Rates of Soil Chemical Processes: Proceedings of a Symposium Sponsored by Divisions S-1, S-2, S-3, and S-9 of the Soil Science Society of America in (S S S a Special Publication)

Rates of Soil Chemical Processes Proceedings of a symposium sponsored by Divisions S-I, S-2, S-3, and S-9 of the Soil Science Society of America in Las Vagas, Nevada, 17 Oct. 1989.

Editors D. L. Sparks and D. L. Suarez Organizing Committee D. L. Sparks R. D. Harter M. C. Amacher P. R. Bloom P. M. Huang

Editorial Committee D. L. Sparks, coeditor D. L. Suarez, coeditor Philip A. Helmke Jerome J. Jurinak Editor-in-Chief SSSA R. J. Luxmoore

Associate Editor-at-Large Jon M. Bartels

SSSA Special Publication Number 27 Soil Science Society of America, Inc. Madison, Wisconsin, USA 1991

Cover Design: Patricia 1. Scullion

Copyright © 1991 by the Soil Science Society of America, Inc. ALL RIGHTS RESERVED UNDER THE U.S. COPYRIGHT LAW OF 1978 (P.L. 94-553) Any and all uses beyond the limitations of the "fair use" provision of the law require written permission from the publisher(s) and/or the author(s); not applicable to contributions prepared by officers or employees of the U.S. Government as part of their official duties. Second Printing 1992 Soil Science Society of America, Inc. 677 South Segoe Road, Madison, WI 53711, USA

Library of Congress Cataloging-in-Publication Data Rates of soil chemical processes / editors, D.L. Sparks and D.L. Suarez. p. ern. - (SSSA special publication ; no. 27) "Proceedings of a symposium sponsored by Divisions S-I, S-2, S-3, and S-9 of the Soil Science Society of America in Las Vegas, Nevada, 17 Oct. 1989~' Includes bibliographical references. ISBN 0-89118-795-2 1. Soil physical chemistry-Congresses. 2. Chemical reaction, Rate of-Congresses. I. Sparks, Donald L., Ph.D. II. Suarez, Donald L. III. Soil Science Society of America. Division S-1. IV. Series. S592.53.R37 1991 91-16288 631.4'l-dc20 CIP

I'rilll~d

ill the United Suucs of Arncricn I~

CONTENTS Foreword Preface Contributors Conversion Factors for SI and non-SI Units

Vll

IX

Xl

Xlll

1 Kinetics of Soil Chemical Reactions-A Theoretical Treatment Chaim Aharoni and Donald L. Sparks

1

2 Methods of Obtaining and Analyzing Kinetic Data Michael C. Amacher................................

19

3 Relaxation Methods for Studying Kinetics of Soil Chemical Phenomena Donald L. Sparks and Peng Chu Zhang...............

61

4 Ion Exchange Kinetics on Reactive Polymers and Inorganic Soil Constituents Domenico Petruzzelli, Friedrich G. Helfferich, and Lorenzo Liberti

95

5 Kinetics of Ion Sorption on Humic Substances K. Bunzl and W. Schimmack

119

6 Kinetics of Sorption/Desorption Processes in Soil Robert D. Harter

135

7 Kinetics of Dissolution of Oxide and Primary Silicate Minerals Paul R. Bloom and Edward A. Nater

151

8 Kinetics of Redox Reactions on Manganese Oxides and Its Impact on Environmental Quality P. M. Huang. . . . .

191

9 Oxidation and Hydrolysis of Ionizable Organic Pollutants at Hydrous Metal Oxide Surfaces Alan T. Stone 10 Modeling Nonequilibrium Reactions of Inorganic Solutes in Soil Columns P. M. Jardine II

Sorption Kinetics of Organic Chemicals: Methods, Models, and Mechanisms Mark L. Brusseau and P. S. C. Ruo

"

..

231

255

281

FOREWORD The soil is one of the most complex chemical systems known with unnumbered reactions occurring at any moment between mineral surfaces and the aqueous phase. When Henry Eyring developed his concepts of chemical kinetics it opened up an area of chemical research that is still proving fruitful 75 years later. This volume can be expected to have a similar effect upon soil chemistry. Few soil chemical reactions go to completion and only through a quantitative understanding of the kinetics of competing reactions can we begin to predict the fate of any chemical species. This is a landmark book and should be of interest to geochemists, ecologists, sediment chemists, engineers, indeed, all earth scientists. Whether one is interested in restoration biology, hazardous waste disposal, acid rain, or mineral cycling, this could prove to be an indispensable work. W. R. GARDNER, president Soil Science Society of America

vII

PREFACE Soil and environmental chemistry have traditionally relied almost exclusively on investigations of equilibria processes. These studies have provided much understanding of soil processes and the conditions under which a specific reaction could occur. More recently it has become evident that knowledge of the rates at which reactions occur is at least equally important both to describe soil processes and to understand the underlying governing mechanismns. In the past decade rates and mechanisms have been increasingly studied and important advances have been made. Interest in this topic led to the organization of a symposium on "Kinetics of Physicochemical Processes in Soils," held in two sessions at the 1989 Soil Science Society of America Annual Meeting in Las Vegas, NV, 15-20 Oct. 1989. This symposium was organized by Division S-2, with S-I, S-3, and S-9 as cosponsors. The book contains 11 chapters, which represent the written contributions from all the invited participants of the symposium. Authors selected are recognized authorities in the field selected both from within SSSA as well as from outside, related fields. The intent of this book is to provide some review but more importantly current knowledge of the application of kinetics to unavoidably heterogeneous soil systems. We hope that this book will prove useful to professionals and students in soil science and related environmental disciplines. Chapter 1 presents a discussion of diffusion models for analyzing slow soil chemical reactions. Chapters 2 and 3 present extensive discussions on experimental methods which can be used to study soil chemical reactions. Chapters 4 and 5 present recent advances in studying the kinetics of ion exchange on inorganic and organic constituents, respectively. Chapter 6 includes a discussion of sorption/desorption phenomena in soil. Kinetics of important weathering reactions in soils, particularly primary silicates and oxides is detailed in Chapter 7. The importance of rates of redox reactions on manganese oxides and their effects on the reactivity of toxic inorganics such as arsenic and chromium is the subject of Chapter 8. Chapter 9 discusses the role of metal oxides in the oxidation and hydrolysis of organic pollutants. Chapters 10 and 11 cover kinetic models used in column studies to predict the fate and transport of inorganic and organic species, respectively. We appreciate the financial support of SSSA, enabling the participation of several non-SSSA scientists from the USA and from abroad in the symposium and in this publication. The editors and other editorial committee members appreciate the careful and thoughtful reviews of the anonymous reviewers. September 1990

DONALD L. SPARKS, coeditor Department of Plant and Soil Sciences University of Delaware, Newark, DE DONALD L. SUAREZ, coeditor U.S. Salinity Laboratory USDA-ARS, Riverside, CA

CONTRIBUTORS Chaim Aharoni

Professor of Chemical Engineering, Department of Chemical Engineering, Technion-Israel Institute of Technology, Technion City, Haifa, Israel

Michael C. Amacher

Research Soil Chemist, USDA-FS, Intermountain Research Station, Logan, UT 84321

Paul R. Bloom

Professor, Soil Science Department, University of Minnesota, St. Paul, MN 55108

Mark L. Brusseau

Assistant Professor, Soil and Water Science Department, University of Arizona, Tucson, AZ 85721

K. Bunzl

Section Head, Gesellschaft fur Strahlen-und Umweltforschung Munchen (GSF), Institut fur Strahlenschutz, D-8042 Neuherberg, Germany

Robert D. Harter

Professor of Soil Chemistry, Department of Natural Resources, University of New Hampshire, Durham, NH 03824

Friedrich G. Helfferich

Professor of Chemical Engineering, Department of Chemical Engineering, Pennsylvania State University, University Park, PA 16802

P. M. Huang

Professor of Soil Science, Department of Soil Science, University of Saskatchewan, Saskatoon, SK, Canada S7N OWO

P. M. Jardine

Staff Research Scientist, Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6038

Lorenzo Liberti

Professor of Water Chemistry and Technology, Istituto Chimica Applicata, Facolta Ingegneria, Universita di Bari, Bari, Italy

Edward A. Nater

Assistant Professor, Soil Science Department, University of Minnesota, St. Paul, MN 55108

Domenico Petruzzelli

Senior Scientist, Istituto di Ricerca sulle Acque, Consiglio Nazionale Ricerche, Bari, Italy

P. S. C. Rao

Professor, Soil Science Department, University of Florida, Gainesville, FL 32611

W. Schimmack

Research Scientist, Gesellschaft fur Strahlen-und Umweltforschung Munchen (GSF), Institut fur Strahlenschutz, D-8042 Neuherberg, Germany

Donald L. Sparks

Professor of Soil Physical Chemistry, Department of Plant and Soil Sciences, University of Delaware, Newark, DE 19717-1303

Alan T. Stone

Associate Professor, Department of Geography and Environmental Engineering, Johns Hopkins University, Baltimore, MD 21218

Donald L. Suarez

Geochemist, U.S. Salinity Laboratory, USDA-ARS, Riverside, California 92501

Peng Chu Zhang

Research Scientist, Research Center, State University of New York, Oswego, NY 13126 xl

Conversion Factors for SI and non-SI Units

xiii

~.

Conversion Factors for SI and non-Sf Units To convert Column 1 into Column 2, multiply by

Column 1 SI Unit

Column 2 non-Sl Unit

<

To convert Column 2 into Column I, multiply by

Length 0.621 1.094 3.28 1.0 3.94 x 10- 2 10

(10 3

kilometer, km m) meter, m meter, m micrometer, JLm (10 -6 m) millimeter, mm (10 -3 m) nanometer, nm (10- 9 m)

mile, mi yard, yd foot, It micron, JL inch, in Angstrom,

A

1.609 0.914 0.304 1.0 25.4 0.1

o

0 2:

-e

.. l"l

:=

Area 2.47 247 0.386 2.47 x 10- 4 10.76 1.55 x 10- 3

hectare, ha square kilometer, km 2 (10 3 m)2 square kilometer, km 2 (10 3 m)2 square meter, m 2 square meter, m 2 square millimeter, mm'' (10- 3 m)2

00

acre acre square mile, mi 2 acre square foot, ft 2 square inch, in 2

0.405 4.05 x 10- 3 2.590 4.05 x 10 3 9.29 x 10- 2 645

0 2: '"'l

> ("'l

.., 0

:= 00 '"'l

0

Volume

..:=> 00

9.73 x 35.3 6.10 X 2.84 x 1.057 3.53 x 0.265 33.78 2.11

10- 3 10 4 10- 2 10- 2

cubic meter, m 3 cubic meter, m 3 cubic meter, m 3 liter, L (10 -3 m 3 ) liter, L (10 -3 m 3 ) liter, L (10 -3 m 3) liter, L (10 -3 m 3 ) liter, L (10 -3 m 3) liter, L (10- 3 m 3)

acre-inch cubic foot, ft 3 cubic inch, in 3 bushel, bu quart (liquid), qt cubic foot, ft 3 gallon ounce (fluid), oz pint (fluid), pt

102.8 2.83 x 10- 2 1.64 x 10- 5 35.24 0.946 28.3 3.78 2.96 x 10- 2 0.473

2: 0 2: 0 2: ,

.. ...., 00

~

2:

00

n

Mass 2.20 x 10- 3 3.52 x 10- 2 2.205 0.01 1.10 x 10- 3 1.102 1.102

gram, g (10 -3 kg) gram, g (10 -3 kg) kilogram, kg kilogram, kg kilogram, kg megagram, Mg (tonne) tonne, t

pound, lb ounce (avdp), oz pound, lb quintal (metric), q ton (2000 lb), ton ton (U.S.), ton ton (U.S.), ton

454 28.4 0.454 100 907 0.907 0.907

0 Z

-e t"'j

lI:l

...

00

0 Z

"l

> o

.., 0

0.893 7.77 x 1.49 x 1.59 x 1.86 x 0.107 893 893 0.446 2.24

10- 2 10- 2 10- 2 10- 2

Yield and Rate kilogram per hectare, kg ha -1 pound per acre, lb acre- 1 kilogram per cubic meter, kg m -3 pound per bushel, bu " ! kilogram per hectare, kg ha -1 bushel per acre, 60 lb kilogram per hectare, kg ha -1 bushel per acre, 56 lb kilogram per hectare, klj ha -1 bushel per acre, 48 lb liter per hectare, L ha gallon per acre tonnes per hectare, t ha -1 pound per acre, lb acre " ! megagram per hectare, Mg ha -1 pound per acre, lb acre " ' megagram per hectare, Mg ha -1 ton (2000 lb) per acre, ton acre."! meter per second, m s-1 mile per hour

lI:l

00

"l

1.12 12.87 67.19 62.71 53.75 9.35 1.12 x 10- 3 1.12 x 10- 3 2.24 0.447

0

lI:l

... 00

> Z 0 Z 0 Z

.... e .....,Z 00

00

10 1000

Specific Surface square meter per kilogram, m 2 kg- 1 square centimeter per gram, em 2 g-1 square millimeter per gram, mm 2 g-1 square meter per kilogram, m 2 kg- 1

0.1 0.001

Pressure 9.90 10 1.00 2.09 x 10- 2 1.45 x 10- 4

(10 6 (10 6

megapascal, MPa Pal megapascal, MPa Pal megagram per cubic meter, Mg m -3 pascal, Pa pascal, Pa

atmosphere bar gram per cubic centimeter, g ern -3 pound per square foot, lb ft - 2 pound per square inch, lb in- 2

(continued on next page)

0.101 0.1 1.00 47.9 6.90 x 10 3 ~

0<1

;.

Conversion Factors for SI and non-SI Units To convert Column 1 into Column 2, multiply by

Column 2 non-SI Unit

Column 1 SI Unit

To convert Column 2 into Column I, multiply by

Temperature 1.00 (K - 273) (9/5 0C) + 32

Kelvin, K Celsius, °C

Celsius, °C Fahrenheit, of

1.00 (OC + 273) 5/9 (OF - 32)

Energy, Work, Quantity of Heat 10- 4

9.52 x 0.239 10 7 0.735 2.387 x 10- 5 10 5 1.43 x 10- 3

joule, J joule, J joule, J joule, J joule per square meter, J m- 2 newton, N watt per square meter, W m- 2

British thermal unit, Btu calorie, cal erg foot-pound calorie per square centimeter (langley) dyne calorie per square centimeter minute (irradiance), cal em -2 min " !

n 3

1.05 X 10 4.19 10- 7 1.36 4.19 x 10 4 10- 5 698

X

10- 2

5.56 x

10- 3

10- 4 35.97

milligram per square meter second, mgm- 2s- 1 milligram (H20) per s~uare meter second, mg m - 2 S milligram per square meter second, mgm- 2s- 1 milligram per square meter second, mgm- 2s- 1

gram per square decimeter hour, gdm- 2h- 1 micromole (H 20 ) per square centimeter second, /Lmol ern - 2 S-l milligram per square centimeter second,mgcm- 2s- 1 milligram per square decimeter hour, mgdm-"2h- 1

<

~... o z

~o ~

Transpiration and Photosynthesis 3.60

o z

"!l

o

27.8

"... 'IJ

180

>-Z

1:::1

10 4 2.78

Z

X 10- 2

oZ

...ciJ e

57.3

radian, rad

Plane Angle degrees (angle), °

Z

1.75

X

10- 2

::l 'IJ

Electrical Conductivity, Electricity, and Magnetism 10 10 4

siemen per meter, S m -1 tesla, T

millimho per centimeter, mmho em -1 gauss, G

0.1 10- 4

cubic meter, m 3 cubic meter per hour, m 3 h- 1 cubic meter per hour, m 3 h- 1 hectare-meters, ha-m hectare-meters, ha-m hectare-centimeters, ha-em

-e

~... o

Water Measurement 9.73 x 10- 3 9.81 X 10- 3 4.40 8.11 97.28 8.1 x 10- 2

82: 2:

acre-inches, acre-in cubic feet per second, ft 3 s-1 U.S. gallons per minute, gal min- 1 acre-feet, acre-It acre-inches, acre-in acre-feet, acre-ft

102.8 101.9 0.227 0.123 1.03 x 10- 2 12.33

"l

> ~

~ i ... "l 00

1 0.1 1

Concentrations centimole per kilogram, cmol kg- 1 milliequivalents per 100 grams, meq 100 g-1 (ion exchange capacity) gram per kilogram, g kg- 1 percent, 0/0 milligram per kilogram, mg kg- 1 parts per million, ppm

~

1 10 1

becquerel, Bq becquerel per kilogram, Bq kg " ' gray, Gy (absorbed dose) sievert, Sv (equivalent dose)

o

2:

r!l e

.....,2:

Radioactivity 2.7 x 10- 11 2.7 X 10- 2 100 100

t:I 2:

00

curie, Ci picocurie per gram, pCi g-1 rad, rd rem (roentgen equivalent man)

3.7 X 10 10 37 0.01 0.01

Plant Nutrient Conversion 2.29 1.20 1.39 1.66

Elemental

Oxide

P K Ca Mg

P 205 K 20 CaO MgO

0.437 0.830 0.715 0.602

~

~:

1

Kinetics of Soil Chemical Reactions-A Theoretical Treatment Chaim Aharoni

Department of Chemical Engineering Technion-Israel Institute of Technology Technion City, Haifa, Israel Donald L. Sparks

Department of Plant and Soil Sciences University of Delaware Newark, Delaware

ABSTRACT Most soil reactions of interest are heterogeneous solid-liquid reactions and take place by a multistep mechanism that comprises transport processes as well as chemical reactions. When the chemical reactions at the solid phase are rapid and are not associated with solid-phase transport processes, the liquid-phase transport processes determine the rate of the overall reaction, e.g., transport in the bulk of the liquid phase, diffusion across the liquid film surrounding the solid particles, diffusion in liquid-filled macropores. In these cases, the kinetics are accounted for by applying the Fick equation or the Nernst-Planck equation with suitable boundary conditions. When the processes taking place at the solid phase are rate determining, it is often observed that a plot of the reciprocal of the rate against the time is S-shaped, and the kinetics are approximated by a sequence of simple equations, each one valid during a limited range of time: the fractional power equation at the beginning of the experiment, the Elovich equation at an intermediate range of time, and the pseudofirst-order equation when saturation is approached. These kinetic phenomena indicate that the reactions at the solid phase are associated with activated diffusional processes, such as surface diffusion or bulk penetration, in which chemical bonds are formed and ruptured along the diffusion path. From the experimentally determined plots of the amount absorbed against time it is possible to deduce whether the rate-determining process is diffusion in a homogeneous medium or diffusion in a heterogeneous medium, and to estimate the parameters of the diffusion process.

Chemical reactions in soils are generally heterogeneous solid-liquid reactions involving a solid component of the soil and the soil solution. The reaction includes chemical processes involving formation or rupture of chemical bonds, Copyright (e) 1991 Soil Science Society of America, 677 S. Segoe Rd., Madison, WI 53711, lJSA. Rules of Soil thrmtcul Procrssrs. SSSA Special Publication no. 27.

2

AHARONI & SPARKS

accompanied by transport processes such as displacement of solutes and sorbates in the liquid phase, solid phase and at the interface. In adsorptiondesportion reactions, a solute originally in the liquid phase becomes bonded to the surface of a solid, or vice versa, a sorbate bonded to a surface becomes a solute in the soil solution. The process of ion exchange involves simultaneous adsorption and desorption of species bonded to charged surfaces by electrostatic forces. In dissolution-precipitation reactions the solid phase and the mobile solute have the same chemical composition and the amount of solid phase decreases or increases as a result of the reaction. In more complex chemical reactions, adsorption is chemical and is followed by formation of new solid phases or new soluble compounds. Soil reactions are generally classified according to the nature of the main chemical process involved: adsorption, ion exchange, dissolution, etc. However, in order to assess the kinetics one should consider the nature and the rate of the transport processes associated with the chemical reaction: flow and diffusion in the soil solution, transport across the solid-liquid interface, diffusion in liquid-filled pores and micropores, and surface diffusion penetration into the solid. An expression for the kinetics of soil reactions can be devised by assigning rate equations to transport and chemical processes and combining these equations. The expression finally obtained has to be validated by comparison to experimental results. Devising a model for slow soil reactions that is rate limited by transport processes at the solid phase is particularly difficult, because of the effects of soil heterogeneity and because in many cases only a limited part of the kinetic isotherm is measurable. The kinetics of slow soil reactions are discussed in this chapter based on the conceptual framework of the kinetics of adsorption (Aharoni, 1984). This treatment predicts that kinetics of slow solidliquid reactions are described by expressions that give an S-shaped curve when plotted as the reciprocal of the rate against the time, and that the empirical equations widely used in the literature are simplified equations to which this expression reduces at some limited ranges of time. Activated diffusion is assumed to take place at the solid phase. This model permits one to distinguish between diffusion in homogeneous and heterogeneous media and to calculate physically based parameters. TRANSPORT PROCESSES IN SOIL REACTIONS Figure 1-1 schematically shows various nonactivated and activated transport processes that may take place in a soil reaction. Nonactivated Processes 1. Transport in the Soil Solution

Transport in the soil solution is the result of convection and flux of solute within the liquid. The solute flux J, in the x direction (mol m -2 s -I) is given by

KINETICS OF SOIL CHEMICAL REACTIONS

3

I I I I

1

12 I I I I

-_ ..~ -_ ..~ -_ ..~ -_ ..~

.. .. .. ..

I I I I I

Film

Liquid

Solid

Fig. I-I. Transport processes in solid-liquid soil reactions-Nonactivated processes: I. Transport in the soil solution, 2. Transport across a liquid film at the solid-liquid interface, 3. Transport in a liquid-filled micropore, Activated processes: 4. Diffusion of a sorbate at the surface of the solid, 5. Diffusion of a sorb ate occluded in a micropore, 6. Diffusion in the bulk of the solid.

Jx

= - D(dc/dx) +

uc

[1]

where c (mol m -3) is the concentration of the solute, u (m' s -I) the velocity of the liquid flow, and D (m 2 s - I) the diffusion coefficient generally assumed to be constant. The second term on the right-hand side of Eq. [1] describes flow of the liquid, and the first term describes the displacement of the solute within the liquid. Transport in the soil solution is sometimes rate determining in largescale field processes. However, in many laboratory experiments the aim is to study the effect of other steps on the kinetics of the overall soil reaction, and in these cases it is useful to eliminate the effect of transport in the soil solution by rapid mixing so that it does not become rate limiting (Sparks, 1989). 2. Transport across a Liquid Film at the Solid-Liquid Interface Solid particles are surrounded by an immobile thin liquid film. The transport across the film can generally be expressed by

[2] where Cliq (mol m -3) and csolid (mol m -3) are the concentrations in the liquid and in the solid just across the film and m (m s -I) is a coefficient of mass transfer. 3. Transport in Liquid-Filled Macropores and Interparticle Voids Wide pores and wide intraparticle voids are capable of containing solution and transport of the solute is essentially diffusion in a liquid phase.

AHARONI & SPARKS

4

However, since the solution in which the transport takes place is confined, the kinetics are affected in various ways: (i) the coefficient of diffusion can differ from the coefficient of diffusion in the bulk solution; (ii) a diffusion path is imposed by the geometry of the pore network; and, (iii) liquid flow is slowed down and its effect generally becomes negligible as compared with the effect of diffusion. Therefore, the transport process in liquid-filled macropores can often be represented simply by Fick's equation J

or

=

-Dp(oclox)

oclot = D p(02c1ox2)

[3a] [3b]

where D p is a coefficient of diffusion. When the macropores are voids in an adsorbing solid component, the amount of solute undergoing diffusion decreases continuously as some of it is taken up by the pore walls. A negative term must then be added to Eq. [3b]. If it is assumed that the uptake is first-order with respect to the solute, Eq. [3b) becomes [4]

where k is a constant. If the diffusing solute is an ion and the pore walls are charged surfaces, the flux may be determined by the gradient of the electrical potential as well as by the concentration gradient. A term for the gradient of the electrical potential is added to Eq. [3a] and the Nernst-Planck equation is obtained J

=

-Dp[(oclox) - c(zeF/RT)(ocP/ox)]

[5]

where ocP/ox is the gradient of the electrical potential, z, is the electrochemical valence of the diffusing ion, F is the Faraday constant, R is the gas constant, and Tis the absolute temperature. The electrical potential can generally be related to the concentrations of the ions in the system and Eq. [5] is then reduced to a function relating the concentration to distance and time. It is often necessary to treat a porous particle or an aggregate of nonporous particles as the medium in which the diffusion takes place instead of considering the pores themselves. Equations similar to the above can be developed for the porous medium using an effective diffusion coefficient. Activated Diffusion Processes 4. Diffusion of the Sorbate at the Surface of the Solid Recent research has shown that surface diffusion (Fig. I-I) often plays an important part in reactions involving solids and there are indications that this applies to soil reactions as well. Surface diffusion results from the fact

KINETICS OF SOIL CHEMICAL REACTIONS

5

that an adsorbate molecule attached at a surface site is capable of moving to a neighboring empty site without desorbing. A jump to a neighboring site implies weakening and breaking of a surface bond while a new bond is being formed and the jump frequency is determined by an activation energy. The process is possible if the activation energy of the jump is small enough so that the frequency is significant and if the activation energy for desorption is high enough so that desorption does not occur. The direction in which any given sorbate molecule moves is random. However, the overall effect is motion from a region of higher surface concentration to a region of lower surface concentration and an expression equivalent to (Eq. [3a)) is applicable. We may therefore write for surface diffusion in the x direction

[6] where Cs is the surface concentration and D s is a surface diffusion coefficient. As D, is determined by the frequency of the jumps by the sorbate molecules it can be expressed as [7]

where Ed is the activation energy for diffusion (which is equivalent to the activation energy for the jumps), and Do is a constant. Surface diffusion is generally slow compared with diffusion processes in the liquid phase, and it can be distinguished by the exponential variation of the diffusion coefficient with temperature. When the diffusing species is an ion and the surface is charged, the effect of the electrical potential gradient can be important and an equation comparable to Eq. [5] must be used J

=

-Ds[(ac/ax) - c(zeF/RT)(acj>/ax)]

[8]

where D, is a coefficient of surface diffusion associated with an activation energy. There are mechanisms by which a gradient of surface concentration is formed and maintained even when all the surface is in contact with the solution. A gradient is formed when certain parts of the surface adsorb more rapidly than other parts; the solute accedes to the surface at these locations and then spreads to the rest of the surface. This process is likely when the surface is heterogeneous and contains reactive regions with a low activation energy for adsorption (Birnholtz et aI., 1984). It can also be determined by porosity as molecules confined in pores have a greater chance of being sorbed (Aharoni et aI., 1989). S. Diffusion of Sorbate Occluded in Micropores If a solute molecule penetrates into a narrow pore with a width only a few times larger than the solute diameter, it cannot bc assumed that the

6

AHARONI & SPARKS

molecule is in the dissolved state. An occluded molecule is always in a sorbed state and any further displacement along the pore is similar to surface diffusion and is given by equations similar to Eq. [6] or [8] (Aharoni and Suzin, 1982a,b). 6. Diffusion Processes in the Bulk of the Solid

Diffusion processes may also take place in the bulk of the solid, e.g., migration of ions along lattice vacancies or along crystal fractures and migration of sorbates in solid materials with a loose structure. These processes are also activated and may obey equations similar to Eq. [6] or [8].

CHEMICAL INTERACTIONS IN SOIL REACTIONS Chemical interactions at the solid phase may comprise: (i) formation or rupture of a bond between sorbate and surface; (ii) further reaction between adsorbed species; and, (iii) rearrangements of the solid structure and formation and disappearance of solid species. It is often incorrect to apply simple kinetic models such as first- or second-order rate equations to such interactions because reacting solid surfaces are rarely homogeneous and because effects of transport phenomena and chemical reactions are often experimentally inseparable (Sparks, 1989). Nevertheless, attempts have been made to treat adsorption as a simple reaction in which the surface and the sorbing solute are reactants and the sorbed solute a product. The adsorption is written S (surface site)

+ A + (adsorbable solute)

~

AS. (adsorbate at surface site)

Assuming first-order kinetics with respect to the solute and first-order kinetics with respect to the number of sites at the surface dq/dt

=

kc a(qo - q)

[9]

where q is the quantity adsorbed at time t, qo is the maximum adsorption capacity of the surface, c is the concentration of the solute in the liquid phase and k and a are constants. The expression a(qo - q) represents the number of available sites at t and k is a constant. If the concentration of the solution does not vary during the process, Eq. [9] becomes, dq/dt

=

ex(qo - q)

[ 10)

where ex is a constant, and integration gives, q/q() = I -

cxp(

trt).

II II

KINETICS OF SOIL CHEMICAL REACTIONS

7

Equations [10] and [11] are seldom applicable for reasons mentioned above. There are, however, cases in which an equation of a different nature with a form similar to Eq. [11] is applicable (see Eq. [15] below). Authors have also fitted data that do not obey Eq. [11] by assuming that several first-order processes take place simultaneously, and using several adjustable values of qo and a, while such fittings lack physical significance.

MECHANISMS OF SOIL REACTIONS It is convenient to classify an overall soil reaction as a slow or rapid reaction. A soil reaction is slow when the kinetics are associated with an energy of activation. Slow reactions are those in which processes taking place at the solid phase are rate determining: whether transport processes (such as surface diffusion, diffusion in micropores, penetration into the bulk, etc.), or chemical interactions. Mechanisms for slow soil reactions are discussed in detail in the following sections. Rapid soil reactions are generally reactions in which transport processes at the solid phase do not take place to a significant extent and in which the rate-determining step is a transport process in the liquid phase. The mechanism for rapid soil reactions can often be elucidated by using models in which, diffusion in the bulk liquid, or film diffusion, or diffusion in liquid-filled pores is rate determining, and by introducing appropriate equations for these processes (see Eq. [1] to [5]) and integrating according to appropriate boundary conditions. The kinetics of rapid soil reactions are sensitive to variations in the experimental conditions that affect the rates of transport-in-liquid processes such as agitation, dispersion of the solid, etc., and experimental results are useful only if these conditions are controlled. These parameters may be manipulated for identification of the rate-limiting process.

APPLICABILITY OF EMPIRICAL EQUATIONS TO SLOW SOIL REACTIONS In many cases the kinetic data obtained experimentally for activated reacI ions do not seem to fit equations derived from theoretical models but can he fitted by some simple empirical expressions. The expressions applicable 10 soil reactions are generally expressions applicable to various other chemicul processes involving solid-fluid reactions. Three simple equations of wide applicability are worth mentioning in this regard. a. The fractional power equation or modified Freundlich equation can be represented [12] q = kt" where k and v are constants and v < I. lis applicability to the sorption of I'ho,sphale by sediments is illustrated in Jiig. 1-2, Plots of log q vs. Jog tare

8

AHARONI & SPARKS

•

200

a.

Cl ::i.

100 50

C"

20 10

0.1

0.2

0.5

1

2

5

10

20

50

time, h Fig. 1-2. Sorption of phosphate by two samples of sediment (from Kuo and Lotse, 1974).

fairly linear with a slope of v = 0.2. Equation [12] is empirical for values of v different from 0.5. For v = 0.5 it is indistinguishable from the parabolic equation associated with diffusion models. b. The Elovich equation can be represented q

=A +

(lib) In(t

+

[13]

to)

where A, b and to are constants; the parameter to is often small at the range of t at which Eq. [13] is applied and thus can be disregarded. Figure 1-3 illustrates the applicability of the Elovich equation to the sorption of phosphate by an Okaihau soil. 1.1 1 0.9 0.8 0.7

8 c- 0.6 c- 0.5

--

0.4 0.3 0.2 0.1 0 -2

0

2

4

In t, hours Fig. 1-3. Sorption of phosphate by an Okaihau soil (from Ryden ("I III., 1977).

5

KINETICS OF SOIL CHEMICAL REACTIONS

9

c. The pseudo-first-order equation can be represented

a/«; = 1 -

(3 exp( -at)

[14]

where qoo, (3, and a are constants, and qoo is the quantity adsorbed at t - 00. The applicability of Eq. [14] can be verified by plotting 10g(1 q/qoo) against t. The conformance of Eq. [14] to K adsorption by clays is illustrated in Fig. 1-4. The equation applicable to experimental results generally differs from a true first-order equation (Eq. [11]) in two ways. 1. The parameter qoo varies with the concentration of the soil solution. If Eq. [14] is written in a differential form one obtains dq/dt

=

[15]

a(qoo - q)

where a(qoo - q) does not represent the number of available sites. 2. The parameter {3 is an adjustable parameter often greater than 1, whereas in a true first-order equation {3 must be equal to 1. A generalized empirical equation can be derived by closely examining the applicability of Eq. [13], [14], and [15] to experimental data. Differentiating these equations and writing them as explicit functions of the reciprocal of the rate, Eq. [12] becomes

= (dq/dt)-I

Z

(1IvK)t 1 -

V

,

[16]

Eq. [13] becomes

Z

=

tdq/dti':' - b(t

+ to)

[17]

and, Eq. [14] becomes Z

=

(dq/ dt) - I

=

(11qoo{3a) exp(at).

time, min 100 120 140 160 180 200220 240

--

.4

8

.6

t,T

.8

tT

o kaolinite • montmorillinite .. vermiculite

T"'

Cl 0

1.0 1.2 1.4 1.6

I lV., I 4, Sorption of K by dllYs (Iron: Spllrks and Jardine. 1984).

[18]

AHARONI & SP ARK~

10

3

~2 c

:::J

ens ... :!:: .c ...

~1

N

OL.--_..l....-_....L...-_....L.._---l.._---1._--I'--_.L.-_....L...-_....L.._---l

o

1

2

34567

8

9

10

time (arbitrary units) Fig. 1-5. Plots of Z YS. t implied by the simple empirical equations: 1. Plot according to Ec [16] implied by Eq. [12],2. Plot according to Eq. [17] implied by Eq. [13], 3. Plot accordir to Eq. [18] implied by Eq. [14].

Equations [16J, [17J, and [18J indicate that the plot of Z vs. 1 for an exper mental isotherm should be convex if Eq. [12J is applicable, linear if Eq. [1: is applicable and concave if Eq. [14J is applicable (Fig. 1-5). Plots of Z vs, 1 for various soil reactions and other solid-fluid process. generally behave in a more complex fashion. They are S-shaped: convex l small I, concave at large I, and linear at some intermediate range of I. Fe example, the plot of Z against 1 for the sorption of phosphate by a Typ Dystrochrept soil depicted in Fig. 1-6 illustrates this S-shaped behavior. Th property of the Z (I) plot suggests that the kinetics of soil reactions ofte obey some complex function that can be approximated by Eq. [12J at sma I, by Eq. [13J at an intermediate I, and by Eq. [14J at large I. There are indications that Z vs. 1 plots result in S-shaped curves, eve in cases when one of the equations given in Eq. [12J to [l4J is applicab over the entire time the rate study is carried out. In many reactions the ra can decrease by many orders of magnitude before saturation is approache however often one uses experimental methods capable of measuring kineti. that vary within a range of say two or three orders of magnitude. In the cases, one obtains experimental points that cover a small part of tl theoretical isotherm; the rate may seem to become zero before tn equilibrium is approached or the measured process may seem to be precede by an instantaneous one. One of the simple equations, Eq. [12], [13J, ar [l4J can be applicable during the entire experiment if all the points mea ured are in its range of validity. It should also he noted that Eq. [12J or [1 cannot be valid when t is large as they give (I • 00 lit I -. 00. These equatioi

KINETICS OF SOIL CHEMICAL REACTIONS

11

200 . - - - - - - - - - - - - - - - - - - - - - . . . ,

z: ,

150

s:

~

0, e, 100 Cl ::::i.

N

50

OL...L-J.....l-J-.J....I..-!-...L.-........-J......l-.............I.....l-J-.J'--L.............l-.............I......l

o

1

2

3

4

time, h Fig. 1-6. Sorption of phosphate by a Typic Dystrochrept soil plotted as Z vs. t. The circles represent the experimental data of Polyzopoulos et al. (1986). The solid line is a curve calculated according to Eq, [191 with an and b n according to Modell (Table 1-1) and T = 10 h (Aharoni et al., unpublished data).

must be superseded at some time by an equation that predicts a finite saturation value of q at t - 00 such as Eq. [14]. As it is often more convenient to plot experimental data as q vs. log t rather than as Z against t, it is useful to consider the plots of q vs. log t. A plot of q vs. In t at the region in which Eq. [12] is obeyed has a slope given by dq/d(ln t) = uk exp(u In t). At the region in which Eq. [13] is obeyed, dq/d(1n t) = lib and at the region in which Eq. [14] is obeyed dq/d(1n t) = qoocx.{3 exp(1n t) exp[ -cx. exp(1n t)]. This means that the plot ofq vs. log t is concave at small t, linear at intermediate t, and convex at large t. The plot q vs. In t for the sorption of phosphate by the < 2-mm fraction of a Chigley gravelly sandy loam (in Fig. 1-7) has these characteristics. The fact that Eq. [12], [13], and [14] are approximations to which the generalized equation reduces at certain limited ranges of coverage explains why no consistent theoretical derivation can be found for these equations. It also explains the fact that there is no correlation between the applicability of any of these equations and the nature of the process; dissimilar processes are fitted by the same equation and similar processes are fitted by different equations.

APPLICATION OF THEORETICAL MODELS TO THE GENERALIZED EQUATION The generalized expression, S-shaped Z(t) plot can be explained by IIH)(.Icls based on diffusion. Equations for diffusion in a homogeneous medi-

12

AHARONI & SPARKS

1

0.9 0.8

0.7 8 0.6

C"

c-

0.5 0.4

0.3 0.2 0.1

00

2

4

6

8

In t, h Fig. 1-7. Sorption of phosphates by the 2-mm fraction of a Chigley gravelly sandy loam plotted as a/a; against In t. The squares represent the experimental data of Enfield (1974). The solid lines are curves calculated according to Eq. (29) with an and bn for Modell (Table I-I) and T = 150 and 180 h (Aharoni et al., unpublished data).

urn lead to S-shaped Z(t) plots in which the final and initial curved parts are dominant. Equations for diffusion in a heterogeneous medium lead to S-shaped Z(t) plots in which the intermediate linear part is dominant. The experimental results correspond to either model.

Diffusion in a Homogeneous Medium If a solute coming from a solution at constant concentration penetrates into a limited space originally empty and moves in that space by a diffusion process, the amount of solute q present in that space at time t is given by n=oo

a/«: - 1 -

E

an exp( -bnt/r).

[19]

n=o

In this equation obtained by integrating Fick's equation,

7

is defined by [20]

where r is the maximum length of the diffusion path, D is the diffusion coefficient which is assumed constant, and q~ is the maximum uptake of solute. In Eq. [19], an and b n are parameters with an infinite number of discrete values determined by the integers n. The relations an(n) and bn(n) depend on the geometry of the system; they are given in Table 1-1 for parallel flux (Modell), for flux converging in a space limited by a circular boundary (Model 2), and for flux converging into II sphere (Model :1). Equation [19]

KINETICS OF SOIL CHEMICAL REACTIONS

13

Table 1-1. Parameters of Eq. [19). [21). [22). and [23)for various geometries of the diffusion flux. Modell t

Model 2*

Model3§

8/r 2(2n + 1)2 7I"2(2n + 1)2/4

4/~~'

6/7I"2 n 2

~~

~2n2

2/71"1/2

4/71"1/2

8/71"2 /2 71"4

4/H <;

1:21

6/71"1/2 6/71"2 71"2

0.238 2.281 0.793 0.192r

0.441 3.136 0.402 0.078r

0.449 3.535 0.333 0.035r

C
AT b2 t2 tp

t Modell: Parallel flux (penetration in slab-shaped particles or surface diffusion into strips with parallel edges).

t Model 2: Flux converging in a space limited by a circular boundary (penetration in cylindrical-shaped particles or surface diffusion in circular surfaces). § Model 3: Flux converging into a sphere. , ~n are the roots of the Bessel equations Jo(X) = o.

is also valid for divergent flux and other more complex geometries. Model I applies to uptake by layered solid materials separated by parallel voids, to occlusion into microporous slab-shaped particles, and to penetration into slab-shaped, nonporous solids. It also applies to surface diffusion into surface strips with parallel edges. Model 2 applies to uptake by narrow cylindrical particles and to surface diffusion into circular areas. Model 3 applies 10 uptake by spheres. For any of these processes, the particles have to be homogeneous and similar in shape, size and diffusivity and the same condiI ions apply to sorbing zones in surface diffusion. Equation [19] (with any set of an and b n) can be rewritten in a form I hat reduces at small I to [21] IIl1d it reduces at large I to

q/qoo

=

1 - k r exp( - arlIT)

[22]

where k, in Eq. [21] and k r and ar in Eq. [22] are parameters determined hv a; and b.; They are given for Models 1, 2 and 3 in Table 1-1. Equation [21] is similar in form to Eq. [12] and it leads to a plot of I VS. 1 that is convex (see Eq. [16]). Likewise, Eq. [22] is similar to Eq. [14] IIl1d leads to a plot of Z vs. I that is concave (see Eq. [18]). This implies that IlIl' plot of Z vs, I corresponding to Eq. [19] is S-shaped, it must be convex nlsillalll and concave at large f, and have an inflection point. This is illusf III I cd in Fig, 1-8 that depicts plots calculated according to Eq. [19], [21], IIlId /221 with an and b; for Modell; nondimensional variables are used (Zr - ItI{f//f/(J<,)/d(t/r)] -I and fIT). This also implies that a plot of q vs. In I If'slIlf,s ill an S-shapcd curve that is concave al small I and convex at large

14

AHARONI & SPARKS

...

N

o

0.5

1.0

t/'t Fig. 1-8. Plots of Z, against t/r calculated according to Eq. [19] (solid line), Eq. [21] (squares), and Eq. [22] (dots) (Aharoni and Suzin, 1982b).

I (see Fig. 1-9a). At an intermediate region, the plot approaches a straight line and can be represented by Eq. [13], which is conveniently formulated in terms of I p , the time at which a plot of Z, vs. lIT has an inflection point.

[23]

Eq. [23] has only one adjustable parameter I p , which depends on T; A r , b, and t, are fixed for each geometry (see Table 1-1).

Heterogeneous Diffusion We now consider a more frequently encountered case: a process in which a solute diffuses in solid media that have different properties. The overall process can be viewed as an array of diffusion processes characterized by their r that includes the effect of the diffusion coefficient and the length of the diffusion path (Eq. [20]). Considering the overall uptake q at time I as the sum of the component uptakes qrf one can write [24] where qroo is the uptake due to the process characterized by T at I - 00, and Tj and T m are the smallest and largest T in the system. Equation [24] can be

15

KINETICS OF SOIL CHEMICAL REACTIONS

solved by introducing a function that relates (qT(lqTOO) to the time such as Eq. [19], and by introducing a distribution function relating qTOO to 7. In soil reactions, the distribution qToo (7) and the rate equations qT((t) are generally poorly known and a precise solution of Eq. [24] is not possible. It is, however, possible to assess some of the characteristics of the kinetics predicted by Eq. [24], by solving it for conditions for which a simple analytical solution can be found and examining the effects that changes in these conditions can cause (Aharoni and Suzin, 1982b). We use the distribution [25]

qTOO (7) = BIT

where B is a constant. Assuming that all the component diffusion processes obey Eq. [19], we add the simplifying assumption that for any time t we can define a variable 7((t) such that all the diffusion processes with 7 > 7( stilI obey Eq. [21] and all the diffusion processes with 7 < 7( already obey Eq. [22]. Introducing these assumptions in Eq. [24] gives q

= rm (BIT)ks(tIT)1/2 dr + T(

P (BIT)[1 T1

- k f exp( - a f tl7)] dr,

[26]

Differentiating according to t, multiplying both sides by t and rearranging gives

where

p

is given by [28]

For 7; sufficiently small and 7m sufficiently large, there is a range of t for which the two negative terms in Eq. [27] are negligible and it reduces to d(q/qrx)/d In t

=

lip.

[29]

Equations [27] and [29] reveal an important characteristic of the plot of q vs. In t, At intermediate time, it is linear as specified by Eq. [29]. At small t and at large t one of the two negative terms in Eq. [27] is not negligiblc and the slope d(q/qoo)/d In t is smaller than at intermediate t. This means I hat the plot q vs. In t is S-shaped, concave at the beginning, convex at the cud, and linear in between (see Fig. 1-9b). The limiting values of 7(viz, 7; and 7m), have two important effects on I he shape of the plot: (i) the extent to which 7; and 7m differ from each other determines the time period over which the plot can be considered linear (the I wo negative terms in Eq. [27] are negligible). At the limit 7; - 0 and 7m • 00, the plot is totally linear and obeys the Elovich equation. At the other IlIlIit T; = T m , the system is homogeneous and the plot is linear near the inI it'd ion point only (compare curves a and IJ in Fig, 1-9); and (ii) the ratio

AHARONI & SPARKS

16

0.8

8 0.6

--

00-

0.4

0.2

o

0123

In t

10

5

15

In t

Fig. 1-9. Plots of a/a; against In t: a. Calculated according to Eq, [19] (an and b m as given for Modell, T = 6 x 10 3_h time units), b. Calculated according to Eq. [27] for Tj = 2 and 9 T m = 2 X 10 .

=

In (7mIT;) determines the slope of the linear part (Eq. [30]) with the slope decreasing when p increases. The maximum slope is the slope for the homogeneous system (0.24 for the slab model). The plot of Z vs. t corresponding to Eq. [27] is,

p

which reduces to Z

[31]

when the two negative terms in Eq. [30] are negligible. The result is a plot of Z vs. t that is also S-shaped but it is convex at the beginnning and concave at the end. The linear intermediate part is important when 7; is small and 7 m is large; its slope increases when p is large, and it is minimum when the system is homogeneous. Although the characteristics of the plot of q vs. In t and the plot of Z vs. t, were derived by using the particular distribution qTOO = BIT, numerical calculations with other distributions show that the distribution chosen has little effect on these characteristics. Thus, they can be considered to be of general validity.

KINETICS OF SOIL CHEMICAL REACTIONS

17

ASSESSMENT OF THE KINETICS OF SLOW REACTIONS

In the preceding discussion it was shown that the kinetics of slow reactions obey rules indicating that the rate is determined by activated diffusion processes taking place in the solid phase. The theoretical treatment leads to useful relations applicable to data because it considers the properties common to the various diffusion processes, and does not attempt to precisely describe each diffusion process. In a complex system like soils the diffusion processes that actually take place cannot be precisely defined, but some characterization of the overall process remains possible. We should distinguish between diffusion in a homogeneous medium and heterogeneous diffusion. In the former case the initial and final curved parts of the Z(t) curve are dominant while the intermediate linear part is of lesser importance and the same applies to the plot of q vs. log t. Data can generally be fitted by Eq. [19] for some simple geometry and an adjusted value of T. The data for the sorption of phosphate by a Typic Dystrochrept soil in Fig. 1-6 was fitted by Eq. [19] for slabs with T = 10 h. The data for the sorption of phosphate by a Chigley gravelly sandy loam in Fig. 1-7 indicate an almost homogeneous process with T varying within the range 150 to 180 h. In diffusion in a heterogeneous medium the intermediate linear part in Ihe Z(t) plot is dominant, and this similarly applies to the plot of q vs. In I: the range of applicability of the Elovich equation is very wide and often 1111 the measured data are in that range (Fig. 1-3). We expect the slope of tlil/oo vs. In t to be smaller than 0.24, and we can use the magnitude of that slope for evaluating a ratio T mIT; that can be used as an index for the heter0llcneity of the system (see Eq. [29] and [28]). The data for the sorption of phosphate by an Okaihau soil in Fig. 3 indicates a ratio T mIT; greater than 10 'ithe actual value cannot be estimated as qoo is not reached, (Aharoni et AI., unpublished data)]. When the results are fitted by one of the simple empirical equations, e,... results in Fig. 1-2, we may assume that the experimental kinetic curve reprcsents a part of the overall curve. The diffusion parameters can be estimAted in some cases but with less certainty. The applicability of kinetics based on diffusional models rather than Ulllni chemical reaction kinetics can be explained by noting that the chemi1111, cad ion is included in the diffusional process. Each step in the diffusion pWn'ss is a chemical reaction involving formation and breaking of chemical bonds. The chemical reaction models regard the surface as a reactant and ".lIl11e that the rate is proportional to the number of available sites. This I, hllscd on the implicit assumption that all the sites are equally available for the reaction, whereas the models based on diffusion assume that the sites Nil unly he reached according to a particular sequence. In both cases the Ifllll'l'lal lire dependence for the overall process is governed by the energy IIr III I Ivai ion I hal characterizes the chemical reaction.

18

AHARONI & SPARKS

REFERENCES Aharoni, C. 1984. Kinetics of adsorption: The S-shaped Z-t plot. Adsorp. Sci. & Techno!' 1:1-29. Aharoni, C., and Y. Suzin. 1982a. Application of the Elovich equation to the kinetics of occlusion, homogeneous microporosity. J. Chern. Soc. Faraday Trans. 1. 78:2313-2320. Aharoni, C., and Y. Suzin. 1982b. Application of the Elovich equation to the kinetics of occlusion, heterogeneous microporosity. J. Chern. Soc. Faraday Trans. 1. 78:2329-2336. Aharoni, C., B. Fubini, and E. Giamello. 1989. Effect of micropore filling on chemisorption by large surface area materials. Adsorp. Sci. & Techno!. 5:297-306. Birnholtz, H., A. Nir, N. Lotan, and C. Aharoni. 1984. Surface diffusion as a rate determining step in activated chemisorption. Can. J. Chern. Eng. 62:233-240. Enfield, C.G. 1974. Rate of phosphorus sorption by five Oklahoma soils. Soil Sci. Soc. Am. Proc. 38:404-407. Kuo, S., and E.G. Lotse. 1974. Kinetics of phosphate adsorption and desorption by lake sediments. Soil Sci. Soc. Am. Proc. 38:50-54. Polyzopoulos, N.A., V.Z. Keramidas, and A. Pavlatou. 1986. On the limitations of the simplified Elovich equation in describing the kinetics of phosphate sorption and release from soils. J. Soil Sci. 37:81-87. Ryden, J.C., J.R. McLaughlin, and J.K. Syers. 1977. Time dependent sorption of phosphate by soils and hydrous ferric oxides. J. Soil Sci. 28:585-595. Sparks, D.L. 1989. Kinetics of soil chemical processes. Academic Press, New York. Sparks, D.L., and P.M. Jardine. 1984. Comparison of kinetic equations to describe potassiumcalcium exchange in pure and in mixed systems. Soil Sci. 138:115-122.

2

Methods of Obtaining and Analyzing Kinetic Data Michael C. Amacher

USDA Forest Service Intermountain Research Station Logan, Utah

ABSTRACT Methods of obtaining and analyzing kinetic data for soil systems are examined in this review chapter. Relaxation methods are used to obtain kinetic data for very fast ion association reactions. Batch methods are used to obtain data for intermediate rate and slow sorption/desorption and precipitation/dissolution reactions. Reactor design, mixing, and separation of solid and liquid phases are all important considerations. Type and rate of mixing are critical in minimizing mass transfer processes (diffusion). Separation of phases is done by centrifugation and filtration, although some types of batch reactors allow in situ measurements. Flow methods and hybrid stirred-flow methods are also used to obtain data for intermediate and slow reactions. Flow rates and reactor design are important considerations. Thin disk methods do not minimize diffusion processes so that reaction kinetics alone cannot he studied by this method. Fluidized bed and stirred-flow reactors overcome many of the limitations and keep many of the desired features of batch and flow methods. The effects of reactant concentrations (solid phase and solute), temperature, pH, ionic strength, and other solution composition variables on rate functions provide valuahie clues for deducing reaction mechanisms. Methods of analyzing data include initial rate, isolation, graphical, rate coefficient constancy, fractional lives, and parameter optimization techniques. Inferring reaction mechanisms from kinetic data is subject 10 many pitfalls, not the least of which is that many models produce results that can adequately describe the data, but are statistically indistinguishable and therefore the correct explanation is unknown.

BASIC KINETIC CONCEPTS

Thermodynamics through the use of state functions describes the properties of systems at equilibrium. Kinetics on the other hand deals with descriptions of time-dependent processes, which are path dependent. These two areas of science together constitute a powerful body of scientific law and theory that can be used to describe both systems and processes. A number of methods (1II'yrij(hl «: 1991 Soil Science Society of America, 677 S, Segoe Rd. Madison, WI 53711, liSA, Rates of Soil Chemical Processes. SSSA Special Publication no. 27. 19

20

AMACHER

have been developed to obtain experimental kinetic data and to analyze the data to arrive at a correct interpretation of the processes responsible for the observed time-dependent phenomena. This chapter reviews the various methods that have been developed for obtaining and analyzing kinetic data for soil systems. First, a few basic kinetic concepts must be introduced because they will be used in the discussions to follow. Consider the following sequence of reactions describing the surface complexation of an oxyanion by a metal oxide surface [RI] SOHt(s)

+

=

U-(aq)

SOHtU-(s)

=

SOH2+U-(s)

SLI-n(s)

+

H 20(l)

[R2] [R3]

where SOH is the metal oxide surface hydroxyl group, SOHt is the protonated surface hydroxyl group, L is the oxyanion ligand of valence n -, SOH2+L n- is the outer-sphere, metal-ligand complex, and SL l-n is the inner-sphere, metal-ligand complex. If these reactions occur as written at the molecular level then they are elementary reactions. The series of elementary reactions shown above comprise the mechanism for the overall reaction

The rate of conversion (reaction rate) of each chemical species in the three elementary reaction steps can now be written [I] d[SOHtJ/dt

=

kl[SOH][H+] - k 2[SOHt]

- k 3[SOHt][L n-] d[Ln-J/dt d[SOHtLn-J/dt

=

=

+

k 4[SOHtL n-]

-k3[SOHn[L n-]

+

k 4[SOH2+U-]

[2] [3]

k 3[SOHn[L n-] - k 4[SOH2+L n-]

- k 5[SOHtU-] d[SLI-nJ/dt

=

+

k 6[SL l-n][H 20]

k 5[SOH2+L n-] - k 6[SL I- n][H 20]

[4] [5]

where the brackets refer to concentrations and the k's are the rate coefficients. Rate of conversion equations for H + and H 20 are not shown because they are quite trivial. These rate of conversion equations are known as rate laws but are not to be confused with fundamental laws of nature. They are best regarded as rate functions and they will be referred to as such in subsequent discussions. Note that rate functions urc written in terms of

OBTAINING & ANALYZING KINETIC DATA

21

concentrations rather than thermodynamic activities. This is because spatial concentrations of colliding molecules determine molecular collision rates and hence reaction rates. Assume that the first reaction (the protonation of the surface hydroxyl group) in the above mechanism occurs instantaneously so that this reaction is always at equilibrium. The rates of the forward and reverse reactions are equal at equilibrium, therefore

[6] Rearranging this equation leads to [7]

where K, is the equilibrium constant for the reaction. Thus, the fundamental link between thermodynamics and kinetics is established. The ratio of forward- and reverse-rate coefficients for an elementary reaction gives the equilibrium constant for that reaction. If the forward-rate coefficient and the equilibrium constant for an elementary reaction are determined from kinetic and equilibrium experiments, then it is not necessary to measure the reverse-rate coefficient. It can be calculated. However, this only applies to rate coefficients for elementary reactions, not for rate coefficients for kinetic processes that include both mass transfer and reaction kinetics. Now assume that the last step in the reaction sequence (the formation of the inner-sphere, metal-ligand complex) is irreversible and that the rate of formation of the outer-sphere, metal-ligand complex is approximately equal to the rate of conversion of the outer-sphere complex to the inner-sphere complex [d(SOHz+U-)/dt == 0]. Therefore

The concentration of the outer-sphere complex is therefore [9]

Setting the rate of formation of the outer-sphere complex equal to its rate ul'conversion is known as the steady-state approximation and the outer-sphere complex is a reactive intermediate under such conditions. A steady state occurs when only a single or some of the elementary reactions in a mechanism arc at equilibrium. Complete equilibrium requires that the rates of forward nnd reverse reactions must be equal for all the elementary reactions and that all species must be at steady state. This is the principle of detailed balancing uud is a consequence of the theory of microscopic reversibility that requires I hal forward and reverse reactions in an elementary process follow the same path. 1ft he last step in the reaction sequence shown above is slow compared In the other two, then that reaction is the rate-determining step. If on the

22

AMACHER

other hand the second reaction is slow compared to the others, then it is the rate-determining step. In a reaction sequence in which the reactions occur in series (consecutively), the slowest reaction is rate determining. Suppose however that an alternate reaction is possible in which the inner-sphere complex is formed directly without going through the outer-sphere intermediate [R5]

If this parallel (concurrent) reaction is faster than Step 2 in the abovementioned reaction sequence, then it will be rate determining. If, however,

Step 2 is faster it will still be rate determining. In a parallel reaction sequence, the faster reaction determines the overall rate. Although slower concurrent reactions still occur, less reactants are consumed by these slower reactions than by the fastest parallel reaction. There are many references (e.g., Frost and Pearson, 1961; Laidler, 1965; Gardiner, 1969; Bernasconi, 1986) that cover the basic concepts of chemical kinetics, and the reader is encouraged to refer to some of these for more detailed and complete information. There is a good chapter on ion-exchange kinetics in Helfferich's (1962) book on ion exchange. An excellent reference on kinetics of geochemical processes is available (Lasaga and Kirkpatrick, 1981). Until recently, reference books on kinetic processes in soils were nonexistent. Fortunately, Sparks (1985, 1986, 1989) has produced two review chapters and a new book to fill this information gap. With these concepts established, a brief discussion of the types of reactions that occur in soil systems is necessary because reaction type will often dictate the choice of method to be used. TYPES OF REACTIONS IN SOIL ENVIRONMENTS Soils and other geochemical systems are quite complex, and therefore there are different types of reactions that can occur concurrently and consecutively in these systems. Figure 2-1 illustrates some of the types of reacIon Association

..

Multivalent Ion Hydrolysis~

.. Gas-Water

Ion Exchange

.

Sorption .. Mineral-Solution~ Mineral Crystallization ,

usee

,

sec

,

min

.!

hr

.t

dy

,,

mo

,

yr

mil

Time Scale Fig. 2-1. Time ranges required to attain equilihrium hy ditTt'lrnl types of reactions in soil environments.

OBTAINING & ANALYZING KINETIC DATA

23

tions that occur in soil systems and the time ranges (presented in readily identifiable time units) required to attain equilibrium by these reactions. The ion association, multivalent-ion hydrolysis, and mineral-crystallization reactions are all homogeneous because they occur within a single phase. The first two of these occur in the liquid phase while the last occurs in the solid phase. The other reaction types are heterogeneous because they involve transfer of chemical species across interfaces between phases. Ion association reactions refer to ion pairing, complexation (inner and outer sphere), and chelationtype reactions in solution. Gas-water reactions refer to the exchange of gases across the air-liquid interface. Ion-exchange reactions refer to electrostatic ion-replacement reactions on charged solid surfaces. Sorption reactions refer to simple physical adsorption, surface-complexation (inner and outer sphere), and surface-precipitation reactions. Mineral-solution reactions refer to precipitation/dissolution reactions involving discrete mineral phases and coprecipitation reactions by which trace constituents can become incorporated into the structure of discrete mineral phases. Reactions in soil environments encompass a wide range of time scales (Fig. 2-1). Furthermore, these reactions can occur concurrently and consecutively. The complexity of reactions in soils that occur over a time continuum defies a simple analysis of the kinetics involved (Sposito, 1986). Numerous methods have been developed to isolate and study the various types of reactions that occur in soils. The choice of method largely depends on the type of reaction to be studied, although some methods are applicable to more than one type of reaction. The sequence of steps that are followed in a typical series of kinetic studies on heterogeneous systems such as soils is shown in the flow diagram of Fig. 2-2. Rarely are all these steps followed in the course of a single study and published as a single paper. Many experiments are usually required to establish a mechanism, which is largely a trial and error process of testing and retesting to rule out alternate explanations for the observed rate funct ions. A lifetime of investigations may be required to establish a particularly complicated mechanism, and in some cases a solution may never be reached. In the following section, some of the various methods for obtaining kinetic data will be described. The advantages and limitations of each method and i I s overall suitability for studying the various types of reactions are also discussed in some detail.

METHODS OF OBTAINING KINETIC DATA Experimental methods for obtaining kinetic data for studying various I vpcs of reactions in soils fall into three broad categories: relaxation methods, hutch methods, and flow methods. Flow methods can be further subdivided 11110 flow methods without mixing and flow methods with mixing. A good u-vicw of these methods is found in Sparks (1989).

24

AMACHER

+

Select kinetic method for reaction to be studied • Relaxation methods

• Batch method.

Propose mechani.m(.) from

• Flow methods

experimental rate function

• Stirred-flow method.

and other data

•

Obtain kinetic data under varying cendtlens

• • •

Test mechani.m(.) by conducting

• Reactant concentrations

experiments designed to

• Temperature

eliminate alternative mechanisms

• pH • Ionic strength

• Solution compo.ition

Refine or reject mechani.m(.)

•

Determine rate function from experimental data

Additionai experiment. to validate

• Initial rate methods

or eliminate revised mechanism(s)

• Isolation methods

• Graphical methods • Rate coefficient constancy • Fractional lives

•

Accapted mechani.m(.)

• Parameter optimization methods

I Fig. 2-2. Flow diagram outlining a typical kinetic study in heterogeneous systems.

Relaxation Methods

Relaxation methods were developed for studying fast reactions (those occurring on time scales of milliseconds, microseconds, or less) such as ionassociation reactions in solution and the more rapid ion-exchange and surfacecomplexation reactions on solid surfaces. They involve the application of a perturbation (e.g., pressure, temperature, concentration jumps, electric field pulses) to a system at equilibrium and then following the return to equilibrium by monitoring some property of the system (e.g., conductivity, fluorescence). The application of relaxation methods to the study of reactions on soil constituents is discussed by Sparks and Zhang (see Chapter 3). This chapter will focus on batch and flow methods that are suitable for studying slower reactions in soils (those occurring on time scales of seconds to years or more). Sorption reactions on soil surfaces may occur over long periods. Although the kinetics of the most rapid of these reactions can only be studied by relaxation methods, batch and flow methods arc applicable to the study of reactions in which loss of solute from solution milo soil surfaces occurs over longer periods.

OBTAINING & ANALYZING KINETIC DATA

25

Suspend known amount of solid phase in known volume of background electrolyte solution or other solution of known composition.

+ Begin mixing and gas flow and adjust pH to desired level.

+ At t=O, add known amount of solute to achieve desired initial reactant concentrations, ionic strength, and total volume.

+ At periodic intervals, sample suspension using sy':inge sampler and filter through membrane filters.

+ Analyze filtrates and separated solid phase.

Fig. 2-3. Flow diagram outlining a typical kinetic experiment using a batch reactor.

Batch Methods Batch methods have long been used to obtain kinetic data for reactions in soils. A unique feature of batch methods is that they are primarily a closed system. After all the reactants are added and mixed together, no additional amounts of reactants are added and products are allowed to accumulate. The only material removed from the system is that removed for analysis, and that is usually a small fraction of the total. Thus, sampling perturbations are typically minor. A typical kinetic experiment using a batch reactor is outlined in the flow diagram in Fig. 2-3. Numerous variations are, of course, possible, but the steps outlined in the flow diagram are fairly typical. Reactor design, mixing techniques, and techniques for separating the solid and liquid phases are all critical to obtaining good data, and each will be discussed in turn. Specialized techniques include in situ monitoring of reactant activities with ion-selective electrodes, which renders phase separation unnecessary, and the use of radionuclides to monitor the ,extent of the reaction.

Batch Reactor Design

A typical batch reactor configuration is shown in Fig. 2-4. The reactor itself is a cylinder constructed of glass or plastic. The best material for minimizing solute sorption onto the reactor walls should be selected. The choice of material is normally based on the solute to be studied. Glass is usual-

26

AMACHER

Syringe Sampler" Combination pH Electrode ..

Stirrer Thermometer Inert Gas Dispersion Tube

Acid or Base Addition

Suspension

Fig. 2-4. Typical batch reactor configuration. pH is controlled by a combination pH electrode and automatic buret connected to an autotitrator; a syringe sampler allows for removal of a subsarnple of suspension; an addition port permits injection of solute; an inert gas is bubbled through the suspension by means of a gas dispersion tube and the system is vented through a gas trap; a thermometer allows for temperature monitoring; and the suspension is mixed with an overhead stirrer.

ly more suited for use with organic solutes, and plastic is usually more suited for some inorganic species (e.g., trace metals). A glass or plastic Erlenmeyer flask makes a suitable low-cost reactor. The size of the reactor is largely dictated by the volume and number of samples to be taken. The reactor should be of sufficient size to obtain an adequate number of samples to accurately describe the kinetics of the reaction, and the volume of each sample must be sufficient to obtain accurate analytical measurements. Normally, a 1- to 2-L-reactor volume is adequate for most studies. The reactor contents can be mixed with an overhead stirrer or from below with a magnetic stirrer. Mixing techniques are critical and are discussed in more detail below. If accurate temperature control is required, the reactor may be surrounded with a jacket through which a fluid (normally water) is pumped to maintain a constant temperature. Alternatively, the reactor can be placed in a constant temperature bath. When temperature must be monitored, the reactor must be equipped with a thermometer as temperatures inside the reactor may vary slightly from the constant temperature bath or jacket because of reactions and mixing. Batch reactors are often equipped with gas dispersion tubes through which an inert gas such as N z or Ar is bubbled through the suspension, This is only necessary if one wants to sweep CO 2 and Oz out of the suspension,

OBTAINING & ANALYZING KINETIC DATA

27

If complete exclusion of CO z and Oz is required, or if exact control of the

gas composition in the reactor headspace is needed, the reactor must be completely sealed from the atmosphere and a gas trap must be used to vent the purge gas and to prevent contact between the reactor headspace and the outside atmosphere, This is normally required only when precise control over redox status is needed. An addition port is provided for the addition of the soluble reactants or other solutes. A simple funnel may be used if the suspension is open to the atmosphere, otherwise a serum stopper for use with a syringe needle is required. The syringe sampler consists of a tube into the suspension the top of which is constructed to allow connection to a Luer-lock syringe (Baxter Scientific Products, McGaw Park, IL). Syringe size depends on the volume to be sampled, but normally a 1O-cm 3-plastic syringe is used. The rubber end of the syringe plunger can sometimes cause contamination problems, especially with Zn. More costly plunger syringes made with Teflon are needed in such cases. The syringe should be filled with inert gas prior to sampling to avoid introducing CO z or Oz into the suspension during sampling if these gases must be excluded. A pH electrode connected to an autotitration instrument (pH meter, controller, and autoburet) is often used to maintain a constant pH (pH-stat) during the reaction. If it is desired to monitor pH changes during the reaction, t hen the pH meter can be connected to a recorder. It should be remembered that autotitration units have finite response times that are longer than many surface-controlled reactions. Thus, pH changes can occur before the autotitrat ion system can fully respond, and there will be some delay between the reaclion and return to pH-stat conditions. A batch reactor of the type just described was first developed and used hy Patrick et al. (1973) to study soils under controlled pH and redox condiI ions. Although not developed to collect kinetic data per se, the Patrick et III. (1973) batch reactor was the forerunner of subsequently developed kinetichatch reactors. Zasoski and Burau (1978) developed a batch reactor designed speci fically for sorption kinetic experiments. The use of the Zasoski and Burau (1978) reactor to obtain kinetic data largely follows the sequence outlined III lig. 2-3. Harter and Lehmann (1983) used a Zasoski and Burau (1978) type reactor to separate rapid ion-exchange (or surface-complexation) reacnuns involving Ni and Cu from slower retention reactions. Van Riemsdijk III1lI l.yklerna (1980a,b) and Van Riemsdijk and de Hann (1981) used a batch u-uctor under pH-stat and P-stat conditions to study P-retention kinetics by ~lIils and soil constituents under constant supersaturation with respect to metal phosphates, Similarly, Phelan and Mattigod (1987) used a pH-stat and Ca~IIII reactor to study the kinetics of P precipitation from supersaturated so1111 ions. These are good examples of specialized adaptations of the basic batch '1'IIr1or 10 study precipitation kinetics. Amacher and Baker (1982) used a IIISllSki and Burau (1978) type reactor to study the kinetics of Cr(lll) oxidanun hy soils and MnOz minerals and the kinetics of Cr(VI) reduction by fulIll'

add.

28

AMACHER

Mixing Techniques The method of mixing and the mixing rate in a batch reactor are critical to obtaining consistent results. The rates of many, if not most, and perhaps all surface-controlled reactions such as ion exchange and surface complexation may be controlled by mass transfer processes such as diffusion through the hydrodynamic film surrounding the solid particles (film diffusion), by diffusion into or through the particle (particle diffusion), or by a combination of the two diffusion processes. Diffusion control occurs when the rate of transfer of the solute to the particle surface is rate limiting (i.e., slower than the more rapid ion-exchange or surface-complexation reaction). Diffusion-controlled ion exchange was first demonstrated for reactions of univalent cations on synthetic ion-exchange resins (Boyd et aI., 1947). Boyd et aI. (1947) also developed the mathematical equations to describe diffusioncontrolled, ion-exchange kinetics. Numerous criteria have been used to distinguish between film and particle-diffusion controlled kinetics, including mixing rate, form of the kinetic equation obeyed by the data, and temperature dependence of the kinetics, but perhaps the most reliable method has been the use of the interruption test (Kressman and Kitchener, 1949). In this test the ion-exchange material is enclosed in a wire-mesh cage attached to the end of a centrifugal stirrer. The reaction is begun by lowering the rotating stirrer with the ion-exchange material in the cage into the solution containing the solute of interest. After a timed interval the reaction is "interrupted" by raising the still rotating stirrer out of the solution. Analysis of the ion-exchange material and solution phases gives the extent of the exchange reaction for the time interval. The process is repeated at various intervals. If particle diffusion is rate limiting, the ion-exchange rate immediately after reimmersion of the particles is greater than before interruption. If film diffusion is rate limiting, then interruption has no effect on reaction rate. The wire-cage apparatus is usable if the particle size of the exchange material is large enough to be contained in the cage where openings must be large enough so that the solution will flow rapidly through the cage. Thus, the wire-cage apparatus cannot be used for clay-sized particles. To solve this problem, Bunzl (1974) attached peat particles to a polyvinylchloride cylinder with a small propeller at the lower end. They were then able to use the interruption test to show that the rate of Pb-H exchange on peat is film-diffusion controlled. In a batch reactor of the type described above it is desirable to reduce or eliminate film diffusion by vigorous mixing of the suspension. If mixing is sufficiently vigorous, particle diffusion may be reduced or eliminated as well. Kressman and Kitchener (1949) showed that mixing was optimum at a stirring speed of 1000 to 1100 rpm for ion exchange in the synthetic resin system. Ogwada and Sparks (1986c) investigated the effect of t ypc and rate of agitation on the kinetics of K sorption by a Chester 1011111 (fine-loamy, mixed, mesic Typic Hapludult). Their original paper pI csenl s the dat a in tabular

29

OBTAINING & ANALYZING KINETIC DATA

..... 0 - 0 Specific Surface - Stirred

. - . Spoclflc Surlaco - Vo"nod

6.25

.....

6.00

Q)

5.75

o

C ..L..

5.50

::l

..o

Q)

Q. (/)

/

--

r o

-
(/)

o

f-

5.25

_~-1Ol 500

i/

'" • /

0 - 0 ka - Stirred . - . ka - Vorlexed

1000

1500

2000

3.000 __

.....

2.500 I c: 2.000

°E

......., 1.500 c

. 1.000

~

2500

Mixing Rate (rpm)

Fig. 2-5. Effect of type and rate of mixing on soil surface area and apparent rate coefficients for K exchange (adapted from Ogwada and Sparks, 1986c). Specific surface is indicated by circles and rate coefficients by squares. Open symbols signify the stirred system, whereas filled symbols signify the vortex mixed system.

form. To clearly show the effect of type and rate of agitation on the specific surface of the soil and their measured apparent rate coefficient for sorption, I heir results are graphed in Fig. 2-5. In the stirred system k a , the apparent rate coefficient for K sorption, increased steadily with increasing stirring rate. A sharp increase in specific surface was observed at the highest stirring speeds indicating that some part ide abrasion was occurring. The increase in surface area could account for 1111 increase in reaction rate. However, k a also increased when specific surlucc did not, indicating that the extent of film-diffusion control on reaction nuc diminished with increasing stirring rate. The type of agitation had a large effect on k a , but not on specific surIucc. In the vortex-mixed system specific surface did increase with vortex rutc, but the increase was not as large as in the stirred system. Furthermore, the specific surface in the vortex system at the lower vortex rates was the 811111e as that in the stirred system at the lower stirring rates. Prolonged agi1111 ion periods are probably required to produce measurable effects on surlul'c area and reaction rate. The difference in k a values between the stirred and vortex-mixed systrills and the dependence of k a on mixing rate in each mixing system indi"'1I1cs Ihat film diffusion was probably the controlling reaction rate in the .'Illed system, that film diffusion control was diminishing as stirring rate 11I1'Il'ascd, that film diffusion was eliminated in the vortex system and now 1'1111 ide-diffusion controlled reaction rate, and that particle-diffusion conIfill diminished with increasing vortex-mixing rate until the exchange reac111111 cont rolled the rate,

30

AMACHER

Studies of the type conducted by Ogwada and Sparks (l986c) are rare, which is unfortunate given the demonstrated importance of the type of mixing and mixing rate on the kinetic results. More quantitative data of the type produced by Ogwada and Sparks (l986c) is needed. Although the effect of agitation rate on the kinetics of P retention in soils has been documented (Barrow and Shaw, 1979), similar data for other solutes and for various soil constituents are lacking. It is expected that the mineralogy of the soil will play an important role in determining whether or not the type and rate of agitation will measurably affect surface area and reaction rates. Ogwada and Sparks (1986c) used the differences in observed rate coefficients between static (no mixing), stirred, and vortex-mixed systems to develop a method for separating and quantifying the rate-limiting step in ion-exchange reactions on soils and clays. By assuming that the steps in the ion-exchange process occurred in series (film diffusion ~ particle diffusion ~ exchange reaction) and by using the steady state approximation (mass transfer rate =:: exchange rate), they developed additive resistance relationships using reciprocals of the rate coefficients for each of the mixing systems Static system

[10]

Stirred system

[11]

Vortex system

[12]

where kos is the observed rate coefficient in the static system with no mixing; k ot is the observed rate coefficient in the stirred system; k ov is the observed rate coefficient in the vortex mixed system; k R is the rate coefficient for the exchange reaction; k p is the rate coefficient for particle diffusion; and k F is the rate coefficient for film diffusion. First-order kinetics is assumed throughout, and the reciprocals of the k's are the additive resistances for the mass transfer and exchange processes. Because kos' k ot' and kov are determined experimentally, the unknown k F and k p values can be calculated by suitable rearrangement of the additive resistance equations. Ogwada and Sparks (l986b) used this approach to show that the rate of K exchange on kaolinite was film-diffusion controlled under static conditions, but the rate of K exchange on vermiculite was both film-diffusion and particle-diffusion controlled under static conditions. Film diffusion and particle diffusion are affected by numerous experimental conditions (Sparks, 1989). In batch systems mixing greatly influences diffusion as already seen with vigorous mixing tending to reduce or eliminate diffusion control. In flow systems to be discussed in a later section, flow velocity affects film and particle diffusion. Hydrodynamic film thickness also affects film and particle diffusion. A decrease in film thickness favors particle-diffusion controlled kinetics. Hydrodynamic film thickness is in turn affected by the type and rate of mixing in a batch reactor, flow velocity in a flow system, hydration of cations, and ionic strength of the background electrolyte solution. Particle size also affects Iilm and parti-

OBTAINING & ANALYZING KINETIC DATA

31

cle diffusion. Film diffusion usually predominates with small particles. Ion concentration is also important. Film diffusion is usually favored in solutions of low ionic concentration. The foregoing discussion has established the importance of mixing in batch reactors. Mixing in batch reactors of the type described above is normally accomplished in one of two ways: from below using a stir bar driven by a magnetic stirrer or from above using a propeller connected to a stirring motor. Either method can promote effective and vigorous agitation that will reduce or eliminate film diffusion. Reduction or elimination of particle diffusion, however, may not be possible in stirred reactors as the mixing rate is usually not as vigorous as with a vortex mixer. The stir bar and magnetic stirrer approach is probably the simplest and easiest to use. Heating of the reactor from the stir plate can be eliminated by placing a heat shield between the stir plate and reactor and by enclosing the reactor in a constant-temperature jacket. Mixing with a stir bar over long periods in a glass reactor suffers from the disadvantage of having quartz introduced into the reactor by the grinding action of the stir bar and sorbent on the glass. The overhead stirrer will eliminate this problem, but propeller design is critical to obtaining good mixing action. The propeller must be positioned near the bottom of the reactor to keep the particles in suspension. Mixing must be vigorous enough to keep sand-sized particles in suspension, and a vortexing action must be created to pull organic matter under the surface that otherwise would float on top. The stratification of soil constituents in batch reactors because of weight differences is a recurring problem, and satisfactory results cannot always be obtained with some soils. In a batch reactor that must be sealed against the outside atmosphere, mixing is most easily accomplished from below with a magnetic stirrer. However, specially designed propellers with bearings and gaskets are available to stir-sealed reactors from above. Regardless of method used, mixing should be as complete, uniform, and vigorous as possible with no unmixed zones in the reactor. When the solute reactant is added, mixing should be complete in less than 5 s. Dyes or other colored solutions can be used to test the mixing process by visual observation. Many batch experiments are of course not conducted in reactors as elaborate as that described above. When centrifuge tubes or Erlenmeyer flasks are used as simple batch reactors, mixing is normally accomplished by vortcxing, reciprocal shaking, or end-over-end shaking in the case of tubes or by rotational or wrist-action shaking in the case of flasks. Separation of Solid and Liquid Phases

This aspect of batch reaction methods is also critical to obtaining good results. Rapid filtration is normally used to separate the solid and liquid phases when samples are removed from a typical batch reactor. When rapid reacI ions are studied, sampling with the syringe sampler must be rapid and reproducible as the reaction is continuing as the sample is taken. A 5-s sampling time is nearly optimal, but it should not exceed 10 s including connec-

32

AMACHER

tion of the syringe to the filter holder. Similarly, filtration time is also critical because the reaction is still proceeding as filtration occurs. Reproducible filtration times are mandatory to obtaining consistent results. The filtration time will depend on the nature of the solid phase as well as the solution/solid ratio. Well-dispersed solid phases with small particle sizes can take longer to filter. Short filtration times are favored by wide solution/soil ratios. One should strive for the lowest, most consistently reproducible filtration time. The pore size of the filter also affects filtration time, with smaller pores yielding longer filtration times. Normally, 0.2- or 0.45-l£m membrane filters are used. The filters and holders must be chemically inert and should not sorb the solute of interest. They also should not release contaminants into the filtrate. Polycarbonate filters have been found to produce consistent results in this regard. The volume of the sampled solution and the weight of the separated solid phase can be determined as a check on whether the original solution/solid ratio in the batch reactor is maintained in the sample. Also, the separated solid phase can be analyzed as a check on the mass balance of the solute in the system. Zasoski and Burau (1978) demonstrated that the solution/solid ratio was not significantly altered by repeated sampling in a batch reactor. For the study of slower reactions, centrifugation is acceptable for separating the solid and liquid phases. However, the reaction will still continue across the solid/liquid interface although at a reduced rate. Centrifugation is valid if the extent of the reaction changes little during the time required for centrifuging and sampling. In Situ Methods

In some cases separation of solid and liquid phases can be avoided by using in situ analysis techniques. The only readily available method for monitoring solutes in batch reactors is the use of ion-selective electrodes. Spectroscopic methods for studying the kinetics of solute reactions on solid surfaces are still largely in the developmental stage. The subject of in situ analysis has already been introduced by discussion of the pH-stat characteristics of the batch reactor. Reactions at electrode surfaces are much the same as reactions at the surfaces of soil constituents. Electrodes have finite response times that may exceed or are on the same order of magnitude as the rapid reactions at soil surfaces. Therefore, the reaction at the soil surface can be largely complete before the electrode can respond to changes in solute activity. Despite this limitation, in situ methods with ion-selective electrodes are preferred over phase separation methods where appropriate because extra steps with additional sources of experimental error are eliminated. A serious limitation on the use of some ion-selective electrodes with soils is the presence of interferences in the soil solution. Interferences are much more readily controlled in studies with pure soil constituents where the chemical composition is known and can be controlled. Ion-selective electrodes with the greatest potential for in situ kinetic studies include those for NH 4 • K, ell, ('u 2 + ,

OBTAINING & ANALYZING KINETIC DATA

33

Cd2+, and Pb z+ . Ogwada and Sparks (1986b) used a K electrode to study the kinetics of K ion exchange. Aringhieri et al. (1985) used Cd2+ and Cu z+ electrodes to study the kinetics of Cd and Cu retention by a Histosol. Jopony and Young (1987) used a Cu 2+ electrode to study Cu desorption kinetics in the presence of an EDTA sink, which lowered Cu 2+ activity and thus initiated desorption. Radiotracer Methods This is a specialized technique so it is considered separately. Radiotracer methods are an excellent means of following the extent of kinetic reactions. The radiotracer is a radionuclide of the solute of interest. Addition of the radiotracer to the system results in isotopic dilution of the chemical species of interest. It is assumed that the radiotracer behaves chemically in an identical fashion as the stable radionuclide. Because radiotracer analysis is often sensitive, low concentrations of solute can be monitored with relative ease. Radiotracer concentrations can be chosen to yield optimal ratios of radiotracer activity to background activity. Corrections for radioactive decay are avoided by counting standards and samples at the same time. Another major advantage is that small aliquots « 1 mL) of solution can be taken for analysis. This makes the method particularly suited to studying reactions in small batch reactors such as centrifuge tubes. Small aliquots of solution removed for analysis alter the solution/soil ratio only slightly and amounts of solute sorbed by the solid phase are readily corrected for the small amount removed by sampling. Radiotracers have long been used to study ion-exchange reactions at or near equilibrium. An example of their use in kinetic studies was provided by Amacher et al. (1986) who studied the kinetics of Cr(VI), Cd, and HgClz(aq) retention by soils using radiotracers to follow the extent of the reactions. Advantages and Limitations Batch methods for obtraining kinetic data have a number of advantages including:

1. There are generally low-cost equipment requirements, and batch reactors are relatively easy to use. 2. Film diffusion and sometimes particle diffusion are eliminated by sufficiently vigorous mixing. 3. Constant solution/solid ratio is readily maintained in some batch reactor systems. 4. Reaction conditions such as pH, ionic strength, and removal of CO z and Oz are easily controlled. Balch methods also have a number of limitations including: I. Desorbed species are not removed and are allowed to accumulate in the inherently closed system of the batch reactor. Thus, unless a unidirectional reaction is being studied, reverse reactions must be taken into account in the data analysis. The accumulation of desorbed

34

AMACHEE

species can sometimes result in secondary precipitation reactions, which further complicates data analysis. 2. The mixing method employed may not produce a uniform suspension and may not be sufficient to limit mass transfer of solute. Furthermore, surface area may be increased by prolonged mixing by some methods. 3. Sampling and phase separation steps are not always uniform and are operator dependent. In the cases of rapid surface reactions sampling and phase separation are not rapid enough to follow the reaction. Despite these limitations batch methods will probably continue to be used to study kinetic reactions in soils where appropriate owing largely to their simplicity. The simplest batch reactor of all (the centrifuge tube) can still be effectively used to obtain kinetic data if the following criteria are met: 1. The reaction(s) are sufficiently slow so that the reactant concentrations will not change appreciably during centrifugation and sampling steps. Even in the case of rapid reactions, this traditional batch method can still be used to study sorption after attainment of steadystate conditions. 2. Small aliquots of sample are taken so that the solution/soil ratio is only slightly altered. Microanalytical or radiotracer techniques permit this approach. 3. pH does not need to be continuously monitored and adjusted. Adjustments in pH or pH measurements are possible with this batch method, but they can only be done at discrete time intervals. Often this is sufficient. 4. Continuous purging with inert gas is not required. Samples can be purged initially and at subsequent intervals if necessary. Tubes can be opened in a controlled atmosphere glove box to avoid contact with CO 2 or O 2 if required. Flow Methods

To overcome some of the problems associated with batch methods, flow methods have been developed and used to obtain data on kinetic reactions in soils and soil constituents. A review of these methods is given by Sparks (1989). A summary of some of the kinetic studies using flow methods is given in Table 2-1. A unique feature of flow methods as contrasted with batch methods is that flow methods are inherently open systems. Solute is continually added to the system with flow methods, and reaction products are continually removed. This unique feature produces special attributes for the flow methods that solve some of the problems associated with batch systems, but also involve some limitations as well. Perhaps the chief advantage of flow methods is the continual removal of reaction products that in batch reactors are allowed to accumulate. Another unique attribute of flow methods is that the solution/soil ratio is much narrower than that used in batch reactors. In the

35

OBTAINING & ANALYZING KINETIC DATA

Table 2-1. Summary of studies using flow methods to obtain kinetic and sorption isotherm data. Type of flow method

Reaction studied

Reference

Miscible displacement (thin disk) Miscible displacement (thin disk) Fluidized bed

Al/NH 4 exchange on soils KINH 4 exchange on soils K exchange on soils

Sivasubramaniam and Talibudeen (1972) Sparks et al. (1980)

Albite weathering as a function of pH K exchange on soils

Chou and Wollast (1974)

Miscible displacement (thin disk) Miscible displacement (thin disk) Miscible displacement (thin disk) Miscible displacement (thin disk) Soil column Stirred-flow reactor Miscible displacement (thin disk) Miscible displacement (thin disk) Miscible displacement (thin disk) Stirred·flow reactor Miscible displacement (thin disk) Stirred·flow reactor Stirred·flow reactor Miscible displacement (thin disk] Htirred·flow reactor Ht.irred·flow reactor

Sparks and Jardine (1981)

K exchange on soils and clays

Sparks and Rechcigl (1982) Jardine and Sparks (1984)

K exchange on soils and clays

Sparks and Jardine (1984)

P sorption by soils under p. stat conditions K exchange on kaolinite Al sorption by clay minerals and peat K exchange on soils

Van Riemsdijk and Van der Linden (1984) Carski and Sparks (1985) Jardine et al. (1985a,b)

K exchange on soils

Data analysis theory and methods NH r N release from soils S04 sorption/desorption in soils Zn, Cd, and Hg sorption by humic acids Data analysis theory and methods P and Si sorption on goethite CalMg exchange on soils NOs sorption/desorption on soils

Ogwada and Sparks (1986a,b,c) Skopp and McCallister (1986) Carski and Sparks (1987) Hodges and Johnson (1987) Randle and Hartmann (1987) Schnabel and Fitting (1988) Miller et al. (1989) Seyfried et al. (1989) Toner et al. (1989)

I'.asoski and Burau (1978) type batch reactor solution/soil ratios are typicallv 011 the order of 100 to I, whereas in flow type reactors the ratio is typicallv less than 1 to 1. Narrow solution/soil ratios are sometimes used in simple rrutrifuge tube batch reactors where ratios from 1:1 to 10:1 are often used. hi II hcrrnore, in flow reactors the solid phase will be reacted with a greater mass of solute (concentration X flow velocity x time) than in batch reacIIlIS (concentration X volume). Two basic types of flow methods can be distinguished: those with mix11111. and those without. The chief limitation of unmixed flow reactors is that IIlass transfer processes are frequently limiting and in the case of fast chemi,nlreactions are probably always limiting. Stirred-flow reactors and fluidized hi'll reactors may often overcome the mass transfer limitation, and indeed IIH'Sl' hybrid techniques may represent the best attributes of batch and flow IIll't hods. Each of these approaches is considered in turn.

36

AMACHER

Thin-Disk Method

This method is also referred to as the miscible-displacement or continuous-flow method. In this method a thin disk of dispersed solid phase is deposited on a porous membrane and placed in a holder. A pump is used to maintain a constant flow velocity of solution through the thin disk and a fraction collector is used to collect effluent aliquots. A diagram of the basic experimental setup is shown in Fig. 2-6. A thin disk is used in an attempt to minimize diffusion resistances in the solid phase. Disk thickness, disk hydraulic conductivity, and membrane permeability determine the range of flow velocities that are achievable. Dispersion of the solid phase is necessary so that the transit time for a solute molecule is the same at all points in the disk. However, the presence of varying particle sizes and hence pore sizes may produce nonuniform solute transit times (Skopp and McCallister, 1986). This is more likely to occur with whole soils than with clay-sized particles of soil constituents. Typically, 1- or 2-g samples are used in kinetic studies on soils with the thin disk method, but disk thicknesses have not been measured. In their study of the kinetics of phosphate and silicate retention by goethite, Miller et al. (1989) estimated the thickness of the goethite disk to be 80 J.tm. The available evidence suggests that thin disks do not minimize masstransfer processes. Comparisons of the thin-disk-flow method with batch methods have shown that apparent rate coefficients are larger in batch systems and that steady-state conditions are obtained sooner (Sparks and Rechcigl, 1982; Ogwada and Sparks, 1986a). In addition, apparent rate coefficients obtained from the thin-disk method may depend on the flow velocity through the disk. Thus, thin-disk methods give rate coefficients for overall kinetic processes including mass transfer and reaction steps. A problem with the thin-disk method that was uncovered by Carski and Sparks (1985) is that the influent solution can be diluted by the solution used to load the solid phase onto the membrane filter, or the washing out of Thin Disk Supported on Membrane Filter

Pump

• 8

I~.·~·~ 18

Reservoir Fig. 2-6. Thin-disk flow method experimental setup. Background solution and solute arc pumped from the reservoir through the thin disk and are collected as aliquots by the 1'1'lIl'llolll'OlIcl:tor.

37

OBTAINING & ANALYZING KINETIC DATA

leftover sorbing solution during desorption ean produce concentration changes not due to sorption or desorption. The dilution and washout effects could erroneously lead one to conclude that sorption and desorption has occurred when in fact there has been no reaction with the solid phase at all. This dilution and washout effect was demonstrated by Carski and Sparks (1985) for B flowing through acid-washed sand where no retention was expected to occur. An additional problem with the thin-disk method is that control over reaction conditions within the thin disk is not usually possible. Although pH and other solution composition variables can be controlled in the influent solution, once the solution contacts the thin disk, direct control with feedhack is no longer possible.

Stirred-Flow Method Stirred-flow methods have long been used by chemical engineers and chemists to obtain kinetic data in homogeneous sytems. They have only recently been used to obtain kinetic data in heterogeneous soil systems (Carski lind Sparks, 1985; Randle and Hartmann, 1987; Miller et al., 1988; Seyfried el aI., 1989). The experimental setup for this method is shown in Fig. 2-7. It is identical to the setup for the thin-disk method except that the stirred-flow reaclor is used in place of the thin disk. Flow through the reactor is maintained III a constant velocity by a pump, and a fraction collector is again used to collect reactor effluent.

Stirrer

Pump

• 8

I~.·~·~ Is

Reservoir Ilv .' 1. Stirred-flow reactor method experimental setup. Background solution and solute are

,,,,,,,pl'd from the reservoir through the stirred reactor containing the solid phase and are , ollcrtcd as aliquots by the fmc Iion collector. Separation of solid and liquid phases is accom,,'''hrd hy 1I membrane flher III the outlc: end of the stirred reactor.

38

AMACHER

@ ~Outlet _

..... Filter

Plunger

Fig. 2-8. Typical stirred-flow reactor (adapted from Carski and Sparks, 1985). This stirredflow reactor can be used in the experimental setup shown in Fig. 2-7.

Various designs of the stirred-flow reactor are possible. Carski and Sparks (1985) developed a relatively simple stirred-flow reactor constructed from a plastic syringe and membrane filter holder (Fig. 2-8). The volume of the reactor is adjustable to allow one to add and maintain a known amount of solution to a known amount of solid phase. Mixing is accomplished by a magnetic stirrer. Miller et al. (1988) developed a stirred-flow reactor in which stirring is accomplished by a propeller connected to a high-torque motor. A special bearing allows the propeller shaft to enter the reactor, but seals the reactor against leaks during solution flow. Stirred-flow reactors retain all the advantages of flow methods in general and eliminate all the problems associated with the thin-disk method. They also retain many advantages of the batch method. Reaction products desorbed into solution are continually removed. Film or particle diffusion is reduced or eliminated by mixing within the reactor. Direct control with feedback of reactor conditions is possible. Although stirred-flow reactors normally have much smaller volumes than conventional batch reactors, it is possible to construct a pH-stat stirred-flow reactor by inserting a microcombination pH electrode and microburette tip into the reactor. The O-rings can provide leak-proof seals where the electrode and burette tip enter the reactor. The electrode and burette tip are connected to an autotitrator as in the conventional batch reactor. Seyfried et al. (1989) showed that the Carski and Sparks (1985) stirredflow reactor is a well-mixed system in the flow velocity range of 0.28 to 2.20 mL min -I. A requirement of the stirred-flow method is f hal f he I ime-

OBTAINING & ANALYZING KINETIC DATA

39

dependent effluent solute concentration curves for any kinetic reaction be significantly different from the dilution curve (time-dependent concentration curve with no solid phase in the reactor) and from the time-dependent effluent solute concentration curve for an instantaneous reaction (Sparks, 1989). Although flow velocity can be increased to distinguish fast reactions from instantaneous ones, practical limits on the rates of reactions that can be distinguished do exist. The fastest reaction that can be measured is that producing a time-dependent concentration curve detectably different from the instantaneous case at the flow velocity and reactor volume conditions used. Seyfried et al. (1989) found that reactions with half-lives of greater than 0.3 min could be detected with a flow rate of 0.83 mL min - I in a reactor volume of 8.3 mL. The slowest reaction that can be studied with this method is that producing a time-dependent concentration curve detectably different from the dilution curve (no solid phase in the reactor). Because flow reactors remove desorbed species, one is tempted to ignore reverse reactions. However, it is only proper to do so when the reaction under consideration is known to be irreversible or when the reverse reaction is negligible compared to the forward one during the observed time frame. As relaxation studies with soil constituents have shown (Hachiya et al., 1979; Hayes and Leckie, 1986; Zhang and Sparks, 1989), reverse reactions can be quite rapid. Thus, the rate of removal of desorbed species in a flow method may not be sufficiently rapid to completely eliminate reverse reactions . •'Iuidized Bed Reactor

This type of reactor, which has its origins in chemical engineering, was used by Chou and Wollast (1984) to study albite weathering, but it can be used to study other types of reactions as well. The basic concept behind a lluidized bed is that the flow rate of the fluid is adjusted to equal the settling late of the particles in suspension. Settling rates of different-sized particles tend to be equalized by frequent collisions with other particles if the suspension density is great enough. It is best to use well-defined size fractions to uchicve this. A homogeneous, rapidly mixed suspension can be achieved with I his method. A diagram of a Chou and Wollast (1984)-type-fluidized bed reactor is shown in Fig. 2-9. The flow velocity needed to maintain particles in suspenvron is provided by pumping rate PI' whereas P z is the rate of addition of new solution and is also the output rate of reacted solution. Changing the I cncwal rate, P z, will control the residence time of the solution in the reac1111. Renewal rate P z must be small in comparison to mixing rate PI to maintnin a small difference in concentration between input at the bottom of the fluidized bed and output at the top of the bed. Chou and Wollast (1984) muinrained P z between 3 and 6070 of PI' The rate of reaction is obtained as I ItI' product of the renewal rate, P z, and the solute concentration difference ItI"I wccn input and output solutions normalized with respect to the total surIIIlT area of the solid phase. Since samples are collected at time intervals, ukulatcd reaction rates lire mcnn values for each time interval.

I

AMACHER

40

+P2 output Overlying Solution

+

Fluidized Bed

Input Solution

Fig. 2-9. Typical fluidized bed reactor experimental setup (adapted from Chou and Wollast, 1984). PI is the flow velocity that maintains the fluidized bed; whereas P 2 is the rate of input and output of solution and solute.

One of the advantages of this method is that vigorous mixing in the fluidized bed eliminates strong concentration gradients. Additionally, solute concentrations can be maintained well below saturation levels for various precipitates, and thus secondary precipitation reactions that complicate data analysis and interpretation can be avoided. The effect of reaction conditions (e.g., pH changes) can be studied by changing the input solution composition without manipulating the solid phase. Column Method with Batch Control This is a hybrid method that combines features of the batch reactor and flow through a soil column to obtain kinetic data. The method was developed by Van Riemsdijk and Van de Linden (1984) and is an advanced version of the P-state method of Van Riemsdijk and Lyklema (1980a,b). It is particularly suited to the study of the continuing slow reaction between phosphate and soils, where small concentration changes over small time intervals render the thin-disk method impractical. In the original P-stat batch reactor method both pH and P were kept constant because after a short reaction time the OH/P ratio of the reaction becomes constant. This approach was particularly useful in studying P retention by oxide surfaces. However, with soils the OH/P ratio changes with different soils and often the pH change during reaction is too small to control accurately. Thus, Van Riemsdijk and Van der Linden (1984) developed a new P-stat method applicable to the study of P retention by soils.

OBTAINING & ANALYZING KINETIC DATA

41

Solution Vessel .Magnetic Stirrer ...

l'ig.2-1O. Column method with feedback control experimental setup (adapted from Van Riemsdijk and Van del' Linden. 1984). MV l • MV2 • and MV 3 are the multiposition valves that allow up to eight columns to be run.

A diagram of the chemical part of the apparatus developed by Van Ricrnsdijk and Van der Linden (1984) is shown in Fig. 2-10. Eight soil columns are connected to eight vessels (only one of each is shown in the diagram). Solution is pumped from a vessel through a column and back into the vessel. A three-way valve makes it possible to pump solution from a vessd through a column independently of other columns. Running eight columns III one experiment is possible because the reaction rate of P with soils is relalively fast at the beginning (analysis at short intervals) and decreases with Ihill' (increase in time between analysis). Measurement in a succeeding column hegins after the reaction rate in the preceding column decreases substantially. Soil is mixed with an equal amount (by weight) of quartz sand and placed III it glass funnel fitted with a 10- to 16-Jtm glass filter plate. The solution ,_ distributed over the surface of the soil column by means of a perforated plutc at the top of the funnel and glass beads on top of the soil. The initial IHIIII ping rate is 25 mL min -I. The solution in the vessel is mixed by a maglit" ic stirrer. 'I'he vessels are connected to Positions 1 through 8 of multiposition valves (MV 1• MV2 , and MV3) . To take a sample from a vessel, MV 1 and MV 2 are _witched to the position corresponding to the vessel to be sampled. Then the 111111 way valve is switched and solution is pumped from the vessel MV\> t 1II01Il(h the four-way valve, through the sample injection valve and one of I hI' s.unple loops, through MV2, and back to the vessel again. After an ali1IIIlIl has been taken by switching the sample injection valve, the four-way vulvc is switched again and air is pumped 10 empty the tubes. thus avoiding

AMACHER

42

contamination of the vessels. The MV3 is used to add phosphate solution to the vessels. By switching the sample injection valve, an aliquot equal in volume to the sample loop is injected in a carrier stream and replaced by exactly the same volume of carrier solution. The composition of the carrier solution is identical to that used in the vessels except for P concentration. Different size sample loops can be used to cover various analytical ranges for P determination. Phosphorus is determined colorimetrically using a molybdate method with an ascorbic acid reductant. The P reagents are added from R 1 and R 2 , color development takes place in the reaction coil, and absorbance is measured by the spectrophotometer. A hydroxide salt is used to clean the tubes. The spectrophotometer, valves, and burette are controlled by a microcomputer and the pumps are run continuously. Details are given in Van Riemsdijk and Van der Linden (1984). Solutions in the vessels are completely mixed within 10 s. The initial 25 mL min -I pumping rate ensures that the solutions in the soil columns are changed within 1 min and the solutions in the vessels are changed within 3 min. The pumping rate decreases with time because of column silting. However, the P retention reaction decreases much faster than the pumping rate, so the decreased pumping rate does not appear to invaiidate the results. However, because this is a column method, diffusion processes are undoubtedly present and thus chemical kinetic data can only be obtained when the reaction and not diffusion is rate limiting. Radiotracer Methods As with the batch reactor method, radiotracers are an excellent means of following the extent of kinetic reactions in flow methods. Flow methods using radiotracers are identical to those where other analytical methods are used to determine the solute of interest except that a radiolabeled solute is used. Radiotracers have been used numerous times in column transport studies but apparently have not as yet been used with thin-disk and stirred-flow methods. Advantages and Limitations Many of the advantages and limitations of flow methods have already been discussed and are summarized here. Advantages include: 1. Low solution/soil ratios are employed that more realistically mimic those found under field conditions. 2. Desorbed species are continually removed from the reactor. Their presence can inhibit reaction completion and can sometimes result in complex secondary reactions that complicate data analysis and interpretation. 3. Phase separation is continual, and if the flow rate remains constant, separation times remain constant. 4. Flow methods are much more readily automated than batch methods. This reduces operator dependence and error.

I

OBTAINING & ANALYZING KINETIC DATA

43

5. Diffusion processes are reduced or eliminated if stirred-flow or fluidized-bed reactors are used. 6. Direct control with feedback of some reaction conditions can be obtained with some methods such as the stirred-flow or the column method of Van Riemsdijk and Van der Linden (1984). 7. Reactions can be studied under constant and controlled solute concentrations with some methods. 8. Input solution composition is readily changed with some methods. Some flow methods, however, do have limitations including: 1. Reaction rates are usually diffusion limiting in thin-disk and column methods. 2. Dilution and washout effects occur with thin-disk and column methods. 3. Direct control over reactor conditions is not possible with thin-disk methods. 4. In the stirred-flow method, time-dependent concentration curves for reactions must be distinguishable from the instantaneous reaction case and from the dilution curve obtained with no solid phase present. It is clear that most of the limitations with flow methods apply to the thin-disk method. Hybrid methods such as the stirred-flow and fluidized bed reactor combine the best features of batch and flow methods and eliminate or control many of the limitations of each. Future progress in the study of reaction kinetics in soils and soil constituents will most likely come from the use of hybrid batch-flow methods and from the use of relaxation methods where rapid chemical reactions can be studied.

Comparison of Batch and Flow Methods Few direct comparisons of batch and flow methods have been done. The most notable are those by Sparks and Rechcigl (1982), Ogwada and Sparks (l986a,b,c), and Miller et al. (1989). Available evidence indicates that there are differences in time to attain equilibrium, half-times of reactions, apparent rate coefficients, and activation energies between batch and thin-disk methods as expected. These differences are mostly due to differences in mass transfer rates between the methods. The work of Ogwada and Sparks (1986a,b,c) clearly established the importance of mixing rates and type of agitation in soil kinetic studies. When mass-transfer processes control reac1ion rates and the rate coefficients obtained are those for the overall kinetic process and not those for elementary chemical reactions, then these apparent or process rate coefficients cannot be used to calculate equilibrium conslants and thermochemical parameters (Ogwada and Sparks, 1986a). Equally disturbing is that sorption parameters (i.e., Langmuir sorption parameters) obtained from batch and thin-disk methods are different (Miller ('I aI., 1989). This was attributed to the fact that batch systems are closed whereas flow systems are open so that the competitive antecedent solute spe('il's is removed. It is apparent Ihat much more work needs to be done on

44

AMACHER

methods development and comparisons. If calculated kinetic parameters are method dependent, then this will obviously limit their usefulness in predicting and understanding solute reactions and transport in soils. Specialized Methods for Studying Desorption Reactions The methods described above can be used to study both sorption and desorption kinetics although the batch method does not readily lend itself to the study of desorption kinetics unless dilution or infinite sink techniques are used. Because desorption studies are approached differently from sorption studies, special techniques are often required, as discussed next. Flow Methods Flow methods, because they readily remove desorbed species, are one of the best methods for studying desorption kinetics. Sparks et al. (1980) used the miscible displacement method to study K desorption kinetics. However, mass transfer processes are clearly rate limiting with this method, and thus great care must be used in interpreting the results. The previous discussion on the limitations of this method is relevant to desorption studies. Stirred-flow or fluidized bed methods can be used to minimize diffusion in desorption experiments, but they have not yet been used specifically for desorption studies. Dilution Methods Dilution of the equilibrium or steady-state solution in contact with the soil has been used to determine the reversibility of sorption reactions (Elrashidi and O'Connor, 1982a,b; Peek and Yolk, 1985). The method is also applicable to kinetic studies (Amacher et al., 1986, 1988). The method is particularly suited to sorption and kinetic experiments conducted in centrifuge tubes. When the sorption reaction has reached apparent equilibrium or a steady state, a portion (or all) of the solution in contact with the soil is replaced by a solution of identical composition to the equilibrating solution except that the replacement solution does not contain the solute of interest. This results in dilution of the solute concentration in remaining equilibrating solution and initiates the reverse desorption reaction. Further step-wise dilutions can be done. The dilution method is not suitable for use with Zasoski and Burau (1978)-type batch reactors, because the solid and solution phases must be separated, so that the fraction of the solution phase can be replaced, and then the phases are remixed. Flow methods are of course readily suited for use with the dilution technique, because the input solution can be easily replaced with an identical solution without the solute of interest, and then desorption occurs during continuous flow. Although it has apparently not been used in this regard, the dilution method can be used as a relaxation method. The dilution step serves as the perturbation of the equilibrium or steady state, and the time required to reattain equilibrium is the relaxation time.

OBTAINING & ANALYZING KINETIC DATA

45

Infinite Sink Methods Infinite sink methods were developed to overcome problems associated with the accumulation of desorbed species in batch experiments. Infinite sinks are ideally suited to the study of desorption kinetics in batch systems. A sink is a solid phase that removes the desorbing species from solution so that a chemical potential gradient is established. Ideally, a sink should be infinite so that an essentially irreversible reaction from the soil to the sink is established (resorption by soil can be neglected and the rate of sorption of the solute from solution by the sink is much greater than the rate of release from the soil so that solute concentration in solution is minimized). The sorption capacity of the sink must be large enough so that it does not become rate limiting. A variety of infinite sinks have been employed including ionexchange resins, strongly sorbing mineral phases, and precipitation sinks. Unfortunately, in practice sinks are not always found to be infinite. Infinite sinks have been used primarily to study P and K desorption kinetics from soils. Ion-exchange resins have been the more popular choice. Recent examples include the studies of P desorption kinetics by Pavlatou and Polyzopoulos (1988) and K desorption kinetics by Sadusky et al. (1987). Van der Zee et al. (1987) used Fe-oxide impregnated filter paper as an infinite sink to study P desorption kinetics from soils. The affinity and capacit y of this sink for P was large enough to maintain negligible P concentrations in solution, and thus it served as an infinite sink. Griffin and Burau (1974) used mannitol as a precipitation sink for B to study B desorption from soils. Two separate pseudo-first-order reactions and a slow reaction were found. Specialized Methods for Separating Reactions As Fig. 2-1 implies there is considerable overlap in reaction times for various reactions in soil systems. Thus, separating the various complex react ions to study their kinetics independently is difficult. Some separation is uchicved by the simple choice of method. For example, relaxation methods lire used to study the kinetics of ion-exchange and surface-complexation react ions independent from any diffusion processes (Sparks, 1989). Harter and lclunann (1983) discussed the use of kinetics to distinguish between the almost lnxruntaneous initial ion-exchange reaction at soil surfaces and concurrent III consecutive slower ion-retention reactions. Jardine and Sparks (1984) used rei vlt rirnethylammonium bromide to block external ion-exchange sites and voul'irmed that there were two K exchange reactions occurring on an Eveshoro loamy sand (Typic Quartzipsamment) corresponding to sites of differt'lIl selectivity. Ogwada and Sparks (1986a,b,c) used different methods pi iuurrily based on mixing technique and rate to delineate and separate differ1'111 eli ffusion processes as already discussed. Pavlatou and Polyzopoulos (l'/HH) used the Aharoni and Suzin (1982a,b) diffusion model to separate timedqwlldenl P desorption curves into regions that could be sequentially dt'snibed by parabolic, Elovich, and exponential equations at small, interrurdiutc, and large times, respectively.

46

AMACHER

The initial fast P retention reaction with soils is usually regarded as a surface-complexation reaction that can be described with the Langmuir equation, whereas the continuing slow reaction is regarded as precipitation and is usually described by first-order kinetics (Sposito, 1986). However, given the complexity of the processes involved there is no clear consensus. Mendoza and Barrow (1987) proposed that the continuing reaction between P and soils is the penetration of sorbed P into the sorbing surface (internal diffusion). Van der Zee et al. (1989) developed a model to describe both the initial P sorption reaction and the continuing slow reaction. The kinetic Langmuir equation was used to describe adsorption, and a diffusion-precipitation model was used to describe the slow reaction. Van der Zee et al. (1989) used the Fe-oxide impregnated filter paper method (Van der Zee et aI., 1987) to measure P desorption kinetics, a column leaching experiment to establish an adsorption isotherm, and total sorption (adsorption + precipitation) was measured by the Van Riemsdijk and Van der Linden (1984) method previously discussed. Using these methods and their model, Van der Zee et al. (1989) were thus able to separate and describe P reactions with soil. Amacher et al. (1988), Selim and Amacher (1988), and Harter (1989) developed nonlinear, second-order, and first-order multireaction models, respectively, to describe element retention by soils. Reactions are distinguished on the basis of mass-action kinetics and these models were found to describe the kinetics of element retention in soils when single-reaction rate functions failed (Amacher et aI., 1986). The approaches of Aharoni and Suzin (1982a,b), Harter and Lehmann (1983), Amacher et al. (1988), Selim and Amacher (1988), and Harter (1989) are model-based approaches in that data analysis methods are used to distinguish reactions. The approach of Van der Zee et al. (1989) is both a model and experimental method-based approach to separating reactions. The other techniques described are primarily experimental. Given the complexity of reactions in soils, it is clear that further work on reaction separation methods is needed.

DATA ANALYSIS METHODS The objective in developing a kinetic expression is to obtain an overall rate function that will describe the observed reaction kinetics. Determination of the rate function also involves determination of the reaction order and rate coefficients. A number of useful methods are available to derive overall rate functions from experimental data and each of these is described here. Initial Rate Method This method depends on measurement of initial rates of an overall reaction before effects of accumulating products (desorbed species) and effects of decreasing reactant concentrations complicate the rate function. The

47

OBTAINING & ANALYZING KINETIC DATA

method depends on the use of sensitive analytical methods (e.g., radiotracer methods) to determine rates at small reaction extents. If the overall rate is sufficiently slow so that no significant chemical changes occur during the measurements, the initial amounts of each reactant can be varied while holding the others constant to find the relationship between initial rate and initial reactant concentration. This relationship is given by log R,

=

log k

,

+

0

nA log C A

[13]

where R, is the initial rate, k: is the pseudo-rate coefficient, nA is the reaction order for Reactant A, and C~ is the initial concentration of A. A plot of R, vs. C~ will be a straight line with slope nA and intercept k ': This equation is applied to each reactant until the reaction orders for all reactants are found (Gardiner, 1969; Lasaga, 1981). The initial rate method has only rarely been applied to soil kinetics studies. Aringhieri et al. (1985) used the initial rate method to establish that the reaction orders for each reactant (element and soil) were unity for Cu and Cd retention by a soil. The overall reaction was thus second-order. The major obstacle to the use of the initial rate method to determine reaction orders is that most ion-exchange and surface-complexation reactions occur so rapidly that the initial rate cannot be accurately determined before I he reverse reaction becomes significant. Flow methods with high flow velocities perhaps offer the best chance of measuring initial rates of some of I he slower reactions because desorbed species are quickly transported away from soil surfaces. Method of Isolation In the method of isolation all reactants except one are present at large concentrations during the reaction. The rate function for the isolated reactum is then determined. This process is repeated for all reactants (Gardiner, 1%9; Lasaga, 1981). For example, if the true overall rate function for the reaction is [14]

where CA and C B are the concentrations of Reactants A and B, respectively, and if the initial concentration of B, C~ , is much greater than Ciso that It docs not vary significantly over the course of the reaction, then the rate Iunct ion can be rewritten as [15] where k = k C~. Thus, the second-order rate function reduces to a first'" dt'r function. The method of isolation is often assumcd in kinetic studies on soils and oilill'llllstiluenls. Frequently, first-order kinetics for the solute of interest I

48

AMACHER

is assumed but never tested, and the reaction sites on the solid phase are assumed to be present in excess of the solute so that the reaction rate does not depend on their concentration. This assumption may be erroneous. Often the quantity of reaction sites on the solid is not known with any degree of certainty. In the case of exchangeable cations, the total quantity of reaction sites is given by the cation exchange capacity (CEC). In the case of other solutes such as transition metals and oxyanion species that can react with metal oxide and organic matter surfaces with variable charge, the total quantity of reaction sites is not known with certainty. It can be estimated by the maximum sorption capacity as determined by the family of Langmuir equations applied to solute sorption data. The real complicating factor, however, is the possible presence of different types of reactions sites in soils that display different reaction kinetics. When this occurs, the quantities of the different types of reaction sites are not known and can only be guessed at. Although the total quantity of reaction sites may be in excess, quantities of some types may be limiting and thus pseudo-first-order kinetics is not obeyed. This situation may occur more often than is realized (Amacher et al., 1988; Selim and Amacher, 1988).

Graphical Methods Often the fit of the data to an assumed integrated rate function is used as a test of the validity of that rate function (Gardiner, 1969; Lasaga, 1981). Many integrated rate functions are linear functions of time so that if the data are plotted according to the integrated rate function and a straight line is obtained, then the data are said to follow that rate function. One of the simplest cases is if the data give a straight line on a plot of reactant concentration on a log scale vs. time, then first-order kinetics is obviously obeyed. Unfortunately, soil kinetic data seldom show correspondence to simple integrated rate functions (Amacher et al., 1986).

Rate Coefficient Constancy Assumed integrated rate functions are again used in this approach. Rate coefficients are calculated for each assumed rate function applied to data sets from kinetic experiments where variables such as initial reactant concentrations were systematically varied. The rate coefficients are then compared to each other. The correct rate function should be the one for which a set of calculated rate coefficients shows only random scatter about the average value for the set. Incorrect rate functions will have rate coefficients that vary systematically with initial concentration and time (Gardiner, 1969). The latter situation is frequently observed for soil kinetic data (Amacher et al., 1988).

I

OBTAINING & ANALYZING KINETIC DATA

49

Fractional Lives Method In this method the time required for a given fractional decrease in starting concentration (frequently the half-time of the reaction) is measured as a function of initial reactant concentrations. A log-log plot of fractional lives vs. initial concentration will give the reaction order (Gardiner, 1969). Often fractional lives methods will be used as a convenient way of analyzing kinetic data. Boyd et al. (1947) and Kressman and Kitchener (1949) used a fractional-lives type approach to analyze their ion-exchange kinetic data. A reaction half-time approach to analyzing soil kinetic data was discussed by Seyfried et al. (1989). Parameter-Optimization Methods In this approach a particular rate function is assumed and nonlinear leastsquares parameter optimization techniques are used to calculate rate coefficients. Many techniques are available, and a computer program developed by Parker and Van Genuchten (1984) is excellent for this purpose. It is basically the maximum neighborhood method of Marquardt (1963). Various statistics are used to evaluate goodness-of-fit of the rate functions to the data including r-square, root mean square, 95070 confidence intervals for computed parameters, and the parameter correlation matrix. The rate function(s) I hat givethe best fit to the data are then assumed to be the most nearly correct. Various rate functions that have been used in soil kinetic studies are summarized in Table 2-2. Most of those listed are mass-action rate functions. I.lovich and mass transfer functions were included because of their imporlance to soil kinetic studies. Strictly empirical rate functions that have no I hcoretical basis whatever were omitted. Integrated forms of the simple mass-action rate functions produce linear equations that are easily tested by graphical methods. The advantage of parameter optimization methods is that the computer programs can be writ(("II to generate statistics for a more quantitative estimation of goodness-ofnl rather than the visual estimation that graphical methods provide. Numerous comparisons of rate functions for describing soil-kinetic data have been done (e.g., Onken and Matheson, 1982; Sparks and Jardine, 1984; lIavlin et al., 1985; Amacher et al., 1986). Often simple single-reaction rate Iunctions do not adequately describe the data, or more than one rate funcI" III will describe the data equally well. Possible reasons for this are that more ihun one reaction is occurring, that mass transfer and reaction processes are lIr('uning together (elementary reactions are not being measured), or that 'hi' kinetics are more complex than the assumed rate function. The failure of single-reaction rate functions to adequately describe soilkllll'lic data led Amacher et al. (1988) and Selim and Amacher (1988) to dev.-lop nonlinear and second-order multireaction rate functions as illustrated lu I'i~. 2-11. The rate functions for the reactions depicted in Fig. 2-11 are 111\1'11 ill Table 2-2. A similar approach was used by Harter (1989) where up

50

AMACHER

to three concurrent reversible first-order rate functions were considered. Many alternative multireaction rate functions will produce time-dependent concentration curves that are statistically indistinguishable. This point was discussed thoroughly by Skopp (1986) in his review of kinetic processes in soils and was amplified by Amacher et al. (1988), Selim and Amacher (1988), and Harter (1989). In such cases where more than one explanation for the observed kinetics is possible, experimental evidence must be used to support a particular mechanism. Curve-fitting alone will not suffice. When using multireaction rate functions to describe kinetic data, the simplest model with the best overall fit to the data and with the lowest parameter standard errors is the most desirable. One must guard against overfitting the data, which occurs by using a model with too many parameters for too few data points. The extra sum of squares principle (Kinniburgh, 1986) can be used to determine if there is any statistically significant improvement in the fit of the model to the data by adding more parameters (i.e., more reactions). Inflated parameter standard errors are an indication of an incorrect model choice or too many parameters. A strong linear dependence Table 2-2. Summary of mass-action and other rate equations used in kinetic studies.

Type

Differential form

Integrated form

Single reaction + Irreversible 1st-order dCldt = -kC 2nd-order dCldt = - k(pIO)[C][Site] nth-order

+ {(b[Co] - a[Siteo])la}kt (lIC n- I) = (lIC(j-I) + (n l)kt

dCldt = -kcn

Reversible 1st-order

2nd-order

nth-order

Elovich

In C = In Co - kt In([C]/[Site]) = In([Co]/[Siteo])

In{[1 + (k 2Ik I)](CICo) dCldt = k '(Cs - C) dCldt = -kI(pIO)[C][Site] + k 2(pIO)[C-Site] dCldt = -kICn + k 2(pIO)S dCldt = -k '(Cs - C)n dSldT = kle -k2s

Mass transfer dSldt = k *(C - C*) (most general form)

(continued

1111 IlI'XI,

(k 2Ik I)) = -(ki + k 2)t In[(Cs - C)/C s - Co)] = - k 't In{[Xs([CollSiteo] - xxs)]/[(x s - x)[Co]2[Siteo]2]} = {([CO]2 [Siteof - x;)/xs}kIt [lI(C - Cs)n-I] = [lI(Co Cs)n-I] + (n - l)k't S = (llk 2) In(k Ik 2) + (lIk 2 ) In(t + to)

Numerous solutions available depending on conditions (film or particle diffusion, geometry, finite or infinite volume) (e.g., Crank, 1976; Helfferich, 1962; Vermeulen et al., 1984) PUKe)

51

OBTAINING & ANALYZING KINETIC DATA

among model parameters will also occur if the model overfits the data. This can be evaluated by examining the parameter correlation matrix. The rate functions in Table 2-2 can be applied to batch kinetic data directly because no transport (flow) processes occur. In flow methods the appropriate transport equation must be coupled to the kinetic rate function to achieve a correct solution. Kinetic-rate functions cannot be applied directly. For the thin-disk method the transport equation (Skopp and McCallister, 1986) is v(J(aClat)

= AJ(qn

- Cout )

-

Vp(aSlat)

[16]

where V is the thin-disk reactor volume (m 3); (J is the volumetric-water content (m 3 m -3); C is the solute concentration in the reactor (mol m -3); A is the cross-sectional area of the thin disk (m 2); J is the flow rate (flux) (m 3 s -1); qn and C out are the influent and effluent solute concentrations; respecTable 2-2. Continued.

Type

Differential form

Multireaction

None available-finite difference approximations used (e.g., Amacher et al., 1988; Selim and Amacher, 1988; and Harter, 1989)

Reversible concurrent nth-order p(aSI/at) 2nd-order

Integrated form

= =

klJcn - k2PSI k a8C m - k 4P S2

p(aS2Iat) p(aSI/at) = k I8[C][SiteI] -

k2P[C-SiteI] = k a8[C][Site2] k4Jl[C-Sit e 2] Irreversible concurrent Ist-order p(psrrr/at) = k irr8C Reversible consecutive Ist-order aSa/at = k SS 2 - k 6Sa nth-order p(aS2Iat) = k a8Cm - k4PS2 p(aS2Iat)

k SP S2

S

+ kGPSa

= concentration of metal retained by soil (mg kg -lor mol kg -1 ); [Site]

= concentration of reaction sites on soil (mg kg -lor mol kg -1); rei-Site] = concentration of solute-site complex (mg kg-lor mol kg-I); C = concentration of solute in solution (mg L -lor mol L -1); Co and [Siteo] = initial reactant concentrations; C. = steady state concentration of solute in solution; x = Co - C; x. = Co - C.; c* = solute concentration at solidIsolution interface; k, k', k I, k 2, k a, »; k s, k 6 , k irr are rate coefficients for various kinetic models; k' is the rate coefficient for the approach to steady state in the reversible l st- and nth-order equations; k* is the mass transfer coefficient; a and II in the integrated irreversible 2nd-order equation are stoichiometric coefficients; p = bulk density (MK m 3); 8 = water content (rna m -a); n and m reaction orders; t = timn; lind subsctipts for S, [Site], and [C-Site] in multireuction models refur tu dlffurnllt reaction sites.

52

AMACHER

51 k1

k2 k3

C

k4

kS

52

k6

53

kirr

5irr Fig. 2-11. Diagram of a multireaction model (adapted from Amacher et al., 1988). C is solute concentration in solution, 8 1 , 82 , 8 3 , and 8 irr are solute concentrations in soil phases, and k l , k 2 , k 3, k 4 , k s, k 6 , and k irr are rate coefficients.

tively (mol m -3); p is the bulk density of the solid on the thin disk, (kg m -3); and S is the concentration of solute on the soil (mol kg -I). The relationships between Sand C that can be coupled to this transport equation are given in Table 2-2. Analytical solutions are available for simple rate functions (e.g., Skopp and McCallister, 1986). Numerical approximations can be used for more complex rate functions. A different transport equation (Schnabel and Fitting, 1988) is used for stirred-flow reactors V(OC/Of)

=

J(qn - C) - m(OS/Of)

[17]

where C is the solute concentration in the reactor and in the effluent, m is the mass of soil in the reactor, and the other terms are defined as before. Schnabel and Fitting (1988)give a solution for the case of first-order kinetics. Numerical approximation techniques can be used for more complex rate functions, but the use of multireaction models in flow systems has not yet become a reality.

EFFECTS OF EXPERIMENTAL VARIABLES ON RATE FUNCTIONS A kinetic study is not complete unless the effects of various experimental variables on the experimental rate functions are determined. By systematically changing experimental variables and determining the effect on the rate function, valuable clues are obtained that will aid in deducing mechanisms to explain the observed rate function. The most commonly manipulated variables in soil kinetic studies include reactant concentrations (both solute and solid phase), temperature, pH, ionic strength, and solution composition (other than pH, ionic strength, and solute concentration).

OBTAINING & ANALYZING KINETIC DATA

53

Reactant Concentrations Obtaining kinetic data over a wide range of initial reactant concentrations is essential to determine unambiguously the correct rate function to describe the data. Unfortunately, systematic variation of initial reactant concentrations is not often practiced in soil kinetic studies. The initial concentration of the solute reactant is the one most often varied, and this is easy to do in both batch and flow methods. Varying the concentration of the solid phase (solution/soil ratio) is not possible in the thin-disk method and can only be done over a narrow range in stirred-flow methods. Wide variations in solution/soil ratios are generally possible only with batch methods. Changing the amount of soil per given volume of solution also changes the amount of reaction sites. It is not unusual to discover that rate coefficients calculated from soil kinetic data using an assumed rate function vary systematically with initial reactant concentrations indicating that the reaction is more complex than that implied by the assumed rate function (Amacher et al., 1988).

Temperature This is one of the most important variables to study, and temperature effects in soil kinetic studies have been frequently reported (e.g., Barrow and Shaw, 1975; Evans and Jurinak, 1976; Sparks and Jardine, 1981; Ogwada lind Sparks, 1986a). Rate coefficients for elementary chemical reactions folIowa temperature dependence that can be described by the well-known Arrhenius equation k

=A

e- E1R T

[18]

where A is the pre-exponential factor, E is the activation energy, R is the universal gas constant, and Tis absolute temperature. The magnitude of the Art ivation energy is often used as a criteria to distinguish between diffusioncontrolled and reaction-controlled kinetics (Sparks, 1985, 1986, 1989). Low Il~'l ivation energies are indicative of diffusion-controlled kinetics, whereas hill,h activation energies are indicative of a chemical reaction. This is logical because chemical bonds are broken and formed in chemical reactions, and lilt' energy barrier that must be overcome can be quite high. Diffusion on IIll' 01 her hand requires no chemical bond breaking of formation, so energy hnuicrs are quite low. Boyd et al. (1947) and Kressman and Kitchener (1949) IIml temperature effect criteria to support the diffusion-controlled kinetic mechanism in their now classic ion-exchange studies. Ogwada and Sparks (ItJH(la,b,c) clearly demonstrated the effect of mixing on activation energy ~1l11ll'S for ion exchange. Under static or low agitation conditions where III ttusion-limiting kinetics occurs, activation energies were low but increased _11111 ply under vigorous mixing conditions where diffusion was no longer 1111111 ing ,

AMACHER

54

pH The effects of pH on sorption isotherms have been studied extensively particularly with oxide surfaces (Anderson and Rubin, 1981; Sposito, 1984), but pH effects in sorption kinetic studies have not received equal attention. In contrast, pH effects in mineral-dissolution kinetic experiments have received a great deal of attention (e.g., Chou and Wollast, 1984; Stumm, 1986; Stone, 1987a,b). Ionic Strength Transition-state theory (Gardiner, 1969); Lasaga, 1981)predicts that rate coefficients for second-order reactions in solution depend on the activity coefficients of the reactants and activated complex and therefore vary with ionic strength (the primary salt effect), and this has been found to be the case. However, the dependence of rate coefficients of kinetic reactions in soils on ionic strength has apparently not been studied. Solution Composition The effects of solution composition (aside from reactant concentrations, pH, and background electrolyte concentrations) on reaction kinetics should also be studied. Using different but chemically related reactants and competitive effects from other species in solution are examples of this approach. For example, Stone and Morgan (1984) examined the effect of different organic compounds on dissolution rates of Mn oxides. FORMULATING MECHANISMS FROM EXPERIMENTAL RATE FUNCTIONS AND OTHER EXPERIMENTAL EVIDENCE Once experimental rate functions are obtained, mechanisms are postulated to account for the experimental findings. Further experiments are carried out to test specific mechanisms, and the mechanisms are further refined based on new experimental results. This process continues until a mechanism that will account for all the experimental findings is generally accepted. Often no single mechanism can completely account for all results, and thus alternate mechanisms are accepted as well. There is no single prescribed procedure for formulating a reaction mechanism. The experimental rate function and other experimental results such as the presence of reactive intermediates are used to arrive at a mechanism. A few examples are cited below. Surface complexation of oxyanions by metal oxides is believed to occur by the following generalized mechanism SOH(s) SOHt(s)

+ H + (aq) = SOHt(s)

+ Ln-(aq) = SOHtLn-(s) = SLI-n(s) + "i>(I)

[R6] [R7]

OBTAINING & ANALYZING KINETIC DATA

55

[R8]

where Step 1 is protonation of the oxide surface, SOH; Step 2 is formation of an outer-sphere complex between ligand, L, and protonated surface, SOHt, followed by formation of an inner-sphere complex and release of water; and Step 3 is direct ligand exchange without going through the outersphere complex intermediate. Some oxyanions such as N0 3 apparently do not form inner-sphere complexes so that the second part of Step 2 and Step 3 are omitted in such cases. Also, some oxyanions may not go through the outer-sphere intermediate so that only Steps 1 and 3 are needed. Steps 2 and 3 imply that formation of outer- and inner-sphere complexes may occur concurrently or consecutively depending on the anion. Sposito (1984) has reviewed the evidence in support of this mechanism, which consists of pH effects, rate studies, and spectroscopic evidence, Zhang and Sparks (1989) used pressure-jump relaxation studies in support of Step 2 as the mechanism of molybdate complexation on the surface of goethite. Similar type mechanisms can be developed for cation complexation on the surface of oxide surfaces as well. Hachiya et al. (1979) and Hayes and Leckie (1986) also used pressure-jump relaxation data to deduce mechanisms for Pb complexation by the surfaces of Al oxide and goethite, respectively.

ASSESSMENT OF FUTURE RESEARCH NEEDS Although the future needs of research on kinetic methods are many, this summary section will focus on only two. First, more work needs to be done on distinguishing between mass transfer (diffusion) kinetics in soils and reaction kinetics. The interruption test is a good means of distinguishing between film and particle diffusion, but it has only been used sparingly on ionexchange resins (e.g., Kressman and Kitchener, 1949) and peat particles (Bunzl, 1974). The work of Ogwada and Sparks (1986a,b,c) has brought the effect of mixing on mass transfer and chemical kinetics into sharp focus. Their work was on ion-exchange kinetics. Similar studies are needed on surface-complexation kinetics of transition metals and oxyanions on metal oxide and organic matter surfaces. The use of relaxation methods (Sparks, 1(89) to study reaction kinetics of surface complexation and ion exchange apart from mass-transfer processes may be particularly rewarding in this I cgard, The principal reason for separating mass-transfer kinetics from react ion kinetics is to be able to calculate thermochemical parameters from react ion kinetic data. This cannot be done if diffusion-controlled kinetics are measured. If the objective is to describe accurately the kinetics of the overall process (mass transfer and reaction), then formal mass-action based rate funcI ions that are somewhat mechanism independent are quite suitable (Amacher \'t aI., 1988; Selim and Amacher, 1988). The second area that needs attention is distinguishing between possible nu-chanisms when different kinetic models can describe the same kinetic data illid arc statistically indistinguishable. The complex kinetic reactions in soils

56

AMACHER

can be described accurately by a number of competing models. Thus, distinguishing among the choices will largely require experimental evidence, not additional theories. More research is needed on separating and measuring reactions independently in soils. Most soil kinetic studies measure the loss of solute from solution in sorption studies or the gain of solute into solution in desorption studies. Little attention is focused on what occurs on the soil surfaces or within soil particles. This undoubtedly reflects the lack of techniques to directly observe the reactions occurring on soil surfaces. The continuing development of surface spectroscopic methods should help progress in this area, particularly for reactions on pure soil minerals where greater progress has been achieved (Davis and Hayes, 1986). The study of soil kinetics has passed through its infancy, but it is still a young science. Maturity will come when the aforementioned and other problems are solved. As is normally the case, experimental validation has not kept pace with theoretical developments. There is a great need for quantitative and unambiguous validation of models.

REFERENCES Aharoni, C,; and Y. Suzin. 1982a. Application of the Elovich equation to the kinetics of occlusion. Part I. Homogeneous microporosity. J. Chern. Soc., Faraday Trans. 1,78:2313-2320. Aharoni, C., and Y. Suzin. 1982b. Application of the Elovich equation to the kinetics of occlusion. Part 2. Analysis of experimental data from the literature. J. Chern. Soc., Faraday Trans. I, 78:2321-2327. Amacher, M.e., and D.E. Baker. 1982. Redox reactions involving chromium, plutonium, and manganese in soils. DOE/DP/04515-1. USDOE, Las Vegas, NV, and Inst. for Res. on Land and Water Resour., Pennsylvania State Univ., University Park, PA. Amacher, M.C., J. Kotuby-Amacher, H.M. Selim, and I.K. Iskandar. 1986. Retention and release of metals by soils-evaluation of several models. Geoderma 38:131-154. Amacher, M.C., H.M. Selim, and I.K. Iskandar. 1988. Kinetics of chromium(VI) and cadmium retention in soils; a nonlinear multireaction model. Soil Sci. Soc. Am. J. 52:398-408. Anderson, M.A., and A.J. Rubin. 1981. Adsorption of inorganics at solid-liquid interfaces. Ann Arbor Sci., Ann Arbor, MI. Aringhieri, R., P. Carrai, and G. Petruzzelli. 1985. Kinetics of Cu and Cd adsorption by an Italian soil. Soil Sci. 139:197-204. Barrow, N.J., and T.C. Shaw. 1975. The slow reactions between soil and anions. II. Effect of time and temperature on the decrease in phosphate concentration in the soil solution. Soil Sci. 119:167-177. Barrow, N.J., and T.C. Shaw. 1979. Effect of solution: Soil ratio and vigour of shaking on the rate of phosphate adsorption by soil. J. Soil Sci. 30:67-76. Bernasconi, C.F. (ed.). 1986. Investigations of rates and mechanisms of reactions. 4th ed. Wiley, New York. Boyd, G.E., A.W. Adamson, and L.S. Meyers, Jr. 1947. The exchange adsorption of ions from aqueous solutions by organic zeolites. II. Kinetics. J. Am. Chern. Soc. 69:2836-2848. Bunzl, K. 1974. Kinetics of ion exchange in soil organic matter. III. Differential ion exchange reactions of Pb 2 + ions in humic acid and peat. J. Soil Sci. 25:517-532. Carski, T.H., and D.L. Sparks. 1985. A modified miscible displacement technique for investigating adsorption-desorption kinetics in soils. Soil Sci. Soc. Am. J. 49:1114-1116. Carski, T.H., and D.L. Sparks. 1987. Differentiation of soil nitrogen fractions using a kinetic approach. Soil Sci. Soc. Am. J. 51:314-317. Chou, L., and R. Wollast. 1984. Study of the weathering of albite at room temperature and pressure with a fluidized bed reactor. Geochim. Cosmochim. Acta 48:22205-2217. Crank, J. 1976. The mathematics of diffusion. 2nd ed, Oxford University Press. New York.

OBTAINING & ANALYZING KINETIC DATA

57

Davis, J .A., and K.F. Hayes (ed.). 1986. Geochemical processes at mineral surfaces. American Chemical Society Symp. Ser. 323. ACS, Washington, DC. Elrashidi, M.A., and G.A. O'Connor. 1982a. Boron sorption and desorption in soils. Soil Sci. Soc. Am. J. 46:27-31. Elrashidi, M.A., and G.A. O'Connor. 1982b. Influence of solution composition on sorption of zinc by soils. Soil Sci. Soc. Am. J. 46:1153-1158. Evans, R.L., and J.J. Jurinak. 1976. Kinetics of phosphate release from a desert soil. Soil Sci. 121 :205-211. Frost, A.A., and R.G. Pearson. 1961. Kinetics and mechanism. Wiley, New York. Gardiner, W.e., Jr. 1969. Rates and mechanisms of chemical reactions. W.A. Benjamin, Inc., Menlo Park, CA. Griffin, R.A., and R.G. Burau. 1974. Kinetic and equilibrium studies of boron desorption from soil. Soil Sci. Soc. Am. Proc. 38:892-897. Hachiya, K., M. Ashida, M. Sasaki, H. Kan, T. Inoue, and T. Yasunaga. 1979. Study of the kinetics of adsorption-desorption of Pb2+ on a v - Al z03 surface by means of relaxation techniques. J. Phys. Chem. 83:1866-1871. Harter, R.D. 1989. A new modeling-compatible solution to the first-order kinetics equation. Soil Sci. 147:97-102. Harter, R.D., and R.G. Lehmann. 1983. Use of kinetics for the study of exchange reactions in soils. Soil Sci. Soc. Am. J. 47:666-669. Havlin, J.L., D.G. Westfall, and S.R. Olsen. 1985. Mathematical models for potassium release kinetics in calcareous soils. Soil Sci. Soc. Am. J. 49:371-376. Hayes, K.F., and J.O. Leckie. 1986. Mechanism of lead ion adsorption at the goethite-water interface. p. 114-141. In J.A. Davis and K.F. Hayes (ed.) Geochemical processes at mineral surfaces. American Chemical Society Symp, Ser. 323. ACS, Washington, DC. Helfferich, F.G. 1962. Ion exchange. McGraw-Hill, New York. Hodges, S.C., and G. Johnson. 1987. Kinetics of sulfate adsorption and desorption by Cecil soil using miscible displacement. Soil Sci. Soc. Am. J. 51:323-331. Jardine, P.M., and D.L. Sparks. 1984. Potassium-calcium exchange in a multireactive soil system. I. Kinetics. Soil Sci. Soc. Am. J. 48:39-45. Jardine, P.M., L.W. Zelazny, and J.C. Parker. 1985a. Mechanisms of aluminum adsorption on clay minerals and peat. Soil Sci. Soc. Am. J. 49:862-867. Jardine, P.M., J.C. Parker, and L. W. Zelazny. 1985b. Kinetics and mechanisms of aluminum adsorption on kaolinite using a two-site nonequilibrium transport model. Soil Sci. Soc. Am. J. 49:867-873. lopony, M., and S.D. Young. 1987. A constant potential titration method for studying the kinetics of Cu 2+ desorption from soil and clay minerals. J. Soil Sci. 38:219-228. Kinniburgh, D.G. 1986. General purpose adsorption isotherms. Environ. Sci. Technol. 20:895-904. Krcssrnan, T.R.E., and J.A. Kitchener. 1949. Cation exchange with a synethetic phenolsulphonate resin. V. Kinetics. Discuss. Faraday Soc. 7:90-103. luidler, K.J. 1965. Chemical kinetics. McGraw-Hill, New York. lusaga, A.C. 1981. Rate laws of chemical reactions. p. 1-68. In A.C. Lasaga and R.J. Kirkpatrick (ed.) Kinetics of geochemical processes. Vol. 8. Reviews in mineralogy. Mineral. Soc. Am., Washington, DC. I nsaga, A.C., and R.J. Kirkpatrick (00.). 1981. Kinetics of geochemical processes. Vol. 8. Reviews in mineralogy. Mineral. Soc. Am., Washington, DC. Marquardt, D.W. 1963. An algorithm for least-squares estimation of non-linear parameters. J. Soc. Ind. Appl. Math. 11:431-441. Mrudoza, R.E., and N.J. Barrow. 1987. Characterizing the rate ofreaction of some Argentincan soils with phosphate. Soil Sci. 143:105-112. Miller. D.M., W.P. Miller, and M.E. Sumner. 1988. A continuously stirred tank reactor for solid/solute adsorption studies. p. 201. In Agronomy abstracts. ASA, Madison, WI. Miller. D.M., M.E. Sumner, and W.P. Miller. 1989. A comparison of batch- and flow-generated anion adsorption isotherms. Soil Sci. Soc. Am. J. 53:373-380. I Iv.wada, R.A., and D.L. Sparks. 1986a. A critical evaluation on the use of kinetics for deterruining therodynamics of ion exchange in soils. Soil Sci. Soc. Am. J. 50:300-305. C 'v.wnda. R.A., and D.L. Sparks. 1986b. Kinetics of ion exchange on clay minerals and soil. I. l.valuation of methods. Soil Sd. Soc, Am. J. 50: 1158-1162.

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Ogwada, R.A., and D.L. Sparks. 1986c. Kinetics of ion exchange on clay minerals and soil. 11. Elucidation of rate-limiting steps. Soil Sci. Soc. Am. J. 50:1162-1166. Onken, A.B., and R.L. Matheson. 1982. Dissolution rate of EDTA-extractable phosphate from soils. Soil Sci. Soc. Am. J. 46:276-279. Parker, J.C., and M. Th. van Genuchten. 1984. Determining transport parameters from laboratory and field tracer experiments. Virginia Agric. Exp. Stn. Bull. 84-3. Patrick, W.H., Jr., B.C. Williams, and J.T. Moraghan. 1973. A simple system for controlling redox potential and pH in soil suspensions. Soil Sci. Soc. Am. Proc. 37:331-332. Pavlatou, A., and N.A. Polyzopoulos. 1988. The role of diffusion in the kinetics of phosphate desorption: the relevance of the Elovich equation. J. Soil Sci. 39:425-436. Peek, D.C., and V.V. Volk. 1985. Fluoride sorption and desorption in soils. Soil Sci. Soc. Am. J. 49:583-586. Phelan, P.l., and S.V. Mattigod. 1987. Kinetics of heterogeneously initiated precipitation of calcium phosphates. Soil Sci. Soc. Am. J. 51:336-341. Randle, K., and E.H. Hartmann. 1987. Applications of the continuous flow stirred cell (CFSC) technique to adsorption of zinc, cadmium and mercury on humic acids. Geoderma 40:281-296. Sadusky, M.C., D.L. Sparks, M.R. Noll, and G.J. Hendricks. 1987. Kinetics and mechanisms of potassium release fro msandy Middle Atlantic Coastal Plain soils. Soil Sci. Soc. Am. J. 51:1460-1465. Schnabel, R.R., and D.J. Fitting. 1988. Analysis of chemical data from dilute, dispersed, wellmixed flow-through systems. Soil Sci. Soc. Am. J. 52:1270-1273. Selim, H.M., and M.C. Amacher. 1988. A second-order kinetic approach for modeling solute retention and transport in soils. Water Resour. Res. 24:2061-2075. Seyfried, M.S., D.L. Sparks, A. Bar-Tal, and S. Feigenbaum. 1989. Kinetics of calciummagnesium exchange on soil using a stirred-flow reaction chamber. Soil Sci. Soc. Am. J. 53:406-410. Sivasubramaniam, S., and O. Talibudeen. 1972. Potassium-aluminum exchange in acid soils. 1. Kinetics. J. Soil Sci. 23:163-173. Skopp, J. 1986. Analysis of time dependent chemical processes in soils. J. Environ. Qual. 15:205-213. Skopp, J., and D.L. McCallister. 1986. Chemical kinetics from a thin disc flow system: Theory. Soil Sci. Soc. Am. J. 50:617-623. Sparks, D.L. 1985. Kinetics of ionic reactions in clay minerals and soils. Adv. Agron. 38:231-266. Sparks, D.L. 1986. Kinetics of reactions in pure and mixed systems. p. 83-178. In D.L. Sparks (ed.) Soil physical chemistry. CRC Press, Boca Raton, FL. Sparks, D.L. 1989. Kinetics of soil chemical processes. Academic Press, San Diego, CA. Sparks, D.L., and P.M. Jardine, 1981. Thermodynamics of potassium exchange in soil using a kinetics approach. Soil Sci. Soc. Am. J. 45:1094-1099. Sparks, D.L., and P.M. Jardine. 1984. Comparison of kinetic equations to describe K-Ca exchange in pure and in mixed systems. Soil Sci. 138:115-122. Sparks, D.L., and 1.E. Rechcigl. 1982. Coparison of batch and miscible displacement techniques to describe potassium adsorption kinetics in Delaware soils. Soil Sci. Soc. Am. J. 46:875-877. Sparks, D.L., L.W. Zelazny, and D.C. Martens. 1980. Kinetics of potassium desorption in soil using miscible displacement. Soil Sci. Soc. Am. J. 44:1205-1208. Sposito, G. 1984. The surface chemistry of soils. Oxford Univ. Press, New York. Sposito, G. 1986. Distinguishing adsorption from surface precipitation. p. 217-228. In J.A. Davis and K.F. Hayes (ed.) Geochemical processes at mineral surfaces. American Chemical Society Symp. Ser. 323, ACS, Washington, DC. Stone, A.T. 1987a. Microbial metabolites and the reductive dissolution of manganese oxides: Oxalate and pyruvate. Geochim. Cosmochim. Acta 51:919-925. Stone, A.T. 1987b. Reductive dissolution of manganese(ll1/IV) oxides by substituted phenols. Environ. Sci. Technol. 21:979-988. Stone, A.T., and U. Morgan. 1984. Reduction and dissolution of manganese(III) and manganese(lV)oxides by organics. 2. Survey of the reactivity of organics. Environ. Sci. Technol. 18:617-624. Stumm, W. 1986. Coordinative interactions between soil solids and water-lin aquatic chemist's point of view. Geoderma 38:19-30.

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Toner, C.V., IV, D.L. Sparks, and T.H. Carski. 1989. Anion exchange chemistry of middle Atlantic soils: Charge properties and nitrate retention kinetics. Soil Sci. Soc. Am. J. 53:1061-1067. van der Zee, S.E.A.T.M., L.G.J. Fokkink, and W.H. van Riemsdijk. 1987. A new technique for the assessment of reversibly adsorbed phosphate. Soil Sci. Soc. Am. J. 51:599-604. van der Zee, S., F. Leus, and M. Louer. 1989. Prediction of phosphate transport in small columns with an approximate sorption kinetics model. Water Resour. Res. 25:1353-1365. van Riemsdijk, W.H., and J. Lyklema. 1981a. The reaction of phosphate with aluminum hydroxide in relation with phosphate bonding in soils. Colloids Surf. 1:33-44. van Riemsdijk, W.H., and J. Lyklema. 1980b. Reaction of phosphate with gibbsite (AI(OHh) beyond the adsorption maximum. J. Colloid Interface Sci. 76:55-66. van Riemsdijk, W.H., and F.A.M. de Haan. 1981. Reaction of orthophosphate with a sandy soil at constant supersaturation. Soil Sci. Soc. Am. J. 45:261-266. van Riemsdijk, W.H., and A.M.A. van der Linden. 1984. Phosphate sorption by soils: II. Sorption measurement technique. Soil Sci. Soc. Am. J. 48:541-544. Vermeulen, T., M.D. LeVan, N.K. Hiester, and G. Klein. 1984. Adsorption and ion exchange. In R.H. Perry and D. Green (ed.) Chemical engineer's handbook. 6th ed. McGraw-Hill, New York. Zasoski, R.J., and R.G. Burau. 1978. A technique for studying the kinetics of adsorption in suspensions. Soil Sci. Soc. Am. J. 42:372-374. Zhang, P.C., and D.L. Sparks. 1989. Kinetics and mechanisms of molybdate adsorption/desorption at the goethite/water interface using pressure-jump relaxation. Soil Sci. Soc. Am. J. 53:1028/1034.

3

Relaxation Methods for Studying Kinetics of Soil Chemical Phenomena Donald L. Sparks

Department of Plant and Soil Sciences University of Delaware Newark, Delaware Peng Chu Zhang

Research Center State University of New York Oswego, New York

ABSTRACT A number of soil chemical phenomena are characterized by rapid reaction rates that occur on millisecond and microsecond time scales. Batch and flow techniques cannot be used to measure such reaction rates. Moreover, kinetic studies that are conducted using these methods yield apparent rate coefficients and apparent rate laws since mass transfer and transport processes usually predominate. Relaxation methods enable one to measure reaction rates on millisecond and microsecond time scales and 10 determine mechanistic rate laws. In this chapter, theoretical aspects of chemical relaxation are presented. Transient relaxation methods such as temperature-jump, pressure-jump, concentration-jump, and electric field pulse techniques will be discussed and their application to the study of cation and anion adsorption/desorption phenomena, ion-exchange processes, and hydrolysis and complexation reactions will he covered.

Many reactions on surfaces of soils and their constituents are extremely rapid-occurring on microsecond and millisecond time scales. Examples of I hcse include some cation and anion sorption/desorption reactions, ionexchange processes, reactions involving hydrolysis of soil minerals, and complexation reactions. The fastest reaction rates that can be measured with most batch, flow, IIl1d stirred-flow techniques is about 1 min (Sparks, 1989; Amacher, 1990). All exception is the batch method of Zasoski and Burau (1978) where reacI "I'yright (el 1991 Soil Science Society of America, 677 S. Segoe Rd., 11';1\, HUll'S of Soil Chrmtcat Procrssrs. SSSA Special Publication no.

61

Madison, WI 5371 I, 27.

62

SPARKS & ZHANG

Table 3-1. Chemical relaxation methods, reaction time scales that can be measured using each method, and ways reactions can be detected using methods. Method

Time rangels]

Method of detection

A. Transient methods 1. t-jump

1-10 -8

Spectrophotometric Fluorimetric Polarimetric Conductometric Spectrophotometric

2. p-jump

3. Electrical-field pulse 4. c-jump

B. Stationary methods 5. Sound absorption and dispersion

6. Dielectric dispersion

5-10- 5 (mechanical pressure release) 5 x 10 -4_5 X 10- 7 (liquid shock wave) 10- 4_10- 8 10 8-10 2 (conventional) 103-10 -3 (stopped flow) 10- 5 _10 -

11

(overall time range for acoustical techniques)

Conductometric Spectrophotometric Spectrophotometric Fluorimetric and many others Power loss or frequency change: resonance or reverberation 00 4-10 6 Hz); light diffraction (10 6_10 8 Hz); impulse echo (10 6-5 x 10 8 Hz); Brillouin scattering Power loss, capacitance change

tions can be observed at 15-s intervals. However, the fastest that one can measure reactions with batch techniques that require centrifugation to obtain a clear supernatant is about 5 min. Bar-Tal et al. (1990) found that reactions faster than 0.6 min could not be measured using a stirred-flow reactor. For reactions that occur on time scales < 15 s, none of the techniques given above is satisfactory. To measure these reactions, one can employ relaxation methods (Table 3-1), such as pressure-jump, temperature-jump, concentration-jump, and electric-field pulse (Bernasconi, 1976; Gettins and Wyn-Jones, 1979; Bernasconi, 1986; Sparks, 1989, 1990). With chemical relaxation methods, the equilibrium of a reaction mixture is rapidly perturbed by some external factor such as pressure, temperature, or electric-field strength. Rate information can then be obtained by following the approach to a new equilibrium by measuring the relaxation time. The perturbation is small and thus the final equilibrium state is close to the initial equilibrium state. Because of this, all rate expressions are reduced to first-order equations regardless of reaction order or molecularity. Therefore, the rate equations are linearized, simplifying determination of complex reaction mechanisms (Bernasconi, 1986; Sparks, 1989). One can divide relaxation methods into those that are either transient or stationary. Transient methods include ternperature-, pressure-, and concentration-jump and electric-field pulse techniques. With these, th.

RELAXATION METHODS AND SOIL KINETICS

equilibrium is perturbed and relaxation time is determined utili/inll some plly,,ical measurement like conductivity. Stationary relaxation methods include sound absorption and dhlpcralon and dielectric dispersion. A sound wave is used to perturb the system thlt causes temperature and pressure alterations on an oscillating electric field. Then, chemical relaxation is measured by determining adsorbed energy (acoustical absorption or dielectric loss), or a phase lag that is dependent on the frequency of a forcing function (Bernasconi, 1986; Sparks, 1989), In this chapter, only transient relaxation methods will be discussed. The objective of this chapter is to discuss the theory of chemical relaxation and its application to the study of soil chemical reaction rates. Transient relaxation techniques including temperature-jump (t-jump), pressure-jump (p-jump), concentration-jump (c-jump) and electric-field pulse will be discussed both as to their theoretical basis and experimental design and application. Application of these techniques to the study of several soil chemical phenomena will be discussed including: anion and cation adsorption/desorption reactions, ion-exchange processes, hydrolysis of soil minerals, and complexation reactions.

THEORY OF CHEMICAL RELAXATION

The following development of chemical relaxation theory is taken from Bernasconi (1976), Schwarz (1986) and Sparks (1989). Let us consider a physicochemical system where a single independent variable z can be observed. The equilibrium of the system can be determined by a parameter (J (e.g., temperature or pressure). Due to changes in (J, the instantaneous equilibrium may vary with time, t. If it were actually established, the variable z would assume a respective value z(t). Should, however, z be different from z(t) the inherent tendency for equilibrium must give rise to a rate, dz/ dt = z(t), which is described as a pertinent function!(x,(J). It can be linearized if the system stays close enough to an appropriately chosen reference state z". (J0 as expressed by f(z,()

= t" + f?(z

-

z~

+ !~«(J

-

(J~

[1]

whcrefOJ?, andff represent the values off(z,(), (JjI(Jz, and (JjI(J(), respecuvcly at Z = zO, (J = (J0. Taking advantage of the equilibrium condition, (',!-t .• f(z,(J) = 0, one readily arrives at

z = f(z,()

- f(z,(J)

= !lO(Z

- z)

[2]

the change in Z is necessarily directed toward Z, the factor j]' must be IIl'Yoal ive. Thus a positive quantity T (having the dimension of time) may be tid ined according to the relation SllIl'C

[3]

SPARKS & ZHANG

64

so that

z=

[4]

-(z - Z)7.

The characteristic parameter 7 is called the relaxation time for the process in question. As one can easily see, the basic relaxation equation [Eq. [4]) is generally applicable over a time range sufficiently close to equilibrium. There the rate can be satisfactorily linearized as expressed in Eq. [2] provided of!oz -:;t=. 0. If of/oz = 0, the variable z is not properly chosen and the system stays at equilibrium despite the perturbation. Equation [4] is a simple linear first-order differential equation. It can readily be solved for any reasonable z(t). This is simple when a timeindependent equilibrium state is considered (e.g., z = constant). Then one immediately obtains

z= z+

z) exp( -

(zo -

fir)

[5]

where Zo is the value of z at t = 0. In other words, the instantaneous deviation from equilibrium fades gradually following an exponential function of time. The actual decay time is measured by 7. The treatment presented thus far applies to systems where only one independent variable is subject to relaxation. Frequently, however, (m > 1) such variables are needed to describe the relaxation properties of interest. Under these circumstances, a set of m relaxation equations of the type given. in Eq. [4] can be established. Accordingly, m relaxation times are determined and in a specific relaxation process each relaxation time will contribute its share to the overall effect in proportion to a corresponding amplitude. The . ensemble of relaxation times and amplitudes is called the relaxation spectrum of the process under consideration. It reflects the underlying molecular rate mechanism. Thus, in principle, experimental relaxation spectrometry offers a way to elucidate kinetic mechanisms. In order to relate the relaxation time 7 to the rate of a reaction, consider the reaction A

+

B

The overall chemical conversion rate

= P

C.

[6]

is then

where CA, CR, and Cc represent the concentrations of A, Band C, respectively, k l and k -I are the forward and backward rate constants, respectively, and K is the equilibrium constant for the reaction. According to the conservation of mass, the change in concentration must conform with the stoichiometry of the given reaction step. An appropriate concentration variable x may be defined which is the difference between Cc and an optional reference value c~. Accordingly, one finds

RELAXATION METHODS AND SOIL KINETICS

65

o

-

Cn -

[8]

X

providing c~ and cZ are the corresponding reference concentrations of A and B, respectively. Progression and regression of a chemical reaction can therefore be described by the single variable x. Employing the expressions in Eq. [8], one finds that the concentration variable x is subject to the differential equation

[9] Equation [9] must be equal to zero if x takes the value oX corresponding to the instantaneous equilibrium condition. Therefore, one can transform the rate expression in Eq. [9] to

In general the instantaneous equilibrium can also vary with t, due to changes in temperature. Then, kl> k_ 1 and/or oX may be complicated functions of t, which results in complex mathematics when one attempts to solve Eq. [10]. A general solution of Eq. [10] can be achieved, however, if the instantaneous equilibrium remains unaltered. In such a case k l and k _I are independent of t and the equilibrium concentrations may be chosen for the reference such that oX = O. Under these circumstances x = cc - Cc = -(CA - CA) = -(Cn - cn). Equation [10] now takes the simplified form

x = k l (x 2 with

u-

CA

+

-

ux)

=*

dx/[x(u - x)]

= - k.dt

[11 ]

cn K- I . Integration readily leads to

In [(u - x)/Ixl]

= In [(u

- xo) Ixl]

+

klut

where Xo is the initial value of x at t = 0 (note that always I 1'/1 + K> 0). Equation [12] can be rewritten as

x

= (u

u - xo) exp(th)

when a characteristic time constant

T

+

Xo

u- x

Xo

[12] = CA

+

[13]

is defined according to [14]

I he situation proves to be even simpler if the initial concentrations differ uuly slightly from their equilibrium values as expressed by an amount

Ixo I -e

f"l

f

el/:S u.

[15]

66

SPARKS & ZHANG

Then, in good approximation it follows from Eq. [10] that x = Xo exp( - th),

[16]

e.g., deviations from the equilibrium concentrations rapidly diminish as a single exponential function of time. This reflects the typical behavior of a relaxation process. In fact, the mathematical problems associated with the general equation (Eq, [10)) are largely eliminated if the actual concentrations and their equilibrium values deviate only slightly from some appropriate reference. Equation [10] can then also be written as [17]

The possible time dependence of the quantities in the brackets are negligible, provided

Then, a (practically) constant relaxation time 7 may be introduced by defining [18]

Accordingly, the basic relaxation equation

x=

-(lh)(x -

x)

[19]

is obtained. This applies to any perturbation function x(t) that is brought about by some modification of an external parameter (e.g., temperature or pressure). Let us assume that at t = 0, a slight stepwise change in a forcing parameter (e.g., a p-jump) is generated in an equilibrium system. The initial concentrations are to serve as the references. Therefore x

=0

for

t < 0, x :::: xo;cO

for

t >0

where Xo is the amplitude that is a function of X. In this case, Eq. [19] readily yields x = xo[1 -

exp(th)]

at

t > O.

[20]

The apparent difference between Eq. [18] and [20] arises from the difference in the way reference concentrations are chosen. Another convenient method of perturbing an existing equilibrium, referred to as a stationary method, involves harmonic oscillations of the foreing parameters (e.g., due to an ultrasonic wave). With the original equilibriurn being the reference and w being an angular frequency, one may then write

RELAXATION METHODS AND SOIL KINETICS

67

Fig. 3-1. Relaxation in a single-step reaction system due to fast displacements of the instantaneous equilibrium state showing a harmonically oxcillating x function that implies a phaseshifted response with a reduced amplitude (from Schwarz, 1986).

x=

Xo cos(wt)

X = Xo exp(iwt), respectively

or

-J -1) where Xo represents the amplitude of the oscillations. An appropriate solution of the relaxation equation can more readily be obtained when the complex version of x is used. Reformulating Eq. [19] as

(i =

TX

IIl1d inserting x

Xo

+

Xo exp(iwt)

X =

exp(iwt) immediately results in x = xo/(1

+

iWT) [exp(iwt)]

Ihat describes the actual oscillations of the concentration variable (Fig. 3-1). ()IIC can find that

x -

I

Xo f

2 2

vl+wr

cos(wt -

1/;)

[21]

wit It '" = tan - I (or). As shown in Fig. 3-1, '" exhibits a reduced amplitude alld a phase lag when compared with the oscillations of the instantaneous f(jllilihrium value.

TRANSIENT RELAXATION TECHNIQUES Temperature-Jump Relaxation Temperature-jump relaxation is the most widely used relaxation method. nrlliasconi (1976) lists several reasons for this: I. Most chemical equilibria are associated with a finite standard enthalpy of reaction IlH and are temperature dependent as shown by the Van't Iloff equation given below (il III A'liI"!'),.

[22]

68

SPARKS & ZHANG Light Source

Monochromator

Sample Cell

Heat Source

Detector

-

TRIGGER

-

Transient Recorder

-

Display .

Computer

-

Printer

Fig. 3-2. Block diagram of t-jump instrument (from Turner, 1986).

where K is the equilibrium constant; P is pressure; T is absolute temperature; and R is the universal gas constant. Thus, the equilibrium can easily be perturbed by changing temperature. 2. The t-jump method method is applicable over a wide time range (l - 10 -8 s) and these times are in the range ofrelaxation times for a large number of inorganic, organic, and biochemical equilibrium reactions. 3. Temperature-jump units can easily be constructed and commercial units are readily obtainable. 4. Temperature-jump can be combined with c-jump (for example, stopped-flow) methods. With t-jump, the temperature of a sample is rapidly changed. Thus, any temperature-dependent equilibrium is perturbed and the concentrations of reactants and products must be altered to the values necessary for equilibrium at the new temperature. If the temperature change is more rapid than the system can react, then the relaxation of the concentration alterations can be measured. This time dependence, which is usually exponential, can then be utilized to derive rate constants at the final temperature for the involved chemical reactions (Turner, 1986). Temperature-jump methods have not been used in soil science. However, they have been widely employed in many areas of chemistry and biochemistry research to study the following types of reactions (Turner, 1986): electron transfer, enzyme catalysis, metal complex formation, nucleic acid folding, proton transfer, spin equilibria, and protein-ligand binding. A typical t-jump instrument is shown in Fig. 3-2. The primary parts are a heat source, a detector to measure concentration changes, and a data acquisition and analysis system (Turner, 1986). Any device that heats a sample up uniformly quicker than the measured relaxation time can be used with t-jump relaxation. A number of devices can do this: thermostated baths, electrical heating (Joule heating), microwave heating, and laser heating. Table 3-2 shows some characteristics of the four heat sources; more detail can be found in Turner (19H6).

I

69

RELAXATION METHODS AND SOIL KINETICS

Table 3-2. Characteristics of heat sources that can be used with t-jump relaxation methods (from Turner, 1986l.

Heat source

Typical heating time

Fastest heating time

Typical temperature K

s Thermostated bath Electric discharge Microwave Laser

10 10- 6 10- 6 10- 8

Solvent limitations

Any 275-283 274 274-283

1 10- 8 10- 7 10- 7

None Conducting Polar Absorption at laser wavelength

A variety of detection systems can be used with t-jump methods. These include: visible/ultraviolet, fluorescence, optical rotation, Raleigh and Raman scattering, and conductivity. Pressure-Jump Relaxation

The p-jump method has several advantages over the t-jump technique. Pressure-jump measurements can be repeated at faster intervals than those with t-jump. With the latter, the solution temperature must return to its inirial value before another measurement can be conducted. This may take 5 min. With p-jump relaxation, one can repeat experiments every 0.5 min. One ran also measure longer relaxation times with p-jump than with t-jump relaxIII ion. As noted earlier, one of the components of a t-jump experiment is II heat source such as Joule heating. Such high electric fields and currents mil destroy solutions that contain biochemical compounds. Such problems ilo 110t exist with the p-jump relaxation method. Of all the transient relaxation methods, p-jump relaxation has been used I he most widely to study interactions at the solid/liquid interface. As will be described later, there are numerous applications of this technique to soil consutuent/inorganic species interactions. Pressure-jump relaxation methods and theory have been reviewed by ~Ilarks (1989). In-depth treatments can also be found in a number of reviews [Tukuhashi and Alberty, 1969; Bernasconi, 1976; Yasunaga and Ikeda, 1986; llllll'lIewald and Knoche, 1979; Knoche, 1974). Pressure-jump relaxation is based on the principle that chemical 'llllilihria depend on pressure as demonstrated below (0 In KIEJP)T

=

AVIRT

[23]

rthnl' A V is the standard molar volume change of the reaction (L) and p

_ p/l'ssure (MPa). For a small perturbation one can also write

AKIK ==

~o

(AVApIHT).

[24]

70

SPARKS & ZHANG

The p-jump occurs because of a quick pressure release or application. Then, the progression in a reaction is followed after the end of the pressure change. Thus, it is imperative that a fast p-jump be used if the method is to be suitable for fast reactions. The first p-jump apparatus was developed by Ljunggren and Lamm (1958). A conductivity cell was filled with the solution of interest and then placed in an autoclave connected to a 15-MPa N tank. The stopcock was rapidly opened to create a rapid pressure increase. With this method, one could obtain a pressure change of 15 MPa in 0.05 s. Ljunggren and Lamm (1958) followed the relaxation time conductometrically. In 1959, Strehlow and Becker described a different p-jump instrument. The autoclave was closed by a metal rupture membrane and the pressure was increased to about 60 MPa. The disc was next punctured by a steel needle and the pressure then dropped to 0.1 MPa within < 100 JlS. The autoclave contained two conductivity cells, one filled with the solution under study and the other containing a nonrelaxing solution such as xylene. By comparing the resistance change of the two cells following a p-jump, disturbances of the measurements tended to cancel each other (Knoche, 1974). Modified forms of the Strehlow and Becker (1959) p-jump apparatus have been widely used and described by others (Hoffman et aI., 1966; Takahashi and Alberty, 1969; Macri and Petrucci, 1970; Knoche, 1974; Knoche and Wiese, 1974; Davis and Gutfreund, 1976). An adaptation of the p-jump apparatus developed by Strehlow and Beck- ' er (1959) was introduced by Knoche and Wiese (1974). A schematic diagram and sectional views of the autoclave for this p-jump instrument using conductivity detection are shown in Fig. 3-3. This type of apparatus has been used by a number of investigators including Zhang and Sparks (1989, 1990) to study reaction rates on soil constituents. A photograph of their particular p-jump apparatus [Dia-log, DIA-RPC, Dia-Log Co., Dusseldorf, Germany] is shown in Fig. 3-4. The main components of the p-jump apparatus include the autoclave, pressure pump, two cells and a vacuum pump. The pressure is built up by the pump with water as the pressure transmitter. The sample and reference cell are covered with a plastic membrane that effectively transmits the pressure. A piece of brass membrane (thickness = 0.03 mm) is clamped on one wall of the autoclave with the bayonet socket. When the pressure in the autoclave gets high enough (9.595 MPa), the brass membrane bursts and the pressure in the autoclave returns to ambient pressure within 70 JlS. After the membrane bursts, the sample suspension having equilibrium at a higher pressure is out of equilibrium due to the instantaneous p-jump. The time required to approach equilibrium at the ambient pressure is then monitored by conductivity detection. The cell filled with the nonrelaxed background electrolyte such as NaN0 3 solution is used as a reference that removes physical effects such as mechanical and temperature disturbances. Water is circulated in the autoclave to maintain a constant temperature (Zhang and Sparks, 1989). Other details of the p-jump relaxation apparat us call he found in Sparks (1989).

71

RELAXATION METHODS AND SOIL KINETICS

> - - . - - - i A 0 Converter

Computer

11

11M 1 3. Schematic diagram and sectional views of the p-jump apparatus: (1) conductivity cells, f.') potentiometer, (3) 4O-kHz generator for Wheatstone bridge, (4) tunable capacitors, (5) 1''''lIlcicctric capacitor, (6) thermistor, (7) IO-lurn helipot for turning bridge, (8) experimen1111 chamber, (9) p-pump, (10) rupture diuphrugm, (II) vacuum pump, (12) pressure inlet, (II) heul exchanger, (14) bayonet .~odel (Irom Knoche und Wiese, 1974).

-.I N

00

'"l:I

>

= N = > 00

.

Fig. 3-4. Dia-log p-jump apparatus (DIA-RPC), (produced by Dia-log Co., distributed by Inrad Interactive Radiation, Inc., Northvale, NJ) used by Zhang and Sparks (1989).

~

Z

~ _

.. _ .

~ · . ~

--_·_"""",-,~

c

~

__

~

.._ _

~ _

~ .

~ _

73

RELAXATION METHODS AND SOIL KINETICS

In the work of Zhang and Sparks (1989), a Dia-log p-jump apparatus and conductivity detector were employed (Fig. 3-4). A digitizer is triggered upon the pressure release and membrane burst and the changes in conductivity of the suspension are monitored. The signals are digitized and then sent to a microcomputer. The results of the relaxation can be read from the computer print-out and displayed on an oscilloscope. Pressure-jump measurements can be detected using either optical or conductivity detection. Since the equilibrium displacement following a p-jump is usually quite small, the very sensitive conductometric detection method is usually preferred. It has been the method of choice by researchers studying the kinetics of reactions at solid/liquid interfaces. This is due to the high sensitivity of conductivity detection and because suspensions are being studied. Optical detection would not be suitable for such systems. However, it should be noted that while conductivity detection is sensitive on an absolute basis, it is necessary that the solution and suspension that one is studying must have adequate buffering and proper ionic strengths. In relaxation methods, small molar volume changes result and thus, even if a low level of inert electrolyte is present, conductivity changes may be undetectable if pressure perturbation of 5 to 10 MPa is used (Takahashi and Alberty, 1969; Sparks, 1989). The specific conductivity, (J (in S m -1), of an electrolyte solution is given as (Bernasconi, 1976) (J

=

(F/1000) E Cj IZj I

Uj

=

(F/l000) p E mj IZj I

Uj

[25]

where F is the Faraday constant; Zj the valence of ion j; Cj the molar and tnj the molality concentrations of ion j; Uj is the electrical mobility; and p is the density of the solution. For a small perturbation ~

(J

= F/1000 (p E +

IZj I

Uj


p E IZj I
Uj

+

E IZj I mj

Uj


Uj


[26]

The first term on the right-hand side of Eq. [26] represents chemical relaxation. The other terms represent "physical effects," i.e., the change in ionic mobility and density as a consequence of pressure and temperature changes. However, problems caused by physical effects can be eliminated by using a reference cell filled with a nonrelaxed solution such as NaN0 3 which has the same temperature dependence on conductivity as the sample cell. The change in conductivity in this case corresponds only to the change ill concentration of reactants or products. A Wheatstone bridge, as shown III Fig. 3-3 and 3-4, can be used to measure the change in conductivity in I he reference and sample cells that are the two arms of the bridge. Optical detection can also be used in p-jump relaxation studies. One of lis major attributes is that one can study systems other than ionic ones, which 1\ 1I0t the case with conductivity detection. Changes in optical properties can be followed rapidly and wit h fine sensitivity utilizing photoelectric transducers

74

SPARKS & ZHANG

or photomultipliers (Eigen and De Maeyer, 1963). Absorption spectrometry can be used with temperature as the forcing variable (Czerlinski, 1960). Fluorescence spectrometry may be used to enhance sensitivity at low concentrations (Czerlinski, 1960). Alternatively, refractometric or polarimetric techniques or measurement of optical rotation may also be utilized (Eigen and De Maeyer, 1963). Other ways to detect p-jump relaxations include measurements of thermal properties of the reaction system such as employing a rapid calorimetric method to determine the heat of reaction. However, a problem with this method is that the time resolution is not very great (Sparks, 1989). Pressure-jump measurements can be evaluated through nondigital and digital methods. Nondigital techniques involve photographing the trace on an oscilloscope screen and then plotting the measured amplitudes vs, time on semilogarithmic paper. Typical oscillograms from p-jump experiments are shown in Fig. 3-5. They resemble a ringing pattern whose frequency is the oscillating frequency of the bridge and whose envelopes correspond to the exponential relaxation decay (Sparks, 1989) that can be seen in Fig. 3-5. Nondigital techniques require photography, the results are often not available until the experiment is finished, and they are generally time consuming and less accurate. Fortunately, digital techniques are available commercially (see later discussion on commercial p-jump units). Krizan and von Strehlow (1974) developed one digitizing interface that can be used in p-jump analysis.

..

250 fls

•

•

a

c

500 fls

•

250 Ils

..

..

b

d

255

Fig. 3-5. Typical oscillograms of p-jump experiments. Relative change in conductivity for pjumps of 13.1 MPa in solutions of 0.05 M InCI 3 , pH = 3.25 (a) at 3lB K showing only pressure decay; (b) at 300.5 K, T = 50 ± 15 JLS; (c) at 273.7 K, T = 2.1 ~ 110"S; (d) solution of 0.10 M
RELAXATION METHODS AND SOIL KINETICS

75

Commercial p-jump instruments can be obtained from Dia-Log Co. and distributed by Inrad Interactive Radiation, Inc. (Northvale, New Jersey 07647) and by Hi-Tech Scientific Limited (Salisbury, Wiltshire, United Kingdom SP27PU). Dia-Log Company makes p-jump units with optical conductivity detection. Relaxation times of 50 to 100 us can be measured. The conductivity range is 0.05 to 200 S m -1, the temperature range is 273 to 343 K, and a sample volume of 0.5 mL or more can be used with a readout digitizer that has a memory of up to 256 values. A microprocessor enables one to automatically process and reduce data. Hi-Tech Limited also produces a p-jump apparatus (PJ-55 p-jump) based on a design by Davis and Gutfreund (1976). A mechanical pressure release valve enables observation after 100 p-s. One can measure changes in turbidity, light absorption, and fluorescence emission in the range of 200 to 850 nm. The PJ-55 unit is thermostated by flowing water from an external circulator through the base of the module. The temperature in the cell is monitored using a thermocouple probe. A hydraulic pump assembly is used to increase pressure up to 40.4 MPa. A mechanical valve release causes the pressure build-up to be applied to the solution in the observation cell. A rapid response ultraviolet/fluorescence optimized S-IO type photomultiplier is used for optical detection and a 12-bit A/D converter interfaces the p-jump unit to a computer.

Concentration-Jump Techniques Another relaxation method that has been widely used is the c-jump technique. There are a number of methods to cause c-jumps. These include (Bernasconi, 1976): (1) diluting the reaction mixture with a small quantity of solvent; (2) adding a solution that is more (or less) concentrated in the reactants; (3) adding a different solvent to change the solvent composition; (4) adding base or acid to create a pH jump and, (5) changing the ionic strength by a salt jump. Bernasconi (1976) notes that if the equilibrium depends on the nature of the solvent, the pH, or the ionic strength, Methods 3, 4, and .~ above can be applied to equilibria of any molecularity. However, Methods I and 2 above can only be applied to equilibria that can be shifted by changing the total concentration of the solutes. All c-jump experiments involve mixing. Thus, the mixing time dictates the shortest relaxation time that can be measured. For very slow reactions (on the order of minutes or longer) ordinary mixing is sufficient (Bernasconi, 1976). I f one wishes to measure shorter mixing times on the order of milliseconds, a stopped-flow technique can be employed. This method has been used to ascertain enzyme mechanisms for a number of organic and inorganIC chemical reactions (Robinson, 1975, 1986). The stopped-flow technique has not been extensively employed in studying kinetics of solid/liquid inter.uiions (Ikeda et al., IlJIl4a).

SPARKS & ZHANG

76

Fig. 3-6. Stopped flow apparatus (SFM-3) of Bio-Logic Instruments and Laboratories (with permission).

In the stopped-flow method two reactants are quickly mixed in a chamber, flow is then rapidly stopped a short distance from the mixing chamber, and some physical property of the reaction system is measured with time (Bernasconi, 1976). , Stop-flow design and construction is thoroughly discussed in a number of review articles (Caldin, 1964; Gibson, 1969; Kustin, 1969; Chance, 1974). Commercial units are available from a number of commercial sources and several different detection systems can be utilized; a stopped-flow instrument from the Bio-Logic Company (Meylan, France) is shown in Fig. 3-6. Further details about commercial stop-flow units can be found in Sparks (1989).

Electric Field Pulse

Of all the transient relaxation methods, the electric-field pulse technique can be used to measure the fastest reaction rates (Table 3-1, )() 4_10 -8 s).

77

RELAXATION METHODS AND SOIL KINETICS 60MQ

Deloy Coble

60kV Power Supply

RG

au

Spork Gop

Trigger Circuli Scope Trigger

A

o

P1

51n lW

Fig. 3-7. Block diagram of square wave dissociation field effect apparatus. The S denotes the sample electrolyte cell. The reference electrolyte cell R has a variable interelectrode distance. Box A denotes a fast oscilloscope and PI and P2 are commercial (Tektronix) high-voltage probes (from Rampton et al., 1967).

Chemical equilibria involving ions and dipolar or polarizable species may depend on electric field strength (E) as shown below (Schelly and Eyring, 1971) iJ In K/iJE

= W*/RT

[27]

where w* is the difference of partial molar' 'polarization" of products and reactants. Thus, if there is a net charge in the number of ions or dipole moments, for a particular reaction, one can apply an electric field to perturb the system. One must usually apply fields of 50 to 100 kV em -I to notice any effect. If the system is a weak electrolyte, dissociation will occur when strong fields are applied. The first electric-field-jump experiment involved perturbation by a single strongly damped harmonic oscillation of the electric field (Eigen and Schoen, 1955). Eigen and De Maeyer (1955) applied a single rectangular high voltage pulse to a chemical system. One major attribute of this approach is that relaxation times can be determined in one experiment. When a square function is used for perturbation, two successive relaxations occur-a forward relaxation when the field is on, and a back relaxation when the field is stopped. The experiments of Eigen and DeMaeyer (1955) employed a square-wave Wheatstone Bridge. A more recent version (Rampton et aI., 1967) of this instrument is shown in Fig. 3-7. A rectangular, approximately 50 kV, pulse is applied to a two-platinum-electrode sample cell that is one arm of an asyrn-

78

SPARKS & ZHANG

metric, high-voltage Wheatstone Bridge. One uses an oscilloscope to capture photographically or digitally an exponential change in sample cell conductance while the high-voltage pulse is still on the bridge. If the sample liquid has a fairly low conductance « 10 -4 (1 em -1) little current passes through the sample cell, the Joule heating t-jump effect is minimal and the determination of the fast transient (with pure water) is easy (Eyring and Hemmes, 1986). The above technique is fine for electric-field pulse experiments where there is no color change associated with the electric-field-induced ionization. If a color change is operational, one may use spectrophotometric detection (Ilgenfritz, 1966).

APPLICATION OF TRANSIENT RELAXATION TECHNIQUES TO SOIL CHEMICAL REACTIONS Anion Adsorption and Desorption on Soil Constituents

Kinetics of anion adsorption/desorption on soil constituents has not been extensively studied (Sparks, 1987, 1989) but it is well-known that a number of anions such as phosphate, sulfate, borate, and selenite and/or selenate play an essential role in plant nutrition, and in soil and environmental quality. Zhang and Sparks (1989, 1990) were the first soil chemists to use relaxation techniques to study the kinetics of soil chemical phenomena. Zhang and Sparks (1989) investigated the kinetics and mechanisms of molybdate adsorption/desorption at the goethite-water interface using p-jump relaxation with conductivity detection. In a static study, a modified triple-layer model (TLM) (Hayes and Leckie, 1986), as well as several other surface complexation models were used to model molybdate adsorption. It was found that the modified TLM model best described the data. It differs from the original model in two ways: (i) the adsorbed ion can be located at both the {3 layer and the a layer rather than only at the {3 layer, that is, the adsorbed ion can form an inner- and/or outer-sphere surface complex, not just an outer-sphere complex; and (ii) the chemical potential and standard and reference states are defined equivalently for both solution and surface speciesleading to a different relationship between the activity coefficients and the interfacial potential than previously used in the original TLM. In the study of Zhang and Sparks (1989), the molybdate adsorption data were modeled assuming both outer- and inner-sphere complexation and were described assuming inner-sphere complexation (Fig. 3-8). The goodness-offit of the data to the modified TLM indicated that only one mole of ligand was replaced by one mole of adsorbed molybdate. In the pH range of 4 to 7 that was employed in this study, the molybdate ion could exist as two species, HMo0 4- and Mool-, with an association constant (K2) of 10- 4 • However, the dominant form of the molybdate anion is Mool- when the pH of the suspension is > 4. Based on the modeling of the data, it was found that the major fraction of the goethite-molybdate suspension is SMo04-

79

RELAXATION METHODS AND SOIL KINETICS

40.0 ,

N

0

L- 1

35.0

Goethite= 15.8 g

30.0

Na MoO =4.5xl0- 3 mol 2 4

~

x -; Cl

-'"

"0

25.0

E

c: 0

a. ~

0

en

20.0 15.0

0

"0

«

~

0

6 0

10.0

0

:2:

---_...........

0.01 M 0.05 M 0.10 M

-- - - ---

5.0 0.0 2

3

5

4

6

7

8

9

pH

Fig. 3-8. Adsorption of Mo04 on goethite vs, pH at three NaN0 3 background electrolyte concentrations. Experimental data are applied to the modified TLM assuming inner sphere surface complexation; symbols represent experimental data and lines represent TLM prediction (from Zhang and Sparks, 1989).

(where S is the goethite surface), with the SHMo04 species existing in a very trace amount (approximately 10- 23_10- 26 mol L -I). Thus, this latter species was ignored in the study of Zhang and Sparks (1989). Additionally, by using the modified TLM, Zhang and Sparks (1989) checked the form of the functional group that was directly reacting with molybdate. It was found that the molybdate anions reacted primarily with the protonated site, the SOHt and not with the neutral one, SOH. For the reactions carried out over a pH range of 4 to 7, the goethite surface is positively charged since the point of zero charge of the goethite is about 8.4. Zhang and Sparks (1989) tried to use neutral sites in their calculations, but the obtained results were not reasonable. Using p-jump relaxation, a double relaxation was observed for molybdate adsorption on goethite (Fig. 3-9). Zhang and Sparks (1989) determined 1 1 I he reciprocal relaxation time constants 71- and 72- from semilog plots of I he relaxation curves. A fast reciprocal relaxation time, 71- 1, was separated from a slow one, 72- 1, based on the significantly different rates of conductivity change as a function of time. The TI- 1 and 72- 1 values increased as molybdate adsorption decreased. Combining the information from the pjump relaxation studies and from overall equilibrium partitioning and the I caction stoichiometry, a two-step reaction was postulated to describe the mechanism of molybdate adsorption on goethite XOH zt

+

MoO]- ~ XOHz' - MoO]

Step I

~

XMo0 4- + H 20 . Step 2

[28]

SPARKS & ZHANG

80

3.0 2.8 Ionic Slrenglh=O.OI M Goelhile=15.8 g L- 1 Na MoO =4.5xI0- 3 mol L-1

Q)

-

-g 2.6 0-

~

2

4

2.4 2.2 2.0 0.0

0.14 0.16 0.18 0.20 Time, S

Q)

0.8

-= :E

Ionic Strenglh=O.Ol M

~

Goelhilf=15.8 g 1"'


0.6

Na MoO =4.5110- 3 mol L-l

Q)

2

.;:::

~ a: 0

0.4

.3'0.2

4

•

•

0.0 L..--'----=-----'------'-_L..--'-----'----..J--"-----' 0.0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Time, S Fig. 3-9. Relaxation curves for molybdate adsorption on goethite: (a) Typical p-jump relaxation curve showing change in conductivity vs. time for the goethite suspension; and (b) semilog relaxation curves for the goethite suspension (from Zhang and Sparks, 1989).

In the first step, the Mo0 4 ion is attracted to the {3 layer by electrostatic or outer-sphere complexation, forming an ion-pair complex with a protonated surface site. In the second step, the Mo04 ion replaces a ligand from the surface site to form an inner-sphere surface complex at the a layer. In this step, the processes of bond breaking and formation are included. Using the kinetic model described in Eq. [28] and the stoichiometry of the overall reactions, i.e., one Mo04 ion replaces one ligand from the protonated surface, Zhang and Sparks (1989) derived the following relationships between 71-1 and 72-1 and intrinsic forward (ki nt and k~nt) and intrinsic backward (k~tl and k~~) rate constants for Steps 1 and 2 [see Zhang and Sparks (1989) for detailed derivations].

[29]

81

RELAXATION METHODS AND SOIL KINETICS

Step 2

= kint 2

rC

exp (F'if;,,) 2RT

[30] where F is the Faraday constant, R is the universal gas constant, T is absolute temperature, and 1/;a and 1/;{j are the electrical potentials at the a and (3 layers, respectively. Rearranging Eq. [29] and [30]

[31]

Step 2

,,-' exp (;:~)

p ~ kj"' [ox (:";)

l

kint exp (-F('if;2~; 2'if;1l») ([XOHtJ + [MoO;])

k;nt

exp (-F('if;" - 2'if;1l») ([XOHtJ + [MoO;-]) + WT

k~tl exp (!y" \

+

kint -2

= k 2int F2

+ k int -2 .

2'if;1l)\

WT

}

j [32]

By plotting the left-hand side of Eq. [31] and [32], i.e., the reciprocal relaxation times with the exponential terms, vs. F I and F 2 in the two separate

equations, one can test the mechanism proposed in Eq. [28]. If linear relaI ionships result, then one can obtain the forward and backward rate con-

82

SPARKS & ZHANG 30,.-----,-------r------r------r----,----,

x

20

t=' a:

~ ~

N

,

:£

u.. 10 I

cr X UJ

'.:OL-._ _---'

o

~

5.0

2.5

__'_

__'_

.....L

7.5

10.0

12.5

....J

15.0

F, X 1000 Fig. 3-10. Plot of 7- 1 exp[ -F("'a - 2"'fj)12RT] VS. F I in Eq, [31] to test the mechanism for Step I as proposed in Eq. [28] (from Zhang and Sparks, 1989).

stants from the slopes and intercepts, respectively for the two steps. As shown in Fig. 3-10 and 3-11 indeed two straight lines resulted indicating Eq. [28] correctly describes Mo0 4 adsorption/desorption on goethite. The intrinsic rate constants, obtained graphically for the first reaction step were k\nt = 4.0 X 103 mol-I L s -I and k~tl = 3.9 X 102 s -I and for the second step they were k~nt = 1.89 mol " ! L s -I and k~~ = 42.34 S -I. 5 I

0 T'"

X

4

~

I-

a: C\I

-

3

0

~

LL

~

a..

>< W I

\-

2

1

OL---------'--------!..----l.-----.....I..------'

o

10

20

30

40

50

F2 Fig. 3-11. Plot of 7- 1 exp(F"'a12R1) vs. F2 in Eq. [32] to test the mechanism for Step 2 al proposed in Eq. [28] (from Zhang and Sparks, 1989).

RELAXATION METHODS AND SOIL KINETICS

83

Thus, the reaction mechanism for Mo04 adsorption on goethite can be described as follows: (i) the Mo0 4 anion that has already diffused close to the goethite surface is attracted to the surface because of the protonated and positively charged surface site and an ion-pair complex is thus rapidly formed; and, (ii) the Mo04 anion reaches the oxide surface to break the bond between Fe and the hydroxyls and a H 20 molecule is released to the bulk solution. Over time, a new bond is established between Mo04 and Fe at the oxide surface. Step 2, which is a ligand exchange process, is slow compared to Step 1. Thus, as can be observed from the magnitude of the rate constants given above, Step 2 is the rate-controlling step in the reaction between Mo04 and goethite. Zhang and Sparks (1990) also studied the kinetics of adsorption/desorption of S04 on goethite using p-jump relaxation. A single relaxation was observed and the T -1 values increased with increases in pH indicating that S04 adsorption rate is pH-dependent. Results from static and kinetic measurements indicated that S04 adsorption on goethite occurred simultaneously with a protonation process as shown below [33] where XOH is a neutral surface site and XOHt -sol- represents a surface complex of S04 and a positively charged surface site. Sulfate adsorption occurs via electrostatic attraction. The intrinsic equilibrium constants obtained from the kinetic measurements, Kk1~etics = klnt/k~tb agreed with those from the static study, ~f~tic (Table 3-3) further indicating that the proposed mechanism in Eq. [33] was correct. Thus, Zhang and Sparks (1990) showed that S04 adsorption occurred at the {3 plane and the complex formed between adsorbed S04 and the surface was outer sphere. Pressure-jump relaxation was also used by others to study anion adsorption/desorption kinetics on soil constituents. These investigations have included the study of the kinetics and mechanisms of acetic acid adsorption on a silica-alumina surface (Ikeda et al., 1982a) and phosphate (Mikami et al., 1983a) and chromate adsorption (Mikami et aI., 1983b), on /,-AI 203 • Double relaxation times on the order of milliseconds were observed in each of these studies. For the adsorption/desorption of acetic acid on a silica-alumina surface (Ikeda et aI., 1982a), the fast relaxation was attributed to a protonationTable 3-3. Intrinsic rate and equilibrium constants for S04 adsorption on goethite as determined from kinetic and equilibrium measurements (Zhang and Sparks, 1990). t k int

k lint

mol ~ I L

-I

S -I

int Kkinetic

Log

int Kstatic

S- 1

0.144

I "I

Log

9.14

9.60

= intrinsic forward rate constant; k . I = intrinsic backward rate constant; Ki:l}.etics intrinsic equilibrium (,un/lI,unt obtained from kinetic measurements; K~~~tic = intrinHie equilibrium conatant uh!.uirll'd from static or equilibrium measurements.

84

SPARKS & ZHANG

deprotonation reaction on the surface and the slower relaxation was ascribed to the adsorption/desorption of the acetate ion, accompanied by the elimination of a water molecule from the surface (ligand exchange). In the study of adsorption/desorption of phosphates on -y-AI203 (Mikami et aI., 1983a) the fast and slow relaxation times were attributed to adsorption/desorption of di- and monovalent phosphate, respectively, on protonated surface hydroxyl groups via electrostatic reactions. The same conclusion was reached from adsorption/desorption of chromate on -y-AI 203 (Mikami et aI., 1983b). The fast relaxation was attributed to CrOl- adsorption and the slow one to HCr04- adsorption by electrostatic attraction. The main difference between the data for phosphate (Mikami et aI., 1983a) and chromate (Mikami et aI., 1983b) adsorption was in the dynamic properties of the monovalent and bivalent ions. Whereas the monovalent and bivalent chromate ion adsorption rates were similar, the adsorption rate of HP0 4- was much faster than that of H 2Pol-. The adsorption rate constants for H 2Pol- and HP04- (4.1 x 105 and 1.1 x 107 mol-I dm ' S-I, respectively) were one to two orders of magnitude larger than those for CrOl- and HCr04- (5.3 X 104 and 9.9 x 104 mol-I dm ' S-I, respectively). The desorption rate constants for H 2Pol- and HP04- (2.3 and 2.7 S-I, respectively) were one order of magnitude smaller than those for CrOl- and HCr04- (1.9 x 10 and 5.2 x 10 s -I, respectively). Accordingly, Mikami et aI. (1983b), concluded that the interaction of chromate with Al oxide was weaker than for phosphates. It has been found that adsorption/desorption of anions such as CI and CI04 on soil constituents is very rapid. In fact, reequilibrium is too rapid to be observed using p-jump relaxation. Fortunately, the electric-field pulse technique can be used for such systems. This method was employed by Sasaki et aI. (1983) to study CI and CI0 4 adsorption on goethite. Two relaxations on the order of microseconds were observed in acidified aqueous suspensions of a-FeOOH with either NaCI or NaCI0 4. The fast relaxation was dependent on the applied electric field intensity and was attributed to a physical diffusion phenomenon. The slower relaxation was independent of the applied electric field intensity and was interpreted in terms of the association/dissociation reaction of counter ions with protonated surface hydroxyl groups as ion pairs [34] Sasaki et aI. (1983) found that the intrinsic equilibrium constant for the aFeOOH-HCI system was one order of magnitude higher than for the aFeOOH-HCI04 system. This indicated that the ion-pair formation reaction in the former system was much more stable than for the latter CI04 system. This finding was further supported by the finding that the stability constant for the ion pair between CI and the metal ions was one to two orders of magnitude larger than the ion pair for the CI0 4 and the metal ions,

85

RELAXATION METHODS AND SOIL KINETICS

Cation Adsorption/Desorption on Soil Constituents Transient relaxation techniques have also been used for determining the kinetics and mechanisms of cation adsorption/desorption at mineral/water interfaces. Hachiya et al. (1979) studied the kinetics of Pb adsorption/desorption on a 'Y-AI203 surface using p-jump and electric-field pulse relaxation. The reaction rate was characterized by a very rapid initial conductivity change that was too fast to measure with p-jump relaxation. Therefore, the more rapid electric-field pulse technique was employed for subsequent investigations. A double relaxation was observed for the Pb adsorption/desorption process. The reciprocal slow relaxation times (75- I) were dependent on the concentration of Pb and the pH of the suspension, but they were independent of ionic strength. The reciprocal fast relaxation times (7[- I) decreased with increasing Pb concentration. Using a Langmuir-type rate equation to describe the adsorption/desorption phenomena, Hachiya et al. (1979) derived a linearized relationship between reciprocal relaxation times and the amounts of adsorbed and free Pb in suspension. The fast relaxation was attributed to adsorption/desorption of Pb on the hydrous oxide surface group AI-OH, while the slow relaxation was ascribed to the deprotonationprotonation process induced by adsorbed Pb. The authors did not consider the effect of surface charge on adsorption. The p-jump technique was also used to study the kinetics of adsorption/desorption of bivalent metal cations such as Ca2+, Mn2+, Zn 2+ , and Co2+ on 'Y-AI203 (Hachiya et aI., 1984). Double relaxations were observed for each system and based on this finding, the authors proposed a two-step mechanism

[35]

Step 2 In Step 1, the hydrated metal ions lose one H 20 molecule and form an intermediate complex with a surface site. The fast relaxation associated with Step 1 was ascribed to simultaneous adsorption/desorption of the metal ions on a major portion of the 'Y-AI203 surface sites. In the second step a metal ion-surface complex is formed that results in the release of a proton. This slow relaxation was attributed to the adsorption/desorption of metal ions on the remaining, multiple type sites of the 'Y-AI203 surface that comprise a small fraction of the total surface sites. Yasunaga and Ikeda (1986) characicrized the first type of surface sites as strong sites and the multiple type sites as weak sites. Linearized rate equations relating reciprocal relaxation times 10 the intrinsic rate constants were developed and validated for the two-step reaction mechanism. A plot of the linearized equation for Step 2 (the faster

SPARKS & ZHANG

86

3

3

,.

III

'I

'b

III N

0 2 ,....

~

2 Q

'I

.::-

I

I-'

o

1.5 [-AIOM(H 20 ): _1]

+ [WI

+ K;". t exp (e1/;s) - kT ([ -AIOH] +

[M(HP)~+]), 10 -3

mol dm- 3

Fig. 3-12. Plot of T~-I YS. t~AIOM(H20):_ tl + IH +] + Kjn! exp( -e1/;s/k1) {[ -AIOH] + IM(H 20);+] where Tr- I is the reciprocal relaxation time for the fast relaxation; -AIOM (H 20),,_1 is a surface complex formed by the adsorption of M(H 20);+; where M is the metal ion; KIn! is the intrinsic equilibrium constant for Step I; 1/;s is the surface potential; and AIOH is the amphoteric surface} (from Hachiya et al., 1984).

step) is shown in Fig. 3-12. Intrinsic rate constants were calculated for both reaction steps for an array of cation/,,-Al203 interactions. Values of kint and k~tl for Step 1, the rate-limiting step, for each reaction system are shown in Table 3-4. Hayes and Leckie (1986) investigated Pb adsorption/desorption at the goethite/water interface using p-jump relaxation. A modified TLM was developed to obtain parameters for surface charge and potential. Three types of information were required to verify the reaction mechanism; (i) overall Table 3-4. Intrinsic forward (krtl and backward (k~i) rate constants for adsorption/desorption of various metal ions on a -y·AI20 s surface at 298 K (Hachiya et al., 1984l. Metal ion Pb 2 + Cu 2 + Zn 2 + Mn 2 + Co 2+

(6.4 ± 1.6) x 10 4 (7.4 ± 2.0) x lOs (5.1 ± 0.8) x 10 2 (3.2 ± 0.5) x 10 (1.5 ± 0.4) x 10

(4.1 ± 1.0) x 10 6 (3.1 ± 0.9) x 10° (1.3 ± 0.2) x 10 6 (1.8 ± 0.3) x 10 6 (6.lJ t I.lJ) x 10 4

87

RELAXATION METHODS AND SOIL KINETICS

Table 3-5. Intrinsic forward (kf't) and backward (k~i) rate constants and the equilibrium constant (Kf't) on goethite as a function of p-jump (.iP) changes (Hayes and Leckie, 1986).

MPa 14 10 7

- - - - - m o l - 1 dm" s -1 1.7 2.4

3.6

X X X

10 5 10 5 10 5

_

4.2 X 10 2 6.1 X 10 2 8.9 X 10 2

4.0 4.0 4.0

X X

X

10 2 10 2 10 2

equilibrium partitioning; (ii) reaction stoichiometry; and (iii) a rate law that correctly related the observed product and reactant changes to 7 -I. A double relaxation was obtained for the goethite system. Combining results from static and kinetic studies, a bimolecular adsorption/desorption reaction mechanism was postulated for the fast relaxation, XOH+

+

Pb 2+ ~ XOPb+

+

H+

[36]

where a Pb2+ adsorbs on a neutral surface site at the a plane and a proton is replaced from the surface. The authors found that the rate-limiting step for the above reaction was the desorption step associated with breaking the surface bond of the inner-sphere, Pb-OH complex. Interestingly, Hayes and Leckie (1986) found that the intrinsic rate constants kl nt and k~\ increased as applied pressure (LlP) decreased (Table 3-5). The authors attributed this to a greater number of high energy sites being perturbed at the higher LlP. This is reflected in the lower value of the rate constants at higher LlP values, which implies a higher activation energy and a lower overall rate (Hayes and Leckie, 1986). Hydrolysis of Soil Minerals It is well-known that the amphoteric properties of hydroxyl groups that exist on the surface of oxide particles play an important role in adsorption phenomena. These groups are characterized by two acidity constants, one for the protonation reaction and the other for the deprotonation reaction, which are functions of the surface potential created by adsorbed ions (Atkinson et al., 1967; Davis et al., 1978). These types of surface reactions on soil minerals have been studied using transient relaxation methods. Astumian et al. (1981) investigated the kinetics of proton adsorption/desorption on oxides in aqueous suspension using p-jump relaxation. Single relaxations were observed for -y-Fe203 (hematite) and Fe304 (magnetite) suspensions. With both suspensions the 7- 1 showed a parabolic dependence on pH, displaying a minimum at pH 3.4. The intrinsic rate constants for the two oxides were very similar. At I = 2 x 10 -3 and 298 K, the proIonation (k~nl) and deprotonation (k~nt) rate constants were 2.4 x 105 mol- I I, s -I and 0.16 s ',respectively, for hematite. For magnetite, they were 1.4 x 10 5 mol -, I, s I und 0.14 s: I, respectively.

SPARKS & ZHANG

88

When proton adsorption/desorption on goethite was investigated, no relaxation was observed. The reason for this is that the acidity constant (Ka ) for goethite (104.3-5.°) is higher than for magnetite (10 3. 5- 4.°) and hematite (10 3. 9- 4 .5) . In general, upon applying a perturbation to a chemical equilibrium, the larger the shift in the equilibrium (relaxation amplitude), the more similar the equilibrium population of the species involved. Therefore, systems with very small or very large equilibrium constants are relatively insensitive to perturbation. Thus, it is not surprising that no relaxations were also observed in Si02 (K; < 10) and -y-AI203 (Ka = 104 .4- 6.° ) suspensions. The relative relaxation amplitudes were found to follow the order of Ti0 2 oc, = 102. 5- 3.°) > magnetite uc, = 103. 5- 4.°) > hematite oc, = 103.9- 4.5) . Astumian et al. (1981) found that relaxations for protonation/deprotonation reactions are observable in the approximate range of 2 < pKa < 4. Ikeda et al. (1981) studied hydrolysis kinetics of a zeolite-NaOH suspension using p-jump relaxation and observed a single relaxation at pH > 11.5. The relaxation could have been caused by Na entering the zeolite cage. Therefore, tetramethylammonium ions, which could not enter the zeolite cage, were added as the base. However, a single relaxation was still observed. Based on these findings the authors concluded that the single relaxation was due to the interaction between the hydroxyl ion and the active site on the zeolite surface. With hydrolysis, a proton on the hydroxyl site was released to the bulk solution to. form a H 20 molecule with a hydroxyl ion. Based on equilibrium and kinetic measurements, the k l and k_ 1 values for the hydrolysis process were 1.6 X 102 mol - I L s - I and 8.7 X 10 - 2 S - I, respectively. Equilibrium constants obtained from kinetic and static studies were very comparable. Similar results were reported for kinetics of hydrolysis on Zeolite X (Na20.AI202.2.5Si02) and Y (Na20.AI203.4.8Si02) surfaces (Ikeda et al., 1982a). Ion-Exchange Kinetics

Ion-exchange kinetics on solids have been studied using p-jump relaxation (Ikeda et al., 1982b; Ikeda et al., 1984b) and stopped-flow measurements (Ikeda et al., 1984a). Ikeda et al. (1984b) noted a single relaxation for NH/ exchange on zeolite. The T -I values were measured at different [NH/] and increased with increases in [NHl]. They proposed a simple ionexchange mechanism given below

S(H)

+

kl

NHl ~ S(NH4) k_ 1

+

H+

[37]

where S is the solid surface. A linearized rate equation was proposed for the exchange mechanism

RELAXATION METHODS AND SOIL KINETICS

89

I

III

'"E 4000 'C I

'0 E

-

+

2000

:I:

+

-

+.. :I: Z

l /)

::::" I

.

0

2 1 ([S(H)] + [NH 4+])/([S(NHn]

3

+ [W))

Fig. 3-13. PlotofT- 1/ {[S(NH 4) ] + (H+]} vs. ([S(H) + [NHl]}/{[S(NH 4) ] S is a zeolite surface (from Ikeda et aI., 1984b).

+

[H+]} where

and it was tested (Fig. 3-13). Linearity resulted, in accordance with the mechanism proposed in Eq. [37]. The k 1 and k -I values and the relationship kl/k_ 1 (K:~n) wer.e calculated. This latter parameter wa~ compared to that determined (K:~al1c) statically and the values were K:~at'c = 0.94 and K:~n = 0.81. The relatively good comparison between the K eq values determined by two independent methods would indicate that chemical kinetics and mechanistic rate laws are being determined (Sparks, 1989). Such favorable comparisons between K:~atic and K:~n have also been noted by Ikeda et aI. (1981) who studied the kinetics of hydrolysis of zeolites using p-jump, by Zhang and Sparks (1990) who investigated S04 adsorption/desorption kinetics on goethite using p-jump relaxation, and by Ikeda et aI. (1984a) who investigated Na-exchange kinetics on zeolite using a stopped-flow method. Kinetics of Li-, K-, Rb-, and Cs-Na exchange on zeolite were studied by Ikeda et aI. (1984a) using a stopped-flow technique with conductivity detection. A conductivity increase with time was noted in the Li-Na system while a decrease with time was observed for the K-, Rb-, and Cs-Na systems (Fig. 3-14). Based on kinetic and equilibrium measurements, the former observation was ascribed to the release of Na induced by Li adsorption and the latter to adsorption of K, Rb, or Cs on sites in the cage of the zeolite. Complexation Reactions in Soil and Aqueous Environments A detailed knowledge of the interactions of metal ions with natural organic and inorganic compounds is needed to understand important chemical processes occurring in soil and natural water systems. Complexation may change the fate of a number of organic species in the soil solution and in the groundwater. In most studies dealing with metal complexes in the aquatic environment only equilibrium measurements have been discussed, and the kinetics has been neglected. However, as Pankow and Morgan (1981) pointed out,

90

SPARKS & ZHANG

... ~

6

t:

::J

>.

-.. III

,Q

III

~

4

2

00 6

CD 'tJ ::J

4

Co

2

-

2

4

6

8

10

2

3

4

5

time,

S

E

III

0

0

Fig. 3-14. Typical reaction curves observed by using the stopped-flow method with electricalconductivity detection at particle concentration (Cp ) of 0.7 g dm -3 and 298 K; (a) Li, b) K, Rb, and Cs [from Ikeda et al., 1984a).

these natural systems never reach complete equilibrium and kinetic processes usually predominate. An example of how kinetic measurements may suggest a mechanism for complex formation between soil compounds is the research of Lopez-Quintela et al. (1984) who studied the reaction between Al ions and citric acid and leaf extract in aqueous solutions. A stopped-flow apparatus was used to study the kinetics and the reaction progress was monitored by electrical conductivity. To avoid conductance changes caused by nonhomogeneous mixing and temperature changes, the two solutions were previously adjusted to equivalent conductances and pH's with inert reagents. Thus, the conductivity changes should be caused by complex formation. At a low pH range (1.4-2.7), only a single relaxation was observed. This was also observed with p-jump-relaxation measurements. The single relaxation obtained with the stopped-flow technique was attributed to the formation of a monodentate complex (AIH 2Cit2+) that was rate determining. At 293.7 K, the stability constants for the monodentate complex, the bidentate complex (AlHCit +) and the tridentate complex (AICit) were 8.2(±1.5) X 102,3.6(±1.6) X 106and5.3(±2.3) X 1O lOdm 3mol- 1s- l , respectively. The rate constants for the formation of AIH 2Cit 2+ and AlHCit+ were 5.4(±O.5) X 103 and 80(±10) dm ' mol " ! S-I, respectively. Complexation reactions between Fe(I1I) and P04 ions play an important role in soil chemistry, water treatment, and corrosion phenomena. Formation of various species have been postulated depending on the experimental conditions, methods of analyses, and interpretation of results. Few studies, however, have reported thermodynamic and kinetic data for these species. Wilhelmy et al. (1985) used stopped-flow with ultraviolet/visible detection to identify the complexes that playa role in formation of ion-solid phases and to determine relevant thermodynamic and kinetic constants. They distinguished between mono- and diphosphate iron species. The proposed mechanisms for the monophosphate iron complex were

91

RELAXATION METHODS AND SOIL KINETICS

Fe H

+ Hzpol-

~ FeHzP01+

[39]

or [40]

or a combination of the above two reactions. They found that the mechanformation is a combination ism for diphosphate iron species [Fe(H zP0 4 of several possible pathways. Wilhelmyet al. (1985) found that a static spectrophotometric procedure was not sufficiently sensitive to detect successive complexation. However, determination of absorbance was an effective method for identifying a series of species in solution. The detection of a ferric diphosphate complex, Fe(H zP04)l , demonstrated the value of using a kinetic technique for characterizing the solution species. Patel et al. (1974) used stopped-flow and t-jump to investigate the kinetics of magnesium-bicarbonate interactions in aqueous solution. Single relaxation times were very short (7 :::::: 5-20 p.s). The best experimental conditions were at pH :::::: 9, since around this pH, conditions due to the formation of both MgHC0 3+ and MgC0 3 gave rise to a relatively large reaction amplitude. At lower pH's, the reaction amplitude was much smaller and experimental measurements were difficult to obtain. The data were interpreted on the basis of a coupled reaction scheme in which protolytic equilibria are established relatively rapidly, followed by a single relaxation process due to the formation of MgHC0 3+ and MgC0 3 • The formation rate constants were determined to be

)n

k r = 5.0 x 105 mol L -I k,

=

1.5 x 106 mol L -I

S-I

(Mg2+-HCOn

S -I

(Mg2+ -coj-).

These results, in conjunction with NMR solvent exchange rate constants ( :::::: 1 5 X 10 S -I), were analyzed in terms of a dissociative mechanism for the rate of complex formation (Patel et al., 1974). Other kinetic studies of complexation using relaxation techniques can be found in Bridger et al. (1983) [hydroxo and chloro complexes of Fe(III)], Bridger et al. (1982) [complexation of Fe(III) by picolinic and dipicolinic acids], Strahm et al. (1979) (complexation of aqueous iron chloride), and Patel and Taylor (1973) (complexation of magnesium pyrophosphates).

SUMMARY

Chemical relaxation theory was presented in this chapter, and a number of transient relaxation techniques including t-jump, p-jump, c-jump, and electric-field pulse were discussed. The application of these methods to important soil chemical processes was also covered including: anion and cal ion adsorption/desorption phenomena, hydrolysis of soil minerals, ionexchange processes, and complexation reactions. Relaxation methods have

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much to offer in the study of rapid soil reactions that often occur on millisecond- and microsecond-time scales. Undoubtedly, soil and environmental chemists will employ these techniques more in future years to study inorganic and organic interactions with soils and soil constituents.

ACKNOWLEDGMENTS

The authors are grateful to the U.S.-Israel Binational Agricultural Research and Development Fund and to the U.S. Borax Corporation for their partial support of this research.

REFERENCES Amacher, M.C. 1991. Methods of obtaining and analyzing kinetic data. p. 19-59. In D.L. Sparks and D.L. Suarez (ed.) Rates of soil chemical processes. SSSA Spec. Publ. 27. SSSA, Madison, WI. Astumian, R.D., M. Sasaki, T. Yasunaga, and Z.A. Schelly, 1981. Proton adsorption-desorption kinetics on iron oxides in aqueous suspensions, using the pressure-jump method. J. Phys. Chern. 85:3832-3835. Atkinson, R.J., A.M. Posner, and J.P. Quirk. 1967. Adsorption of potential determining ions at the ferric oxide-aqueous electrolyte interface. J. Phys, Chern. 71:550-558. Bar-Tal, A., D.L. Sparks, J. Pesek, and S. Feigenbaum. 1990. Analysis of adsorption kinetics using a stirred-flow chamber: I. Theory and critical tests. Soil Sci. Soc. Am. J. 54:1273-1278. Bernasconi, C.F. 1976. Relaxation kinetics. Academic Press, New York. Bernasconi, C.F. (ed.). 1986. Techniques of chemistry, Vol. 6, Investigations of rates and mechanisms of reactions. Part 2. 4th ed. Wiley, New York. Bridger, K., R.C. Patel, and E. Matijevic. 1982. Thermodynamics and kinetics of iron (III) ion by picolinic and dipicolinic acids. Polyhedron 1:269-275. Bridger, K., R.C. Patel, and E. Matijevic. 1983. Thermodynamic and kinetic studies of hydroxoand chloro-complexes of iron (III) in ethanol/water mixtures. J. Phys. Chern. 87: 1192-1201. Caldin, E.F. 1964. Fast reactions in solution. Blackwell, Oxford. Chance, B. 1974. Rapid flow methods. p. 187-210. In G.G. Hammes (ed.) Investigation of rates and mechanisms of reactions. 3rd ed. Wiley, New York. Czerlinski, V.G. 1960. Eine Versuchsanordnung Zur Anwendung der Temperatursprunsmethode auf biologische systeme. Z. Elektrochem. 64:78-79. Davis, J .S., and H. Gutfreund. 1976. The scope of moderate pressure changes for kinetic and equilibrium studies of biochemical systems. FEBS Lett. 72: 199-207. Davis, J .A., R.O. James, and J .0. Leckie. 1978. Surface ionization and complexation at the oxide/water interface. I. Computation of electrical double layer properties in simple electrolytes. J. Colloid Interface Sci. 63:480-499. Eigen, M., and L. DeMaeyer. 1955. Untersuchungen uber die kinetik der neutralisation. I. Z. Electrochem. 59:986-993. Eigen, M., and 1. Schoen. 1955. Stodpannungsverfahren znr untersuchung seln schnell verlaufender ionenreakionen in wasseriger losung. Z. Elektrochem. 59:483-494. Eigen, M., and L. DeMaeyer. 1963. Relaxation methods. Tech. Org. Chern. 8:895-1054. Eyring, E.M., and P. Hemmes. 1986. Electric field methods. p. 219-246. In C.F. Bernasconi (ed.) Techniques of chemistry, Vol. 6, Investigation of rates and mechanisms ofreactions. Part 2. 4th ed. Wiley, New York. Gettins, W.J., and E. Wyn-Jones (ed.), 1979. Techniques and applications of fast reactions in solution. Reidel Publ., Dordrecht, The Netherlands. Gibson, Q.H. 1969. Rapid mixing: Stopped flow. p. 187-228. In K. Kustin (cd.) Methods in enzymology. Vol. 16. Academic Press, New York.

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Gruenewald, B., and W. Knoche. 1979. Recent developments and applications of pressure jump methods. p. 87-94. In W.l. Gettins and E. Wyn-lones (ed.) Techniques and applications of fast reactions in solution. Reidel Publ., Dordrecht, The Netherlands. Hachiya, K., M. Ashida, M. Sasaki, H. Karr, T. Inoue, and T. Yasunaga. 1979. Study of the kinetics of adsorption-desorption of Pb H on a -y-Alz0 3 surface by means of relaxation techniques. 1. Phys. Chern. 83:1866-1871. Hachiya, K., M. Sasaki, T. Ikeda, N. Mikami, and T. Yasunaga, 1984. Static and kinetic studies of adsorption-desorption of metal ions on a -y-Alz0 3 surface. 2. Kinetic study by means of pressure-jump technique. 1. Phys. Chern. 88:27-31. Hayes, K.F., and 1.0. Leckie. 1986. Mechanism of lead ion adsorption at the goethite-water interface. p. 114-141. In 1.A. Davis and K.F. Hayes (ed.) Geochemical processes at mineral surfaces. Proc. Am. Chern. Soc. Syrnp. Ser. 323, Chicago, IL., 8-13 Sept. 1985. ACS, Washington, DC. Hoffman, H., 1. Stuehr, and E. Yeager. 1966. Studies of relaxation effects in electrolytic solutions with the pressure-step methods. p. 227-255. In B.E. Conway and R.G. Barradas (ed.) Chemical physics of ionic solutions. Wiley, New York. Ikeda, T., 1. Nakahara, M. Sasaki, and T. Yasunaga. 1984a. Kinetic behavior of alkali metal ion on zeolite 4A surface using the stopped-flow method. 1. Colloid Interface Sci. 97:278-283. Ikeda, T., M. Sasaki, R.D. Astumian, and T. Yasunaga. 1981. Kinetics of the hydrolysis of zeolite 4A surface by the pressure-jump relaxation method. Bull. Chern. Soc. Jpn. 54:1885-1886. Ikeda, T., M. Sasaki, K. Hachiya, R.D. Astumian, T. Yasunaga, and Z.A. Schelly. 1982a. Adsorption-desorption kinetics of acetic acid on silica-alumina particles in aqueous suspension, using the pressure-jump relaxation method. 1. Phys. Chern. 86:3861-3866. Ikeda, T., M. Sasaki, and T. Yasunaga. 1982b. Kinetics of the hydrolysis groups on a zeolite surface using the pressure-jump relaxation method. 1. Phys, Chern. 86:1678-1680. Ikeda, T., M. Sasaki, and T. Yasunaga. 1984b. Kinetic studies of ion exchange of NH 4+ in zeolite H-ZXM-5 by the chemical relaxation method. 1. Colloid Interface Sci. 98:192-195. Ilgenfritz, G. 1966. Ph.D. diss. George August Univ., Goettingen, Germany. Knoche, W. 1974. Pressure-jump methods. 1974. p. 187-210. In G.G. Hammes (ed.) Techniques of chemistry, Vol. 6, Investigations of rates and mechanisms of reactions. 3rd ed. Wiley, New York. Knoche, W., and G. Wiese. 1974. An improved apparatus for pressure-jump relaxation measurements. Chern. Instrum. (NY) 5:91-98. Krizan, M., and H. von Strehlow. 1974. On the evaluation of chemical relaxation measurements with sampling techniques and on-line processing. Chern. Instrum. (NY) 5:99-108. Kustin, K. (ed.). 1969. Methods in enzymology. Vol. 16. Academic Press, New York. Ljunggren, S., and 0. Lamm. 1959. A relaxation method for the determination of moderately rapid reaction rates near chemical equilibrium. Acta Chern. Scand. 12:1834-1850. Lopez-Quintela, M., W. Knoche, and 1. Veith. 1984. Kinetics and thermodynamics of complex formation between aluminum (III) and citric acid in aqueous solution. 1. Chern. Soc. Trans. 80:2313-2321. Macri, G., and S. Petrucci. 1970. Pressure-jump relaxation kinetics of magnesium (II), manganese (II), nickel (II), cobalt (II), copper (II) and zinc (II) m-benzenedisulfonates in anhydrous methanol at 25°. Inorg. Chern. 9:1009-1014. Mikami, N., M. Sasaki, K. Hachiya, R.D. Astumian, T. Ikeda, and T. Yasunaga, 1983a. Kinetics of the adsorption-desorption of phosphate on the -y-Alz0 3 surface using the pressurejump technique. 1. Phys. Chern. 87:1454-1458. Mikami, N., M. Sasaki, T. Kikuchi, and T. Yasunaga. 1983b. Kinetics of adsorption-desorption of chromate on -y-Alz0 3 surface using the pressure-jump technique. 1. Phys. Chern. 87:5245-5248. Pankow, 1.F., and 1.1. Morgan. 1981. Kinetics for the aquatic environment. Environ. Sci. Tech. 15:1155-1164. Patel, R.C., F. Garland, and G. Atkinson. 1974. Dynamics of magnesium-bicarbonate interactions. 1. Solution Chern. 4: 161-174. Palel, R.C., and R.S. Taylor. 1973. Kinetics of binding of pyrophosphate to magnesium ions. J. Phys. Chern. 77:2318-2323. Rampton, D.T., L.P. Holmes, D.1.. Cole, R.P. Jensen, and E.M. Eyring. 1967. Square wave dissociation field cffect II1'1'11 ruIus. Rev. Sci. Instrum. 38:1637-1640.

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Robinson, B.H. 1975. The stopped-flow and temperature-jump techniques-principles and recent advances. p. 41-48. In E. Wyn-Jones (ed.) Chemical and biological applications of relaxation spectrometry. Reidel Publ., Dordrecht, The Netherlands. Robinson, B.H. 1986. Rapid flow methods. p. 9-29. In C.F. Bernasconi (ed.) Techniques of chemistry, Vol. 6, Investigation of rates and mechanisms of reactions. Part 2. 4th ed. Wiley, New York. Sasaki, M., M. Morlya, and T. Yasunaga, 1983. A kinetic study of ion-pair formation on the surface of a a-FeOOH in aqueous suspension using the electric field pulse technique. J. Phys. Chem. 87:1449-1453. Schelly, Z.A., and E.M. Eyring. 1971. Step perturbation relaxation techniques. J. Chem. Ed. 48:A639-654. Schwarz, G. 1986. Theoretical basis of chemical relaxation. p. 27-39. In C.F. Bernasconi (ed.) Techniques of chemistry, Vol. 6, Investigation of rates and mechanisms of reactions. Part 2. 4th ed. Wiley, New York. Sparks, D.L. 1987. Kinetics of soil chemical processes: Past progress and future needs. p. 61-73. In L.L. Boersma (ed.) Future developments in soil science research. SSSA, Madison, WI. Sparks, D.L. 1989. Kinetics of soil chemical processes. Academic Press, New York. Sparks, D.L. 1991. Chemical kinetics and mass transfer processes in soils and soil constituents. In Y. Corapcioglu and J. Bear (ed.) Transport processes in porous media. Kluwer Publ., Dordrecht, The Netherlands. (In press). Strahm, U., R.C. Patel, and E. Matijevic. 1979. Thermodynamics and kinetics of aqueous iron (III) chloride complex formation. J. Phys. Chem. 83:1689-1695. Strehlow, von H., and M. Becker. 1959. Ein Drucksprung-Verfahren Zur Messung der Geschwindig keit. Z. Elektrochem. 63:457-461. Takahashi, M.T., and R.A. Alberty. 1969. The pressure-jump methods. p. 31-55. In K. Kustin (ed.) Methods in enzymology. Vol. 16. Reidel Publ., Dordrecht, The Netherlands. Turner, D.H. 1986. Temperature-jump methods. p. 141-189. In C.F. Bernasconi (ed.) Techniques of chemistry, Vol. 6, Investigation of rates and mechanisms of reactions. Part 2. 4th ed. Wiley, New York. Wilhelmy, R.B., R.C. Patel, and E. Matijevic. 1985. Thermodynamics and kinetics ofaqueous ferric phosphate complex formation. Inorg. Chem. 24:3290-3297. Yasunaga, T., and T. Ikeda. 1986. Adsorption-desorption kinetics of the metal-oxide-solution interface studied by relaxation methods. p. 230-253. In J.A. Davis and K.F. Hayes (ed.) Geochemical processes at mineral surfaces. Proc. Am. Chem. Soc. Symp. Ser. 323, Chicago, IL. 8-13 Sept. 1985. ACS, Washington, DC. Zasoski, R.T., and R.G. Burau. 1978. A technique for studying the kinetics of adsorption in suspension. Soil Sci. Soc. Am. J. 42:372-374. Zhang, P., and D.L. Sparks. 1989. Kinetics and mechanisms of molybdate adsorption/desorption at the goethite/water interface using pressure-jump relaxation. Soil Sci. Soc. Am. J. 53:1028-1034. Zhang, P., and D.L. Sparks. 1990. Kinetics and mechanisms of sulfate adsorption/desorption on goethite using pressure-jump relaxation. Soil Sci. Soc. Am. J. 54:1266-1273.

4

Ion-Exchange Kinetics on Reactive Polymers and Inorganic Soil Constituents Domenico Petruzzelli

Istituto di Ricerca sulle Acque Consiglio Nazionale delle Ricerche Bari, Italy Friedrich G. Helfferich

Department of Chemical Engineering Pennsylvania State University University Park, Pennsylvania Lorenzo Liberti

Istituto Chimica Applicata Facolta Ingegneria Universita di Bari Bari, Italy

ABSTRACT The assessment of the fate (dispersion, retention, degradation), the quantification of transport phenomena, and the relative concentrations of a chemical in the different natural compartments (air, water, soil, and biota) is one of paramount importance in evaluating the chemical "mobility" in and through different phases. Among others, ion-exchange phenomena at the water-soil interface are of primary importance in soil and environmental chemistry, and research from both thermodynamic and kinetic viewpoints is necessary. With regard to kinetic aspects, despite the huge amount of work performed on reactive polymers, (e.g., ion-exchange resins and/or membranes) insufficient literature in reference to inorganic soil constituents (e.g., clays, oxides, and zeolites) exists. In general, due to the extreme subdivision of the constituent particles of natural exchangers, they are usually considered as "quasihomogeneous" with the liquid phase. Thus homogeneous kinetic theory can be used to describe their reaction mechanisms. Recent studies have shown that mass transfer phenomena, either in the liquid and/or the solid phase, could playa relevant role in determining general kinetic behavior of these systems in addition to those strictly related to the pure chemical reactions. After a general overview of the basic principles of ion-exchange kinetics on reactive polymers, we shall apply these principles to clays, oxides and zeolites, which serve as models for heterogeneous soils. Copyright © 1991 Soil Science Society of America. 677 S. Segoe Rd .• Madison. WI 53711. lJSA. RaIl'S of Soil Chrmtcut Processes. SSSA Special Publication no. 27.

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Once a chemical has been introduced into the environment, the assessment of its transfer phenomena between natural compartments (air, water, and soil) and its concentrations in the respective phases (gas, liquid, solid) is an indispensable prerequisite for the estimation of the chemical's environmental impact (exposure, accumulation in the food chain, and ecotoxicity) on living organisms, including humans. Land disposal of wastewaters for groundwater recharge, and eventual reuse for irrigation, for example, is among the operations most widely blamed for dissipation of pollutants in the environment. Nevertheless, the interest in water reuse by land disposal, as an additional resource supplementing the hydrologic balance, is growing, especially in those areas (such as the Mediterranean basin) where increasing water demand is accompanied by insufficient rainfall and scant local supplies of freshwater. This combination leads to water shortages and a systematic deficit in the general water balance in the summertime (Ciavatta and Vianello, 1987). Reclamation of treated wastewaters by land disposal has long been discouraged, mainly for sanitary reasons. This, in our opinion, reflects the concern that not enough is known about the transport and fate of potentially hazardous wastewater constituents (biorefractory organic molecules, heavy metals, and biological agents) in the surface and subsurface environments. It is known that chemicals reach bodies of water by transportation through soil after generic manmade operations of land "disposal" of liquids. Examples of this include: irrigation with low-quality waters, groundwater recharge operations involving partially treated wastewaters, and excessive fertilization and pesticide practices. Understanding the transport and fate of pollutants in soils is among the most challenging and demanding current research topics. Predictions of mobility and transport of chemicals in the natural compartments usually rely on models and mathematical simulations. The effectiveness of these hinges on a fundamental knowledge of the reactions and interactions of the pollutant substrate at the boundaries of the respective compartments, governing its behavior in the different phases (gas, liquid, and solid). Phenomena have to be identified, characterized, and quantified with respect to kinetics and thermodynamics to provide a comprehensive and predictive model of the natural system under consideration. Thermodynamic aspects of ionic reactions on inorganic soil constituents (clays, oxides, zeolites, and minerals) have received considerable attention over the years. These studies allow quantification of interactive phenomena, but fail to provide insight into the dynamics, mechanisms, and facets of great importance for construction of effective models. Kinetic studies, on the other hand, have been less extensive and systematic. This is in part because of the fine subdivision of the solids and their correspondingly large specific surface areas as well as the low rates of liquid convection in soils. Interactive phenomena at liquid-solid interfaces are usually considered sufficiently fast for local equilibrium to be maintained. Also, the fact that soils are very complex mixtures of different constituents may well have discouraged many investigators from attempting a thorough

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kinetic characterization, as was conducted on synthetic reactive polymers (Helfferich and Hwang, 1988). Unfortunately, thermodynamics and kinetics alone are insufficient to predict migration and fate of pollutants and toxic substances in the environment. They indicate what happens momentarily and locally, given the presence of the participants and the conditions at the time. What is really needed, however, is the "global" picture of travel and change over long distances and time. This is produced by a complex interplay of transport phenomena (convection and diffusion) with reactions (decay of organics, redox reactions of inorganic ions, and precipitation and dissolution) and transfer between phases (adsorption, ion exchange, and possibly liquid-liquid partitioning if a water-insoluble liquid phase is present or formed). Such combinations control both the usually very slow penetration of geological strata and the faster transport in aquifers and the like. For example, a toxic metal ion may slowly be released into an aquifer by dissolution of a mineral or salt of low solubility, then be carried by liquid-phase convection, later to be redeposited elsewhere as a result of ion exchange, a redox reaction, or reprecipitation by another anion released by dissolution of a different mineral. Such "metasomatic processes" have long been known to geologists (Korzhinski, 1970) and their environmental impact has been recognized (Hahne and Kroontje, 1973; Griffin et al., 1977; Khalid, 1980). However, only in recent years have first steps been taken to establish quantitative physicochemical models (Miller and Benson, 1983; Walsh et al., 1984; Bryant et al., 1986; Dria et al., 1987; Kim and Cussler, 1987; Novak et al., 19889; Helfferich, 1989), drawing in part on concepts and mathematics originally developed for chromatography and enhanced oil recovery (Helfferich and Klein, 1970; 1981; Hirasaki, 1981). The most comprehensive theoretical framework to date, including convection, redox reactions, and adsorption, is that proposed by Bryant, Schechter, Lake, and others of the University of Texas (Bryant et al., 1986; Dria et al., 1987; Novak et al., 1988). The present review, however, is confined to kinetics of local, momentary ion-exchange phenomena. After a brief overview of kinetic models commonly used to interpret ionic reactions on soil constituents (essentially based on kinetic theory of homogeneous systems), current kinetic models of heterogeneous systems will be examined in order to identify the limitations of their application to inorganic soil constituents.

REASONS FOR KINETIC STUDIES

A kinetic study of an ion-exchange process has different objectives. The basic scientist, engaged in fundamental research, may be attempting either 10 ascertain the reaction mechanisms in a system or to confirm an existing rate theory. The applied researcher, at a certain stage of a new application, will be interested in how kinetic behavior is related to thermodynamic aspects of the system (i.e., equilibria and selectivity) and to the performance of the ion exchanger in pruct kill sell ings. The design engineer may need to deter-

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mine mass transfer coefficients and related parameters for design and optmization of a new installation. The scientist interested in mass transfer phenomena will find in ionexchange kinetics a fascinating field of study. This is true of work with synthetic reactive polymers or natural, usually inorganic, ion exchangers. It is especially challenging to study ion-exchange kinetics in soils, one of the least investigated areas in soil science.

EXPERIMENTAL METHODS

In soil science, even more than in areas that employ synthetic reactive polymers, the selection of an appropriate experimental technique is of vital importance if one is to obtain conclusive and reliable kinetic information (Kressman and Kitchener, 1949; Zasoski and Burau, 1978; Liberti, 1983; Petruzzelli and Boghetich, 1983; Carski and Sparks, 1985; Sparks, 1985a,b; and Amacher, 1990). In the following discussion, some details on batch and shallow-bed techniques for rate measurements, as well as methods for direct monitoring of ion diffusion in the solid phase will be covered (Petruzzelli and Boghetich, 1983). Other details of kinetic methodologies can be found in the chapter by Amacher (1990). A comprehensive description of relaxation methods, increasingly adopted to follow fast reactions on soil constituents, is found in the chapter by Sparks and Zhang (1990). Batch Techniques

With this technique, appropriate amounts (by volume or weight) of the ion exchanger and solution, of known initial composition, are placed in a vessel with a thermostat and vigorously agitated while the time dependence of a representative variable of the system (e.g., pH, concentration, electrochemical potential, radioactivity) in one or both phases is continuously monitored. Effective agitation of the system is essential to avoid local nonuniformities and to provide well-defined hydrodynamic conditions. Paddle or magnetic stirrers may cause breakup of particles, abrasion, and changes in the surface structure of the solid particles, by a shearing effect, and affect the kinetic behavior. An ingenious solution to this problem is offered by the KressmanKitchener centrifugal stirrer reactor (Kressman and Kitchener, 1949), in which the ion exchanger is confined in a wire-mesh basket in the core of a centrifugal stirrer (Fig. 4-1A). The solution is driven through the reactor by centrifugal action and leaves through radial holes, thus there is rapid recirculation and excellent liquid-solid contact without shearing effects onto the particles. Fig. 4-1B shows an automated, computerized monitoring system that records the measured variable as a function of time. Unfortunately, the Kressman-Kitchener reactor is not easily adapted to soil systems because of their fine particle size. A variation of 1his reactor

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SOIL ION-EXCHANGE KINETICS

A

..

8

UT

p Fig. 4-1. Batch apparatus for study of ion-exchange kinetics: A) Kressman-Kitchener stirrerreactor, and B) automated system for kinetic monitoring where M = stirrer; UT = ultrathermostat; RE = stirrer-reactor; E = potentiometer; R = recorder; DAS = data acquisition system; C = computer; P = plotter; EL = electrodes; b = baffles; T = thermometer; and PA = pneumatic pump (from Petruzzelli and Palmisano, 1981).

that helps in overcoming this problem is the so-called "Completely Mixed Batch Reactor" (CMBR), illustrated in Fig. 4-2, and the Carberry reactor shown in Fig. 4-3 (Hand et al., 1981). In CMBR, the ion exchanger is suspended in the liquid, which is agitated by a reciprocal shaker or, better, a paddle stirrer designed to minimize mechanical damage of the ion exchanger. For kinetic monitoring, I he suspension must be centrifuged or filtered to separate the liquid und solid for analysis. This is the principal disadvantage

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- l - - - - E l E (T RIC

MOTOR REA CTAN1'---l~

SAMPLE PORT

INJECTION

PORT

BAFFl£

Fig. 4-2. Completely mixed batch reactor (CMBR) for study of ion-exchange kinetics.

REACTANT

~

ELEC TRIC

AGITATOR

MOTOR

SHAFr

f;;J--. SAM PL E PORT

INJECTION PORT

BAFFCE

BASKET CONTAINING

EXCHANGER Fig. 4-3. Carberry reactor used in studies of ion-exchange kinetics on soils. SAMPLE

PORT

EXCHANGER MATERIAL

MAGNETIC STIRRING BAR

PUMP

Fig. 4-4. Shallow-bed apparatus for study of ion-exchange kinetics.

of the CMBR, as in some cases, centrifugation or filtration requires more time than does the actual kinetic process. However, Zasoski and Burau (1978) have developed a filtration batch technique that largely overcomes this drawback. Shallow-Bed Techniques With this method, a thin layer of the exchanger material is placed in a small column and a solution of constant composition is passed through the column at a constant and well-defined flow rate (Fig. 4- 4). The lime de-

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pendence of a representative variable of the system is continuously monitored in the effluents. An advantage of the shallow-bed technique, also called "miscible displacement" by soil scientists, is that the composition of the solution in contact with the ion exchanger remains virtually constant. In particular, the concentration of the ion released by the ion exchanger does not build up in the liquid, as it does in a batch method of finite volume. This greatly simplifies the interpretation of the experimental results. Moreover, complete conversion from one ionic form to another can be effected in a single experiment. The miscible displacement technique perfected by Sparks and coworkers (Sparks et aI., 1980; Carski and Sparks, 1985)is increasingly being recommended over batch studies, particularly if ion-exchange kinetics is related to mass transport under simulated field conditions (Murali and Aylmore, 1983). In summary, shallow-bed techniques have the following advantages over batch techniques for studying ion-exchange kinetics on soil constituents: (i) closer resemblance to phenomena under field conditions, (ii) ability to measure faster reactions, (iii) no need for liquid-solid separation prior to analysis, and, (iv) greater ease of evaluation as the composition of the liquid is held constant. Direct Monitoring Techniques The techniques mentioned thus far provide an "indirect" picture of what is happening in the solid phase since it is necessary to deduce variations in that phase from those in the liquid by means of mass balance approaches. Experimental kinetic curves (e.g., fractional conversion vs. time) are then correlated with models to establish the molecular mechanism. In some cases, the correlation of kinetic data with mathematical models may be misleading as different physical mechanisms may lead to the same mathematical description (Boyd et aI., 1947; Helfferich et aI., 1985a). To avoid the uncertainties in interpretation, and to gain a deeper insight into what is really occurring in the solid phase, a "direct" visualization of ion diffusion in the solid phase is highly desirable. Autoradiography and/or x-ray microprobe analysis (Petruzzelli and Boghetich, 1983) are two prominent techniques that make this possible. Autoradiography, a radioanalytical technique, requires tagging one of the participating ions with a radioisotope. After "freezing" the diffusion pattern in the solid phase by quenching the process at a predetermined time or conversion level with a suitable agent (e.g., acetone), a single exchanger particle is sliced into micron-thick cuttings and the equatorial section is tightly faced to a film sensitive to nuclide radioemission so as to map the spatial radioisotope distribution in the sample. The magnified map provides a direct picture of the pattern produced by diffusion and so can confirm or refute hypothetical mechanisms (Fig. 4-5). Microprobe analysis is based on the detection of the characteristic x-ray emission from an ion with which the ion exchanger has been partially or completely loaded. The emission is induced by scanning the material with an elec-

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Fig. 4-5. Autoradiographs of 804 radioisotopic distribution on cuttings of equatorial sections of single resin beads at different fractions of conversion, F; (a) micrograph (xlOO) of bead cuttings, (b) isotopic *804 - 804 exchange reaction, (c) forward CI - *804 exchange reaction, (d) reverse *804 - CI exchange reaction. [(*refers to the labelled ion)(from Petruzzelli and Boghetich, 1983)].

tron beam of sufficient energy to excite the x-ray emission of the ion of interest (Fig. 4-6). Instrumentation is expensive, but results are more accurate than those that can be obtained with autoradiography.

QUASI-HOMOGENEOUS SOIL SOLUTION MODELS It is common practice in soil science to use kinetic theory of homogeneous reactions as an approximation for reactions occurring in soil-solution systems. The rationale is that the very fine subdivision of the soil particles (clays, minerals, oxides, zeolites, humic acids, etc.) allows the system to appear homogeneous except on a very small scale. A number of "homogeneous models" have been proposed to interpret kinetics of ionic reactions on inorganic and organic soil constituents. These include zero-order equations (with the rate of release of the ionic species independent of the amount left in the exchanger material) (Keeney, 1973; Reddy et aI., 1978), classical first-order (Sawhney, 1966; Sparks and Jardine, 1984) and "multiple first-order" equations (Griffin and Jurinak, 1974; Jardine and Sparks, 1984; Carski and Sparks, 1987) (the multiple terms IIIl' attributed

103

SOIL ION-EXCHANGE KINETICS

0.8 0.4

0.4 F "'.6

0.4

\ 180

120

60

0

60

120

180

240

+----jtm

Fig. 4-6. X-ray microprobe analysis of 804 distribution along equatorial axis of single resin bead at different fractional conversion, F (from Petruzzelli and Boghetich, 1983).

to kinetic sites of different reactivities), the Elovich equation, originally derived for the chemisorption of gases onto solid surfaces (Chien et aI., 1980; Onken and Matheson, 1982), and, the parabolic diffusion law (Sparks and Jardine, 1984, Evans and Jurinak, 1977), no longer a strictly "homogeneous" model since it incorporates a solid-phase diffusion coefficient into the equation for a first-order homogeneous reaction. Table 4-1 lists these models as reported in recent publications by Sparks (Sparks, 1985a, 1989). The inrerested reader is referred to these publications for more details on kinetic models. The interpretation of ion-exchange kinetics in terms of homogeneous I heory is mathematically exact in most cases, but shortcomings are present and can be attributed to: the effect of poorly identified solid-phase structural and morphological parameters on ionic migration (Sparks et aI., 1980; Nkedi'l'uble 4-1. Equations for homogeneous models for correlation of kinetic data in soil systems.'] 1. 2. 3. 4.

Elovich Parabolic diffusion law First-order Zero-order

C, = a + bin t C,jC", = b t l/ 2 log(l - CtlC oo) = a - bt (1 - C,jC oo) = a - bt

'{', = liquid phase concontrution of the ion of interest at time 1/

und II are constunt« (from Spnrk», 19Hfia, with permission).

t

=

too; t

= time; and

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PETRUZZELLI ET AL.

Kizza et al., 1984; Srivastava et aI., 1989), the presence of different reactive sites on the solid (Jardine and Sparks, 1984; Carski and Sparks, 1987), and the influence of chemical reactions such as precipitation, dissolution, complexation, or neutralization that accompany ion exchange (Griffin and Jurinak, 1974).

HETEROGENOUS MODELS The idea that the mechanism of ion exchange is mass transfer rather than a chemical reaction dates back to the work of Warburg (1913) and Schulze (1913, 1914) on glasses. Unfortunately, this work is largely forgotten. The first group of scientists to present a systematic analysis of possible ion-exchange mechanisms was Boyd et al. (1947), who identified diffusion in the liquid and solid phases and the actual exchange reaction at the surface sites as necessary steps for ion exchange to occur. They also argued that the slowest of these steps will control the overall rate. These views were immediately and widely accepted for synthetic ion exchangers. In soils, mass transfer is usually considered to be sufficiently fast for local equilibrium to be maintained (this is essentially based on the assumption of extreme subdivision of particles). However, exceptions occur depending on the type of soil constituent one is dealing with, and, in particular, if the soil constituent is coated with anything that retards accessinto the solid phase (humic and/or colloidal substances). In such cases, mass transfer could play a relevant role in kinetic behavior. Boyd and his early successors (Kressman and Kitchener, 1949; Schlogl and Helfferich, 1957) described diffusion in terms of Pick's law, with fluxes proportional to the respective concentration gradients (Crank, 1970) [1]

where J, is the flux of the ion i; D, is the individual diffusion coefficient; and q is the concentration of the ion i. However, in interdiffusion of ions of different mobilities, Fick's law fluxes would be unequal and disturb electroneutrality. Here, the first, minute deviation from local electroneutrality generates an electric potential gradient (diffusion potential) that produces electric transference of ions superimposed on diffusion. This is the mechanism by which the system manages to balance the fluxes so as to maintain electroneutrality (Schlogl and Helfferich, 1957; Helfferich, 1962a; Helfferich and Hwang, 1988). The flux now obeys the Nernst-Planck equation (Nernst, 1888; 1889; Planck, 1890)

«o,

grad

ordinary diffusion

q +

DjZPi F/RT grad

electric transference

[2]

SOIL ION-EXCHANGE KINETICS

105

where Zi is the ionic valence; F is the Faraday constant; R is the gas constant; T is the temperature; and cI> is the electric potential. One should note that the electric transference term is proportional to the concentration of the respective ion while the diffusion term is not. As a result, the "correction" for the electric transference is large for a counter ion at high concentration but small or none at trace levels. Thus, the ion moves essentially according to Fick's law. With interdiffusion of two counter ions, the diffusion coefficient of the minority ion (the ion present at lower concentration) essentially dictates the flux (Helfferich, 1962a). Rate-Controlling Steps In a binary exchange reaction [3]

(where overbars refer to the ion in the solid phase) five steps must be considered as possibly controlling the overall rate (Boyd et aI., 1947): 1. Mass transfer of Ion B from the bulk liquid to the surface of the solid particle 2. Diffusion of Ion B from the particle surface to the exchange site 3. An exchange reaction of B for A at the site 4. Diffusion of Ion A from the exchange site to the particle surface 5. Mass transfer of Ion A from the particle surface into the bulk liquid. In the liquid phase, convection contributes to mass transfer in addition to diffusion; in the narrow pores of the solid this contribution is usually considered to be negligible. With rare exceptions, ionic-exchange reactions are very fast compared with mass transfer phenomena. The exchange reaction (Step 3) therefore is usually expected to be at equilibrium and thus not rate limiting. In fact, rate control by an exchange reaction, although theoretically possible, has so far never been demonstrated. Moreover, the constraint of electroneutrality couples the opposing fluxes of Ions A and B in each of the two phases. Accordingly, two steps remain in contention as possibly rate controlling: interdiffusion of the exchanging ions in the particle, and mass transfer of t he ions in the liquid phase. Commonly, mass transfer in the liquid is modeled as diffusion in a fieI itious liquid film adhering to the particle "Nernst film" (Nernst, 1889; Planck, 1890). Intraparticle diffusion and film diffusion are the two possible rate-controlling steps (Helfferich, 1962a). A criterion that can be used to predict which of these two steps is rate controlling is to equate the half-times calculated for ideal intraparticle- and ideal film-controlled exchange. This leads to a dimensionless Helfferich numher (He) defined as [Hclffcrich, 1962a] /It'

[4]

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PETRUZZELLI ET AL.

where C and D are the concentration and diffusion coefficient respectively, in the solid phase, 0 is the thickness of the liquid film around the particle; r" is the mean radius of the exchanger particles; and (XAB = (CACBICBCA)' is defined as the separation factor of Ion A relative to Ion B [Helfferich, 1962a].

Systems with He 41: 1 are controlled by intraparticle diffusion; those with He ~ 1 are controlled by liquid-phase mass transfer. Accordingly, intraparticle-diffusion control is favored by: high liquid-phase concentration, C; low ion-exchange capacity, C; large particle size, r "; tight structure of the exchanger material (low value of D); effective agitation of the system (low value of film thickness, 0); and, preference of the ion exchanger for the ion taken up from the solution. The last effect is interesting in that forward and reverse exchange of the same two counter ions under identical conditions can be controlled by different mass transfer steps. The physical cause for film rate control for an ion selectively taken up is that the concentration at the particle surface remains low up to high conversion, so that the large initial concentration difference across the "film" is maintained until the process is almost complete. Opposite conditions (He 41: 1) tend to favor rate control by mass transfer in the solid phase. In the range He = 1, both mass transfer steps affect the rate. The criterion based on the Helfferich number is derived for ion exchange with quasi-homogeneous (e.g., gel-type) particles and with no reaction such as neutralization or complex formation. In macroporous ion-exchange resins (Weatherly and Turner, 1976; Patell and Turner, 1980; Yoshida et al. 1985; Yoshida and Kataoka, 1985), in zeolite pellets consisting of micron-sized crystals fused together [Breck, 1974; Barrer, 1978], and in many types of soils (Ogwada and Sparks, 1986), the two potentially rate-controlling steps are diffusion in the macropores (or wider intraparticle channels) or within the gel-type microregions (or microcrystals). Mass transfer in the external liquid film can usually be ruled out since it is usually faster than mass transfer in the macropores. Chemical reactions at the functional group can affect ion-exchange rates even more profoundly. A slow exchange reaction, although possible, but usually not observed, would exclusively control the overall rate. Even a fast reaction at equilibrium can retard ion exchange by orders of magnitude, namely, if either or both exchanging ions in the ion exchanger are largely immobilized by bond formation with fixed groups (Barrer et al., 1963; Schwarz et al., 1964). Low rates on highly selective chelating ion exchangers are a case in point. Many experimental criteria have been suggested for identification of the rate-controlling step. The majority are based on curve fitting to idealized rate laws and are unreliable. The two best methods are the so-called "interruption test" and the determination of the dependence of the rate on particle size.

SOIL ION-EXCHANGE KINETICS

107

Table 4-2. Dependence of ion-exchange rates on various experimental parameters. Experimental parameter

Liquid-phase mass transfer

Intraparticle diffusion

Particle size (r"] Solution concentration (C) Separation factor (ocij) Stirring rate (rpm) Exchanger capacity (C) Interruption test Temperature (T)

Proportional to lIro Proportional to C See text Sensitive Proportional to lIC Not sensitive Kinetic increment 4%/oK

Proportional to lIro 2 Independent Independent Independent Independent Sensitive Kinetic increment 6%/oK

In the interruption test (Kressman and Kitchener, 1949), the ion exchanger is temporarily separated from the liquid. If the rate is controlled by mass transfer in the liquid, the rate upon reimmersion is the same as at the time of separation, the quasi-stationary state in the film is very quickly re-established. If the rate is controlled by intraparticle diffusion, concentration gradients within the particle have time to relax, and the rate is faster upon reimmersion. This comparison is independent of specific mechanisms and algebraic forms of rate laws. If controlled by mass transfer in the liquid, the exchange rate is proportional to the specific surface area and thus is inversely proportional to the particle radius or diameter. If controlled by intraparticle diffusion, the rate is, in addition, inversely proportional to the distance diffusion has to cover from particle surface to center, and so is inversely proportional to the square of the particle radius or diameter. If exchange were controlled by a reaction at the exchange site, the rate would be independent of particle size. Again, the comparison is independent of specific models or equations. A special case, however, arises with macroporous materials. Here, if the rate is controlled by diffusion within the microregions or crystals, it is inversely proportional to the square of the diameter of the crystals, but independent of the size of the macroparticles (provided they have the same microstructure) . Table 4-2 shows, as an example, a summary of the effects of experimental variables on the ion-exchange rate controlled by intraparticle diffusion, and by liquid-phase mass transfer. Further details and special situations will become apparent in the discussion of rate laws to follow. Rate Laws and Models

Three general classes of kinetic models that may apply to systems with rate control by mass transfer in the liquid or by interdiffusion in the particle with or without chemical reaction will be briefly reviewed here (for more detail, see [Helfferich, 1962a; Helfferich and Hwang, 1988]). In particular I he following models will be examined: liquid-phase mass transfer with linear driving force, Nernst-Planck models for intraparticle diffusion without reacI ion, and, Nernst-Planck models for intraparticle diffusion with accompanyIII~ react ion.

PETRUZZELLI ET AL.

108

Common assumptions of all of these models are: constant individual diffusion coefficients of the exchanging ions (e.g., A, B) in each phase, constant binary separation factors, <XAB' (selectivity), spherical particles of uniform and constant size, ion-exchange equilibrium at the particle surface, and, no convective transport of solvent. Liquid-Phase Mass Transfer With Linear Driving Force The simplest approach to rate laws is based on Fick's law, Eq. [1], which postulates the flux of any species to be proportional to the concentration gradient (Crank, 1970). When liquid-phase mass transfer is the ratecontrolling step, this is equivalent to assuming a constant mass-transfer coefficient (so-called "linear driving force approximation" [Vermeulen et al., 1984]). For quasi-stationary conditions in the film, a constant diffusion or masstransfer coefficient, and if the compositon of the bulk solution is constant, the fractional conversion, F(t), becomes

where D is the diffusion coefficient of ions in the liquid-phase; 0 is the film thickness; C is the concentration of ions in the liquid phase; C is the ion exchange capacity; r" is the particle radius; and t is time. Here, we are assuming that initially Ion A is in the exchanger and Ion B is in solution. Of special interest is the limiting case of very high preference of the exchanger for the entering ion (<XAB ~ 1). Here, the fractional conversion is a linear function of time until almost complete conversion. This is because the high selectivity for the ion being taken up maintains the original concentration difference across the film until exchange is almost complete (Helfferich et al., 1985a). Nernst-Planck Intraparticle Diffusion without Reactions This is the most widely used model for ion-exchange kinetics (Schlogl and Helfferich, 1957; Plesset et al., 1958). Combining the Nernst-Planck equation (Eq. [2]) with the constraints of electroneutrality and zero net charge transfer yields

J,

=

-DAB

grad

q (i = A,B)

[6]

where DAB is a variable interdiffusion coefficient given by

The material balance for A or B (oC/o/),

- div

J,I

[8]

109

SOIL ION-EXCHANGE KINETICS

is integrated to obtain the radial concentration profile q (r) and from it the momentary rate and eventually the fractional conversion as a function of time. Because of the nonlinearity of Eq. [6], numerical methods must be used. A computer program for such calculations is available and includes the effect of additional mass-transfer resistance in the liquid (Helfferich and Petruzzelli 1985; Petruzzelli et al., 1987). Some numerical solutions have been tabulated (Helfferich, 1963) and explicit approximations given (Schlogl and Helfferich, 1957; Plesset et al., 1958). In multi-ion systems the Nernst-Planck equation (Eq. [2]) applies to each ion. A set of simultaneous partial differential equations must be solved, as Eq. [6] and [7] can no longer be used (Bajpai et aI., 1974; Plicka et al., 1984; Hwang and Helfferich, 1987). This is also true if the presence of coions in the ion exchanger is to be accounted for (Spalding, 1971).

Nernst-Planck Intraparticle Diffusion with Fast Reaction Of particular interest in soil science is ion exchange accompanied by reactions such as dissociation, neutralization, hydrolysis, and complex formation. Such reactions affect both equilibria and kinetics. The effect on kinetics is particularly strong if the reactions results in binding and thus immobilization of ions on whose diffusion ion exchange depends. Cases in point are exchange reactions involving H on weak-acid exchangers and of metal ions forming covalent bonds chelating with fixed groups. Although the reaction may be fast enough to remain at local equilibrium, immobilization of the ions retards the process and produces entirely different diffusion patterns and mathematics (Helfferich, 1965). In cases with reactions consuming the ion taken up by the ion exchanger, conversion proceeds by a shell-core mechanism: a sharp boundary between a fully converted outer shell and a still entirely unconverted core advances from the particle surface to the center. Examples are neutralization of weak-acid or weak-base materials by base or acid, respectively, and uptake of metal ions forming bonds with fixed groups (chelating resins). The mathematics of shell-core kinetics is relatively simple, leading to F(t)

=1

- {1/2

+

sin[(l/3) sin -I(l-1/2DxCtt/ro 2C)]}

[9]

where index x refers to the rate-controlling ion; * refers to the concentration in equilibrium with the liquid; Ct refers to the concentration in equilibrium with the liquid; C is the ion-exchange capacity (Helfferich, 1965; Hellferich and Hwang, 1988). More generally, fast reactions can be accounted for within the NernstPlanck model by inclusion of a source-or-sink term R, in the material balance div J, + R,

rIO]

110

PETRUZZELLI ET AL.

where R, gives the quantity (mol) of species i formed (if positive) or consumed (if negative) per unit volume and time. A computer program for such calculations is available (Hwang and Helfferich, 1986, 1987). The participating ions are now coupled not only through the electric potential gradient, common to their flux equations, but also through the reaction terms. Mass action-type equilibria are assumed, with provision for multispecies systems that include coions and neutral species such as solvent molecules. It is the most general model of ion-exchange kinetics developed to date. A computer program for such calculations is also available (Hwang and Helfferich, 1987). Nernst-Planck Equations in Liquid-Phase Mass Transfer A brief comment should be made concerning the use of the NernstPlanck equations for ion transport across the liquid film (e.g., Copeland and Marchello [1969], Kataoka et al. [1987]). This is a nonlinear, three-ion problem because of the presence of at least one coion at comparable concentration. The Nernst film model relies on the assumption of a linear concentration gradient in the liquid film. The film has no physical reality, and the calculation of nonlinear concentration profiles in it overburdens the model and offers little improvement over the much simpler linear driving force approximation. For higher accuracy, more refined and complex hydrodynamic models would have to be used (Van Brocklin and David, 1975).

LIMITATIONS OF THE NERNST-PLANCK APPROACH AS APPLIED TO ION-EXCHANGE PHENOMENA IN SOILS The Nernst-Planck model is based on limiting laws for ideal systems. It accounts only for diffusion and electric transference of ions, not for electroosmotic solvent transfer in the ion-exchanger phase, swelling or shrinking of the ion-exchange material, variations of activity coefficients and diffusivities, and possible slow structural relaxation of the exchanger matrix. It also postulates the existence of individual diffusion coefficients for ions. Concentration-dependent activity coefficients can be accommodated with relative ease by an added term (e.g., [see Helfferich, 1962a; Brooke and Rees, 1968] and variations in diffusivities are easily included in numerical calculations (Helfferich and Petruzzelli, 1985; Hwang and Helfferich, 1986). In both instances, however, a fair amount of additional experimental information is required to establish the dependence on composition. Electro-osmotic solvent transfer and particle-size variations are more difficult to deal with, and no readily manageable models have been developed to date. A subtle difficulty here is that, as a rule, there is not only a variation in equilibrium solvent content with conversion to another ionic form, but that the transient local solvent content is a result of dynamics (electro-osmosis) and so not accessible by thermodynamic considerations (Helfferich, 1962b). Theories based on the Stefan-Maxwell equations or other forms of thermodynamics of ir-

111

SOIL ION-EXCHANGE KINETICS

reversible processes, avoiding the introduction of individual diffusion coefficients and accounting for dynamic interactions other than through the electric field, have been developed (Lightfoot and Scattergood, 1965; Graham and Dranoff, 1982; Schlogl, 1983). However, they are more complex and still fail to account for the variation of diffusivity parameters with solvent content of the ion exchanger. Slow relaxation phenomena are perhaps the most serious possible complication in that they introduce a memory effect ("non-Fickian" behavior, e.g., see Parks [1953]). Zeolites, with their rigid crystal structure, pose special problems relevant to phenomena in soils. For example, the water content is found to change, in accordance with the space available for solvent in the intracrystalline cavities, when a counter ion is exchanged for another of different crystalline radius (Barrier, 1980). In turn, the change in water content affects the ionic mobilities. It must also be recognized that, because of the usually much finer subdivision of natural ion exchangers in soils as compared with commercial synthetic resins, surface phenomena may playa more prominent role. Among these effects are: water is more structured at the interface than in the bulk liquid; ions and water molecules are less mobile at the interface because of stronger interactions; the dielectric constant of water is lower than in the bulk solution; and surface charges produce an electric double layer (Horst, 1~~. • Although structural studies of the mineral-water interface have been extensive, the effects of the above-mentioned phenomena on mass transfer and reactions are still largely unresolved (Yasunaga and Ikeda, 1986).

COMMENTS ON MECHANISMS OF ION EXCHANGE WITH INORGANIC SOIL CONSTITUENTS The most prominent inorganic soil constituents with ion-exchange properties are oxides, clays, minerals, and zeolites. Each have their own characteristics, which will be briefly reviewed here. Oxides Oxides in soils, as the end product of "weathering" of natural rocks, have dense, three-dimensional crystal structures and are reduced to very fine particle size. Ion exchange on oxides has long been demonstrated to be essentially confined to only the very first hydrated surface layers (Davis and Leckie, 1978). From a kinetic point of view, the fine subdivision and absence of inI raparticle mass transfer allows oxide microcrystals to be considered as quasicontinuous with the liquid phase. Homogeneous kinetic models are reasonable lor these materials and provide an adequate description in most cases (Yasunaga and Ikeda, 1986). Rate control by mass transfer has been invoked in cerlain cases for synthesized lind compacted oxides and attributed to the oxides'

PETRUZZELLI ET AL.

112

porous structure (Nkedi-Kizza et aI., 1984; Paterson and Rahman, 1985). Hydrous oxides are amphoteric, with surface charges dependent on protonation or hydroxylation in accordance with the pH of the contacting liquid

-

OH0-

,.L hydroxylated form (cation exchanger)

H

I

0

,.L

H

-

H

\/ 0+

H+

,.L

[11]

protonated form (anion exchanger)

hydrous oxide

Soil scientists and physical chemists tend to view this situation somewhat differently. The former see it as the acid-base reaction (Eq. [11]) at the surface; the latter, as an equilibrium uptake of anion and cation of acid HA or base B (see Eq. [12]) regulated by the Donnan potential and followed by the respective reaction (Paterson and Rahman, 1985)

B

i

HA

1

[12]

This is a phenomenon that could be classified as a special case of ion exchange accompanied by a neutralization reaction. In those terms, protonation or hydroxylation of a porous oxide could be described kinetically with the shell-core model (see Eq. [9]), the rate-controlling ion being H + or OH -, respectively. Clay Minerals Aluminosilicates such as montmorillonite, kaolinite, illite, and vermiculite are solids. that have structures readily accessible to counter ions. The excess negative charge resulting from isomorphic substitution of Al for Si is primarily distributed over the three adjacent surface 0 atoms of the layer, , where it is electrically balanced by mobile, exchangeable cations. Thermodynamically, ion exchange can be interpreted in terms of the interlayer electrostatic interaction between surface charges and hydrated cations in accordance with the classical Eisenman theory (Eisenman, 1983). A comprehensive description has recently been given by Maes and Cremers (1986). Most kinetic results have to date been correlated on the basis of homogeneous kinetic theory, with only a few exceptions (Srivastava et al., 1989). Nevertheless, mass transfer effects are likely to warrant inclusion. Here, special attention to water behavior at the mineral surface will be called \ for.

SOIL ION-EXCHANGE KINETICS

113

There is general agreement, supported by experimental evidence, that water molecules in contact with or in close proximity to the solid surface have properties different than those in the bulk solution. Over what distance this is true is still controversial (Giese and Costanzo, 1986). Two conflicting models for water adsorption on clay mineral surfaces have been proposed. The first limits the influence to a range equivalent to four or five layers of water molecules ( ::::: 0.1 nm), the second extends the effect much farther out, up to 30 to 40 layers (::::: 10 nm). Water structure is, of course, affected not only by the clay surface, but also by the charge-dipol interactions with the counter ions (hydration). Moreover, the presence of thermodynamically different exchange sites on natural clays (Maes and Cremers, 1986) must be expected to affect the kinetic behavior of the exchanging ions. Extensive experimental evidence on the presence of different exchange sites on mica and vermiculite is available. Here, low rates are attributed to interlattice exchange sites, intermediate rates, to the exposed edge sites, and rapid rates, to readily available external sites (Sparks and Jardine, 1984).

Zeolites

Natural zeolites are aluminosilicates with rigid, three-dimensional crystal lattices containing cavities connected by windows. The size and shape of these varies greatly from one material to another. In a few instances, e.g., analcite-leucite, the crystal structure may change discontinuously with conversion to another ionic form (Barrer and Hinds, 1953). Moreover, most zeolites contain several physically and crystallographically distinct exchange sites with different accessibility and selectivity (Barrer and Falconer, 1956). Another peculiarity of zeolites is that, under certain conditions, they may not be able to accommodate as many metal counter ions as are needed to compensate for the negative charges of the aluminosilicate matrix. Such imbalance can cause exchange to remain incomplete (Barrer et aI., 1956; Barrer and Sammon, 1956; Barrer, 1980) or lead to hydrolysis, pH changes, and other anomalies (Helfferich and Klein, 1970; Barrer, 1980). Still another complication in certain zeolites such as basic cancrinite, with channels that are not interconnected, is that exchanging ions, although able to move by themselves, cannot pass one another and thus exchange cannot take place (Barrer and Sammon, 1956). Finally, the rigid and regularly repeating crystal structure creates preferential directions for counter ion movement, making it anisotropic. Fick's law and the Nernst-Planck equations imply that the interior of the ion exchanger can be viewed as quasi-homogenous. This is not a poor premise for synthetic resins, in which local nonhomogeneities and anisotropies may momentarily exist, but are time averaged as the flexible matrix undergoes continuous rearrangement ("breathes"). It may also be acceptable for materials with easily accessible exchange sites. In zeolites, with rigid windows whose size does not much exceed that of the ions and with "nooks" (hat may be permanently inaccessible to larger ions, the application of the

PETRUZZELLI ET AL.

114

equations remains problematic, even if a term accounting for activitycoefficient gradients is added. Because of the rigid crystal structure and small window size, ionic diffusion in zeolites is slow and the activation energy is high (Barrer, 1980). Except on samples of very fine particle size, the exchange rate is controlled by intracrystalline rather than liquid-phase mass transfer.

CONCLUSIONS

A sound understanding of the mechanisms of ionic reactions at the liquid-solid interface is important in soil science both for its own sake and for effective analysis and prevention or correction of problems related to the migration and fate of chemicals in the environment. With respect to ion-exchange kinetics, the great complexity of soils has resulted in a penchant for the easy approximations of homogeneous models, even where the premise of a quasi-continuum of liquid and solid is hard to accept. The theory of heterogeneous systems offers the Nernst-Planck equations, but these also can provide no more than an approximation for migration of ions in soil constituents. The most important limitation in applying the classic Nernst-Planck theory to soils is the inability to account for the unusual behavior of water. An inclusion for the effects produced by water in minerals and on mineral surfaces may well be the key to a more accurate description of ion-exchange kinetics in soils. Certainly also important are dynamic interactions between the participants, including water, beyond the effect of the electric fields. Nonequilibrium thermodynamics can account for these at least in principle, but at this stage has not produced a theory or model that is manageable enough for practical application to soils. To become generally accepted, any new theory or model will have to demonstrate that its improvement outweigh its greater complexities. Finally, however, before starting any modelistic improvement of the Nernst-Planck theory to render it applicable to "natural reactive polymers," a great deal of experimental effort has to be devoted to the investigation of different systems under different experimental conditions in order to have a clear and comprehensive idea of all factors determining kinetic behavior.

REFERENCES Amacher, M.C. 1991. Methods of obtaining and analyzing kinetic data. p. 19-59. In D.L. Sparks and D.L. Suarez (ed.) Rates of soil chemical processes. SSSA Spec. Pub!. 27, Madison, WI Bajpai, R.K., A.K. Gupta, and M. Gopala-Rao, 1974. Single particle studies of binary and ternary cation exchange kinetics. AIChE J. 20:989-995. Barrer, R.M. 1978. Zeolites and clay minerals as sorbents and molecular sicvcs. Academic Press. New York.

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Barrer, R.M. 1980. Zeolite exchangers. Some equilibrium and kinetic aspects. p. 273-290. In L.V.C. Rees (ed.) Zeolites. Proc. 5th Int. Conf. Zeolites, Naples, Italy. 2-5 June 1980. Heiden & Son Ltd., London. Barrer, R.M., R.F. Bartholomew, and L.C.V. Rees. 1963. Ion exchange in porous crystals. II. The relationship between self and exchange diffusion coefficients. J. Phys, Chern. Solids. 24:309-317. Barrer, R.M., W. Buser, and W.F. Grutter. 1956. Synthetic fajausit. I. Properties and base exchange character. Helv. Chim. Acta. 39:518-530. Barrer, R.M., and J.D. Falconer. 1956. Ion exchange feldspatoids as a solid-state reaction. Proc. R. Soc. London A236:227-249. Barrer, R.M., and L. Hinds. 1953. Ion exchange in crystals of analcite and leucite. J. Am. Chern. Soc. 75:1879-1888. Barrer, R.M., and D.C. Sammon. 1956. An ion sieve reagent for cesium-alkali metal separation. J. Am. Chern. Soc. 78:675-682. Boyd, G.E., A.W. Adamson, and L.S. Myers. 1947. Exchange adsorption of ions by organic zeolites. II: Kinetics J. Am. Chern. Soc. 69:2836-2848. Breck, D.W. 1974. Zeolite molecular sieves: Structure, chemistry and use. Wiley, New York. Brooke. N.M., and L.C.V. Rees. 1968. Kinetics of ion exchange. Part I. Trans. Faraday Soc. 12:3383-3392. Bryant, S.L., R.S. Schechter, and L.W. Lake. 1986. Interactions of precipitation/dissolution waves in ion exchange in flow through permeable media. AiChE J. 32:751-757. Carski, R.H., and D.L. Sparks. 1985. A modified miscible displacement technique for investigating adsorption-desorption kinetics in soils. Soil Sci. Soc. Am. J. 49: 1114-1116. Carski, T.H., and D.L. Sparks. 1987. Differentiation of soil nitrogen fractions using a kinetic approach. Soil Sci. Soc. Am. J. 5:314-317. Chien, S.H., W.R. Clayton, and G.H. McClellan. 1980. Kinetics of dissolution of phosphate rocks in soils. Soil Sci. Soc. Am. J. 44:260-264. Ciavatta, C., and G. Vianello. 1987. Carta del deficit idrico dei suoli dell'Italia meridionale ed insulare. Acqua Aria. 3:317-327. Copeland, J.P., and J.M. Marchello. 1969. Film diffusion controlled ion exchange with a selective resin. Chern. Eng. Sci. 24:1471-1474. Crank, J. 1970. The mathematics of diffusion. Oxford Univ. Press, London. Davis, J.A., and J.O. Leckie. 1978. Surface ionization and complexation at the oxide-water interface. J. Colloid Interface Sci. 67:90-107. Dria, M.A., S.L. Bryant, R.S. Schechter, and L.W. Lake. 1987. Interacting precipitation/dissolution waves: The movement of inorganic contaminants in groundwater. Water Resour. Res. 23:2076-2090. Eisenman, G. 1983. The molecular basis of ionic selectivity in macroscopic systems. p. 121~156. In L. Liberti and F.G. Helfferich (ed.) Mass transfer and kinetics of ion exchange. NATOASI Symp. Ser. no. 71 M. Nijhoff, The Hague, Netherlands. Evans, R.L., and J.J. Jurinak. 1977. Kinetics of phosphate release from a desert soil. Soil Sci. 121 :205-211. Giese, R.F., and P.M. Costanzo. 1986. Behavior of water on the surface of kaolin minerals. p. 37-53. In J.A. Davis and K.F. Hayes (ed.) Geochemical processes at mineral surfaces. ACS Symp. Ser. no. 323, ACS, Washington, DC. Graham, E.E., and JK.S. Dranoff. 1982. Application fo the Stefan-Maxwell equation to diffusion in ion exchangers. Ind. Eng. Chern. Fundam. 21:360-369. Griffin, R.A., A.K. Au, and R.R. Frost. 1977. Effect of pH on adsorption of chromium from landfill leachate by clay minerals. J. Environ. Qual. Health A12:43l-449. Griffin, R.A., and J.J. Jurinak, 1974. Kinetics of the interaction of phosphates with calcite. Soil Sci. Soc. Am. Proc. 38:75-80. Hahne, H.C.H., and W. Kroontje. 1973. Significance of pH and chloride concentration on behavior of heavy metal pollutants: Mercury (II), cadmium(II), zinc(II), and lead(II). J. Environ. Qual. 2:444-450. Hand, D.W., J.C. Crittenden, and W.E. Thacker. 1981. User oriented solutions to the homogeneous surface diffusion model: Batch reactor solutions. Proc. 54th Annual Conf. Water Pollution Control Federation, Detroit, MI. 4-9 Oct. 1981. Water Pollution Control Federation, Alexandria, VA. l lclfferich, F. 1962a. Ion exchange. McGraw-Hili Publ. Co., New York. lid fferich, F. 1962h. Ion exchnnae kinetics. Ill. Experimental test of the theory of particle diffusion controlled Ion eXdllllllll'. .I. I'hys. Chern. 616:39-44.

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Helfferich, F. 1963. Revised tables for ion exchange kinetics. J. Chern. Phys. 38:1688-1691. Helfferich, F. 1964. A simple identification reaction for natural zeolites. Am. Mineral. 49: 1752-1753. Helfferich, F. 1965. Ion exchange kinetics. V. Ion exchange accompanied by reactions. 1. Phys. Chern. 69:1178-1187. Helfferich, F. 1981. Theory of multicomponent, multiphase displacement in porous media. Soc. Pet. Eng. J. 21:51-62. Helfferich, F.G. 1989. The theory of precipitation/dissolution waves. AIChE J. 35:75-87. Helfferich, F.G., and Y.L. Hwang. 1988. Ion-exchange kinetics. In K. Dorfner (ed.) Ion exchangers. De Gruyter, Berlin. Helfferich, F., and G. Klein. 1970. Multicomponent chromatography. M. Dekker, New York. Helfferich, F.G., D. Petruzzelli, L. Liberti, and R. Passino. 1985a. Anion exchange kinetics in resins of high selectivity. Part II. The case of chloride/sulphate exchange. Isr. J. Chern. 26:8-16. Helfferich, F.G., and D. Petruzzelli. 1985b. Diffusion with variable diffusion coefficients. Rep. no. r/107, Consiglio Nazionale Ricerche, Rome. Hirasaki, G.J. 1981. Application of the theory of multicomponent, multiphase displacement to three component, two phase surfactant flooding. Soc. Pet. Eng. J. 21:191-198. HOrst, J., W.H. Holl, and S.H. Eberle. 1990. Application of surface complex formation model to exchange equilibria on ion exchange resins. Part I. Weak acid resins. React. Polym. 13:209-231. Hwang, Y.L., and F.G. Helfferich. 1986. Computer program for multispecies ion exchange kinetics including fast reversible reactions. Dep. Chern. Eng., Pennsylvania State University, University Park, PA. Hwang, Y.L., and F. Helfferich. 1987. Generalized model for multispecies ion exchange kinetics including fast reversible reactions. React. Polym. 5:237-253. Jardine, P.M., and D.L. Sparks. 1984. Potassium-calcium exchange in a multireactive soil system: I. Kinetics. Soil Sci. Soc. Am. J. 48:39-45. Kataoka, T., H. Yoshida, and T. Uemura. 1987. Liquid-side ion exchange mass transfer in a ternary system. AIChE J. 33:202-210. Keeney, D.R. 1973. The nitrogen cycle in sediment water systems. J. Environ. Anal. 2:15-29. Khalid, R.A. 1980. Chemical mobility of cadmium in sediment-water systems. p. 258-294. In J.O. Nriagu (ed.) Cadmium in the environment. Part I: Ecological cycling. Wiley, New York. Kim, J.L., and E.L. Cussler. 1987. Dissolution and reprecipitation in model systems of porous hydroxyapatite. AIChE J. 33:705-710. Korzhinskii, D.S. 1970. Theory of methasornatic processes. Oxford Univ. Press, Lohdon. Kressman, T.R.E., and J.A. Kitchener. 1949. Cation exchange with a synthetic phenolsulphonate resin. Disc. Faraday Soc. 7:90-104. Liberti, L. 1983. Planning and interpreting kinetic investigations. p. 181-206. In L. Liberti and F. Helfferich (ed.) Mass transfer and kinetics of ion exchange. NATO-ASI Symp. Servo no. 71, M. Nijhoff, The Hague, Netherlands. Lightfoot, E.N., and E.M. Scattergood. 1965. Suitability of the Nernst-Planck equation for describing electrokinetic phenomena. AIChE J. 1:175-182. Maes, A., and A. Cremers. 1986. Highly selective ion exchange in clay minerals and zeolites. p. 254-295. In J.A. Davis and K.F. Hayes (ed.) Geochemical processes at mineral surfaces. ACS Symp. Servo no. 323, ACS, Washington DC. Miller, C.W., and L.W. Benson. 1983. Simulation of solute transport in a chemically reactive heterogeneous system: Model development and applications. Water Resour. Res. 19:389-398. Murali, V., and L.A.G. Aylmore. 1983. Competitive transport during solute transport in soils: 3. A review of experimental evidence of competitive adsorption and an evaluation of simple competition models. Soil Sci. 136:279-290. Nernst, W. 1888. Zur kinetic der in losung befindlichen korper. Z. Phys. Chern. (Munich) 2:613. Nkedi-Kizza, P., J.W. Biggar, H.M. Selim, M.T. Van Genuchten, P.J. Wierenga, J.M. Davidson, and D.R. Nielsen. 1984. On the equivalence of two conceptual models for describing ion exchange during transport through an aggregated oxisol. Water Resour. Res. 20:1123-1130. Novak, C.F., R.S. Schechter, and L.W. Lake. 1988. Rule-based mineral sequences in geochemical flow processes. AIChE J. 34: 1607-1614. Ogwada, R.A., and D.L. Sparks. 1986. Kinetics of ion exchange on day minerals and soil: II. Elucidation of rate limiting steps. Soil Sci. Soc. Am. J. 50:1162 111>9,

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Onken, A.B., and R.L. Matheson. 1982. Dissolution rate of EDT A-extractable phosphate from soils. Soil Sci. Soc. Am. J. 46:276-279. Parks, G.S. 1953. An experimental study of the influence of various factors on the time dependent nature of diffusion in polymers. J. Polym. Sci. 11 :97-115. Patell, S., and J .C.R. Turner. 1980. The kinetics of ion exchange using porous exchangers. J. Sep. Process. Technol. 1:31-39. Paterson, R., and L. Rahman. 1985. The mechanism of ion exchange on microcrystals of inorganic oxide-hydroxydes. p. 306-311. In L. Liberti and J .R. Millar (ed.) Fundamentals and applications of ion exchange. NATO-ASI Symp, Ser. no. E-98. M.Nijhoff, The Hague, Netherlands. Petruzzelli, D., and G. Boghetich, G. 1983. Investigation on reactive polymers using autoradiography and scanning electon microscopy. Environ. Prot. Eng. 1:5-12. Petruzzelli, D., L. Liberti, R. Passino, F.G. Helfferich, and Y.L. Ywang. 1987. Chloride/sulfate exchange kinetics: Solution for combined film and particle diffusion control. React. Polym. 5:219-226. Petruzzelli, D., and N. Palmisano. 1981. Rilevazione ed elaborazione automatica di dati potenziometrici nello studio cinetico di un processo a scambio ionico. Teen. Automazione 15:1-3. Planck, M. 1890. Uber the erregung von electrizitat und warme in elektroliten. Ann. Phys, (Leipzig). 39:161. Plicka, J., J. Cabicar, K. Stamberg, and M. Fabian. 1984. The kinetics of ion exchange sorption in ternary systems. p. 331-236. In D. Naden and M. Streat (ed.) Ion exchange technology. Ellis Horwood, Chichester, United Kingdom. Plesset, M.S., F. Helfferich, and J.N. Franklin. 1958. Ion exchange kinetics. A non-linear diffusion problem: II. Particle diffusion controlled exchange of univalent and bivalent ions. J. Chern. Phys. 29:1064-1069. Reddy, K.R., W.H. Patrick, and R.E. Phillips. 1978. The role of nitrate diffusion in determining the order and rate of denitrification in flooded soils. Soil Sci. Soc. Am. J. 42:268-272. Sawhney, B.L. 1966. Kinetic of cesium sorption by clay minerals. Soil Sci. Soc. Am. Proc. 30:565-569. Schlogl, R. 1983. Non-equilibrium thermodynamics: A general framework to describe transport and kinetics in ion exchange. p. 207-212. In L. Liberti and F.G. Helfferich (ed.) Mass transfer and kinetics of ion exchange. NATO-ASI Symp. Ser. no. E-71. M. Nijhoff', The Hague, Netherlands. Schlogl, R., and F. Helfferich. 1957. Comment on the significance of diffusion potential in ion exchange. J. Chern. Phys. 26:5. Schulze, G. 1913. Versuche uber die diffusion von Ag in glas. Ann. Phys. (Leipzig). 40:335-367. Schulze, G. 1914. Die ionendiffusion im permutit und natrolite. Z. Physik Chern. 89:168-178. Schwarz, A., J.A. Marinsky, and K.S. Spiegler. 1964. Self exchange measurement in a chelating ion exchange resin. J. Phys. Chern. 68:918-924. Spalding, G.E. 1971. Predictive theory of coion transport accompanying particle diffusion controlled ion exchange. J. Chern. Phys. 55:4991-4995. Sparks, D.L. 1989. Kinetics of soil chemical processes, Academic Press, New York. Sparks, D.L. 1985a. Kinetics of ionic reactions in clay minerals and soils. Adv. Agron. 38:231-266. Sparks, D.L. 1985b. Kinetics of reactions in pure and mixed systems. p. 83-142. In D.L. Sparks (ed.) Soil physical chemistry. CRC Press, Boca Raton, FL. Sparks, D.L., L. W. Zelazny, and D.C. Martens. 1980. Kinetics of potassium desorption in soil using miscible displacement. Soil Sci. Soc. Am. J. 44:1205-1210. Sparks, D.L., and P.M. Jardine. 1984. Comparison of kinetic equations to describe potassiumcalcium exchange in pure and in mixed systems. Soil Sci. 138:115-122. Sparks, D.L., and P. Zhang. 1991. Relaxation methods for studying kinetics of soil chemical phenomena. p. 61-94. In D.L. Sparks and D.L. Suarez (ed.) Rates of soil chemical processes. SSSA Spec. Pub!. 27, Madison, WI. Srivastava S.K., R. Tyagi, N. Pant, and N. Pal. 1989. Studies on the removal of some toxic metal ions. Part II. Removal of lead and cadmium by montmorillonite and kaolinite. Environ. Technol. Lett. 10:275-282. Van Brocklin, L.P., and M.M. David. 1975. Ionic migration effects during liquid-phase controlled ion exchange. AIChE Symp. Ser. 71:191-201. Vermeulen, T., G. Klein, and N.K. Hiester. 1984. Adsorption and ion exchange. p. 16-1 to 16-40. In Perry's chemicul engineers handbook, 6th Ed., McGraw Hill, New York. Walsh, M.P., S.L. Hrynnl , I..W. Luke, and R.S. Schechter. 1984. Precipitation and dissolulion of solids llllelldlllll flow IhlOlI~h porous media. AIChE .1.30:317-328.

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5

Kinetics of Ion Sorption on Humic Substances K. Bunzl and W. Schimmack

Gesellschaft fur Strahlen-und Umweltforschung Munchen (GSF) Institut far Strahlenschutz Neuherberg, Germany

ABSTRACT Toxic heavy metal ions and radionuclides can be deposited on the soil surface where they are sorbed to a considerable extent also by soil organic matter. To improve predictions of the behavior of these ions in soils we investigated in stirred batch experiments the sorption rates of Pb2+, Cu2+, Cd 2+, Zn2+, Ca2+ and, at trace concentrations ("" 10 -9 M) 137CS +, 85Sr2+, 65Zn2+, 109Cd2+ and 57C02+ on sphagnum peat and humic acid. Interruption tests showed that film diffusion is the ratedetermining step for sorption of these metals on the humic substances. Accordingly, corresponding rate equations were derived for various initial and boundary conditions. The experimental and theoretical results show: (i) the half-time (t1l2) for sorption increases with decreasing concentration of the metal ions in solution, except at very low concentrations, where it becomes constant; (ii) at a given concentration of the metal ions in solution, 1112 increases, the more the adsorbent prefers the sorbed ion (high separation factor a). At very low concentrations, however, 1112 becomes independent of a; (iii) the 11/2 for sorption decreases if the adsorbent initially contains the metal ion that will be sorbed. The magnitude of this decrease is small, however, when the ion is sorbed preferentially (high values of a); and (iv) the 11/2 for sorption of radionuclides at trace concentrations, but at finite concentrations of the supporting electrolyte, increases with increasing distribution coefficients (Kd ) . At very high K d values, however, 1112 is almost independent of the K d value. As a result, the 1112 for the sorption of 85Sr, 65Zn, 109Cd and 57Co (Kd above 15 000 L kg - I) were almost identical ("" 55 s) while l37Cs (Kd = 220 L kg - I) is sorbed much faster (1112 = 8 s).

Metal ions, such as Pb2+, Cu2+, Cd2+ or Zn2+ can be deposited on the soil surface via sewage sludge, fertilizers, atmospheric fallout or waste water. In addition, a variety of radionuclides such as 137Cs +, 9OS r 2+ or 6OC02+ can also be deposited on soils from radioactive fallout or discharges from the nuclear industry. In most soils these cations are sorbed to a considerable exCopyright (C) 1991 Soil Science Society of America. 677 S. Segoe Rd., Madison, WI 53711. t ISA. Rates of Soli ('hrmlml Processes. SSSA Special Publication no. 27. 119

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120

tent not only by clay minerals or sesquioxides, but also by humic substances. In many cases the extent of sorption controls the accumulation of these ions in the top of the soil profile, their migration to the groundwater, and their availability for plant uptake. For detailed predictions of the behavior of these ions in the soil, however, not only the sorption equilibria, but also the corresponding rates have to be studied. This information is especially needed in developing ion-transport models that do not assume that the equilibrium between the moving liquid phase and the soil is attained instantaneously (Van Genuchten and Cleary, 1979). As shown by Sparks (1989) in his comprehensive treatment of this subject, our present knowledge on the rates of ion sorption by soil humic substances is rather limited. For that purpose we will first briefly summarize some of our kinetic data obtained earlier for the sorption of several divalent metal ions on peat and humic acid suspensions at solution concentrations of the metals between 5 . 10 -5 and 5 . 10 -4 mole L - I (Bunzl et aI., 1976a,b) and then present some recent data on the sorption rates of several radionuclides by peat at trace concentrations (i.e., less than 10 -9 mol L -I). The kinetics and equilibria of the following systems were investigated in well-stirred batch experiments: (i) HCl-washed peat, suspended in water, to which a given amount of a metal ion (Me)(Pb2+, Cu2+, Cd 2 + , Zn2+ or Ca2+) was added; (ii) humic acid particles, partially saturated with a metal ion and suspended in water, to which an additional amount of this metal ion was added, and (iii) HCl-washed peat, suspended in HCl at pH 3.82, to which a trace amount of a radionuclide 37Cs, 57CO, 85Sr, 65Zn, 109Cd) was added. Interruption tests indicated that diffusion of the ions across a liquid layer (film) of unstirred solution surrounding the peat particles is the ratecontrolling step (Bunzl, 1974a). Accordingly, rate equations for film diffusion-controlled, ion-exchange processes for the boundary and initial conditions of our experiments are derived and compared to experimental results.

e

MATERIALS AND METHODS Theoretical Considerations According to the theory of irreversible thermodynamics, the differential equation for a film diffusion-controlled, ion-exchange process of Counter Ions 1 for Counter Ions 2 is (Bunzl, 1971; Bunzl, 1974b) [I]

where XI = zIC/C is the equivalent fraction of Ions 1 in the ion exchanger, ZJ, Z2 are the valencies of the Counter Ions Band D, respectively, and ric, r2e are the stoichiometric coefficients for ionization of the two electrolytes BrleArla and D r2cfl r2a present in solution (A is the common coion); C 1 is the concentration of the Counter Ion I in the ion exchanger (mol of ion L ····1

121

ION SORPTION KINETICS

ion exchanger) and C is the ion exchange capacity in moles of charge per liter ion exchanger; ai is the equivalent separation factor; CI and Cz are the concentrations (in mol/L) of the two counter ions in solutions at time t. The rate coefficient R is given as [la] where F/ V is surface to volume ratio of the ion exchanger (for spherical particles of radius r, F/ V = 3/r). The D I and D z are diffusion coefficients and are functions of the four diffusion coefficients D II , D 12, D Zb D zz (Bunzl, 1971), describing isothermal diffusion in the corresponding electrolyte solution involving Counter Ions 1 and 2 and the common coion (they can be determined by independent measurements in this solution, but as yet very few data are available); and 0 is the film thickness. In accordance with the two kinds of batch experiments described later, we will solve Eq. [1] for two different initial and boundary conditions, namely (i) the sorption of metal ions at arbitrary solution concentrations and (ii) the sorption of ions in trace amounts in the presence of a supporting electrolyte. Sorption of Metal Ions at Arbitrary Solution Concentrations Initially, the ion exchanger will contain the Counter Ion 1 at a given equivalent fraction XI,o, where XI,o can also be zero. The solution (V in L) will contain initially only the Metal Ion 1 at a given concentration CI,O (mol L -I). Because the reaction proceeds with the exchange of equivalent amounts of counter ions, the total equivalent concentration in the solution remains constant and is denoted as c. In this case C (mole L -I) = rlcZlcl,O' The amount of ion exchanger employed shall be Q mole' If we integrate Eq. (1) for the boundary conditions of a batch experiment, we obtain for the uptake of the Ion 1, characterized by its equivalent fraction XI in the ion exchanger as a function of time t F o, ==---=.

r sC +

t

= E-

AXr

+

BX

+

P

In - - : - ' - - -I- - - 2A AXi,o + BXl,o + P

FA - ERI2 2AS

~

+ (BI2) + AXI 0] " AXI,o][S + (BI2) + AXIl

[S - (BI2) - AXIl [(S [S -

(BI2) -

where

=

Q (ai - 1)/V, R = [Q XI 0(1 - ai)/V] - ai(c I ' P = az (c + Q X1,0/V), E = I - ai D z/ Db F = aiDz/D ,• and S = (8 z/4 - PA)I/l.

A

+

Q/V),

[2]

BUNZL & SCHIMMACK

122

At the half-time (tin> of the ion-exchange process, the ionic composition X; is given by

= XI,O +

X;

0.5(XI , 00

XI,o)

-

where XI 00 is the corresponding equilibrium ionic composition at t given (except for a1 = I) as

=

XI,oo

[(b z

+

4aH)112 -

b]l(2a).

[3] 00,

[4]

Here

a

= Q(I -

b

V) [cd = (QI I

ad)/V, - XI 0(1 - cd)] '

H= az[(QIV) X I ,O + c].

+

ale, and

Inserting XI ,00 from Eq. [4] in Eq. [3], and subsequently X; from Eq. [3] for XI in Eq. [2], the t llZ can be calculated. Because the resulting rate equation is rather complicated, it is not reproduced here, but will be discussed later. Equations for ion-exchange processes controlled by film diffusion were given by Helfferich (1962) for ions of different mobilities for the case ad = I (no selectivity), or for a1 -.r. I, but then only for ions of equal mobilities. No such restrictions were assumed in the derivation of the rate equation given above.

Sorption of Ions in Trace Amounts in the Presence of a Supporting Electrolyte

In this case the ion exchanger contains initially only Counter Ions 2, i.e., XI,o = O. The solution contains initially the counter ions at trace concentrations only (CI - 0) and the Ions 2 at a concentration Cz ,0 (supporting electrolyte). To obtain the corresponding rate equation we first extend Eq. [2] to include also the case Cz ,0 -.r. O. With help of the corresponding material balance equation we find the constants A, B, P, E, Fand S in Eq. [2] now as A' Q(ai - I)/V, B' - -ai(c - rzcZz Cz 0 + QIV) - rzcZz cz,o, I ' P' az(c - rzcZz Cz 0), I ' E' 1 - az DzID I , F' aiDzlD I , and (B ,z/4 - P'A ')112. S'

The equilibrium uptake is given as XI,oo

=

[(b'z

where a' - Q(1 - ai)1 V, b' - ai(c rzczz Cz 0 I ' H' az (c - rzcZzcz,o).

+

4a'H,)112 -

b']/(2a')

+ QI V) + rzczz cz,o, and

[5]

ION SORPTION KINETICS

123

The fractional attainment U(t) of the equilibrium is given for the present case, where Xl ,0 = 0, as

o<

U(t)

< 1

[6]

To obtain U as a function of time, we insert Xl from Eq. [6] together with Xl , 00 from Eq. [5] in Eq. [2], using the values for A I, B I, pi, E I, F ', S I and a I, b I, H I given above and calculate the limits for U = fit) when Cl - 0, i.e., C - Z2r2er2 ,o. In this case the uptake of the Counter Ion 1, Xl(t), as well as the total amount of ions taken up, Xl , 00' approach zero, but the limit for U(t) = Xl(t)1Xl ,00 is not indeterminate. The resulting rate equation is

(F DI)I( V 0) . t The t l /2 at U

=

= [- odc In(1

- U)]/[r2eZ2C2,O

+

ai QI V].

[7]

0.5 becomes

(F Dl)/(V 0) . tl/ 2

=

laiC In(2)]/[r2eZ2c2,o

+

aiQIV].

[8]

If trace amounts of ions are sorbed in the presence of a supporting electrolyte, the distribution coefficient K d is usually used rather than ai to characterize the eqilibrium. It is defined as

K

d -

amount of ion sorbed per mass of ion exchanger amount of ion in the solution per solution volume

[9]

where C I is the total capacity of the ion exchanger in moles of charge per kilogram. The C I is related to C (in mole L -I, as defined above), by C I = CI p, where p is the specific gravity of the ion exchanger. The relation between K d and ai for the sorption of trace amounts at constant concentration of C of the supporting electrolyte is [10] If we recall that Q = V C = m C I, where m is the mass of ion exchanger used, and substitute Eq. [10] in Eq. [7] and [8] we obtain for the sorption rate and the t1/ 2 ' respectively, (F DI)/(V 0) . t

=

[-p K d In(1 -

(F D)/(V 0) . t l/2

=

U)][Kd (mlV)

+

+

1].

[p K d In(2»)/[Kd(ml V)

1]

[11] [12]

Eq. [II] is identical to an equation given by Helfferich (1962), derived for the exchange of two isotopes of the same counter ion, if we substitute

124

BUNZL & SCHIMMACK

in this equation Cc/c = K d P, V = mlp, and 31r = FIV (r = radius of the particles). Equation [11], however, was derived from Eq. [2], which considers the selectivity and the diffusion potential arising from the different mobilities of the counter ion (Bunzl, 1971). The above result then shows that even if these effects are considered, the simple rate equations for isotopic exchange hold also for the exchange of different ions, if one ion is present at trace concentrations only. Equations [11] and [12] will be used later to discuss the rates observed for sorption of different radionuclides on peat. Finally, two limiting cases shall be considered. If the experimental conditions are selected in such a way that K d (ml V) ~ 1, Eq. [12] reduces to (F D,IV 0) . 11/2

= p (Vim)

In(2)

which means that the 11/2 is independent of the K d value. If Kd(ml V) we obtain

[13] ~

1

[14]

which shows that in this case the half-time increases proportional to the Kd value of the trace ion. Applicability of the Theory The theory given is based on the assumption that metal ions are sorbed onto the functional groups of insoluble humic substances by reversible ionexchange processes. In the following we will, therefore, discuss briefly the resulting limitations and strengths of the theory. First, we have to assure that the humic substances investigated are insoluble. This does not seem to be a severe limitation because most humic materials in soils or sediments occur in insoluble forms (Stevenson, 1985) either as macromolecular complexes or in combination with clay materials. A partial solubility of the humic material may, however, occur if the pH of the solution for the sorption experiment is selected too high. Many parameters as, e.g., pH, the ionic strength or the metal saturation affect the pKa's of the functional groups and thus the interactions between the metal ions and the humic material. Fortunately, however, detailed information on these interactions is not required, as long as film diffusion is the rate determining step of the sorption process. All we have to know in this connection is according to Eq. [8] or [11] the separation factor ex (or the K d ) and the ion-exchange capacity C. These quantities depend of course on the above interactions, but they can be determined independently and without any detailed information on the sorption mechanism. Besides, we have to keep in mind that the rate equations derived are for homogeneous ion-exchanger particles. This implies that the particles are monodisperse (same ratio of surface to volume, see Eq. [Iaj), and that each particle has the same sorption properties, as characterized by its ion-exchange capacity and separation factor (or K d ) . For a given particle, however, it is

ION SORPTION KINETICS

125

acceptable that it contains many nonidentical functional groups with different pKa's, as long as these groups are distributed evenly within the particles. For this reason it is important that the humic material investigated is sieved to a uniform particle size and that, in addition, it is not composed of particles with different sorption properties. The above theory will of course not hold, if film diffusion is not the rate-determining step. This can be the case if e.g., the desorption process is very slow or even almost irreversible (e.g., as a result of conformational changes of the polydispersed molecular aggregates). Therefore, before any rate equations are applied, the rate-determining step should be confirmed (e.g., by interruption tests). Peat and Humic Acid Material

The sphagnum peat and the humic acid used for the sorption of metal ions Pb, Cu, Cd, Zn and Ca were described earlier in detail (Bunzl, 1974a). The apparent ion-exchange capacities of the peat at pH 4.0 were (in mole kg -I): 0.8 Ca H , 1.0 Zn H , 1.2 Cd H , 1.3 Cu H , and 1.3 Pb 2 + . For this purpose the peat was suspended repeatedly with the corresponding metal nitrate solutions until in equilibrium a ratio of metal ions/hydrogen ions (in mol.) in solution of approximately 500:1 was present. The leaf-like particles were shredded and wet sieved to a particle size of 0.2- to 0.5-mm diam. and converted to H + by repeated washings with HN0 3 • The humic acid (supplied by F. Roth, Karlsruhe, Germany) was purified by dissolution in NaOH and subsequent precipitation by HCI, and 3.8 Cu H . The apparent ion-exchange capacities were (in the same units as above) 1.3 Ca H , 1.5 Zn H , 1.9 Cd 2 + . The particle size was approximately 10 to 30 p.m. Because the peat used above was no longer available at the time when the sorption of the radionuclides was investigated, sphagnum peat from another raised bog (Konigsdorf', Bavaria) had to be used. It was shredded, wet sieved to a particle size 0.3 to 0.8 mm, and converted to H + form by repeated washings with HN0 3 • Its ash content was 101o, the cation exchange capacity for Ca 2 + peat 0.65 mole kg-I. Procedure

The following procedures were used to determine the kinetics of sorption of metal ions or radionuclides on peat and humic acid: 1. A 1.0-g sample of wet peat as H + was suspended in 200-mL deionized water in a reaction vessel and thermostated at 298 K. To avoid abrasion of the particles, a two-blade stir paddle was used for vigorous mixing (470 rpm) rather than a magnetic stirrer. The sorption process was initiated instantaneously by addition of 1.0 mL of a solution containing the metal ions as N0 3 using a piston pipette. The ion-exchange process thus initiated resulted in an equivalent release of H 30 +. Since the equivalent conJuctivity of the H 30 + appearing in solution is considerably greater than that if the disappearing metal ions, the electrical conductivity of the solution in-

126

BUNZL & SCHIMMACK

creases at the same rate as the sorption of the metal ions. (The absence of other sources and sinks for H + in the sysem was confirmed by adding a known amount of H + to suspended H-saturated peat and recording the pH). With help of an immersed conductivity electrode and after calibration, the rate of the metal sorption can thus be monitored continuously. At the end of each sorption experiment the pH was measured and the amount of metal ions in the solution was determined using atomic absorption spectrometry. Details can be found in Bunzl et aI. (l976a). 2. In 2oo-mL deionized water 0.1 g of humic acid particles were suspended at 298 K, stirred at 430 rpm, 0.02 mmol, metal ions added, and the sorption rate measured as described above. At the end of the first experiment, the humic acid particles, (which were now partially saturated with the metal ion) were allowed to settle, the supernatant solution was withdrawn, the particles in the reaction vessel were washed with deionized water, resuspended again in 200 mL water, 0.02 mmol, metal ions added as before, and the sorption rate was determined. This procedure was repeated several times for each metal ion. More details of this technique have been given previously (Bunzl et al., 1976b). 3. 0.5-g wet peat (corresponding to 0.125-g dry weight) as H + were suspended in 100 mL of a HCl solution at pH 3.82, thermostated, and stirred as above. The reaction was initiated by adding 1 mL of a solution containing a known amount of the nuclides (137 Cs, 85Sr, 57Co, 65Zn and I09Cd as Cl), The resulting concentrations of the radionuclides in the solution were about 10 -9 M. Ion pairing between the metal ions and Cl at these low concentrations will be negligible. At various times a I-mL aliquot of the suspension was withdrawn by a pipettor, filtered quickly by using a membrane filter (cellulose acetate, 0.4 ~m), and the activity of the filtrate analyzed. Because the opening of the pipettor tip was large enough to withdraw the peat particles together with the solution, the solid-to-solution ratio in the reaction vessel was not changed by taking the aliquots. Sampling and filtration were achieved in about 5 s. The activity of each radionuclide in the solution was determined by using a Ge-detector and a multichannel analyzer. From the initial and final activity of each radionuclide in the solution, the amount sorbed as a function of time can be obtained and, after attainment of equilibrium, also the K d value can be obtained according to Eq. [9]. In experiments with a blank, it was confirmed that the amounts of radionuclides lost during the experiments by sorption on the walls of the reaction vessel, the stirrer, and the filtration unit were negligible. The error (l standard deviation) for the 11/2 determined was approximately ± 5% for Experiments 1 and 2 and about ± 10010 for Experiment 3. RESULTS AND DISCUSSION Effect of Concentration and Separation Factor The 11/2 observed for the sorption of Pb 2 + , Cu H , Cd 2 + . Zn 2 + and Ca + on H + peat as a function of the four initial concentrations of these 2

127

ION SORPTION KINETICS

metals in the solution phase are shown in Fig. 5-1 (bottom). Because H + are released by the peat while metal ions are sorbed, the pH in the solution decreases to some extent during the sorption process. The pH observed after attainment of the equilibrium depends, therefore, on the amount of metal ions taken up. When Cu2+ was sorbed on peat, the resulting pH values in equilibrium for the four concentrations (0.025, 0.05, 0.125 and 0.25 mmol L -I) employed were: 4.3, 4.0, 3.8, and 3.7, respectively. Similar values were obtained for the uptake of the other metal ions. Fig. 5-1 shows that the t l /2 decreases with increasing initial concentration of the metal ions in solution. Besides, the half-times for the sorption of the metal ions were longer for the heavy metal ions Pb2+, Cu 2 + , Cd 2+, and Zn 2 + as compared to Ca. From the sorption equilibria attained, the separation factor a~e can be obtained. The resulting values depend on the concentration and are shown in Fig. 5-1 (top). Independent of the concentration, however, the order for the selective uptake by peat was always Pb2+ > Cu2+ > Cd 2 + = Zn 2 + > Ca2+. To compare these observations in a qualitative way with the theoretical considerations given above, we can use Eq. [2-4], to calculate the t l /2 as a function of the initial concentration rlcZl"cl,O = C of the metal ions. Because the peat did not initially contain any metal ions, we put XI 0 = O. The values of the other constants were arbitrarily selected as Q/V ' 0.01 mole L -I; D 2/D I = 2 (because the diffusion coefficient of the H 30 + released is certainly larger than that of the metal ion sorbed); and C = 1 mole L -I. The resulting t1/ 2 ' calculated as the dimensionless quantity (FD 2)/(Vo) . t l /2' is shown in Fig. 5-2 for three different values of the separation factor

ai.

:h 10

...011

o

Ctl

u..

c

0

...Ctl

Ctl Q.

8 6

Metal concentration in solution:

'0 0.025 m~~IH-' ~ .. 0...5 mmol _ O 0.125 mmolL-'... L -, l:llI 0.25 mmol L -,

4

2

Q)

en

0 30 25

:§: 20 Q)

E 15 i= 10 "iii

J:

5 0

Fig. 5-1. Half-times (bottom) and separation factor aite (top) for the sorption of several divalent metal ions by H + -peat as a function of the initial concentration of the ions in solution (top),

128

BUNZL & SCHIMMACK

160 ~ '-<>

120

C

80

-

I> ILL

~

40 1.10- 6

1.10- 4

1.10- 2

initial cone. (mole L-l) Fig. 5-2. Half-time for the sorption of a Counter Ion I by an ion exchanger as a function of i~ initial concentration in solution. The (1/2 is plotted as the dimensionless quantity (FDz/VO) . (I/Z calculated according to Eq. [2-4J. Initially, the ion exchanger shall not contain the Ion 1 (Xl,O = 0), and the solution contains only the Ion I (CZ.o = 0). Parameter is the separation factor ad.

The theory of film diffusion-controlled, ion-exchange processes then predicts that the 11/2 decreases with increasing solution concentration. In addition, at a given concentration, the 11/2 decreases, if the selectivity a of the ion exchanger for the ion sorbed decreases. Only at very low concentrations does the 11/2 become independent of the separation factor. This can explain the strong decrease in the 1 112 with increasing concentrations that was observed for all the metal ions that were investigated (Fig. 5-1, bottom), because the separation factor a decreases in addition with increasing concentration (Fig. 5-1, top). Because Ca2+ is sorbed least selectively by peat (smallest value of a), it is, according to Fig. 5-2 also understandable, why we observe at each given concentration longer 11/2 for the sorption of the heavy metal ions as compared to Ca 2+. In addition, however, the 1112 depends also on the ternary diffusion coefficients D I and D 2 of the ions in the aqueous film. As yet, these values are not available for the system Me(N0 3h/HN03 investigated here. On the basis of the well-known limiting equivalent conductivities of these ions we can estimate, however, that of the metal ions used here, Pb 2 + should have the highest diffusion coefficient (Robinson and Stokes, 1968; Weast, 1987). This might explain why Pb 2 + does not exhibit the longest 1112 (see Fig. 5-1), as predicted from its high separation factor. The short 11/2 of Ca2+, on the other hand, can only be explained by its low separation factor, because its limiting equivalent conductivity and hence its diffusion coefficient is intermediate between those of the other ions. Effect of Initial Metal Content of Adsorbate In Fig. 5-3 (bottom) we show the 11/2 for the sorption of metal ions by humic acid particles. In this case the amount of metal ions added to the suspension was always constant (0.02 mrnol.), but the initial metal content of the humic acid particles was selected as 0.2, 0.4,0.6 and O.R 11101, kg . I dry

129

ION SORPTION KINETICS

:li J: 10 -.l

... o

8

III u.. I:: o

6

(j

-...

Initial 00.21110'e kg -1 metal 1':Ol0.4 mole kg- 1 content: .0.6 mole kg- 1 il:ll0.8 mole kg- 1

1

4

III III

Co

(l)

2

en

0 '----_--'---"< ",-_-,-50,---------------,

~

40

(l)

E i=

30

:= 20 III ::r:::

10

0 Cu 2 +

Cd 2 +

Zn 2 +

Ca 2 +

Fig. 5-3. Half-times (bottom) and separation factor afte (top) for the sorption of several metal ions by suspended humic acid particles as a function of their initial metal content. The amount of metal ions added was always constant (0.02 mmol.).

atr

humic acid. The corresponding separation factors as a function of the metal content are also given in Fig. 5-3 (top). The data show that for a given metal ion the /I/Z decrease considerably with increasing initial metal content of the humic acid for the sorption of Zn2+ and Ca z+ . For the sorption of Cd2+ this effect is smaller. In the case of Cu z+ a decrease of the /I/Z is not observable. Again we can compare these results with the corresponding theoretical predictions for film diffusion-controlled, ion-exchange processes. For that purpose, we calculated the /I/Z according to Eq. [2-4] as a function of the initial equivalent fraction XI,D, by putting c = 0.0001 mole L -I, Q/ V = 0.01 mole L -I, D z/ D I = 2 and C = 1 mole L -I. The values used for the separation factor were 10, 1.1 and 0.1. The resulting /I/Z, plotted again as the dimensionless quantity (FDz)/(Vo) . /I/Z are illustrated as a function of XI ,D in Fig. 5-4. The half-time can be seen to decrease with increasing initial metal content of the ion exchanger. At low initial metal contents the /1/z decreases less if the separation factor is high; at high metal contents the opposite is observed. The physical reason for this behavior is the following: with increasing initial metal contents of the ion exchanger the absolute rate for the sorption of additional metal ions will decrease because the concentration gradient across the film (the driving force) becomes smaller. On the other hand, the additional amount of ions sorbed by the ion exchanger will also be smaller, if the ion exchanger initially contains these ions. The calculations show that the latter effect obviously prevails. As a result, the /I/Z, which is a measure of the rate relative to the amount of ions sorbed, decreases.

BUNZL & SCHIMMACK

130

200

-I> ~

~

1

160

Q2:

. -. 120

--'"

Q ILL

--

80 40 0

0.2

0.4

x.,

0.6

0.8

1

Fig. 5-4. Half-time for the sorption of a Counter Ion I by an ion exchanger as a function of its initial equivalent fraction Xl,o of the ion. The solution shall always contain initially only the Ion I at a concentration of 0.0001 mole L -I. The t 1/2 is plotted as the dimensionless quantity (FD2/Vli) . t1/ 2 , calculated according to Eq. [2-41. The parameter is the separation fac1 tor (X2'

The theoretical predictions illustrated in Fig. 5-4 are in qualitative agreement with the experimentally observed values, where we also found that the t 1l 2 decrease continually already at low initial metal contents of the humic acid particles for the sorption of Zn 2 + and Ca 2 + , because the separation factor for these metal ions is comparatively small (see Fig. 5-3). For Cu 2 + , which has the highest separation factor, the t 1l2 remains almost constant, as predicted from Fig. 5-4. In addition to the effect of the initial metal content, however, the t 112 will decrease in the present case to some extent because the separation factor decreases with increasing metal content (see Fig. 5-3, top). With respect to the predictions for the t 1l 2 as a function of X"a according to Eq. [2-4], we want to make two further remarks. First, if the total concentration c of the counter ions in the solution becomes very small, the curves shown in Fig. 5-4 will have the same half-time at X, a = 0, because then t'/2 is independent of cd (see Fig. 5-2). Second, we should keep in mind that the predicted decrease of the t'/2 with increasing values of X, ,a is only true if D 2/D, > 1. If D 2/ D, < 1, the calculations predict an increase of the t 1l 2 with increasing values of XI,a. As mentioned above, however, this latter assumption can certainly not be true for the present experiments, where the Ion 2, which is released by the humic acid particles, is the very mobile H 30+.

Effect of the Distribution Coefficient at Trace Concentrations The experimental results obtained for the sorption of trace quantities of the radionuclides l37Cs, 85Sr, 57CO, 65Zn and 109Cd are illustrated in Fig. 5-5. The t 1l 2 determined for the divalent metal ions were very similar and considerably higher than those observed for l37Cs. The corresponding distribution coefficients Kd are shown also in Fig. 5-5. Again, they are rather similar for the four divalent metal ions (between 15 000 L kg -1 for 85Sr and 23 000 for 57CO) and by about a factor of 70 smaller for IJ7Cs. This differ-

131

ION SORPTION KINETICS

60 .-.

50 ~

-Q)

40 ~

E

30 ~

iii

20 ~ 10 ~

Ul

i= J:

o

-

~

-

-

-

n

10 5

-

.-. 10' ~

b,

-

r-

-

-

~

--.., ...I

10 3 -

~ 10 2

-

10' Fig. 5-5. Half-time (top) and distribution coefficient K d (bottom) for the sorption of several radionuclides at trace concentrations by a peat suspension at pH 3.82.

ence in the K d values is not surprising, because the complex formation between the weakly acidic functional groups of humic substances and metal ions is well-known (Schnitzer and Khan, 1972; Stevenson, 1982). Cesium, in contrast, which can only be present as a monovalent ion, and thus not be bound in coordinate linkages, is sorbed to a much smaller extent. These observations may be compared with the theoretical predictions for film diffusion-controlled, ion-exchange processes given above. If we plot the experimentally determined fractional attainment U of the equilibrium as In(l - U) vs. times, we should obtain straight lines at trace concentrations (Eq. [11]). This is indeed observed (not shown here), but above U = 0.7, deviations occur. Most likely this is due to the fact that the peat particles used are to some extent polydisperse. Even though they were wet sieved to a diameter of 0.3 to 0.8 mm, this does not mean that they all have the same surface to volume ratio (F/V) because their geometrical shapes can be different. For polydisperse mixtures, however, deviations from the simple In(l - U) vs. t relation have to be expected (Bunzl, 1978). However, even if the peat particles used were to some extent polydisperse, the theoretical predictions for monodisperse particles should qualitatively be correct also for polydisperse mixtures, as long as the deviations are small. For this purpose we can use Eq. [12] that relates the tl/ 2 and the K d value at trace concentrations. For illustration, we plotted in Fig. 5-6 (according to Eq. [12]) the dimensionless half-time (FD(/Vo . tl/2 as a function of the K d (L kg -1). The parameter is the ratio m/V (m = mass of ion exchanger (kg); V = solution volume (L). For the specific gravity we put p = 1 kg L -I. Figure 5-6 shows that the tl/ 2 will increase with increasing K d , especially at low values for mass/volume and K d • For high values of the distri-

132

BUNZL & SCHIMMACK

10'

-

..-. ~

I>

--- 102

--

0.01

..-.

C

I!:!;:. 10'

mlV (kg L"):

0.1 10 2

10 3

10'

10 5

Kd (L kg-1) Fig. 5-6. Half-time for the sorption of trace quantities of a counter ion by an ion exchanger as a function of the distribution coefficient K d • The (1/2 is plotted as the dimensionless quantity (FD]/Vo) . (1/2' calculated according to Eq. [12). Parameter is the ratio (mass m of ion exchanger)/(solution volume V).

bution coefficient and mass/volume, the tl/ 2 become rather independent of the K d • This is in agreement with the experimental observations shown in Fig. 5-5. Because in our experiments mass/volume was 0.001 25 kg L -1 and the K d values of the divalent metal ions were above 15 000 L kg -1, we are according to Fig. 5-6 already in a region where the tl/ 2 is almost independent of the K d • Because the diffusion coefficients D Me , as estimated from their limiting equivalent conductivities (Weast, 1987) are also rather similar, it is thus not surprising that we find within experimental error the same t I 12 for 85Sr, 57CO, 65Zn and 109Cd. In contrast, 137Cs, which has a of only 220 L kg -1 should at the above value of mass/volume exhibit a smaller tl/ 2 (see Fig. 5-6). Again this is in agreement with the experimental observation (see Fig. 5-5). If we use Eq. [12] to calculate the ratio of the tin for the sorption of two different ions A and B at the same experimental conditions, we obtain

s;

DB [K t I 12 ,A d B(m/V) ' D A [Kd,A (m/V) tl/ 2,B

+ 1] «;,A + 1] Kd,B

[15]

This relation can be applied to the experiments illustrated in Fig. 5-5, because all quantities on the right side of Eq. [15] are either known (Kd and m/ V), or can be estimated (DB/ D A)' For the distribution coefficient of the divalent metal ions Me (Sr, Co, Zn, Cd) we found approximately the same values (Fig. 5-5, bottom). For this reason we can put Kd,Me :::::: 15 000 L kg -1 dry weight. For the distribution coefficient of Cs we put Kd,cs = 220 L kg -1 (Fig. 5-5, bottom). The m/V = 0.001 25 kg dry weight per liter. The ratio D Me/ D c s in the film can be estimated from the limiting equivalent conductivities of these ions as about 0.7. If, therefore, the indices A and B in Eq. [15] denote the metal ions Me and Cs, respectively, we can insert the above values to obtain tl12,Me/tl/2,Cs :::::: 6, where Me denotes Sr, Co,

ION SORPTION KINETICS

133

Zn, and Cd. Experimentally (Fig. 5-5, top), we observed for this ratio a value of (55 ± 3)/(8 ± 2) = 7 ± 2, which is in good agreement with the above estimate.

CONCLUSIONS

The 11/2 for the sorption of several divalent metal ions by peat particles were between a few seconds and 1 min for our experimental conditions. The theory of film diffusion-controlled, ion-exchange processes predicted qualitatively correct, to which extent the 11/2 of the sorption depended on the concentration, the separation factor (for trace concentrations on the distribution coefficient), the initial metal content of the peat, and the ratio peat/solution volume. If we want to apply the results obtained here to describe the kinetics of metal sorption in a natural soil, we have to consider two opposing effects. First, the ratio dry peat/solution volume in our experiments (m/ V :::::: 0.001 kg dry weight L -1) is much smaller than present in a natural peat water system. Figure 5-6 shows that for very low K d values the effect of mass/volume on the 11/2 is rather small. At high K d values, however, an increase in mass/volume of one order of magnitude will result in a corresponding decrease of the 11/2' Thus, for the sorption of metal ions, which usually exhibit rather high K d values, the sorption in a natural peat/solution system will proceed considerably faster than observed in our experiments. On the other hand, the vigorous agitation used in our batch experiments is not present in a natural peat bog. As a result, the thickness (0) of the Nernst film around the particles in a natural system will be much larger and the sorption rate correspondingly slower (see e.g., Eq. [12]). Thus, unless one has detailed information on the local boundary conditions of the system, it is difficult to predict values for the 11/2 of the sorption of metal ions on a natural soil. Experimental and theoretical results obtained from experiments as described above, however, can serve to predict at least qualitatively the effect of various parameters on the sorption rate.

REFERENCES Bunzl, K. 1971. Reactions of ion exchangers with salts of low solubility. Z. Phys. Chern. N. F. 75:118-136. Bunzl, K. 1974a. Kinetics of ion exchange in soil organic matter. III. Differential ion exchange reactions of Pb H in humic acid and peat. Soil Sci. 25:517-532. Bunzl, K. 1974b. Kinetics of differential ion exchange processes in a finite solution volume. 1. Chromatogr. 102:169-180. Bunzl, K. 1978. Kinetics of ion exchange in polydisperse systems. Anal. Chern. 50:258-267. Bunzl, K., W. Schmidt, and B. Sansoni, 1976a. Kinetics of ion exchange in soil organic matter. IV. Adsorption and desorption of Pb H , Cu H , Cd 2 + , Zn H and Ca H by peat. J. Soil Sci. 27:32-41. Ilunzl, K., A. Wolf, 1I11l! II. SIIIiSOlii. 1976b. Kinetics of ion exchange in soil organic matter. V. Differential ion excbungc reactions of Cu 2 + , Cd 2 + , Zn 2 + and Ca H ions in humic acid. Z. Pflunzcncrnnelu . lIodclikd. 137:475-485.

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Helfferich, F. 1962. Ion exchange. McGraw-Hill Book Company, Inc., New York. Robinson, R.A., and R.H. Stokes. 1968. Electrolyte solutions. Butterworths, London. Schnitzer, M., and S.U. Khan. 1972. Humic substances in the environment. Marcel Dekker Inc., New York. Sparks, D.L. 1989. Kinetics of soil chemical processes. Academic Press., Inc., San Diego. Stevenson, F.J. 1982. Humus chemistry. John Wiley & Sons, New York. Stevenson, F.J. 1985. Geochemistry of soil humic substances. p. 13-52. In G.R. Aiken et aJ. (ed.) Humic substances in soil, sediment, and water. John Wiley & Sons, New York. van Genuchten, M. Th., and R.W. Cleary. 1979. Movement of solutes in soil: Computer simulated and laboratory results. p. 349-386. In G.H. Bolt (ed.) Soil chemistry, B. Physicochemical models. Elsevier, Amsterdam, Netherlands. Weast, R.C. 1987. Handbook of chemistry and physics. 68th ed. The Chemical Rubber PubJ. Co., Cleveland, OH.

6

Kinetics of Sorption/Desorption Processes in Soil l Robert D. Harter

Department of Natural Resources University of New Hampshire Durham, New Hampshire

ABSTRACT Kinetic techniques are increasingly being used to characterize soil sorption/desorption processes and results of such studies are being used as sorption model input. There are benefits and limitations to the approach, and to avoid misuse of kinetics researchers should be aware of both. The initial choice among the many techniques should be based on appropriateness of the technique for modeling a process within the soil system. Without such basis, it is more difficult to develop a modeling strategy. Given an appropriate model, empirical data such as rate of sorption and reaction half-times and calculated information such as rate constants and thermodynamic quantities are assessable. In interfacing data from kinetics studies with models, one must always remember, however, that the heterogeneous nature of soils makes proper assignment of sorption mechanisms tenuous. It appears that the rate-determining processes during metal sorption by soil may be exchange reactions for the first few minutes then intraparticular diffusion until an equilibrium is established, but complete characterization of soil sorption kinetics is not so easily attained. For example, the effects of certain quantities (e.g., temperature) commonly varied in kinetics experiments are not always attributable to the sorption reaction itself, but may also alter the sorbent. Given these constraints, it is possible to make some tentative mechanism assignments and to calculate apparent rate coefficients for the reactions.

In continuing efforts toward characterization of soil sorption processes, soil chemists have been examining the potential of kinetics investigations (Aringhieri and Pardini, 1989; Carski and Sparks, 1985; EIkhatib and Hem, 1988; EIkhatib et al., 1984; Harter and Lehmann, 1983; Hodges and Johnson, 1987; Jardine et al., 1985; Lehmann and Harter, 1984; Ogwada and Sparks, 1986; Randle and Hartmann, 1987; Sharpley, 1987). Aharoni and Sparks (1991) have discussed the complexity of measuring reaction rates in soil systems and Amacher (1991) has provided an overview of current methodology. It is the 1 Scientific

contribution no. 1686 from the New Hampshire Agricultural Experiment Station.

Copyright (c) 1991 Soil Science Society of America, 677 S. Segoe Rd., Madison, WI 53711, I IS", Rates of Soil ('hm/lml /"11/'('.1'.1'('.1'. SSSA Special Publication no. 27, I3S

136

HARTER

purpose of this paper to explore some applications of kinetics (specifically, batch techniques) to metal sorption by soil and to provide perspective on the use of kinetics in modeling soil sorption phenomena. We must evaluate our underlying objectives in conducting sorption/ desorption research before we can evaluate the utility of kinetic approaches for this research. The perspective and rationale for the use of kinetic studies are, in turn, the bases of conceptual models against which empirical data are tested. Research objectives are often forgotten in the excitement of data acquisition and under the pressure of interpretations, but results and interpretations are only meaningful when they can be related to the questions that were being addressed. Regardless whether sorption research is motivated by environmental, plant nutritional or other concerns, system description requires certain types of information. At a minimum, it is usually helpful to know the amount of sorbate retained by the sorbent and the partitioning of sorbate between solid and solution. Isotherms are quite adequate for this purpose. If movement of ions is of concern, the rate of sorption (or sorption kinetics) becomes important. Methodology for acquiring such information is relatively well-established and interpretations are typically noncontroversial. Results, however, are limited to the system studied. This may be adequate for the task at hand, but the prospect of individually describing every sorbate/sorbent combination usually encourages attempts toward predictive modeling whereby applicability is broadened to systems not actually studied. Prediction, in turn, requires information not directly available from empirical studies: sorption mechanisms must be deduced and system parameters such as rate constants and distribution coefficients must be defined. In many cases, thermodynamic properties of the system are also useful for modeling input. The Langmuir equation has proved useful for summarizing adsorption isotherm data, and the equation has been used to provide modeling input. Use of the equation has, however, been extended beyond appropriate applicability (Veith and Sposito, 1977; Harter and Smith, 1981; Sposito, 1982; Harter, 1984). Kinetics can be used as input for adsorption modeling, but this technique also has both benefits and limitations. Misuse of kinetically derived data can only be avoided through familiarity with the technique's limitations as well as its advantages. This discussion is intended to provide guidance to some techniques by which useful information can be acquired from kinetics experiments.

METHODOLOGY Amacher (1991) has discussed a variety of techniques by which reaction rates can be ascertained. These techniques can generally be divided into two basic categories, depending on the experimental conditions employed. Inflowthrough experiments a solution is passed through a thin layer of soil. The desired solution ionic composition is maintained and reactants arc constant-

SORPTION/DESORPTION KINETICS

137

ly removed, forcing the net reaction to go in one direction. Batch experiments, on the other hand, utilize "static" conditions in which forward and reverse reactions are allowed to proceed until an equilibrium is established. These latter studies are compatible with isotherm studies, whereas flowthrough experiments are compatible with breakthrough type studies. Discussion in this paper will be limited to batch conditions, but the generalprincipIes are applicable to results of flow-through experiments as well. Both batch and flow-through experiments can provide useful information and the choice of methodology depends on research objectives and the soil system to be modeled. Flow-through experiments might logically be used to model sorbate reactions in soil macropores during leaching events. At any given sorption site, the sorbate concentration in solution will be relatively constant and desorbed ions will be removed in the leachate. Conversely, batch experiments more nearly model reactions in micropores where chemical processes may approach or reach equilibrium. Batch kinetics model events after perturbation caused by evapotranspiration or diffusion to or from the micropores. Mechanisms of retention are similar in either situation, but expression of the mechanism will vary. Practically, measurement of reaction rates in soil systems is usually limited to observing changes in reactant. This means that observations will be related to the most rate-limiting step, since this will control the amount of reactant observed at any given time. Unfortunately, diffusion rates are often the rate-limiting step, so observation of reaction kinetics often depends on the ability to negate or interpret diffusion processes. This ability differs, depending on the experimental technique chosen.

CAPABILITIES OF KINETIC APPROACHES

Laying aside, for the moment, all application problems, let us examine the inherent capabilities of kinetics. Reaction rates are the most obvious and most readily available output of these experiments. As with adsorption isotherms, empirical sorption or desorption data can simply be plotted as a function of time and the progress of the reaction can be visually examined. Such information as half-reaction time and time to establish a new equilibrium can be directly obtained from the plot. If, however, the objective of the research is to provide input for generalized sorption models, more quantitaI ive information will be necessary. It is usually possible to calculate rate coefficients, but mechanism postulation is necessary. Equations are used in coefficient calculation, and developmerit of the required equations is based on knowledge of the reactions occurring in the system. If the system studied is relatively simple, it may be possible to deduce mechanisms from curve shape. The postulate can someI imes be confirmed by ancillary measurements in the experimental system (c.g., increase of the same-charge ion in solution would indicate an exchange reaction). In other cases, confirmation of mechanisms may require additional lesls.

HARTER

138

On the more theoretical level, once the system is sufficiently defined to determine the forward- and reverse-rate coefficients, thermodynamic quantities can be calculated. If the reaction is first-order, the ratio of rate coefficients is the thermodynamic equilibrium constant, from which the change in Gibbs free energy can be obtained. By using multiple equilibration temperatures, enthalpy change can be calculated (Harter and Smith, 1981).

APPLICATION PROBLEMS

Application of chemical theory to heterogeneous systems such as soils almost always comes in conflict with system complexity. Commonly used kinetic techniques are based on the assumption that the reactions are either unidirectional or discrete, but soil sorption reactions are often both reversible and multiple. The combination of multiple reversible reactions makes evaluation tedious and tenuous. It is seldom possible to be definitive in calculating rate coefficients attributed to a specific reaction. These difficulties are compounded by the difficulty of measuring reactants and products in a colloidal system and by the probability that reaction energy varies as the reaction proceeds. Attempts to conduct kinetic experiments at varying temperatures are equally frustrating. Temperature effects are not limited to sorption kinetics, but the sorbent surfaces themselves can be affected by temperature. Cation exchange capacity, particularly of amorphous and organic surfaces (Wada and Harada, 1971) is temperature dependent, as is the stability of soil minerals (Mattigod and Kittrick, 1980). In turn, specific sorption will be affected by mineral stability due to associated surface changes. In soil systems, one of the largest challenges is to isolate reaction kinetics from diffusion. While diffusion gradients in the bulk solution can be minimized by rapid stirring, the contribution of diffusion across the double layer and in intraparticle spaces is difficult to ascertain. Since diffusion is also affected by temperature (Skogley and Schaff, 1985), this becomes a problem in attempts to obtain thermodynamic information for the system.

BASIS FOR MECHANISM DECISIONS

Evaluation of results from kinetics experiments and assignment of mechanisms to the processes involved requires a clear understanding of the thermodynamic basis for the reactions. Before proceeding, therefore, it is appropriate to briefly review reaction driving forces. In their simplest form, rates of reaction are probability functions dependent upon energy relationships between the reaction components. In any reaction both the reactants and products represent an energy base with an activated energy state occurring between the two. By way of example, a hydrated ion must lose at least one water of hydration before it can enter the Stern layer. This means the ion will gain hydration energy to form an activated stale before it can ap-

139

SORPTION/DESORPTION KINETICS

proach the surface closely enough to lose reaction energy and drop to a new base energy level (Shainberg and Kemper, 1966). Under given conditions, both reactants and products have a certain probability of gaining enough energy to attain the activated energy state, whereupon their probability of becoming a reactant or a product is equal. The probability of becoming activated depends on both the activation energy (Ea) to be gained and the number of ions in the base energy state. Equilibrium, then, is an expression of the point at which the probability of a product achieving the activated energy state is exactly equal to that of the reactant obtaining this energy. Thus, the ratio of reactant to product at equilibrium is proportional to the ratio of their activation energies. In kinetics, the probability of achieving activation energy is expressed as a rate coefficient. The forward- and reverse-rate coefficients (k) are directly dependent on activation energies, as expressed by the integrated Arrhenius equation (Atkins, 1978) k

=A

exp( -EalRn

[1]

where A is an equation coefficient dependent on system conditions, E a is the activation energy, R is the gas constant, and T is absolute temperature. Since for a first-order reaction the thermodynamic equilibrium constant (K) is the ratio of the forward- to reverse-rate coefficients, it is directly dependent on the relative magnitude of the forward- and reverse-activation energies. Thus when K = 1, activation energies in the forward and reverse directions are equal and the entity of interest has equal probability of occurring as product or reactant. Therefore, K < 1 means the forward-activation energy is greater than reverse-activation energy and K > 1 indicates the opposite.

ASSIGNING MECHANISMS TO SOIL PROCESSES

Soil chemists have generally classified soil sorption processes as either "specific" or "nonspecific" reactions. Reaction mechanisms termed "specific sorption" are usually considered irreversible. This is reasonable on a practical level when it becomes difficult or impossible to remove a sorbed ion from specific sorption sites. As indicated, however, irreversibility is in reality a probability function with the probability of the reactant achieving activation energy being much greater than that of the product achieving activation energy. As a result, at equilibrium little or no material will remain in the reactant form. Irreversibility, therefore, has approximately the same meaning as "insolubility" of precipitates in that dissolution of a bonded ion is dependent upon the probability of the ion gaining sufficient energy to break the bond(s) with which it is held. Insolubility is usually equated to very low, but not zero, reactant concentration. When the forward-rate coefficient (k r) is much larger than the reverserate coefficient (k,) the logical outcome of a reaction is only trace quanti-

140

HARTER

ties of reactant remaining in the system at equilibrium. If more than trace reactant remains at equilibrium, either the reaction is not irreversible or another condition has intervened in the reaction. One example of an intervening condition is the exhaustion of one reactant in a nonfirst-order reaction. Sorption reactions by nature must be secondorder, depending on both sorbate and sorbent in the system. This introduces an unwanted complexity to sorption kinetics research, but it can be circumvented. Sorption sites on any given sorbent are relatively constant, whereas sorbate can be easily varied. Therefore, if the sorbate present in the system is substantially less than the number of sorption sites, the reaction will be directly dependent on sorbate concentration and reaction will occur as if it is first-order. This type of condition is usually referred to as "pseudofirst-order. " A changing dependence of reactions on sorbate concentration is commonly evident in adsorption isotherms. A direct dependence is expressed by a straight line, the C, or constant partition isotherm of Giles et al. (1974). Most sorption isotherms will contain a constant partition portion, indicating a pseudo-first-order relationship, at very low equilibrium concentrations (Fig. 6-1). By examining the isotherm, therefore, the concentration range over which the reaction is pseudo-first-order can be ascertained. As a confirmation, a plot of the fraction of added adsorbate remaining in solution (CICo) as a function of time will be independent of the initial concentration (Co) over this concentration range (Harter, 1989). This will only be true of a first-order or pseudo-first-order reaction. Figure 6-2a presents a typical loss of NiH from solution as a function of time. (In the sorption of NiH to soils, equilibrium is usually reAdsorbed (mmol kg- 1)

l o

--o

----

o

--------- ------o

2

o o

Isotherm data Kinetics data Constant Partition Langmuirian Isotherm

0[9-------'----------'------'-------'---------"

o

0.02

0.04

0.06

0.08

0.1

Equilibrium Concentration (mrnol C) Fig. 6-1. Adsorption isotherm for Ni 2 + retention by Christiana B (Typic Paleudult) horizon, demonstrating the linear nature of such isotherms at low sorbate eoncentrutions.

141

SORPTION/DESORPTION KINETICS

Cone. (mmol L-

1

)

0.016 0.014 0.012 0.01 0.008 0.006

DODD

o

DO

0.004 0.002 O'----------'--------'---------'----------'---------L-------'

o

10

20

30

40

50

60

Time (min)

C/C o

1lt1-----------------------------,

0.8

0.6

0.2

f.-

I

I

I

I

10

20

30

40

O'--------~------'-----'--------~------'----~

o

50

60

Time (min) Fig. 6-2. Kinetics of NiH sorption by a Christiana B horizon (0.016 mol L -1 NiH added; soil solution ratio .. I: I(0); (a) Solution concentration as a function of time, (b) Ratio of NiH remaining to Nl 2 + added as a function of time. The solid line represents a first-order reversible reaction with k r' - 3.26 and kr' = 1.848 (K' = 1.76).

142

HARTER

established within 10-30 min after NiH addition.) The equilibrium NiH concentration is about 0.006 mol L -1, which is in the linear range of Fig. 6-1, so sorption should be a direct function of sorbate concentration. As previously noted, an irreversible reaction will proceed to completion unless sorption sites become restrictive. If sorption were affected by the availability of sites, the equilibrium data point should fall on the curvilinear portion of the isotherm. Therefore, combining these two observations, we can reasonably assume that the reaction is reversible and pseudo-first-order. Based on this information, it is possible to proceed with development of a first-order reversible reaction. As suggested by Harter (1989), it is convenient to convert sorbate concentration in solution to fraction remaining at time, t. Using this approach, the data were adequately modeled by a single reaction (Fig. 6-2b) with apparent rate coefficients k( = 3.26; kr' = 1.848; and the apparent thermodynamic equilibrium constant, K' = 1.76. Considering that the reaction appears to be completed within 2 min, cation exchange is the probable sorption mechanism. Having successfully modeled the data, there is a temptation to consider the point to be proven and the work to be done. Unfortunately, individual models are not always unique to a data set, so a mechanism consistent with the model must be postulated and confirmed by independent means. (While agreement of a model with a mechanism does not provide a priori knowledge of the kinetic system, inability to match the two does argue for rejection of the theory developed.) For the data illustrated (Fig. 6-2), cation exchange "fits" the known system characteristics. To confirm a cation exchange hypothesis, Ni 2+ sorption by an exchange reaction should be accompanied Cone. (mmol C1

)

0.014 r - - - - - - - - - - - - - - - - - - - - - - - - - - ,

o

0.012 - o~ ¢

U ~ITI:b

0 0

0

L

0.01 r O o

0

00

0

Cb 0 0

0 000000

o

o 0 0

0 0 0000 0

0000000

0

0 0

000 0.008 0.006 0.004 0.002

o

Nickel lost

<> Cations gained

I

I

I

I

I

10

20

30

40

50

60

Time (min) Fig. 6-3. Nickel lost from and cation gain to solution after adding 0.016 mol L- 1 NiH to a Christiana B horizon (soil/solution ration = I: 1(0).

SORPTION/DESORPTION KINETICS

143

by a stoichiometric increase in solution concentration of desorbed cations. Indeed, when Ni2+ sorption is plotted along with cation desorption as a function of time (Fig. 6-3), we do find near equality between Ni2+ lost from and cation gain to solution. The slight data plot discrepancy is not of major concern, because three different techniques were used in its accumulation. Nickel sorbed was assumed to be that lost from solution, Ca 2 + and Mg2+ were measured directly in the equilibrium solution, and H + was calculated from OH - demand during the experiment. Let us now consider sorption of Ni2+ by a Paxton B horizon (coarseloamy, mixed, mesic, Typic Fragiochrept) (Fig. 6-4). Again, Ni2+ lost from solution is balanced by cation gain to solution, so an exchange mechanism can be reasonably assumed. Note, however, that the shape of the curve is different. Nickel sorption by this soil cannot be modeled by a single firstorder reversible reaction (Fig. 6-5a). Harter (1989) suggested that these types of data can be modeled by assuming multiple first-order reversible reactions, and the data can be successfully simulated if two reactions are assumed (Fig. 6-5b). One of the suggested reactions has an apparent equilibrium constant similar to that calculated for the Christiana B horizon (clayey, kaolinitic, mesic, Typic, Paleudult), but note that it is the slower of the two model reactions. Importance cannot, therefore, be placed on this similarity without additional supportive evidence that there is a similarity between the reactions indicated. Great caution must be exercised in interpreting multiple-reaction models containing several independent parameters. A four-parameter model will not be unique to a data set (Sposito, 1982). In addition, there is no evidence of 0.016

C

Cone. (mmol 1 ) ,----------------------~

o

0.014

o

0

00

0.012

o

DO 0

0.006 0.004

o

0.002

Nickel lost

o

Cations gained

O~--'----'----'---l---'------'---------.J'---------.J-----.J-----'-----'------'--'

o

5

10

15

20

25

30

35

40

45

50

55

60

Time (min) Fig. 6-4. Nickel lost from and cation gain to solution after adding 0.016 mol L -1 NiH to a Paxton B (Typic IIrllllochrcpt) horizon (I: 100 soil/solution ratio).

HARTER

144

CIC o 11lt-----------------------------,

0.8

O'----"-------'----'------'--.L----'-------L----'--L----'----L--~

o

5

10

15

20

25

30

35

40

45

50

55

60

Time (min) CIC o 11lt-----------------------------,

0.8

0.6

0.4

0.2

O'-----'----'------''-----'------'------'---'------'------''----'---------L-----'-' o 5 10 15 20 25 30 35 40 45 50 55 60

Time (min) Fig. 6-5. Nickel sorption by Paxton B horizon (0.016 mol L -I NiH added, soil/solution ratio = 1:1(0). a) Model represents a first-order reversible reaction with ki = 0.475; and k( = 0.21 (K' = 2.26). b) Model represents two independent reversible first-order reactions having kil = 1.25; k(l = 1.70 (K' = 0.74); kh = 0.16; and kr'z = 0.105 (K' = 1.52).

a multiple reaction in the experimental data collected. It is apparent that exchange has occurred (Fig. 6-4) and logic might indicate the possibility of two exchange mechanisms, but data available does not support such an assumption. Not only must a mechanism be postulated for each of the sug-

SORPTION/DESORPTION KINETICS

145

-,

Cone. (mmol L )

0.03 DO DODD 0000000

0

DODD

0.025

0000

00000000000

0

o

0

DO 0

0

0

00 0 0 0 0 0

~

8

0.02 0.015 0.01 0.005

o

Nickel lost

o

Cations gained

0 0

5

10

15

20

25

30

35

40

45

50

55

60

Time (min) Fig. 6-6. Nickel lost from and cation gain to solution after adding 0.040 mol L -1 Ni 2+ to a Paxton A (Typic Fragiochrept) horizon (1:100 soil/solution ratio).

gested reactions, but the mechanism must also be confirmed. Lacking this ability, a multiple-reaction kinetic model can never be better than a datafitting device. Sorption of Ni2+ by the Paxton A horizon provides one more clue to processes involved. Adsorption/desorption response of this soil (Fig. 6-6) is at slight variance to that of the Paxton B horizon. While the Ni2+ sorption curve appears similar and is modelable by two first-order reversible reactions, the cation desorption curve is not similar to that of the B horizon. After an initial rapid desorption comparable to Ni2+ sorption, cation gain to solution lags behind Ni2+ loss from solution. This response is suggestive that intraparticle diffusion may be playing a role in this horizon. Therefore, a single first-order reversible reaction model was used for this soil (Fig. 6-7a), and the difference between the model and empirical data was assumed to be diffusion. A plot of the difference as a function of square root of time (Fig. 6-7b) is linear over the first 10 min. Linearity of a (1/2 plot is usually taken as evidence of a diffusion process. In confirmation, the difference between cations desorbed and the model (Fig. 6-7c) was examined and plotted against (1/2 (Fig. 6-7d). The (1/2 plot is linear for I h, which is in general conformance to expectations. Diffusion of Ni2+ out of solution should occur more rapidly than diffusion of cations into solution. This indicates that the multiple-reaction model of Harter (1989) should be modified to account for diffusion processes.

146

HARTER C/Co

1[i1----=.-------------------~---_,

0.8

t-

o.e 0.4

, 0000

0.2

0000000

ooooooooo[

000000

I-

,

,

,

5

10

15

20

,

I

I

I

,

,

I

25

30

35

40

45

50

55

60

Time (min)

6C/Co 0.3

001IIJJ 00000000 0000000

0.25

o

00

o

0.2 0.15 0.1

O~-~-'----'----'--------'-------l---L----'------'

o

1

2

3

4

I~ Time

5

6

7

8

Fig. 6-7. Kinetics of NiH sorption and associated cation release by Paxton A horizon (0.040 mol L -1 NiH added, soil/solution ratio = 1:1(0). (a) Ratio of NiH remaining to NiH added as a function of time. The model represents a first-order reversible reaction with kj = 0.65; and k( = 0.95 (K' = 0.68). (b) Difference between NiH remaining in solution and the first-order kinetic model (Fig. 7a), as a function of (112. The line indicates the area of direct relationship. (c) Cation release during the reaction. The solid line represents (l - CICO> or the inverse of the first-order model presented as a solid line in Fia. 6-7a. (d) Difference between cation gain to solution and the first-order kinetic model (Fla. 6-7c), as a function of (1/2. The line indicates the area of direct relationship.

147

SORPTION/DESORPTION KINETICS

C/Co 0.8 , - - - - - - - - - - - - - - - - - - - - - - - - - - - ,

o 0.6

f-

0000 0

0 0 00 0 0 0 0 00

0

I'd" 0.4'f>r

0.2

,

0 0

5

10

,

,

15

20

25

30

,

,

,

,

35

40

45

50

60

55

Time (min) 6C\Co 0.35 0

0.3 0.25 0.2 0.15 0.1 0.05 0 0

1

2

3

4

5

6

7

8

'\j Time Fig. 6-7. Continued.

SUMMARY From the limited data presented herein it is obvious that the understanding of sorption kinetics is a complex undertaking, but not a hopeless one. It appears that sorption by some soils only occurs via exchange on external surfaces, whereas sorption by others may involve multiple reactions and/or diffusion processes. The latter is a particular problem in attempting to de-

148

HARTER

fine sorption mechanisms. The development of diffusion gradients in the solution (and probably those across the double layer of charged external surfaces as well) can, however, be minimized by rapidly stirring the system. Stirring will not affect the development of intraparticular diffusion gradients, and rate of intraparticular reactions will be diffusion controlled. Intraparticular diffusion should be minimal in sandy soils, but will probably be a major contributor to sorption dynamics in fine-textured surface soils. It is also apparent that the dynamics of the sorption processes cannot be studied in isolation. Mechanism postulation and confirmation requires both an integrated experimental approach and investigation of sorption on a variety of sorbents. It has been demonstrated, for example, that interpretation of kinetic processes under "static" conditions requires consideration of associated sorption isotherms, and that insight to processes can be gained by comparison of different sorbents. While it may never be possible to unequivocally "prove" a particular sorption mechanism(s), it is possible to build up a body of information from which reliable predictions can be made. As a final cautionary note, erroneous results can be replicated by replicating experimental conditions. Such erroneous results can usually be detected by careful comparison to all information available. At minimum, batch sorption kinetics studies should be conducted in parallel with isotherm studies. It is also beneficial to use multiple start concentrations and multiple sorbents.

REFERENCES Aharoni, C., and D.L. Sparks. 1991. Kinetics of soil chemical reactions-a theoretical treatment. p. 1-18. In D.L. Sparks and D.L. Suarez (ed.) Rates of soil chemical processes. SSSA Spec. Pub!. 27. SSSA, Madison, WI. Amacher, M.C. 1991. Methods of obtaining and analyzing kinetic data. p. 19-59. In D.L. Sparks and D.L. Suarez (ed.) Rates of soil chemical processes. SSSA Spec. Pub!. 27. SSSA, Madison, WI. Aringhieri, R., and G. Pardini. 1989. Kinetics of the adsorption of potential-determining ions by positively charged soil particle surfaces. Soil Sci. 147:85-90. Atkins, P.W. 1978. Physical chemistry. W.H. Freeman and Co., San Francisco, CA. Carski, T.H., and D.L. Sparks. 1985. A modified miscible displacement technique for investigating adsorption-desorption kinetics in soils. Soil Sci. Soc. Am. J. 49:1114-1116. Elkhatib, E.A., and LL. Hem. 1988. Kinetics of phosphorus desorption from Appalachian soils. Soil Sci. 145:222-229. Elkhatib, E.A., O.L. Bennett, and R.J. Wright. 1984. Kinetics of arsenite sorption in soils. Soil Sci. Soc. Am. J. 48:758-762. Giles, C.H., D. Smith, and A. Huitson. 1974. A general treatment and classification of the solute adsorption isotherm I. theoretica!. J. Colloid Interface Sci. 47:755-765. Harter, R.D. 1984. Curve fit errors in Langmuir adsorption maxima. Soil Sci. Soc. Am. J. 48:749-752. Harter, R.D. 1989. A new modeling-compatible solution to the first-order kinetics equation. Soil Sci. 147:97-102. Harter, R.D., and R.G. Lehmann. 1983. Use of kinetics for the study of exchange reactions in soils. Soil Sci. Soc. Am. J. 47:666-669. Harter, R.D., and G. Smith. 1981. Langmuir equation and alternate methods of studying "adsorption" reactions in soils. p. 167-182. In R.H. Dowdy et a!. (ed.) Chemistry in the soil environment. Spec. Pub!. 40. ASA, Madison, WI. Hodges, S.C., and G.C. Johnson. 1987. Kinetics of sulfate adsorption and desorption by Cecil soil using miscible displacement. Soil Sci. Soc. Am. J. 51:323-331.

SORPTION/DESORPTION KINETICS

149

Jardine, P.M., J.e. Parker, and L.W. Zelazny. 1985. Kinetics and mechanisms of aluminum adsorption on kaolinite using a two-site nonequilibrium transport model. Soil Sci. Soc. Am. J. 49:867-873. Lehmann, R.G., and R.D. Harter. 1984. Assessment of copper-soil bond strength by desorption kinetics. Soil Sci. Soc. Am. J. 48:769-772. Mattigod, S.V., and J .A. Kittrick. 1980. Temperature and water activity as variables in soil mineral activity diagrams. Soil Sci. Soc. Am. J. 44:149-154. Ogwada, R.A., and D.L. Sparks. 1986. Kinetics of ion exchange on clay minerals and soil: 11. Elucidation of rate-limiting steps. Soil Sci. Soc. Am. J. 50:1162-1164. Randle, K., and E.H. Hartmann. 1987. Applications of the continuous flow stirred cell (CFSC) technique to adsorption of zinc, cadmium and mercury on humic acids. Geoderma 40:281-296. Sharpley, A.N. 1987. The kinetics of soil potassium desorption. Soil Sci. Soc. Am. J. 51:912-917. Shainberg, I., and W.D. Kemper. 1966. Hydration status of adsorbed cations. Soil Sci. Soc. Am. Proc. 30:707-713. Skogley, E.O., and B.E. Schaff. 1985. Ion diffusion in soils as related to physical and chemical properties. Soil Sci. Soc. Am. J. 49:847-850. Sposito, G. 1982. On the use of the Langmuir equation in the interpretation of "adsorption" phenomena: 11. The "two surface" Langmuir equations. Soil Sci. Soc. Am. J. 46:1147-1152. Veith, J.A., and G. Sposito. 1977. On the use of the Langmuir equation in the interpretation of "adsorption" phenomena. Soil Sci. Soc. Am. J. 41:697-702. Wada, K., and Y. Harada. 1971. Effects of temperature on the measured cation-exchange capacities of Ando soils. J. Soil Sci. 22: 109-117.

7

Kinetics of Dissolution of Oxide and Primary Silicate Minerals Paul R. Bloom and Edward A. Nater Soil Science Department University of Minnesota Saint Paul, Minnesota

ABSTRACT Under earth surface conditions between pH 4 and 10, the rates of primary silicate and oxide dissolution are controlled by surface reactions. For many oxides and hydroxides as well as some silicates, dissolution reactions can be modeled by surface complexation theory, which states that reaction rates are proportional to the population of surface complexes with H +, OH -, or ligands. The rate of release is controlled by the detachment of the complexes from the surface. This theory, however, fails to explain many observations induding the dissolution of oxides at low pH, which is first-order with respect to solution H + , the dependence of rates on ionic strength, and the incongruent nature of the initial dissolution of most silicates. Rapid hydrolysis of charge balancing cations in silicates results in rapid release from surfaces. Even after removal of surficially exposed cations, the reaction is commonly incongruent. Much, but not all, of the nonlinear rates observed in silicate dissolution can be explained by the presence of high energy sites, such as dislocation outcrops, twinning planes, or damaged sites on ground mineral surfaces. These sites dissolve more rapidly than the bulk of the mineral, causing the high initial rates and producing etch pits, which results in increased surface area. The exact nature of the material remaining on reacted mineral surfaces (indicated by incongruence) is the subject of debate.

The stability of minerals has long been of interest to soil scientists. One of the major processes occurring during the development of soils is the formation of secondary minerals from primary minerals. Plant nutrition in natural environments is dependent on mineral nutrients supplied by mineral weathering. Soil acidification, whether it results from natural processes of soil development or is accelerated by anthropic acidic deposition, is mediated by weathering processes. The inherent stability of minerals in soils is a function of both equilibrium solubility and kinetic factors. Some minerals, such as anatase (TiO z), have very low equilibrium solubilities and their stability is very high even in well-drained soils under high rainfall. For many minerals, however, Copyright @ 1991 Soli Science Society of America, 677 S. Segoe Rd., Madison, WI 53711, USA. Rates of Sr,1I Ch,ml/'lJll'ro/'esses. SSSA Special Publication no. 27. 151

152

BLOOM & NATER

kinetic considerations are important in determining long-term stability in soils. For example, feldspars and amphiboles, both important classes of minerals that supply base cations in soils, are not thermodynamically stable in soil environments. The rates of the processes involved in the hydrolysis of ions at the surfaces of these minerals determine their stability, rather than equilibrium solubilities. The study of weathering kinetics has occurred over the last 50 yr (Correns and Von Engelhardt, 1938) and has been an especially active area of research in the last decade. Excellent reviews of mineral weathering kinetics are included in volumes edited by Drever (1985), Colman and Dethier (1986), and Stumm (1987), and in the book authored by Sparks (1989). Other recent reviews on topics related to weathering kinetics have been authored by Aagaard and Helgeson (1982), Helgeson et al. (1984), Velbel (1984), Murphy and Helgeson (1987a,b), Wieland et al. (1988), and Brady and Walther (1989). The mineral dissolution reactions discussed in this chapter are generally surface controlled. For these reactions, the rate of diffusion of reaction products from the reaction surface into the bulk solution is more rapid than the rate of release of products from the surface (Berner, 1981; Dibble and Tiller, 1981). Consequently, reaction rates are independent of the rate of stirring and measured Arrhenius activation energies (determined from the temperature dependence of measured rates) are greater than the activation energies for the diffusion of reaction products in solution. Activation energies for some soil minerals are shown in Table 7-1. Mineral dissolution reactions are often considered to be hydrolysis reactions because water is consumed during the dissolution reaction. For example, in the dissolution of orthoclase in acidic solutions, four moles of water are needed for each mole of orthoclase dissolved

In Eq. [1], protons are shown to be important in determining the equilibrium of the hydrolysis of a silicate mineral. Protons are important factors in determining dissolution rates of silicates, oxides, hydroxides, and hydrous oxides. Because of the relatively high Arrhenius activation energies of surface-controlled reactions, temperature is an especially important factor in determining dissolution rates. Anions that bind to mineral surfaces can Table 7-1. Operational Arrhenius activation energies comparing dissolution with diffusion. Mineral Gibbsite. AI(OH)a Labradorite Ca1.0SNao.s6Ko.o6AlaSis016 Bronzite Mgo.77Feo.2aSiOa Diffusion in H 20 Diffusion in solids

E A' kJ mol -1

References

60-70 45

Erich and Bloom, 1987 Erich and Bloom, 1987, unpublished data Grandstaff, 1977

44 <20

85-600

Lasaga, 1981 a Lasala, 198 III ... ---_._-

OXIDE AND SILICATE DISSOLUTION KINETICS

153

also influence dissolution rates. For minerals that contain component ions that can be reduced to species with greater mobility (e.g., Fe H to Fe 2 +), reducing agents can be important in determining rates of dissolution.

RATE EQUATIONS A mineral dissolves to form an aqueous product, P. Assuming that the reverse reaction is negligible, then the overall rate of formation of P by a dissolution reaction can be described by the equation

[2] where R is the rate in moles per second, k is a rate constant, [A] and [B] are the concentrations of solution components A and B that contribute to the rate of dissolution, a and b are the orders of the reaction with respect to A and B, and S is the surface (interfacial) area (m'). There is no consistency in the literature on the use of concentrations or activities in rate equations. The theory of activated complex formation, discussed below, does explain the effect of ionic strength on homogeneous solution reactions where the ionic charge of the activated complex is known (Lasaga, 1981a; Stumm and Morgan, 1981). Usually concentrations are used in the rate expression and the rate constant is corrected for the effects of ionic strength. For heterogeneous reactions of the type discussed in this chapter it is not possible to calculate activity coefficients of activated complexes on surfaces, and rate constants cannot be corrected for the effects of differing ionic strengths. In this chapter we will use concentrations in the rate equations. Some authors (e.g., Helgeson et al., 1984; and Holdren and Speyer, 1987) consider S to be the "reactive surface area" and not the total surface area. This adjustment is made to account for preferential weathering at high energy sites on mineral surfaces that results in the creation of both reactive and nonreactive portions on mineral surfaces. Although it is theoretically and mechanistically interesting, the concept of reactive surface is of little practical importance because it is not possible to measure the reactive surface area. Rate constants can also be expressed in terms of mass of mineral, in which case, S in Eq. [2] is replaced by the mass. In a reaction where solubility equilibrium can be attained, the reverse reaction rate can be significant as the reaction proceeds, and Eq. [2] becomes [3]

where k, is the forward rate constant, k, is the rate constant for precipitation, C and D are components involved in the precipitation reaction, and c and d are orders of reaction with respect to C and D. According to the principle of microscopic reversibility

154

BLOOM & NATER

[4] where K is the solubility constant (Lasaga, 1981a). The theory of activated complex formation can be applied to mineral dissolution (Lasaga, 1981a; Wieland et al., 1988). The rate constant, k, is then related to the activation energy, E A , of formation of an activated complex of the rate-limiting step by the following equation k

=A

exp( -EA/RT)

[5]

where A is an integration constant related to the probability of the formation or decomposition of the activated state, R is the gas constant, and T is the absolute temperature. For an elementary reaction, the activation energy, E A , is the difference between the total free energies of the activated state and the ground state EA

= E{activated)

-

E{ground)·

[6]

In the case of a multistep reaction, the measured E A may not be an activation energy of an elementary reaction. For example, if in a two-step reaction the rate-determining step is preceded by a rapid equilibriumcontrolled reaction, the Ml of the first reaction contributes to the measured activation energy (Stumm and Morgan, 1981). The activation energy determined by the temperature dependence of the reaction is then only an apparent activation energy. When two or more different phases react to form product P (e.g., the simultaneous dissolution of anorthite and hornblende to release Ca ions), the overall instantaneous rate of formation of P is the sum of the individual rates of formation of P from all sources, providing there are no significant interactions between the different reactions (Bamford and Tipper, 1969) n

dP{total/ dT

=

Ek

i8j

[7]

i = I

where the subscript i denotes different phases. Because mineral surfaces are not homogeneous, Eq. [7] can be applied to the dissolution of a single mineral, in which case the subscript i denotes different crystallographic faces or types of reaction sites. Mineral dissolution, like crystal growth, is anisotropic and rates differ at different crystallographic faces. Also rates are higher at high energy surface sites, such as twin boundaries, cleavage planes, and dislocations (Blum and Lasaga, 1987). OXIDES AND HYDROXIDES (EXCLUDING SILICA)

The dissolution reactions of oxides, oxyhydroxides and hydroxides of trivalent and divalent metals are of interest to soil and environmental scientists

155

OXIDE AND SILICATE DISSOLUTION KINETICS

because some of these minerals are important components of soils and sediments. They also represent a set of structurally simple minerals whose study can provide insights into processes involved in the dissolution of the more complex silicate minerals, which will be discussed later. When oxide and hydroxide minerals dissolve there is no question of nonstoichiometric removal of components from mineral surfaces as for many silicates. Neither is there any question of the possibility of the formation of depleted surface layers that may affect rates as has been proposed for many silicates. The rate plots are typically linear which is often not the case for silicates.

Proton and Hydroxide Mediated Dissolution The dissolution of oxide and hydroxide minerals is pH dependent. In acidic solutions, the dependence of the rate of reaction on proton concentration, [H +], can be described by [8]

where R is the rate of release of the metal ion in moles per second, k is a rate constant, S is the surface area, and n is the order of the reaction with respect to [H +]. The logarithm of R is then related to solution pH by log R

=

log k

+ log S - n log 'YH

-

n pH

[9]

where 'YH is the activity coefficient for H +. When the ionic strength is constant, the n log 'YH term can be eliminated and the ionic strength effect is incorporated into the rate constant. In Eq. [2], [5], and [8], the dissolution of a mineral is treated as an isotropic attack of mineral surfaces by H +. The dissolution of goethite, however, is more rapid at the (010) and (001) faces than at the (100) face and dissolution rates in 0.5 MHCl vary with variations in crystal shape, which produces different relative exposures of these faces (Cornell et al., 1974). Other factors can also cause differential rates of dissolution of mineral surfaces (Blum and Lasaga, 1987). Crystal defects, such as twinning planes and dislocations, create high energy sites for surface attack. The excess surface energy of very finely divided crystallites, sharp points, or crystal edges also increases dissolution rates. A detailed account of the overall rate of dissolution of a mineral based on Eq. [7] would require a knowledge of the rate constant and surface area for each different crystal face and the rate constant and abundance of every type of high energy site. Equations [2], [5], and [8], however, are very useful approximations and in many cases are applicable. If finely divided material is removed by pretreatment, e.g., with HCI (Bloom and Erich, 1987) or HF (Stumm et al., 1985), the initial rate of release of metal ions from hydroxide minerals is linear with time (Fig. 7-1). At acid pH values, the rate of reaction increases with decreasing pH (Furrer and Stumm, 1986; Pulfer et al., 1984; Bloom and Erich, 1987). For samples with

156

BLOOM & NATER

0.1 M KN03

40

Fig. 7-1. Release of Al from 0040 g of gibbsite in 200 mL of 0.1 M KN0 3 solution. The pH was adjusted with HN03 (from Bloom and Erich, 1987).

similar crystal morphologies, the rate is proportional to surface area (Cornell et al., 1974; Bloom, 1983; Pulfer et al., 1984). At sufficiently low pH, the rate of dissolution of oxides and hydroxides is approximately first-order with respect to H +. The data of Surana and Warren (1969) for the dissolution of goethite suggest a first-order dependence on concentrations of H 2S04 and HCI0 4 , and on H + activity in HCI at concentrations > 0.5 M. Part of the difficulty in determining the difference between dependence on concentration and H + activity may be due to the specific effects of anions and the effects of ionic strength that will be discussed later. Bloom and Erich (1987) showed that in 0.1 MKN0 3 (with HN0 3 added to adjust the pH) the dissolution of gibbsite [AI(OHh] is first-order with respect to [H "l at pH <2.5 (Fig. 7-2). An earlier study (Bloom, 1983) reported reaction orders> 1.5 due to a failure to control ionic strength. For pH >2.5, the reaction was much less dependent on [H+]. Bloom and Erich (1987) modeled the higher pH reaction as a zero-order reaction and for the pH range 1.2 to 4.0, their data corresponded well (r 2 = 0.99) to rates calculated from the sum of two reactions: a first-order reaction with a rate constant of 1.4 X 10 -9 mol m -2 s -I and a zero-order reaction with a rate constant of 1.0 x 10 -12 mol m -2 s -1. They also showed that the rate of dissolution of gibbsite by the pH-independent reaction is of the same order of magnitude as the rate of dissolution of alkali feldspars at pH 5, which led them to conclude that kinetic stability is a factor for gibbsite in soils. Pulfer et al. (1984) showed that the dissolution of bayerite [Al(OH)3] is first-order with respect to [H +] in 1.0 M KNO J , in the pH range of 3.0 to 4.0. The first-order rate constant, however, is 100 times that

157

OXIDE AND SILICATE DISSOLUTION KINETICS

00.1

M KN03 A 0.1 M K 2S04 00.0001 M KHz P0 4

w ~

a: -10

o

9 -11

-12L_----J'---_----J._ _ 1.5 2.0

----L~===~!::=~ 3.0

3.5

40

pH Fig. 7-2. Variation of log of rates (mol m -2 s -1) for dissolution of gibbsite in solutions containing nitrate, sulfate, or phosphate. The slopes suggest first-order dependence on [H + I at pH <2.5 for sulfate and nitrate solutions and zero-order dependence in phosphate (from Bloom and Erich, 1987).

obtained by Bloom and Erich (1987) for gibbsite. The higher rate constant was, in part, due to the effect of the higher KN0 3 concentration on rate (discussed below), but this cannot explain most of the difference in rate constants. The greater rate of proton attack on bayerite may explain why the first-order reaction occurs at a higher pH in bayerite. The data of Furrer and Stumm (l986) for o-A1 203 dissolution in 0.1 M NaN0 3 suggests an order dependence of 0.4 with respect to solution [H +] in the pH range of 4.0 to 6.0 and little pH dependence in the pH range of 2.5 to 3.5. The lack of pH dependence at pH <4.0 seems to further substantiate the assumption of Bloom and Erich (1987) of a zero-order reaction in the pH range of 2.5 to 4.0 for gibbsite. Stumm et al. (1985) plotted log R vs. the log of the quantity of protons adsorbed and obtained a plot with a slope of 3.1 (Fig. 7-3). They suggested that adsorption of three protons in the vicinity of a surface Al is a necessary precondition for removal of a surface AI 3+. The apparent zero-order reaction in the pH range of 2.5 to 4.0 was attributed to proton saturation of the surface. The data of Carroll-Webb and Walther (1988) for corundum (AI203) show an order dependence on [H+] of only 0.15 in the pH range 1 to 8. They reported that dissolution was first-order dependent on adsorbed protons, and attributed the difference in their results from those of Furrer and Stumm (1986) to the difference in pH range used and to possible surface alterations caused by the H 2S04/HF pretreatment used by Furrer and Stumm (1986). Both Furrer and Stumm (1986) and Carroll-Webb and Walther (1988) concluded that the rate-controlling step is the detachment of protonated metal ions from the surface.

158

BLOOM & NATER

-

....

-8.0

',c

N

'E

-8.2

0

E

-

-8.4

:I:

c::

-

-8.6

:I:

Q)

C'CS

c::

-8.8

Cl

0

1

-9.0

Surface

-6.0

log

u-

-5.8

prolonatlon

-5.6 2

OH2+} , mol mI I I I. 6

5

pH

(solution)

4 3

Fig. 7-3. Variation in log of rate of release of Al 3+ from o-A1203 with log of concentration of surface protonated sites (from Stumm et aI., 1985; reprinted by permission of Kluwer Acad. Pub!.)

At high concentrations of NaOH, the dissolution of gibbsite is rapid and first-order with respect to NaOH activity (Packer and Dhillon, 1968; Scotford and Glastonbury, 1972). Comparison of the data for gibbsite dissolution at 41°C in 1.0 M NaOH (Scotford and Glastonbury, 1972) with estimated rates for gibbsite dissolution in 1.0 M HN0 3 (Bloom and Erich, 1987) at the same temperature suggests that the dissolution rate in NaOH is about four orders of magnitude greater than in HN0 3 • The apparent activation energies, however, are quite similar in HN0 3 (68 kJ mol-I; Bloom and Erich, 1987) and NaOH (63 kJ mol-I; Scotford and Glastonbury, 1972). The data of Carroll-Webb and Walther (1988) suggest that for corundum, first-order attack by OH - occurs in the pH range of 8 to 11. The authors, however, concluded that the reaction showed a fourth-order dependence on adsorbed hydroxyls. Ligand-Promoted Dissolution Binding of complex-forming ligands to oxide and hydroxide surfaces increases dissolution rates. Stumm and Furrer (1987) suggest that in acidic solutions the measured rate of dissolution of an oxide or hydroxide can be treated as the sum of the rate of the proton-promoted reaction (RH ) plus the rate of the ligand-promoted reaction (RL ) [IOJ

159

OXIDE AND SILICATE DISSOLUTION KINETICS 18 16

14

a:..J 12 ..J

~

~

10 8 6

4

Orgonlo lIgondo

2

1t:....,.......===¥:==;='=1 J

~~ x

• U'L}

'24 28

Concentration surface complex

Fig. 7-4. Variation in log of rate of release of A1 3 + from o-Alz0 3 with concentration of surface complexes with organic ligands (from Stumm et aI., 1985; reprinted by permission of Kluwer Acad. PubI.)

The rates of dissolution of o-Alz0 3 promoted by the multidentate ligands, citrate, salicylate, and oxalate, are proportional to the quantity of ligand adsorbed (Fig. 7-4) (Furrer and Stumm, 1986). These ligands form five- and six-memberedring bidentate chelation complexes. The adsorption of benzoate ions, however, was not effective in increasing dissolution rates because benzoate does not form strong complexes with AI. Stumm and Furrer (1987) attributed the acceleration of the rates to the negative charge brought into the coordination sphere of Al by the complexing ligands. Fluoride ions greatly increase the dissolution rate of aluminous minerals. Zutic and Stumm (1984) found that for their rotating disk electrode study of Alz0 3 dissolution, the surface reaction was sufficiently rapid to be diffusion controlled at [F -] > 10 -6 M. Pulfer et ai. (1984) showed that the rate of dissolution of bayerite was increased by a factor of more than 100 in 10 -4 M fluoride, compared to dissolution without fluoride in 1.0 M KN03 • Pulfer et al. (1984) stated that the increase in rate was approximately second-order with respect to both [H +] and [F -] in the pH range of 4 to 6. Their model for the rate of fluoride-mediated dissolution (R F) is [11]

where [=AI(OH)F -] is a surface fluoride adsorption site. They developed a predictive equation for adsorbed F - involving five different surface equilibrium constants and the surface capacitance. A mechanism that is fourth-order in solution components and first-order in a surface component is difficult to accept as an elementary reaction. It is also hard to conceive of a multistep reaction of the type that would yield a rate expression like Eq. [II].

160

BLOOM & NATER

Phosphate ions, like F -, adsorb strongly on aluminous mineral surfaces at low pH, and have been shown to accelerate gibbsite dissolution at pH < 3 (Bloom and Erich, 1987). The rate of gibbsite dissolution in 1.0 x 10-4 M phosphate at pH 3.0 is more than 30 times the rate in 0.1 M KN0 3 (Fig. 7-2). The data of Bloom and Erich (1987) show an apparent 0.88-order dependence on solution phosphate. Their data suggest that dissolution is not a simple function of the quantity of P04 adsorbed. The reaction is also pH independent. The apparent dependence of P04-promoted dissolution on solution P04 rather than adsorbed P contrasts with the results of Stumm et al. (1985) for organic ligands. Stumm et al. (1985), however, studied the reaction rates at higher pH values (3-6). As with proton-promoted dissolution, the reaction mechanism at higher pH may be different from mechanisms occurring at low pH. The rate-controlling step for phosphate- and possibly fluoridemediated dissolution may not be the detachment of the complex from the surface. If surface detachment is sufficiently rapid, surface complex formation may be rate limiting. Sulfate ions form weak complexes with Al but can promote the rate of gibbsite dissolution (Fig. 7-2)(Bloom and Erich, 1987). In the pH range of 1.75 to 3.0, the dissolution rate for gibbsite in 0.10 M KZS0 4 is first-order (slope = 1.0) with respect to [H +] and greater than 40 times as fast as in 0.10 M KN0 3 (Bloom and Erich, 1987). The apparent order of the reaction with respect to sol- concentration in solution is 0.36 (Bloom and Erich, 1987). Nitrate salts also can have an effect on dissolution. Bloom and Erich (1987) found an apparent 0.56-order dependence on N0 3- for concentrations of 0.08 to 1.0 M. Similar rates were found for Ca(N0 3)z, Mg(N0 3)z, and KN0 3 when the N0 3- concentration was constant. The more weakly bonding sol- and N0 3- ions may contribute to proton attack by affecting the surface charge of the mineral. Phosphate, however, binds to surface Al ions with enough strength to destabilize AI-OH bonds. The simple first-order dependence of the rate of gibbsite dissolution on [H+] in KZS04 is not easy to interpret given the protonation (pKa = 2.1) of S04 in the pH range studied (Bloom and Erich, 1987). Thus at the lowest pH studied, 1.6, the majority of S04 was in the form of HS04- while at the highest pH studied, 3.8, most of the S04 was in the form of soi'. The protonated sulfate ion might be expected to have a different effect on the rate than the divalent ion. A similar difficulty occurs in understanding the apparent zero-order dependence on [H +] of P04-promoted dissolution. The pKa for protonation of H zP04- is 2.2. Zero-order dependence on [H +] of ligand-promoted dissolution, however, has also been demonstrated for the dissolution of hematite in 0.1 M EDTA, HEDTA, DTPA, and CDTA in the pH range of 2 to 6. The rate for hematite dissolution in 0.1 M NTA, however, increases with decreasing pH (Chang and Matijevic, 1983). These chelating ligands, however, were studied at much higher concentrations than the other ligands discussed.

OXIDE AND SILICATE DISSOLUTION KINETICS

161

Surface Complex Formation and Dissolution Mechanisms The low fractional orders found for the influence of [H +] and complexing ligands on the dissolution of oxides and hydroxides can be explained by the surface complexation theory (Wieland et al., 1988). For conditions where the detachment of product ions from the surface is rate limiting, the rate is given by the general rate equation [12]

where X a is the mole fraction of dissolution active sites; P is the probability of finding a specific site with the proper coordination environment for formation of an activated complex; and S is the surface concentration of sites (mol m -2). For proton-promoted dissolution, the probability term, P, can be described by P

=

[4!/j!(4 - J)!](XHY

[13]

where j is the number of adjacent sites that must be protonated for the release of a metal ion and XH is the mole fraction of the possible protonated sites that are protonated. The values of j were determined to be 2 for BeO and 3 for FeOOH and o-A1 203 (Furrer and Stumm, 1986; Zinder et al., 1986). For proton-promoted dissolution, the adsorption of protons can be predicted using the constant capacitance model for the formation of protonated sites on oxide surfaces (Sposito, 1983; Hayes and Leckie, 1987). The rate can then be related to the quantity of protonated sites, [= MOHl], by the equation [14]

This approach seems to fit the data of Stumm and coworkers for dissolution of oxides and hydroxides in dilute acids, but Carroll-Webb and Walther (1988) suggest for corundum thatj = 1, and that the required number of protons adjacent to an Al to promote detachment from the surface need not be equal to the number required to convert the Al in corundum to Al 3+ . At sufficiently low pH, the dissolution of Al(OH)3 is first-order with respect to protons in solution (Pulfer et al., 1984; Bloom and Erich, 1987) and dissolution cannot be explained by the surface complexation model. For this reaction, protonation rather than detachment of surface sites appears to be rate controlling. Carroll-Webb and Walther (1988) have also tried to apply the surface complexation model to the dissolution of corundum in basic solutions. They concluded that the rate-controlling step has a fourth-order dependence on adsorbed OH -. This is not consistent with the formation and detachment of AI(OH)4- from the surface. Their data, however, suggest a first-order dependence on solution [OH "I that is consistent with what others have

162

BLOOM & NATER

found for AI(OH)3 at higher NaOH concentrations (Packer and Dhillon, 1968; Scotford and Glastonbury, 1972). Dissolution at basic pH values may be dependent on the rate of OH - attack of the surface rather than the rate of detachment of AI(OH)4-' The surface complexation theory can also be used to explain the effect of ligands on dissolution. The rate of dissolution of o-Al20 3 and BeO is wellcorrelated with the quantity of adsorbed bidentate carboxyl and carboxylphenol ligands (Furrer and Stumm, 1986). With FeOOH and Fe203' however, the nonreductive (in the dark) dissolution in the presence of oxalate was proportional to the product of adsorbed oxalate and protons (Zinder et aI., 1986). This suggests that proton adsorption on the nearest neighbor may be necessary for release of an Fe-oxalate complex from the surface. The partial-order dependence of AI(OH)3 dissolution on N0 3- and sol- (Bloom and Erich, 1987) may be due to a dependence on surface complex formation. This explanation, however, is not completely consistent with the first-order dependence on [H +] in these salts at low pH. The N0 3- and sol- may be influencing the rate of H + attack by their effect on the density of surface positive charges (McBride, 1989). The rate of dissolution of gibbsite is increased by additions of phosphate and sulfate without changing the apparent activation energy (Bloom and Erich, 1987). Thus, if the detachment step is rate controlling, the formation of P04 and S04 complexes is not accelerating the rate by lowering the activation energy of detachment. This seems to be at odds with the surface complexation model because a decrease in the energy involved in detachment should lower the activation energy. It may be, however, that for some ligands a decrease in the activation energy does occur. Different mechanisms may hold at different pH values. A more detailed understanding of reaction mechanisms awaits further research. Reductive Dissolution Under reducing conditions, the dissolution of some oxide and hydroxide minerals of transition metals is greatly accelerated. This includes the environmentally important oxide/hydroxide minerals of Mn(III/IV), Fe(III), Co(III), and Pb(IV) (Stone, 1986). The lower valence ions produced by reduction, e.g., Fe2+ and Mn 2+ , are much more mobile in aqueous systems than the ions of higher oxidation states. Various natural and synthetic organic compounds can act as reducing agents in reductive dissolution (Table 7-2). These compounds, when adsorbed to a mineral surface, can undergo oxidation and transfer electrons to surface Table 7-2. Reducing agents that promote the dissolution of Mn(IV) and Fe(III) oxide minerals. Phenols Catechols Hydroquinones a-hydroxy-benzoic acids

Ascorbic acid Pyruvic acid Oxalic acid

163

OXIDE AND SILICATE DISSOLUTION KINETICS

3r-----------------, Mn oxide added (x 10 -5 M)

...

4.21 3.51 c 2.87 A 2.10 o 1.44

v o

2 'g

CD II)

III CD CD

a:: +

o"--__ o

CII

........j'---_ _- - ' -

C ~

5

---'--

15

-'

20

ions. Stone (1986), Stone and Morgan (1987), and Sparks (1989) have recently reviewed these reactions. Only a brief discussion of reductive dissolution will be given here. The rate of release of Mn 2+ from a Mn(I1I/IV) oxide is a function of the concentration of reductant in solution and oxide. The data in Fig. 7-5 and 7-6 show that with increasing concentrations of oxide or p-methylphenol the rate of release of Mn 2 + increases. With sufficient time the rate plots are curved (Fig. 7-6) due to the consumption of Mn oxide, because the reductant was in excess (Stone, 1987). At lower reductant concentrations the reaction is first-order with respect to concentration of reductant added (Stone and Morgan, 1984; Stone, 1987). The reduction is pH dependent with the rate increasing at lower pH. This is not surprising because reduction reactions consume protons and the adsorption of ligands is pH dependent.

..... CD

....

III

I

a:: c c E 0

..- ... :I

0

II) II)

Q

I

..J 0

....E 10- 3

Concentration of p-Methylphenol (M) Fig. 7-6. Variation in rate of Mn 2 + released from a Mn(III/IV) oxide with increasing concentrations of p-methylphenol in 0.001 M acetate buffer. (Reprinted with permission from Stone, 1987, Copyright 1987, American Chemical Society.)

164

BLOOM & NATER

Reductive dissolution reactions can be described by a three-step reaction sequence (Stone, 1986). The steps are (i) adsorption of the reductant forming either an inner- or outer-sphere surface complex, (ii) electron transfer from a reducing agent to a surface metal ion, and (iii) release of the reduced ion. For Mn(III/IV) oxides the reductive step is complicated by the necessity for Mn(lV) to be reduced first to Mn(III) then to Mn(II). All natural Mn oxides, however, contain both Mn(lV) and Mn(III) (McKenzie, 1989). Even laboratory MnOz preparations contain some Mn(lII).

SILICATES Silicate mineral weathering is more complex than the dissolution of oxides and hydroxides. The primary silicates, those silicates of most interest in weathering studies, are not stable in aqueous environments at earth surface temperatures. For these minerals, solution equilibrium with respect to soluble mineral components is not a factor in determining stability, and only the forward dissolution rate needs to be considered. Investigations of the dissolution of freshly crushed materials often show nonstoichiometric release of mineral components that can affect the rates of dissolution, even over long-term laboratory experiments. This is especially common in experiments conducted at pH values < 4 or > 9, where dissolution mechanisms differ from those controlling weathering reactions at circumneutral conditions. Nonlinear dissolution rates are also frequently observed when freshly ground silicates are used. The complexities involved in silicate weathering have caused difficulties for interpretation of laboratory dissolution data and have been the basis of heated controversies concerning the mechanisms of dissolution. This difficulty has been exacerbated by attempts to make direct comparisons of the results of dissolution experiments conducted in different pH regions. Because the extrapolation of rate and mechanistic data obtained from low or high pH weathering studies to more neutral conditions is a potential source of error, and because the majority of soils have pH values between 4 and 9, the interpretations made in this paper will be restricted to the pH range of 4 to 9, unless otherwise stated. Variation in Rates with pH Dissolution of most primary silicates is pH dependent, as illustrated by the release of Si from anorthite (CaAlzSizOs) after four successive pHadjusted, 3-d rinses (Fig. 7-7) (Amrhein and Suarez, 1988). For anorthite there is little or no pH dependence at pH values from 5 to 9. At higher and lower pH values, however, the dissolution rate increases. In a review of feldspar hydrolysis kinetics, Helgeson et al. (1984) utilized the data of Chou and Wollast (1984) for albite and Siegel and Pfannkuch (1984) for microcline to show that for pH < 2.9 the rate of feldspar dissolution approaches firstorder with respect to [H +]. At pH values greater than 8. the reaction has

165

OXIDE AND SILICATE DISSOLUTION KINETICS 0.9 o First rinse

0.8

• Cumulative Si release of 4 rinses

0.7 0.6 ~

E 0.5

ci 0.4 0.3 0.2

0.1

o L..........:::::~::::i:::::~~~ 3

4

5

6

7

8

9

10

pH Fig. 7-7. The cumulative release of Si to solution vs. pH for four sequential rinses of anorthite with pH adjusted 0.005 M NaCI. Anorthite (50-100 /Lm) at 6.67 g L -1 was suspended in rinse solution for 3 d before replacement with fresh solution (Reprinted with permission from Amrhein and Suarez, 1988, Copyright 1988, Pergamon Press pic.)

an apparent order dependence on [OH-] of 0.4, but in the mid-pH range little dependence on pH was observed. First-order dependence on H + for the low pH dissolution of silicates is not universal but it has been observed in silicates other than the alkali feldspars, including forsteritic olivine [(Mg,FehSi04 , Grandstaff, 1986] and nepheline [(Na,K)AISi0 4 , Tole et aI., 1986] in the pH range of 3 to 6. In bronzite [(Mg,Fe)SiOa, Grandstaff, 1977] and diopside (CaMgSi 204 , Schott et aI., 1981), the acid dissolution reaction has an apparent order dependence on [H +] of 0.5. Murphy and Helgeson (l987a) suggest that the 0.5-order dependence is general for pyroxenes. The initial process in the dissolution of feldspars is replacement of surface mobile cations (primarily Na +, K +, and Ca2+) by protons (Nash and Marshall, 1956; Garrels and Howard, 1959). This process is rapid and initially reversible, but becomes less so with time. The replacement is complete even at high solution concentrations of the mobile ion and occurs over a wide pH range (Murphy and Helgeson, 1987a). The reactions for microcline, an alkali feldspar, and anorthite are KAISi30 s + H + - HAISi30s (microcline) CaAI2Si20H + 2H + - HzAlzSizOs (anorthite)

+

K+

+ Ca z+ .

[15]

[16]

166

BLOOM & NATER

The slow decomposition of the silicate structure due to the disruption of AI-O and Si-O bonds by proton adsorption of the type shown in Eq. [15] and [16] may account for the pH-independent reaction (Murphy and Helgeson, 1987a). At low pH, proton adsorption at sites other than the cation exchange sites may account for the pH dependence. The partial orders with respect to [OH -] observed for most silicate mineral dissolution reactions can be explained by the surface complexation model (Blum and Lasaga, 1988; Brady and Walther, 1989). Brady -and Walther (1989) showed that slope plots of log R vs. pH for quartz and other silicates at 25°C is not inconsistent with a value of 0.3. Plots of the log of absorbed OH - vs. pH also have slopes of about 0.3, suggesting a first-order dependence on negative charge sites created by OH - adsorption. Because of the similarity of quartz with other silicates and difference with the dependence of aluminum oxides and hydroxide dissolution on solution [OH -], Brady and Walther (1989) concluded that at pH > 8 the "precursor site" for development of the activated complex in the dissolution of silicates is Si. This conclusion is supported by the evidence that the rates (mol em -2 s -I) at pH 8 are inversely correlated with the site potential for Si (Smyth, 1989). Thus it seems that at basic pH values, silicate dissolution is dependent on the rate of detachment of H 3Si04- from negative charge sites. Blum and Lasaga (1988) used the surface complexation model to explain the effect of H + on the dissolution of freshly ground forsteritic olivine and albite. Their experimental data for a forsteritic olivine showed an apparent 0.56-order dependence on [H +] in the pH range of 2 to 6, which corresponded to a first-order dependence on adsorbed protons. This contradicts with the data of Grandstaff (1986), which shows first-order rate dependence on [H +] for naturally weathered forsteritic olivine. Using the albite dissolution data of Chou and Wollast (1985a), in the same pH range, which showed an apparent dependence on [H +] of 0.49, they also found a first-order dependence with respect to protons adsorbed in excess of the protons exchanged for Na +. The H + exchanged for Na + was similar across the pH range of 2 to 12. The low pK for the protonation of silica surfaces ( < 2.4 for quartz, Parks, 1967) suggests that the site of surface protonation is Al in an aluminosilicate like albite (Brady and Walther, 1989). Wieland et al. (1988) reasoned that if the rate of removal of surface ions is rate controlling, the energetics of binding of the most stable ion in a surface should correlate with the rate of dissolution. They plotted the Madelung (site) energies for the most stable ion (Si4 + for silicates) against the rates of dissolution at pH = 5.0 for 14 different oxide and silicate minerals and obtained a general trend for decreasing rates with increasing site energies. If the diopside and quartz data are removed from the plot, however, much of the observed trend disappears. The inverse correlation that Brady and Walther (1989) showed with site potential of Si at pH 8.0 suggests that the site for Si is more important at pH > 8. This is expected if Brady and Walther (1989) are correct about the role of Si sites in high pH dissolution.

167

OXIDE AND SILICATE DISSOLUTION KINETICS

Ligand-Promoted Dissolution The rates of dissolution of most aluminosilicates (Henin and Pedro, 1965; Huang and Keller, 1970; Huang and Kiang, 1972) and silicates (Jergensen, 1976; Bennett et aI., 1988) increase in the presence of complex-forming ligands, notably carboxylic and phenolic acids. This has frequently been observed in studies of the weathering of rock in contact with lichens, fungal hyphae, and other microbes (Robert and Berthelin, 1986, and numerous references contained therein). Inorganic ligands, such as fluoride, also enhance the rate of dissolution (Amrhein and Suarez, 1989). Amrhein and Suarez (1989) applied the surface complexation model (Wieland et aI., 1988)to the dissolution of anorthite in the presence of fluoride and oxalate ions. They observed enhancement of dissolution rates in the presence of the ligands and a strong pH-ligand interaction in the pH range 5 to 9, even though the reaction was nearly pH independent in that range in the absence of complex-forming ligands. The rate of dissolution was linearly related to the surface concentration of absorbed ligands. Similar results were observed for the ligand-promoted dissolution of microcline (Nater and Huang, 1988), where the rate of release of Al and K was highly correlated with the AI-ligand complexation constant for several low molecular weight aliphatic acids at pH 4.50 (Fig. 7-8), suggesting that surface complexation of structural AI by the ligands is the mechanism causing the enhanced release of Al and K. The rate of Si release was not correlated with the AI-ligand complexation constant (r 2 = 0.003), however, implying that its release occurred via some other mechanism, most probably simple hydrolysis. These results differed from those found by Manley and Evans (1986), who studied the effects of organic acids on the dissolution of albite and microcline. They observed that the ligand-promoted rate of dissolution 78011 ~

'"E

'0

oS CD
'"

Gi

[;1] AI

68-11

• 81 .. K

58011

R"2

48011

= 0.003

•

38-11

•

II:

'0

II
II:

28011

R"2 = 0.957

18011

Oe+O

2

3

4

5

6

7

8

Log Keq

Fig. 7-8. The rate of release of AI, K, and Si from microcline during ligand promoted dissolution vs. the log of the aqueous Al-ligand stability constant (data from Nater and Huang, 1988).

168

BLOOM & NATER

was influenced more by the strength of the acid than the magnitude of the AI-ligand stability constant. The pH was not controlled in their study, however, and varied from 3.82 (oxalic acid) to 4.37 (caffeic and vanillic acids). The rate of quartz dissolution is also enhanced by organic acids. The addition of the polyphenolic acids catechol (1,2-dihydroxybenzene), 4-nitropyrocatechol (4-nitro-l,2-dihydroxybenzene), and 3,4-dihydroxybenzoic acid, which are known to complex silica, produced a two- to three-fold enhancement of the rate of dissolution of quartz and some aluminosilicates (Jergensen, 1976), suggesting that a surface complexation reaction is involved. Interestingly, the rate of quartz dissolution was also enhanced in the presence of 20 mmol kg -1 concentrations of citrate, oxalate, and salicylate (Bennett et aI., 1988), although these carboxylic acids were not previously known to form complexes with silica. Ultraviolet absorption difference spectral evidence, however, suggests complex formation with these ligands. The aqueous silica peak shifted towards longer wavelengths (from 190-195 nm to 240 nm) in the presence of citrate, oxalate, and pyruvate at near neutral pH. Acetate, which did not produce any rate enhancement, also did not cause any silica peak shift. Not all silicate minerals show a rate enhancement in the presence of organic ligands, however. Oxalate concentrations of 0.5 and 1 mM produced no significant effects on the dissolution rate of tremolite nor on the steadystate release of Si from oligoclase (Mast and Drever, 1987). Oxalate did increase the rate of release of Al from oligoclase in the pH range 4 to 9; however, the dissolution reaction was incongruent (the Al to Si ratio was less than stoichiometry) in the absence of oxalate and congruent in its presence. Large transient spikes of Al were released at pH 4, 5, and 7, and of Si were released at pH 9 when oxalate was added to or removed from the system. In order to avoid sample grinding effects on dissolution kinetics, Grandstaff (1986) separated a forsteritic olivine (Fod from naturally weathered beach sands. The rates of dissolution were measured in pH 4.5, 1 mM solutions of the organic ligands EDTA, citrate, oxalate, succinate, phthalate, acetate, and tannic acid, and in pH 4.5, 1 mM KCI. Significant increases in the dissolution rate were observed for most ligands (110 times higher for EDTA than for KCI), and were shown to be proportional to the strength of the aqueous Mg-ligand complexation constant (Grandstaff, 1986). The rates of dissolution were also affected by the concentration of ligands present, and were proportional to the square root of the free ligand concentration. Formation of Etch Pits Mineral surfaces examined by optical and electron microscopy clearly show etch pits that indicate that most, if not all, silicate minerals dissolve preferentially at certain sites (Fig. 7-9). These etch pits are small, rounded, almond-shaped, rectilinear, or lens-shaped hollows. They may be more or less evenly distributed across the surface or concentrated in u few loci. They

o ...~ ot"'l > Z o

...

00

t::

£ t"'l

...o 00 00

oe-

...S

o z

~

z

§ ("l

00

Fig. 7-9. Etch pits formed on hornblende surfaces after weathering in a pH 4.0,0.01 M lithium acetate buffer solution (from Zhang et aI., 1990; reprinted by permission from Elsevier Science Pub!.)

... ~

170

BLOOM & NATER

have been observed in weathered feldspars (Wilson, 1975; Berner and Holdren, 1979), quartz (Petrovich, 1981; Blum et aI., 1990), pyroxene and amphiboles (Schott and Berner, 1985), hornblende (Zhang et aI., 1990), olivine (Grandstaff, 1978, 1986), garnets (Velbel, 1984; Ghabru et aI., 1989), and other minerals. The presence of etch pits indicates a surface-controlled dissolution mechanism (Berner, 1981) wherein dissolution reactions are initiated at high energy sites. Linear defects (edge dislocations and screw dislocations) and planar defects (twinning planes, grain boundaries, and stacking faults) are naturally occurring features in crystals. Low to moderate defect densities « 105_10 8 cm ") are formed during crystal growth (Nielsen, 1964), while higher densities (> 10 12 cm -2) may result from structural deformation induced by geologic forces or sample preparation (Petrovich, 1981). An excellent discussion of defects is presented in Lasaga (1981b). Where dislocations intersect the surface, they provide an access for solution to react with high energy sites. Simulations of dissolution around screw dislocations have been made using Monte Carlo methods (Fig. 7-10) (Blum and Lasaga, 1987). Model calculations made without including strain fields around the dislocation produced a small (-25070) rate enhancement when the solution was far from saturation. When strain fields were included in the calculations, however, ,'_"

---, ----,-

n :.

"

,,-

,:

I

..

o

-

:

I

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%

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DISTANCE (blocks) Fig. 7-10. Graphical results of a Monte Carlo simulation of progressive dissolution and etch pit formation around a screw dislocation in quartz. Etch profiles illustrate the removal high energy material adjacent to the dislocation with time (reprinted wilh permission from Blum and Lasaga, 1987; Copyright 1987, John Wiley & Sons.)

or

OXIDE AND SILICATE DISSOLUTION KINETICS

171

dissolution proceeded very rapidly down the core of the dislocation. The predicted rate decreased markedly with distance from the dislocation center due to relaxation of the strain field and a corresponding decrease in free energy. Although dislocations have been related to weathering features and have been implicated in the initially rapid rate of dissolution, they may have less effect on the overall long-term rate of dissolution than has been previously assumed. Studies have shown that dissolution rates for silicate and oxide minerals increase only by a factor of two to three when the dislocation density is increased by two to three orders of magnitude by mechanical deformation (Holdren et aI., 1988; Murphy, 1988; Casey et aI., 1988a; Blum et aI., 1990). Blum et aI. (1990) showed that, after about 800 h of reaction, the dissolution of quartz in distilled water and in 0.2 M HF was almost independent of the dislocation density (from less than 105 ern -z to approximately 5 x 10 10 cm-z) for solution compositions far from equilibrium, even though the morphology of grains weathered in 0.2 M HF was substantially different for low (few etch pits) and high (numerous etch pits) defect density materials. Theoretical arguments indicate that dislocation densities should have a larger effect for solutions near equilibrium. Blum et aI. (1990) hypothesize that the major rate-limiting step in the dissolution reaction is the removal of silica from high strain areas surrounding dislocations, and that increasing the number of dislocations does not significantly increase the number of sites available for this process. Surface Area and Surface Reactivity The rate of dissolution is not strictly a function of the surface area of the interface, as indicated in Eq. [2], but is actually related to the reactive surface area (Helgeson et al., 1984), an ill-defined term relating the surface area and its reactivity to the rate of reaction. In theory, the reactivity of the surface is a function of the free energies and relative surface areas of different crystal faces, the abundance and type of surface defects present, sample treatment history, and other factors (Helgeson et aI., 1984). Modification of Eq. [2] to account for variations in surface reactivity gives [17]

where () is the surface reactivity term (Helgeson et al., 1984), and all other terms are the same as defined in Eq. [2]. Factors other than dislocation abundance affect surface reactivity. As discussed previously, increasing the dislocation density by mechanically inducing deformations did not increase the dissolution rate in proportion to the number of defects (Holdren et al., 1988; Murphy, 1988; Casey et aI., 1988a; Blum et aI., 1990). However, natural and induced dislocations may differ in reactivity. Mineral grains having different sizes may also have different surface reactivities due to dislocation density-particle-size interactions. Holdren and

172

BLOOM & NATER

1:

region

1 1.

.....Gl

-.. CG

~

::J

.c .....

.5

-.'"

1

c:

CD 'C

-o

CD

CD 'C

region

2

co

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.

o

~

~

c

c:

Q

CD CD

CD

o

c:

In (surface area) Fig. 7-11. The effect of decreasing particle size (represented by increasing surface area) on the bulk rate of dissolution. Three regions are described: Region 1, particle dimensions are significantly greater than the distance between dislocation outcrops; Region 2, particle dimensions are smaller than or equal to the distance between adjacent dislocations; Region 3, particle dimensions are sufficiently small that excess surface energy increases the rate of release (reprinted with permission from Holdren and Speyer, 1985, Copyright 1985, Pergamon Press plc.)

Speyer (1985, 1987) examined particle-size-reaction rate relationships for 10 feldspar samples of varying composition in pH 3.0 H'Cl, The samples were ground and then separated into six size fractions, ranging from > 600 I-tm to < 37 I-tm. The specific surface area (particle size)-dissolution rate relationships for the alkali feldspars they examined could be divided into three regions on a graph (Fig. 7-11). In Region 1, which corresponds to the largest particle sizes, the bulk reaction rate (mol kg! S-I) increases linearly with surface area; i.e., the specific reaction rate (mol m-2 S-I) is constant throughout this region. This corresponds to particle sizes that have mean particle dimensions that are significantly greater than the distance between adjacent reactive sites. In Region 2, the bulk reaction rate does not increase linearly with increasing surface area and may even decrease with decreasing particle size. In this region, particle dimensions are smaller than, or of the same order as, the mean distance between dislocations, and further increases in the specific surface of the particles do not produce corresponding increases in the numbers of defects intersecting the surface, demonstrating that the dissolution rate is controlled mainly by reactions at dislocations. In Region 3, the smallest particle-size region, the bulk reaction rate increases with decreasing particle dimension, due to excess surface energy resulting from small particle size.

173

OXIDE AND SILICATE DISSOLUTION KINETICS 100...------------------,

:::E

~

----0--

---0--

10

c::

-..

AI 51

Na

0 :;: «I

e GI o c::

1

0

0

o

50

100

150

200

250

300

Time (h)

Fig. 7-12. Initial, nonlinear dissolution of albite in pH 5.1 HCI in a continuous flow fluidized bed reactor. Reaction product concentrations were maintained below saturation for all secondary phases (data from Chou and Wollast, 1984).

This same particle-size-reaction rate relationship did not hold for some members of the plagioclase feldspar series (Holdren and Speyer, 1987). For these minerals, the bulk reaction rate was proportional to surface area over almost all of the particle-size range studied, with only slight decreases occurring for the smallest « 37 ~m) particle-size fraction. Consequently, the specific reaction rate (mol m-2 S·I) was constant over almost the entire particle-size range measured, corresponding to Region 1. The second region, if it existed, did not occur within the particle-size range studied, suggesting that the mean distance between rate-controlling sites was smaller than the diameter of all but the smallest particle-size fraction studied.

Nonlinear Rates Most investigators have observed a decrease in the rate of dissolution as weathering reactions proceed (Fig. 7-12). Commonly, the initial rate of weathering decreases by an order of magnitude within the 1st d of reaction, and may decrease by an additional one to three orders of magnitude within 2 wk to 1 yr or more. This decrease is not due to the presence of a reverse reaction, as it can be readily observed in continuous-flow reactor systems where dissolution product concentrations are carefully maintained at very low levels (Chou and Wollast, 1984; Holdren and Speyer, 1985). The dissolution rate may be nonlinear even after extensive weathering; curvilinear rates have been observed after more than 400 d of reaction for labradorite at pH 4 (Erich and Bloom, 1987, unpublished data). This phenomenon has been related to several mechanisms: 1. Rapid dissolution of very fine particles produced during sample grinding (Holdren and Berner, 1979; Fung and Sanipelli, 1982; Talman and Nesbitt, 19HH).

174

BLOOM & NATER

2. The rapid dissolution of structurally damaged surface sites produced during sample grinding (Petrovich, 1981). 3. Preferential dissolution at naturally occurring crystal imperfections, such as dislocations, twinning planes, and other structural defects (Berner and Holdren, 1979; Berner and Schott, 1982; Lasaga, 1981b; Brantleyet aI., 1986; Schott and Petit, 1987; Blum and Lasaga, 1987). 4. Formation of a leached layer (Chou and Wollast, 1984). 5. Precipitation of secondary products on surfaces of dissolving minerals, thus producing a diffusional barrier to the release of ions from the solid (Wollast, 1967). In general, the first three mechanisms require the presence of sites or particles with higher free energies than the bulk phase of the mineral. For very fine particles, the surface energy increases as a function of the radius of curvature of the solid-solution interface (Nielsen, 1964). This increase generally is not significant except for very small ( < 1 I-tm) crystallites. Likewise, sites on mineral surfaces damaged by abrasion or pressure deformation have higher bulk free energies than similar, undamaged sites (Petrovich, 1981) due to a loss of physical and cyrstallographic integrity. Sites of structural defects, dislocations, and other crystal imperfections also have higher energies than more perfectly crystalline portions of the mineral due to the presence of unsatisfied bonds, localized charge imbalances, or bond strain. Because the total free energy (bulk plus surface free energy) of these sites or particles is higher than that of more perfectly crystalline sites, the activation energies involved in creating the activated state, Eq. [5], are reduced, thereby producing more rapid dissolution rates. Each high energy site or particle behaves as if it were a separate phase and dissolves more or less independently of the rest of the mineral. Thus, by combining Eq. [5] with Eq. [7], the rate equation for the dissolution of a mineral sample containing a number of different high energy microsites or microphases as well as the bulk phase can be theoretically described

dP -

dt

=

E n

i=1

8 iA exp

(-Ei) -

[18]

RT

where A is the integration constant and the subscript i denotes microsites or microphases having different activation energies. Although the total quantity and surface area of these higher energy microsites or microphases is small relative to that of the bulk phase, they can significantly affect the overall dissolution kinetics. Because they dissolve more rapidly than the lower energy bulk phase material, they increase the overall rate of dissolution. As each high energy microphase dissolves, however, it no longer contributes to the overall dissolution rate, which then decreases infinitesimally (Talman and Nesbitt, 1988). Under this scenario, the rate of dissolution will not become completely linear as long as two or more phases having significantly different free energies are present within

OXIDE AND SILICATE DISSOLUTION KINETICS

175

the sample. With sufficient removal of surface material, linear rates, measured per unit of surface area, should be observed. Thus, for a naturally weathered olivine, separated from a beach sand of an undetermined age, the rate of dissolution was linear (Grandstaff, 1986). Precipitate layer and leached layer dissolution mechanisms can also cause nonlinear dissolution rates. The precipitate layer hypothesis proposes that a more or less coherent, contiguous layer of secondary product precipitates on the reactant surfaces of the mineral that is dissolving. Consequently, reactants released from the surface must diffuse through the precipitate layer to reach the bulk solution. As the layer thickens, the diffusional path lengthens, and the integrated rate of diffusion decreases. If the integrated rate of diffusion of reaction products from the surface is lower than the rate of reaction at the surface of the primary mineral, then the dissolution reaction becomes diffusion controlled. Although the precipitate layer can explain the observed nonlinearity, it has been discounted by most researchers because avoidance of the formation of secondary products by maintenance of undersaturation with respect to secondary phases does not eliminate nonlinear kinetics (Chou and Wollast, 1984). The importance of secondary phase formation on dissolution rates under field conditions has also been discounted by many researchers (Berner and Holdren, 1979). Electron microscope studies (Wyart et al., 1963; Berner and Holdren, 1979) of mineral surfaces weathered in soil and geologic environments have provided almost no evidence for the presence of a coherent precipitate layer capable of providing such a diffusional barrier. One possible exception is the weathering of Fe-bearing minerals in well-oxidized solutions for which thin Fe (hydr)oxide layers have been observed (Schott and Berner, 1983). The clay and oxide coatings commonly observed on mineral surfaces in soils are typically patchy and well-hydrated. Although the rate of diffusion of reaction products through these materials is slower than through pure aqueous solutions, the diffusion rates are still faster than the rate of release from the mineral surface (Berner, 1981) and therefore not rate limiting. The leached layer hypothesis proposes that one or more components of a mineral (usually charge-balancing cations such as Na, Ca, or K, and sometimes structural AI) are released to solution faster than the remaining components (Chou and Wollast, 1984). A leached residual layer, depleted in the more mobile components but still retaining some degree of structural integrity, forms on the mineral surface. The more mobile components of the mineral must then diffuse through the residual layer, which has a relative enrichment of silica and sometimes alumina, in order to reach the solution interface. As the reaction progresses, the leached layer thickens and the length of the cation diffusion path increases, causing a decrease in the rate of cation release and the overall reaction rate, thereby producing the observed nonlinear rates. While this mechanism has been verified for the dissolution of natural and manmade glasses (Lanford et aI., 1979; White, 1983), it has not conclusively been shown to occur in the dissolution of feldspars at pH levels (4-8) commonly found in soils. Spectroscopic analyses of the surfaces

176

BLOOM & NATER

of naturally and artifically weathered feldspars have shown that a leached layer thicker than one or two unit cells does not form under these pH conditions (Petrovic et aI., 1976; Holdren and Berner, 1979). Deep (120 nm) altered layers have been observed by Auger electron spectroscopy (AES) on the surfaces of hornblende naturally weathered at pH 5.1 (Mogk and Locke, 1988), although other x-ray photoelectron spectroscopic (XPS) studies of artifically weathered amphiboles and pyroxenes (Schott et al., 1981) have not shown alteration deeper than about 1.7 nm at pH 6.0. It seems more likely that a leached layer could form in the inosilicates, which have one-dimensional silicate chains held together by charge-balancing cations, than in the tectosilicates, which have a three-dimensional aluminosilicate framework. Surface-sensitive spectroscopies have identified altered surface layers on feldspars weathered at pH levels higher than 8 or lower than 4 (Casey et al., 1989a; Hochella et al., 1988; Hellman et al., 1990). Over the last few years, researchers have shown that many cases of nonlinear dissolution kinetics are caused by artifacts of sample preparation. Holdren and Berner (1979) found that particles < I-J.tm diam. disappeared rapidly during weathering, with a corresponding decrease in the initially high rate of dissolution. They found that washing feldspar samples for 5 min in 0.5 M HF removed the fine particles and produced linear dissolution kinetics. However, others (Perry et aI., 1983) have shown that fluoride ions penetrate the mineral structure and may significantly affect the kinetics of dissolution, so this pretreatment has generally been abandoned. Petrovich (1981a) demonstrated that damaged sites were produced during sample grinding and contributed to increased initial rates of dissolution. Eggleston et al. (1989) found that damaged sites apparently underwent a slow annealing or self-healing process during several months of storage, thus decreasing the initial dissolution rates. Other sample pretreatments (sonification, washing in water, acetone, or acid) also produced significantly different initial dissolution rates, but these differences also disappeared rapidly, as the rates observed after 50 to 100h of weathering were the same for all sample pretreatments (Eggleston et al., 1989).

Incongruence Initial dissolution of primary silicates is typically incongruent; that is, the stoichiometric ratio of elements released to solution is not the same as that found in the bulk phase of the mineral. An excellent example of incongruent dissolution (Fig. 7-13) is presented by Chou and Wollast (1984). They reacted albite with aqueous solutions in a fluidized bed reactor and maintained solution concentrations of the reaction products below saturation for potential secondary products. Even so, the molar ratio of Na/Si initially released to solution was almost an order of magnitude higher than that of the bulk albite. Dissolution incongruence has posed a particularly difficult theoretical problem for researchers working on mineral dissolution problems. Incongruence has been fully or at least partially attributed to the following mechanisms:

177

OXIDE AND SILICATE DISSOLUTION KINETICS 100 r - - - - - - - - - - - - - - - - - - - - - ,

e

Gi E 10 o

•• •

:cu

~ s o

~

~

• ••• • • • ~

n

~

~

o

a: -

.1

~_~

o

0

0

1 "'"'00 u

_ _........._ _ 100

•

~

AI

Na

Stoichiometry __

~_--l.

200

~_----'

300

Time (h)

Fig. 7-13. Incongruent dissolution occurring during the initial dissolution of albite in pH 5.1 HCI in a continuous flow fluidized bed reactor. Reaction product concentrations were maintained below saturation for all secondary phases (data from Chou and Wollast, 1984.)

1. Rapid, initially reversiblehydrolysis and exchange of charge-balancing cations in the outermost surface layer (approximately one or two unit cells thick) for hydronium ions (Nash and Marshall, 1954; Garrels and Howard, 1959). 2. Formation of secondary precipitates (Lagache, 1961a,b; Holdren and Berner, 1979; Petrovic et aI., 1976; Schott and Berner, 1983; Wyart et al., 1963; Parham, 1969). 3. Formation of a leached layer (Chou and Wollast, 1984). 4. Formation of highly hydrated, thread-like remnants of the silicate framework (Tazaki and Fyfe, 1987; Nater and Bouabid, 1990). 5. Presence, in some instances, of two or more phases having different compositions (Gardner, 1983; Inskeep et aI., 1991). 6. Hydration along crystallographic planes of weakness and the release or exchange of ions (Petit et aI., 1987; Schott and Petit, 1987). It is widely accepted that a portion of the incongruence is due to the initial exchange of charge-balancing cations for hydronium ions (Eq. [15] and [16]) or other cations (Nash and Marshall, 1956; Garrels and Howard, 1959). For alkali feldspars, the exchange appears to affect only the outermost layer of cations. For anorthite, the inosilicates, and some other minerals, however, the exchange reaction may involve more than one or two unit cells, but the depth of removal is commonly no more than 1.5 to 3.0 nm. Mechanisms 2,3, and 4 above all depend on the formation of some type of secondary solid phase, such as a precipitate or altered surficial material, having a composition different from that of the bulk mineral. The three mechanisms described, however, each affect the mechanism and kinetics of dissolution in different ways. Nearly all researchers agree that the precipitation or formation of secondary phases ill the dominant mechanism causing incongruence in natural

178

BLOOM & NATER

systems that become oversaturated with respect to secondary minerals. Precipitation, however, cannot explain the incongruence observed in laboratory experiments where solution ion activity products have been maintained below saturation for most potential secondary products. It is difficult to imagine how precipitates form under these conditions. Secondary precipitates are commonly observed in laboratory studies of Fe-bearing minerals due to the low solubility of Fe3+ (hydr)oxides. Some researchers contend that the dissolution reaction occurs via a leached layer mechanism as discussed in the previous section. Surface-sensitive spectroscopies such as XPS (Petrovic et al., 1976; Holdren and Berner, 1979), secondary ion mass spectroscopy (SIMS) (Beusen and Gijbels, 1983), and solid-state nuclear magnetic resonance (NMR) spectroscopy (Yang and Kirkpatrick, 1989) have failed to produce evidence of leached layers thicker than about 0.5 to 1.5 nm on feldspars (with the exception of labradorite, which will be discussed later) weathered in the pH range of 4 to 8, eventhough the dissolution reaction was clearly incongruent. The incongruence observed is sufficient to account for a uniform leached layer from 3 to > 10 nm, depending on reaction conditions. Because these techniques have relatively low lateral resolution (spot sizes range from a few I-tm to several mm in diameter), it has been hypothesized (Chou and Wollast, 1985b) that the leached layers form only over the most reactive sites, and thus could not be observed. Recent studies have shown the formation of altered surface layers thicker than one or two unit cell layers on feldspar surfaces, in apparent support of the leached layer theory. Thick (> 100 nm), silica-rich surface layers were detected by XPS on feldspar samples weathered in solutions having pH < 3 (Caseyet aI., 1988b) or >9 (Hellman et al., 1990). At these extreme pH values, the rate of release of Al and charge-balancing cations to solution is much faster than the rate of hydrolysis of silica. Under these conditions, oversaturation with respect to amorphous silica could occur, and a highly hydrated, residual leached or precipitated layer of silica could form. However, this layer is probably too porous and discontinuous to be a diffusion-limiting mechanism, but would still account for incongruence under these conditions (Hellmann et al., 1990). Whether the altered layer formed by a leached layer process or by simple precipitation from oversaturated solutions was not determined. Hydrated remnants of the aluminosilicate structure of feldspars have been observed in naturally weathered (Tazaki and Fyfe, 1987) and laboratoryweathered (Nater and Bouabid, 1990) samples through the use of ultrahigh resolution transmission electron microscopy (Fig. 7-14). Feldspar lattice planes at crystal edges expand from 1.4 to 1.7-2.0 nm upon hydration. Thread-like structures also form, apparently by loss of charge-balancing cations and solid-state transformations of Si and Al structures (See Tazaki and Fyfe, 1987). Only a small portion of the surface is affected, however, the majority of the surface displays unexpanded lattice images extending to the very edge of the crystal. It is possible that hydrated lattices and threads form on the surfaces of members of other silicate groups, particularly the inosilicates, but they have not been observed so far.

OXIDE AND SILICATE DISSOLUTION KINETICS

179

The presence of two or more phases in a mineral sample will produce incongruent dissolution with respect to the bulk composition of the mineral if the two phases have significantly different rates of dissolution, even if each phase dissolves congruently with respect to its own composition (Gardner, 1983; Inskeep et al., 1991). This mechanism has been overlooked by most researchers, but is particularly important in feldspars, where several large miscibility gaps occur and perthites, antiperthites, peristerites, Huttenlocher intergrowths, and Beggild intergrowths readily form (Ribbe, 1983). These

Fig. 7-14. Lattice images of the edge of a weathered microcline grain removed from a lateritic crust, I1ha Bela, Brazil. Note the curved, expanded lattices (1.67 to 2.0 nm d-spacings) of the hydrated frinlleH compared to the straight, unexpanded lattices (0.74 and 1.43 nm) of the nonhydrated mlnerul (reprinted with permission from Tazaki and Fyfe, 1987, Copyright 19117, (anad/an J",mlll/lIll·:(/rth Sciences).

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500nm

Fig. 7-15. The "corrugated" surface produced during weathering of labradorite (AnS4) due to the more rapid weathering of the more calcic lamellae. Beggild intergrowths (mostly 75-85 nm thick) are clearly visible (from Inskeep et al., 1991).

exsolved phases have exsolution lamellae that vary in thickness from as little as 2 to 4 nm to more than 250 nm, depending on melt composition, temperature of crystallization, and rate of cooling. The composition of the different lamellae affects their individual dissolution rates. In labradorite, for example, the more calcic phase appears to dissolve about four times faster than the more sodic phase (Inskeep et al., 1991), thus causing incongruent dissolution and producing a "corrugated" surface on the weathered grains (Fig. 7-15). Although little is currently known about the overall contribution of exsolved phases to incongruence, it is probably more important than has been previously recognized. Several researchers have reported the apparent formation of thick layers (> 50 nm) of altered composition on the surface of labradorite using scanning AES (Hochella et al., 1988; Caseyet al., 1989a), XPS, and SIMS (Muir et al., 1989; Inskeep et al., 1991). Almost all labradorites have exsolution lamellae, however, because their compositional range falls in the middle of a large miscibility gap in the plagioclase series (Ribbe, 1983). As discussed, differential weathering of the more calcic and more sodic phases produces a corrugated surface. The systemic elevation of the more sodic phase above the more calcic phase introduces a significant bias into AES and XPS analyses that mimics the development of a thick uniform leached layer (Inskeep et al., 1991). A well-known example of hydration along crystallographic planes of weakness and the consequent exchange or release of components along those planes occurs during the weathering of micas, where K or other cations are released from the interlayers by hydration, exchange, and charge-reduction processes. Recent studies of laboratory-weathered albite and diopside using hydrogen depth profiling by resonant nuclear reaction (Petit ct aI., 1987;

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Schott and Petit, 1987) have demonstrated that water penetrates these mineral structures to a depth of approximately 100 nm within 75 d. Secondary ion mass spectrometry showed that all elements, with the exception of Fe, were slightly depleted (nearly congruently) to depths up to 150 nm. No clear relationship was evident between the penetration of water and the loss of cations and other constituents of the mineral, although they must surely be related. Only a slight relative depletion of Ca with respect to Si to a 1.5-nm depth was observed on the surface, even though the surface and near surface structure had obviously been altered. The reaction producing the loss of material appears to be the penetration of molecular water into the crystal along linear dislocations and twinning planes and the resultant nearly congruent dissolution of material along those planes. The Monte Carlo simulation of dissolution of Blum and Lasaga (1987) predicts rapid penetration of water and the concurrent dissolution of materials along dislocation cores due to strain energy. Change in Surface Area The weathering of freshly ground primary aluminosilicates causes an increase in the BET-Ng-measured surface area of the sample (Grandstaff, 1978; Caseyet al., 1989b). Grandstaff (1978) observed a four-fold increase in the surface area of forsterite grains during the first 120 h of reaction in a pH 2.6, 0.1 M acetic acid-sodium acetate buffer solution. Scanning electron micrographs of the weathered forsterite grains showed the presence of large numbers of etch pits and other features associated with surface-controlled reaction mechanisms. Grandstaff (1978) attributed the increase in surface area to increasing surface roughness. Although a very limited quantity of secondary, clay-sized particles were observed on the surface, it was not sufficient to account for the observed increase in surface area. The surface area of labradorite increased by a factor of 30 after 318 h of reaction in pH 2.0 HCl solution (Casey et al., 1989b). The increased surface area observed under these low pH conditions resulted from the formation of a highly porous, short-range ordered polymeric Si-O precipitate several tens of nanometers thick on the surface of the feldspar. Calculations made using the adsorption/desorption isotherms indicated that most of the pores had radii between 2.0 and 8.0 nm. Because thick Si-O layers are not observed on samples that have been weathered at pH > 4.0, the results of this study probably have little applicability to natural soil systems. Zhang et al. (1989) showed a three-fold increase in the surface area of hornblende after weathering for 40 d in pH 4.0, 0.01 M acetic acid-lithium acetate buffer due to the formation of etch pits. The BET-N2 adsorption/desorption isotherms of the weathered material showed pronounced hysteresis (Zhang, Bloom, and Nater, 1990, unpublished data). Analysis of the isotherms showed that some of the N2 was absorbed in pores having radii between 1 and 13 nm, indicating that narrow, apparently deep pores formed during the 59 d of weathering. These results appear to be in general agreement with hydrogen depth profiling results of Petit et al. (1987) for di-

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opside, which showed the formation of deep (100 nm) hydration pits after 75 d of weathering.

SUMMARY AND CONCLUSIONS The rate-controlling step for dissolution of an oxide or primary silicate mineral generally involves a surface reaction. For surface-controlled dissolution, the rate-controlling step is either the detachment of silica or a metal ion from the surface or the attack of the surface to form precursor sites for detachment. Surface detachment controlled kinetics can be modelled using the surface complexation rate model (Wieland et al., 1988) that models rates as a function of the surface concentration of surface complexation sites that are precursors for dissolution. In this model, the formation of precursor sites is rapid compared to the rate of detachment and the concentration of sites can be described by surface complexation theory (Sposito, 1983). The surface complexation rate model explains the partial orders often observed for the effects of H +, OH -, and ligand concentrations on dissolution rates. There is, however, some debate about the nature of precursor sites. For oxides, Stumm and coworkers (Stumm and Furrer, 1987) have shown that in order to form a precursor site in the pH range of 4 to 6, the number of protons adsorbed at a precursor site should be the number required to form a free metal ion, e.g., three H + for AI. Carrol-Webb and Walther (1988) argue that the precursor sites for Al z0 3 involve only one proton at each site. Blum and Lasaga (1989) have drawn a similar conclusion about the acid-mediated dissolution of olivine and albite. The OH - -mediated dissolution of silicates, including quartz, at pH > 8 is generally first-order with respect to the number of OH - adsorption sites. This results in reaction rates that are about O.3-order with respect to [OH "]. Many dissolution reactions, however, are not dependent on adsorbed H + or OH -, but are first-order with respect to solution concentrations of these ions. Examples of reactions that are first-order with respect to [H +] include: feldspar dissolution at pH < 2.9; nepheline dissolution in the pH range of 3 to 6; and the dissolution of naturally weathered olivine (Grandstaff, 1986). The results of Grandstaff (1986) for olivine contradict the previously mentioned conclusions of Blum and Lasaga (1989) concerning a first-order dependence on H + adsorption sites for freshly crushed olivine. The dissolution of aluminum oxides and hydroxides is first-order with respect to [OH-] at pH >8. The dissolution of oxides and silicates in the presence of O-containing organic ligands that form bidentate complexes with surface metal ions is a function of the concentration of complexation sites on the surface. In some cases, the precursor site for detachment may involve protonation as well as surface complexation. Some data suggest that at high concentrations of ions that form strong surface complexes, the rate-controlling step may involve surface attack.

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Electrolytes, like KN03 , can strongly affect dissolution rates of oxides. At acid pH values, this effect is probably due to an increase in surface protonation when the pH is maintained constant and salt strength is increased. Silicate minerals dissolve preferentially at high energy sites, such as dislocations, abraded areas, or twinning planes, causing the formation of etch pits (Lasaga, 1981b). The relationship between surface area and dissolution rate is complex, and is dependent on surface reactivity: a function of the free energies and relative surface areas of different crystal faces; the abundance and type of surface defects present; sample treatment history; and other factors (Helgeson et aI., 1984). Because these characteristics vary widely for different samples, and even for different particle-size fractions of the same sample, dissolution rates may not necessarily be proportional to initial surface areas (Holdren and Speyer, 1987). Many of the problems observed during silicate mineral dissolution are related to artifacts of sample preparation. For example, the rate of dissolution of a freshly ground mineral sample decreases with time, even though its surface area increases. Sample grinding, especially dry grinding, produces numerous submicron-sized particles that adhere strongly to the mineral grain surface. These particles have excess surface energy resulting from very small interfacial radii, and thus dissolve more rapidly than the bulk of the mineral, increasing the initial rate of dissolution (Holdren and Berner, 1979). Because they reform bonds with the freshly cleaved surface, these particles are extremely difficult to remove from the surface except by harsh chemical treatments, which produce their own pretreatment artifacts. Grinding produces surface abrasion and associated bond disruption and bond strain (Petrovich, 1981). Abraded sites also have higher energy, and dissolve faster, than the bulk mineral. As these high energy sites and particles dissolve, they no longer contribute to the dissolution reaction, which decreases in rate causing the observed nonlinearity (Talman and Nexbitt, 1988). Abraded areas apparently can undergo a process of self-annealing, illustrated by the observation that the initial dissolution rates of ground samples decrease over a period of several months of storage in moisture-free conditions (Eggleston et aI., 1989). The initial dissolution of freshly ground silicates also tends to be incongruent, although most dissolution reactions attain a steady-state with essentially congruent dissolution after some time. One exception occurs in the dissolution of mineral samples containing exsolved phases of different composition (Inskeep et aI., 1991), where the dissolution reaction may remain congruent for more than a year (Erich and Bloom, 1987, unpublished data). During the initial stages of dissolution, H + exchanges for chargebalancing cations in the outermost one or two unit cell layers (Nash and Marshall, "956; Garrels and Howard, 1959), producing an altered layer generally no thicker than about 0.5 to 1.5 nm. The presence and thickness of this layer has been verified by XPS (Holdren and Berner, 1979), SIMS (Beusen and Gijbels, 1983), and solid state NMR (Yang and Kirkpatrick, 1989). Further incongruence, however, poses a difficult theoretical and analytical problem as il CUll he caused by several mechanisms. During the dissolution

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of feldspars at pH 4 to 9, the extent of incongruence (total disparity in reaction product concentrations) commonly observed before the reaction becomes congruent predicts the formation of a uniform cation-depleted surface layer from 3 to 10 or more nanometers thick, in general disagreement with surface spectroscopic data. The initially incongruent reaction indicates that material having a composition different from that of the bulk mineral is present on the surface at steady state. The nature of this surficial material is a matter of debate, but it appears relatively certain that it is not uniformly distributed across the surface of the mineral or it would be observed by XPS. The low lateral resolution of XPS, however, prevents detection of materials that do not cover more than about 5 % of the exposed surface area. Precipitation of secondary products explains most of the incongruence occurring in natural systems, but cannot explain that observed in laboratory experiments where solution concentrations are maintained below saturation for all secondary products. Some researchers have argued that a more or less structurally intact leached surface layer forms during weathering, and that it poses a diffusional barrier to further dissolution (Chou and Wollast, 1984). Although this argument explains both the nonlinear dissolution rates and incongruence, recent advances in the understanding of the role of high energy sites and particles in increasing initial dissolution rates offer a better explanation for the nonlinear rates. Leached surface layers may form at localized sites of dissolution because of differences in the rate of detachment of silica and the other components of the mineral. If the formation of leached layers is highly localized, as hypothesized by Chou and Wollast (l985b), their existence cannot be verified by current spectroscopic techniques. Samples weathered at pH values < 4 and > 9 do show the existence of uniform, thicker (up to a 100 nm or more) altered surface layers, but these are apparently so highly hydrated and porous that they do not present a diffusional barrier to continued dissolution of the sample (Casey et al., 1989b). High resolution TEM studies of weathering fragments of naturally and artifically weathered (pH = 4.5) feldspars, however, have shown the existence of highly hydrated weathering fragments (Tazaki and Fyfe, 1987; Nater and Bouabid, 1990). Because these fragments are highly hydrated, they may not form much of a barrier for diffusion in the near-surface region. Other evidence concerning surface hydration clearly indicates that water molecules penetrate deeply into surfaces, presumably in dissolution pits or along dislocations (Petit et al., 1987). Surface area studies with hornblende indicate the formation of numerous etch pits having diameters between 1 and 13 nm (Zhang, Bloom, and Nater, 1990, unpublished data).

REFERENCES Aagaard, P., and H.C. Helgeson. 1982. Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions. I. Theoretical considerations. Am. J. Sci. 282:237-285.

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Amrhein, C., and D.L.Suarez. 1.:. 1988. The use of a surface complexation model to describe the kinetics of ligand·~omottl~ted dissolution of anorthite. Geochim. Cosmochim. Acta 52:2785-2793. Bamford, C.H., and c.m. Tipripper. 1969. Comprehensive chemical kinetics, Vol. 2. The theory of kinetics. Elielier, N! New York. Bennett, P.C., M.E. Melcer, D .[]).I. Siegel, and J.P. Hassett. 1988. The dissolution of quartz in dilute aqueois solutb01lc:ms of organic acids at 25' C. Geochim. Cosmochim. Acta 52:1521-1530. Berner, R.A. 1981. Kincti~ ofwtw weathering and diagenesis. p, 111-134. In A.C. Lasaga and R.J. Kirkpatrick (ed.)Kin~icsof lof geochemical processes. Vol. 8, Reviews in mineralogy. Mineral. Soc., Washington,DC. Berner, R.A., and G.R,HoldreJl...en, Jr. 1979. Mechanism of feldspar weathering. II. Observations of feldsparirm soiIiCJOils. Geochim. Cosmochim. Acta 43:1173-1186. Berner, R.A., and J.Sc~ott.lQI 1982. Mechanism of pyroxene and amphibole weathering. II. Observations of soilgraio.s.,r-J,s. Am. J. Sci. 282:1214-1231. Beusen, J.-M., and RGijbels . . • . 1983. Alteration in the surface composition of some silicate minerals after hydrothermaIsoal treatment, studied by SIMS. p. 257-275. In S.S. Augustithis (ed.) Leaching andiliffusiolloion in rocks and their weathering products. Theophrastus Pub. S.A., Athens. Bloom, P.R. 1983. Ttelnetics 1) cs of gibbsite dissolution in nitric acid. Soil Sci. Soc. Am. J. 47:164-168. Bloom, P.R., and M.S,Erich.19Qr1987. Effect of solution composition on the rate and mechanism of gibbsite dissolution in ao, acid solutions. Soil Sci. Soc. Am. J. 51:1131-1136. Blum, A.E., and A.C.L~aga. 11_ 1988. Monte Carlo simulations of surface reaction rate laws. p. 255-292. In W.E.~tlll11lI1 OlJll (ed.) Aquatic surface chemistry. John Wiley & Sons, New York. Blum, A.E., and A.C.Lasaga.1 ~l 1988. Role of surface speciation in the low-temperature dissolution of minerals. Nature 33 t031 :431-433. Blum, A.E., R.A. Yund,and A..O.A.C. t.asasa. 1990. The effect of dislocation density on the dissolution rate of quartz. GeOllieochim. Cosmochim. Acta 54:283-297. Brady, P. V., and J .V. W~ther. I' I _ 1989. controls on silicate dissolution rates in neutral and basic pH solutions at 25'(, Geo-ceeochim. Cosmochim. Acta 53:2823-2830. Brantley, S.L., S.R. Crane, DAA_A. Crerar, R. Hellman, and R. Stallard. 1986. Dissolution at dislocation etch pitlin qU8l'lsaartz. Geochim. Cosmochim. Acta 50:2349-2378. Carroll-Webb, S.A., an~J.v." Walther. 1988. A surface complex reaction model for pHdependence of corunuum au and kaolinite dissolution rates. Geochim. Cosmochim. Acta 52:2609-2623. Casey, W.C., M.J. Can.ad R.N... A. Graham. 1988a. Crystal defects and the dissolution kinetics of rutile. Geochin.tosmoc» ochim. Acta 52:1545-1556. Casey, W .H., H.R. Westrich, anQn_TId G. W. Arnold. 1988b. Surface chemistry of labradorite feldspar reacted with a~ueo~1I : e s solutions at pH 2, 3, 12. Geochim. Cosmochim. Acta 52:2795-2807. Casey, W.H., H.R. We~rich, n.'.D.W. Arnold, and J.E. Banfield. 1989a. The surface chemistry of dissolving labradnrite felel,-eldspar. Geochim, Cosmochim. Acta 53:821-832. Casey, W.H., H.R. Westrich, T. I.~. Massis, J.F. Banfield, and G.W. Arnold. 1989b. The surface of labradorite felds~~ aflenl::er acid hydrolysis. Chern. Geol. 78:205-218. Chang, H., and E. Matij~ic. I~H::8g83. Interactions of metal hydrous oxides with chelating agents. IV. Dissolution onerrratile ..l.e. J. Colloid Interface Sci. 92:479-488. Chou, L., and R. Wollan 19~4. ,t4. Study of the weathering of albite at room temperature and pressure with a fluilired bed~d reactor. Geochim. Cosmochim. Acta 48:2205-2217. Chou, L., and R. Wollast.l~8SII ..si5a. Steady-state kinetics and dissolution mechanisms of albite. Am. J. Sci. 285:96~l93. Chou, L., and R. WoIJast.198Sh ..deb. Study of the weathering of albite at room temperature and pressure with a fludull! bell nJ=:l reactor. (Reply to a comment by R.A. Berner, G.R. Holdren, Jr., and J. Schott).Geochlrl'niaim. Cosmochim. Acta 49:1659-160. Colman, S.M., and D.P,Dethil!r ..l,er. 1986. Rates of chemical weathering of rocks and minerals. Academic Press, New York . ,. k. Cornell, R.M., A.M. Pomer, BIIl.I~ nd J.P. Quirk. 1974. Crystal morphology and the dissolution of geothite. J. InorjNud, •.•. Chern. 36: 1937-1946. Correns, C.W., and W.vonEnsC'lIbselhardt. 1938. Neue untersuchungen uber die verwitterung des kallfeldspate». Chem,Erd~ II~ 12:1-22.

=

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Dibble, W.E., Jr., and W.A. Tiller. 1981. Non-equilibrium water/rock interactions-I. Model for interface-controlled reactions. Geochim. Cosmochim. Acta 45:79-92. Drever, J.I. 1985. The chemistry of weathering. D. Reidel, New York. Eggleston, C.M., M.F. Hochella, Jr., and G.A. Parks. 1989. Sample preparation and aging effects on the dissolution rate and surface composition of diopside. Geochim. Cosmochim. Acta 53:797-804. Fung, P .C., and G .G. Sanipelli. 1982. Surface studies of feldspar dissolution using surface replication combined with electron microscopic and spectroscopic techniques. Geochim. Cosmochim, Acta 46:503-512. Furrer, G., and W. Stumm. 1986. The coordination chemistry of weathering: I. Dissolution kinetics of o-A120 3 and BeO. Geochim. Cosmochim. Acta 50:1847-1860. Gardner, L.R. 1983. Mechanics and kinetics of incongruent feldspar dissolution. Geology 11:418-421. Garrels, R.M., and P. Howard. 1959. Reactions of feldspar and mica with water at low temperature and pressure. Clays Clay Miner. 6:68-88. Ghabru, S.K., A.R. Mermut, and R.J. St. Arnaud. 1989. Characterization of garnets in a Typic Cryoboralf (Gray Luvisol) from Saskatchewan, Canada. Soil Sci. Soc. Am. J. 53:575-582. Grandstaff, D.E. 1977. Some kinetics of bronzite orthopyroxene dissolution. Geochim. Cosmochim. Acta 41:1097-1103. Grandstaff, D.E. 1978. Changes in surface area and morphology and the mechanism of forsterite dissolution. Geochim. Cosmochim. Acta 42:1899-1901. Grandstaff, D.E. 1986. The dissolution rate of forsteritic olivine from Hawaiian beach sand. p. 41-59. In S.M. Colman and D.P. Dethier (ed.) Rates of chemical weathering of rocks and minerals. Academic Press, New York. Hayes, K.F., and J.O. Leckie. 1987. Modelling ionic strength effects on cation adsorption at hydrous oxide/solution interfaces. J. Colloid Interface Sci. 115:564-572. Helgeson, H.C., W.M. Murphy, and P. Aagaard, 1984. Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solution. II. Rate constants, effective surface area, and hydrolysis of feldspar. Geochim. Cosmochim. Acta 48:2405-2432. Hellmann, R., C.M. Eggleston, M.F. Hochella, J. Crerar, and D.A. Crerar. 1990. The formation of leached layers on albite surfaces during dissolution under hydrothermal conditions. Geochim. Cosmochim. Acta 54:1267-1282. Henin, S., and G. Pedro. 1965. The laboratory weathering of rocks. p. 29-39. In E.G. Hallsworth and D.V. Crawford (ed.) Experimental pedology. Butterworths, London. Hochella, M.F., Jr., H.B. Ponader, A.M. Turner, and D.W. Harris. 1988. The complexity of mineral dissolution as viewed by high resolution scanning Auger microscopy: Labradorite under hydrothermal conditions. Geochim. Cosmochim. Acta 52:385-394. Holdren, R.G., Jr., and R.A. Berner. 1979. Mechanism of feldspar weathering. I. Experimental studies. Geochim. Cosmochim. Acta 43:1161-1171. Holdren, R.G., Jr., and P.M. Speyer. 1985. Reaction rate-surface area relationships during the early stages of weathering - I. Initial observations. Geochim. Cosmochim. Acta 49:675-681. Holdren, R.G., Jr., and P.M. Speyer. 1987. Reaction rate-surface area relationships during the early stages of weathering - II. Data on eight additional feldspars. Geochim. Cosmochim. Acta 51:2311-2318. Holdren, R.G., Jr., W.H. Casey, H.R. Westrich, M. Carr, and M. Boslough. 1988. Bulk dislocation densities and dissolution rates in a calcic plagioclase. Chern. Geology 70:79. Huang, W.H., and W.D. Keller. 1970. Dissolution of rock-forming silicate minerals in organic acids: Simulated first-stage weathering of fresh mineral surfaces. Am. Mineral. 55:2074-2094. Huang, W.H., and W.C. Kiang. 1972. Laboratory dissolution of plagioclase ft;jdspars in water and organic acids at room temperatures. Am. Mineral. 57:1849-1859. Inskeep, W.P., E.A. Nater, P.R. Bloom, D. Vandervoort, and M.S. Erich. 1991. Characterization of laboratory weathered labradorite surfaces using x-ray photoelectron spectroscopy and transmission electron microscopy. Geochim. Cosmochim. Acta 55:787-800. Jergensen, S.S. 1976. Dissolution kinetics of silicate minerals in aqueous catechol solutions. J. Soil Sci. 27:183-195. Lagache, M., J. Wyart, and G, Sabatier. 1961a. Dissolution des feldspaths alcalins dans I'eau pure ou chargee de CO 2 a 200· C. C.R. Seances Acad. Sci. Ser. 2. 253:2019-2022.

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Lagache, M., J. Wyart, and G. Sabatier. 1961b. Mechanisme de la dissolution des feldspaths alcalins dans l'eau pure ou chargee de CO 2 a 200· C. C.R. Seances Acad. Sci., Ser. 2. 253:2296-2299. Lanford, W.A., K. Davis, P. Lamarche, T. Laursen, R.J. Groleau and R.H. Doremus. 1979. Hydration of soda-lime glass. J. Non-Cryst, Solids 33:249-266. Lasaga, A.C. 1981a. Transition state theory. p. 135-169. In A.C. Lasaga and R.J. Kirkpatrick (ed.) Kinetics of geochemical processes. Vol. 8, Reviews in Mineralogy. Mineral. Soc. Am., Washington, DC. Lasaga, A.C. 1981b. The atomistic basis of kinetics: Defects in minerals. p. 261-319. In A.C. Lasaga and R.J. Kirkpatrick (ed.) Kinetics of geochemical processes. Vol. 8, Reviews in mineralogy. Mineral. Soc. Am., Washington, DC. Manley, E.P., and L.J. Evans. 1986. Dissolution of feldspars by low-molecular weight aliphatic and aromatic acids. Soil Sci. 106-112. Mast, M.A., and J.1. Drever. 1987. The effect of oxalate on the dissolution rates of oligoclase and tremolite. Geochim. Cosmochim. Acta 51:2559-2568. McBride, M.B. 1989. Surface chemistry of soil minerals. p. 35-88. In J .B. Dixon and S.B. Weed (ed.) Minerals in soil environments. Soil Sci. Soc. Am. Book Ser. I, SSSA, Madison, WI. McKenzie, R.M. 1989. Manganese oxides and hydroxides. p. 439-466. In J.B. Dixon and S.B. Weed (ed.) Minerals in soil environments. Soil Sci. Soc. Am. Book Ser. I, SSSA, Madison, WI. Mogk, D.W., and W.W. Locke, III. 1988. Application of Auger electron spectroscopy (AES) to naturally weathered hornblende. Geochim. Cosmochim. Acta 52:2537-2542. Muir, I.J., G.M. Bancroft, and H. W. Nesbitt. 1989. Characteristics of altered labradorite surfaces by SIMS and XPS. Geochim. Cosmochim. Acta 53:1235-1241. Murphy, W.M. 1988.Dislocationsand feldspar dissolution: Theory and experimental data. Chern. Geology 70:163. Murphy, W.M., and H.C. Helgeson. 1987a. Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions. III. Activated complexes and the pHdependence of the rates of feldspar, pyroxene, wollastonite, and olivine hydrolysis. Geochim. Cosmochim. Acta 51:3137-3153. Murphy, W.M., and H.C. Helgeson. 1987b. Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions. IV. Retrieval of rate constants and activation parameters for the hydrolysis of pyroxene, wollastonite, olivine, andalusite, quartz, and nepheline. Am. J. Sci. 289:17-101. Nash, V.E., and C.E. Marshall. 1956. The surface reactions of silicate minerals. I. The reactions of feldspar surfaces with acidic solutions. Missouri Univ. Agric. Exp. Stn. Res. Bull. 613. Nater, E.A., and R. Bouabid. 1990. Micromorphology of the initial weathering products of feldspars. p. 525-530. In L. Douglas (ed.) Soil micromorphology: A basic and applied science, Vol. 19, Developments in soil science. Elsevier, New York. Nater, E.A., and P.M. Huang. 1988. The effect of organic acids on the kinetics of microcline weathering. p. 202. In Agronomy Abstracts, ASA, Madison, WI. Nielsen, J.W. 1964. Kinetics of precipitation. Macmillan Co., New York. Packer, A., and H.S. Dhillon. 1968. Reactions of aluminum hydrate powders with aqueous sodium hydroxide solutions. Chern. Ind. (London) 1968:1806-1807. Parham, W.E. 1%9. Formation of halloysite from feldspar: Low temperature, artificial weathering versus natural weathering. Clays Clay Miner. 17:13-22. Parks, G.A. 1967. Aqueous surface chemistry of oxides and complex oxide minerals: Isoelectric point and zero point of charge. p. 121-160. In R.F. Gould (ed.) Equilibrium concepts in natural water systems. Vol. 67. Advances in Chemistry Series, ACS, Washington, DC. Perry, D.L., L. Tsao, and K.A. Gaugler. 1983. Surface study of HF- and HF/H2S04-treated feldspar using Auger electron spectroscopy. Geochim. Cosmochim. Acta 47:1289-1291. Petit, J.-C., G.D. Mea, J.-C. Dran, J. Schott, and R.A. Berner. 1987. Mechanism of diopside dissolution from hydrogen depth profiling. Nature 325:705-707. Petrovic, R., R.A. Berner, and M.B. Goldhaber. 1976. Rate control in dissolution of alkali feldspars. I. Study of residual feldspar grains by x-ray photo-electron spectroscopy. Geochim. Cosmochim. Acta 40:537-548. Petrovich, R. 1981. Kinetics of dissolution of mechanically comminuted rock-forming oxides and silicates - I. Deformution and dissolution of quartz under laboratory conditions. Geochim. Cosmochim. Aclu 4~:16ti5-1674.

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Pulfer, K., P.W. Schindler, J.C. Westall, and R. Grever. 1984. Kinetics and mechanism of dissolution of bayerite (oy-AI(OH 3» in HNOrHF solutions at 298.2° K. J. Colloid Interface Sci. 101 :555-564. Ribbe, P .H. 1983. Exsolution textures in ternary and plagioclase feldspars; Interference colors. p. 241-270. In P.H. Ribbe (ed.) Feldspar mineralogy. 2nd ed. Vo!. 2. Reviews in mineralogy. Mineralogical Society of America, Washington, DC. Robert, M., and J. Berthelin. 1986. Role of biological and biochemical factors in soil mineral weathering. p. 453-495. In P.M. Huang and M. Schnitzer (ed.) Interactions of soil minerals with natural organics and microbes. SSSA Spec. Pub!. No. 17, SSSA, Madison, WI. Schott, J., R.A. Berner, and E.L. Sjoberg. 1981. Mechanisms of pyroxene and amphibole weathering. I. Experimental studies of iron-free minerals. Geochim. Cosmochim. Acta 45:2133-2135. Schott, J., and R.A. Berner. 1983. X-ray photoelectron studies of the mechanism of iron silicate dissolution during weathering. Geochim. Cosmochim. Acta 47:2233-2240. Schott, J., and R.A. Berner. 1985. Dissolution mechanisms of pyroxenes and olivines during weathering. p. 35-53. In J.1. Drever (ed.) The chemistry of weathering. D. Reidel, New York. Schott. J., and J.-C. Petit. 1987. New evidence for the mechanisms of dissolution of silicate minerals. p. 293-315. In W.E. Stumm (ed.) Aquatic surface chemistry. John Wiley & Sons, New York. Scotford, R.F., and J.R. Glastonbury. 1972. The effect of concentration on the rates of dissolution of gibbsite and boehmite. Can. J. Chern. Eng. 50:754-759. Siegel, 0.1., and H.O. Pfannkuch. 1984. Silicate mineral dissolution at pH 7 and near standard temperature and pressure. Geochim. Cosmochim. Acta 48:197-201. Smyth, J. 1989.Electrostatic characterization of oxygen sites on minerals. Geochim. Cosmochim. Acta 53:1101-1110. Sparks, D.L. 1989. Kinetics of soil chemical processes. Academic Press, New York. Sposito, G. 1983. On the surface complexation model of oxide-aqueous solution interface. J. Colloid Interface Sci. 91:329-340. Stone, A.T. 1986. Adsorption of organic reductants and subsequent electron transfer on metal oxide surfaces. p. 446-461. In J.A. Davis and K.F. Hayes (ed.) Geochemical processes at mineral surfaces. ACS Symp. Ser. 323, ACS, Washington, DC. Stone, A.T. 1987. Reductive dissolution of manganese (III/IV) oxides by substituted phenols. Environ. Sci. Techno!. 21:979-988. Stone, A.T., and J.J. Morgan. 1984. Reduction and dissolution of manganese(lII) and manganese(IV) oxides by organics. 1. Reaction with hydroquinone. Environ. Sci. Techno!. 18:450-456. Stone, A.T., and J.J. Morgan. 1987. Reductive dissolution of metal oxides. P. 221-254. In W.E. Stumm (ed.) Aquatic surface chemistry. John Wiley & Sons, New York. Stumm, W.E. (ed.). 1987. Aquatic surface chemistry. Wiley Interscience, John Wiley & Sons, New York. Stumm, W.E., and G. Furrer. 1987. The dissolution of oxides and aluminum silicates; Examples of surface-coordination-controlled kinetics. p. 197-219. In W.E. Stumm (ed.) Aquatic surface chemistry. Wiley Interscience, John Wiley & Sons, New York. Stumm, W.E., and J.J. Morgan. 1981. Aquatic chemistry. 2nd ed. John Wiley & Sons, New York. Stumm, W., G. Furrer, E. Wieland, and B. Zinder. 1985. The effects of complex-forming ligands on the dissolution of oxides and aluminosilicates. p. 55-74. In J.1. Drever (00.) The chemistry of weathering. D. Reidel, The Netherlands. Surana, V.S., and I.H. Warren. 1969. The leaching of geothite. Min. Metal!. C. 78:C133-139. Talman, S.J., and H.W. Nesbitt. 1988. Dissolution of populations of ultrafine grains with application to feldspars. Geochim. Cosmochim. Acta 52:1467-1471. Tazaki, K., and W.S. Fyfe. 1987. Primitive clay precursors formed on feldspar. Can. J. Earth Sci. 24:506-527. Tole, M.P., A.C. Lasaga, C. Pantano, and W.B. White. 1986. The kinetics of dissolution of nepheline (NaAISi04 ) . Geochim. Cosmochim. Acta 50:379-392. Velbel, M.A. 1984. Natural weathering mechamisms of almandine garnet. Geology 16:631-634. White, A.F. 1983. Surface chemistry and dissolution kinetics of glassy rocks at 25°C. Geochim. Cosmochim. Acta 47:805-815. Wieland, E., B. Wehrl, and W. Stumm. 1988. The coordination chemistry of weathering: Ill. A generalization on the dissolution of minerals. Geochim. Cosmochlm. Acta 52:1969-1981.

OXIDE AND SILICATE DISSOLUTION KINETICS

189

Wilson, M.J. 1975. Chemical weathering of some primary rock-forming minerals. Soil Sci. 119:349-355. Wollast, R. 1967. Kinetics of the alteration of K-feldspar in buffered solutions at low temperature. Geochim. Cosmochim. Acta 31:635-648. Wyatt, J., A. Oberlin, and C. Tchoubar, 1963. Etude en microscopie et microdiffraction electroniques de la boehmite formee lors de I'alteration de l'albite. C.R. Seances Acad. Sci., Ser. 2. 256:554-555. Yang, W.-H.A., and R.J. Kirkpatrick. 1989. Hydrothermal reaction of albite and a sodium aluminosilicate glass: A solid-state NMR study. Geochim. Cosmochim. Acta 53:805-819. Zhang, H., P.R. Bloom, and E.A. Nater. 1989. Surface area and hornblende weathering. p, 323. In Agronomy Abstracts, ASA, Madison, WI. Zhang, H., P.R. Bloom, and E.A. Nater. 1990. Morphology and chemistry of hornblende dissolution products in acid solutions. p, 551-556. In L. Douglas (ed.) Soil micromorphology: A basic and applied science, Vol. 19, Developments in soil science. Elsevier, New York. Zinder, B., G. Furrer, and W. Stumm. 1986. A coordination chemical approach to the kinetics of weathering. II. Dissolution of Fe(lII) oxide. Geochim. Cosmochim. Acta 50:1861-1869. Zutic, V., and W. Stumm. 1982. On the role of surface complexation in weathering reactions. Dissolution kinetics of hydrous alumina in the presence of organic ligands. p. 613-621. In H. van Olphen and F. Verniale (ed.) Int. Clay Conf. 1981. Developments in sedimentology, Vol. 35. Elsevier, New York.

8

Kinetics of Redox Reactions on Manganese Oxides and Its Impact on Environmental Quality P. M. Huang

Department of Soil Science University of Saskatchewan Saskatoon, Saskatchewan, Canada

ABSTRACT Manganese oxides are very reactive components in soils and associated environments. The objective of this chapter is to integrate the existing information on the kinetics of redox reactions on the surface of Mn oxides pertaining to transformations of certain metalloids, metals, and organics common in soils and sediments. Manganese oxides can oxidize the toxic As(III) to the less toxic As(V). The rate constants of Mn oxides to deplete As(III) vary with their crystallinity, specific surface, point of zero charge, and surface coatings. Trace metals such as Cr(Ill), Pu(III), and Co(III) have been shown to be oxidized by Mn oxides. Oxidation of trace metals can substantially influence their solubility, mobility, and toxicity. Further, the oxidation of Fe(II) by Mn oxides has been proven. Manganese oxides, which have different structural and surface properties, differ in their ability to influence the crystallization processes of hydrolytic products of Fe. The surface of Mn oxides catalyzes the oxidative polymerization of many polyphenolics, the polycondensation of pyrogallol and glycine, and the formation of humic substances. The rate and degree of the abiotic polymerization of phenolic compounds varies with the kinds of Mn oxides, the chemistry of phenolic compounds, and the pH of the systems. Many organics can be oxidatively decomposed during the reduction of Mn oxides that can lead to the mobilization of Mn in nature. The kinetics and mechanisms of these redox reactions on the surfaces of Mn oxides, thus, deserve increasing attention in the study of soil and environmental quality.

The oxide and oxyhydroxide minerals of Mn are widely distributed in soils and sediments (Jenne, 1968; McKenzie, 1989). In terrestrial and aquatic environments, Mn oxides and oxyhydroxides occur as coatings on other soil and sediment particles and as discrete particles; they exist in close associaCopyright © 1991 Soil Science Society of America, 677 S. Segoe Rd., Madison, WI 53711, USA. Rates of Soil Chemica! Processes. SSSA Special Publication no. 27. 191

HUANG

192

tion with many other chemical species (Hem, 1978; Taylor and McKenzie, 1966; Crerar and Barnes, 1974; McKenzie, 1989). Manganese oxides and oxyhydroxides are very reactive components of natural environments. They strongly sorb many ions and playa very important role in many redox reactions. Manganese oxides promote the oxidation of As(III) (Oscarson et aI., 1981a, 1983a), Cr(lll) and Pu(III) (Amacher and Baker, 1982), Co(ll) (Murray and Dillard, 1979; Dillard and Schenck, 1986) and possibly other trace metals (Hem, 1978). The oxidation of metalloids and trace metals can substantially influence their solubility, mobility, and toxicity. They also substantially influence the formation of Fe oxides and oxyhydroxides (Krishnamurti and Huang, 1987, 1988). Further, Mn oxides also catalyze the degradation of organics, the formation of humic substances and organic N complexes (Shindo and Huang, 1982, 1984a). The objective of this chapter is to integrate the existing information on the rates and processes of redox reactions on surfaces of Mn oxides pertaining to transformations of certain metalloids, metals, and organics common in soils and sediments. CONVERSION OF ARSENIC(III) TO ARSENIC(V)

Arsenic is a labile element present in all environmental substrates and it can exist in several oxidation states and forms in the environment (Ferguson and Gavis, 1972; Bramin and Foreback, 1973; Andreae, 1978). The biological availability and the toxicological effects of As depend on its chemical state (Webb, 1966; Ferguson and Gavis, 1972). Arsenite, As(III), is much more toxic than arsenate, As(V). Oscarson et al. (l981a) reported that birnessite, one of the most common Mn oxides in soils and sediments, is a very effective oxidant with respect to As(III). The appearance of As(V) in solution after adding solutions of various concentrations of As(III) to Mn(IV) oxide (Table 8-1) shows that As(III) is converted to As(V) by Mn(lV). In a control experiment, no detectable As(III) is oxidized in the absence of Mn(IV) oxide. Manganese (II) is more soluble than Mn(lV) (Stumm and Morgan, 1980), and the high concentrations of Mn in solution in the As(III)-Mn(IV) oxide systems relative to the As(V)-Mn(IV) oxide system is, thus, further evidence that Mn(IV) is reduced to Mn(lI) by As(III). The decrease in the Mn concentration in soluTable 8-1. Oxidation of As(III) and sorption of As by Mn(lV) oxide (Oscarson et al., 1981a). As(III) or As(V) added /Lg mL- 1 100 300 500 1000 300

t ND

As(lII) As(III) As(III) As(III) As(V)

= not detectable.

As(lII)

As(V)

Mn

Final pH

- - - - /Lg mL -1 in solution - - - -

NDt 63.2 ± 7.0 213 ± 4 665 ± 5

ND

83.5 186 205 216 298

± 1.4:j: ± 5

± 1 ± 4 ± 1

:j: Mean ± SD; n = 3.

0.41 8.08 6.06 4.61 0.06

± 0.12 ± 0.36

± 0.60 ± 0.86

± 0.02

7.1 7.1 7.3 7.5 7.5

193

KINETICS OF REDOX REACTIONS

tion with the increase in the initial As(III) concentration from 300 to 1000 /-tm mL -1 is attributed to an increase in the formation of a sparingly soluble manganese-arsenate complex, Mn3(As04)z. This interpretation is substantiated by the fact that the solubility product of Mn3(As04h (Hess and Blanchar, 1976) is much lower than the ion product, (Mn2+)3(As043- ) 2, of the equilibrated solutions in the As(III)-Mn(IV) oxide systems. Sediments from five lakes in southern Saskatchewan, Canada, oxidize As(III) to As(V) (Oscarson et al., 1980). The concentration of As(III) and the ratio of As(III) to As(III) + As(V) in solution indicate that sediments from all five lakes oxidize As(I1I) (700 /-tg As 70 mL -1) within 48 h (Fig. 8-1A). The oxidation of As(III) is not detectable within 72 h in the absence c:

o

6.0

+'

:J

~

A

5.0

c ___ Buffalo Pound 0- .. -0 Pasqua &---6 Echo .......... Mission c; - -.(J Katepwa

I

..J

E

2.0

Cl

::t

1.0

-----_.•>------>. ~ (J)

B

1.5

« I

..J

E

0.5

Cl ::t

01-_---I:._ _L - _ - L_ _L 1.0

~ (J)

:::......._ _.1--_----'-_---'

C

« +

u;

«

Time (h)

Fig. 8-1. The oxidation of As(III) to As(V) and the sorption of As by lake sediments as a function of time. (A) concentration of As(III) in solution, (B) concentration of As(V) in solution, and (C) As(III)/As(III) + As(V). Ten micrograms per milliliter of As(III) were added initially. During the reaction period, the pH of the As-sediment suspensions ranged from 8.0 to 8.2 for the Buffalo Pound sediment and from 7.3 to 7.6 for the other four sediments (Oscarson et al., 1980).

194

HUANG

of sediment. Although, As(V) is the thermodynamically stable species in oxygenated water at common pH values (Penrose, 1974), the kinetics of oxidation of As(III) with O2 is very slow at neutral values (Kolthoff, 1921). Sorption of As occurs simultaneously with the oxidation of As(III) to As(V) (Fig 8-1). With the exception of the Buffalo Pound sediment, over 90% of the added As is sorbed by the sediments within 72 h (Fig 8-1A, B). Arsenic is strongly sorbed onto Al and Fe oxides and the edge of clay minerals (Huang, 1975; Walsh and Keeney, 1975; Fordham and Norrish, 1979) through ligand exchange (Parfitt, 1978; Huang, 1980). The variation in the concentration of As(V) in solution at the end of the reaction periods (Fig. 8-1B) is attributed to the differences in the nature and surface properties of the sediments. The oxidation is not affected by flushing N2 or air through the sediment suspensions, nor does the addition of HgCl 2 to the system eliminate the conversion of As(III) to As(V). This indicates that the oxidation of As(III) to As(V) is an abiotic process. When freshwater lake sediments were treated with hydroxylamine hydrochloride or sodium acetate, which are effective extractants for the removal of Mn (Oscarson et al., 1981b), the oxidation of As(III) to As(V) by the treated sediments was greatly decreased relative to untreated samples of the sediments (Table 8-2). Although the hydroxylamine hydrochloride treatment also removes Fe oxide, the evidence obtained from colorimetry and x-ray photoelectron spectroscopy shows that a redox reaction between Fe oxide and As(III) does not occur within 72 h, indicating that the kinetics of the redox reaction between As(III) and Fe(III) is relatively slow. This supports evidence that Mn oxide is a primary sediment component responsible for the oxidation of As(III). Manganese is present in both the colloidal and noncolloidal particlesize fractions of freshwater sediments (Oscarson et al., 1981b). The depletion (oxidation plus sorption) of As(III) by the sediments involves at least two rates: one rate before (dashed lines) and one after 30 min (Fig. 8-2). However, because of experimental limitations involved in obtaining accurate, meaningful data for the time period < 30 min, rates and energies of depletion of As(III) were not evaluated for this time period. The depletion of As(III) by sediments after 30 min follows first-order kinetics. The rate constant increases with increasing temperature from 278 to 298 K (Table 8-3). The heat of activation for the process varies from 13.8 to 35.6 kJ mol "" for the sediments, indicating that the depletion of As(III) is predominantly a diffusion-controlled process. The ability of Mn oxides to deplete As(III) varies with their crystallinity and specific surface (Oscarson et aI., 1983a). The depletion of As(III) by Mn oxides follows first-order kinetics. The rate constants for the depletion of As(III) by birnessite and cryptomelane at 298 K are 0.267 and 0.189 h -I, respectively (Table 8-4). On the other hand, the rate constant of the depletion of As(III) by pyrolusite at 298 K is 0.44 x 10 -3 h -I. Pyrolusite is highly ordered and has a low specific surface; conversely, birnessite and cryptomelane are poorly crystalline and have relatively high specific surfaces.

195

KINETICS OF REDOX REACTIONS

Table 8-2. Effect of NH 20H-HCI-, NaOAc-, and N 2-flushing treatments on the oxidation of As(III) by lake sediments (Oscarson et al., 1981bl.t As(lII)

Treatment

-p.g mL

As(III)/ [As(III) + As(V)]

As(V) -1

Final pH

Final Eh(V)

0 0 0.55 ± 0.03' 0.82 ± 0.05

8.0§ 8.2 7.2 7.5

0.39§ 0.24 0.25 0.39

0 0 0048 ± 0.03 0.90 ± 0.03

7.6 7.8 7.2 7.5

0049 0041

0 0 0.77 ± 0.01 0.84 ± 0.01

7.6 7.9 7.5 7.5

0.19 0.27 0.39

in solutionBuffalo Pound Lake

None N 2 flushing NH 2OH-HCI NaOAc

0 0 4.32 ± 0.32 6.97 ± 0.63

1.60 1.70 3.59 1.54

± ± ± ±

0.02:j: 0.27 0.24 0.36

Pasqua Lake None N 2 flushing NH 2OH-HCI NaOAc

0 0 2.99 ± 0.28 5.48 ± 0.62

1.04 1.14 3.25 0.58

± ± ± ±

0.01 0.07 0.08 0.15

0.24 0.28

Katepwa Lake None N2 flushing NH 2OH-HCI NaOAc

0 0 5.55 ± 0040 6.68 ± 0.08

0.28 0.80 1.68 1.26

± ± ± ±

0.03 0.15 0.02 0.04

0044

t Initial As(III) concentration was 10 p.g mL -1. :j:X + SD; n = 3.

§ The precision of the pH and Eh measurement is ±0.1 and ±0.01 V, respectively. , The error of the ratio was calculated by the conventional expression for the exact differentiation of a function of two variables; the computation is as follows:

I

As(V) [As(III) + AS(V)]2

I

I.1As (III) I +

I -

As(III) [As(III) + As(V1l2

I

I.1As(V)

I

where As(lII) and As(V) are the concentrations of the respective As species in solution in micrograms per milliliter and .1As(III) and .1As(V) are the standard deviations of the above values.

The relatively high specific surface of birnessite and cryptomelane may be in part attributed to their porous nature. An ethylene glycol monoethylether molecule has a cross-sectional area of 0.4 nrrr' (Eltantawy and Arnold, 1973) and it, thus, could penetrate the pores in the structure of birnessite and cryptomelane. This would further explain why the specific surface of birnessite and cryptomelane and their rate constant for the depletion of As(lII) are much higher than those for pyrolusite. The rate constants for the depletion of As(III) by birnessite are significantly greater than are the rate constants for its depletion by cryptomelane, even though the specific surface of cryptomelane is greater than that of birnessite (Table 8-4). Birnessite has a greater negative charge density than cryptomelane at pH 7 (McKenzie, 1981). Because As(V) is also negatively charged at pH 7, the repulsive interaction energy would be greater between birnessite and As(V) than it would be between cryptomelane and As(V). This is apparently the reason why birnessite does not sorb a detectable amount of As(V) and cryptomelane sorbs a substantial amount (218 ± 5 mmol As kg - 1 of Mn02) of As(V) (Oscarson et aI., 1983a). Differences in point-of-zero

...

: PASQUA

BUFFALO POUND

~

KATEPWA

.... 3

s

;:

C>

eo

~

1.0

z z

~ o.a .-.oJ

E 0.6

~til


0.4

• 278K

g

... 298K

02

... OJ'

o

I

,

6

12

I

18

"

240

I

•

6

12

I

18

I

I

24 0

TIME (h) Fig. 8-2. First-order plots of As(IlI) depletion in solution by the lake sediments (Oscarson et al., 1981c).

,

,

6

12

I

18

"

24

=

e > 2: o

197

KINETICS OF REDOX REACTIONS

Table 8-3. Rate constants and Arrhenius heats of activation for the depletion (oxidation plus sorption] of As(lIl) by the lake sediments (Oscarson et al., 1981c). Rate constants x 10 2 , h- 1 Sediment Buffalo Pound Pasqua Katepwa

278 K

298 K

Arrhenius heats of activation, kJ mol -1

4.1 4.8 6.9

11.3 13.5 10.3

35.2 35.6 13.8

charge (pzc) of birnessite and cryptomelane and their ability to sorb As(V) explain why the rate constants of As(III) depletion are greater for birnessite relative to cryptomelane even though cryptomelane has the greater surface area. Because little As(V) is sorbed from solution by birnessite upon the oxidation of As(III) and less total As is sorbed by birnessite than by cryptomelane, the electron-accepting sites on the surface of birnessite are blocked to a lesser extent than those on the surface of cryptomelane. Therefore, the subsequent rate of depletion of As(III) from solution is greater for birnessite than for cryptomelane. Manganese nodules often exhibit "onionskin" layering of Fe(III) oxides (Arrhenius, 1963). The surfaces of many soil Mn concretions, composed predominantly of birnessite, are coated with ferruginous and siliceous material (Taylor et al., 1964). The intermixing or coating of various chemical species with/on Mn oxides could substantially alter their redox and sorption/desorption behavior and profoundly affect the mobility and fate of many nutrients and pollutants in natural environments. However, there is only limited information in the literature on the subject. Oscarson et al. (l981b) hypothesized that a coating of carbonates on Mn oxides was responsible for a retardation in the rate of oxidation of As(III) by some freshwater lake sediments. Oscarson et al. (l983b) reported that the rate constants for the depletion (oxidation plus sorption) of As(lII) are generally substantially smaller for the Mn oxide with higher levels of coatings of Fe and Al oxides and CaC0 3 than they are for the untreated MnOz and the MnOz with low levels of coatings (Table 8-5). The rate constant is always less for the high level relative to the low level of Fe and Al oxide and CaC03 coatings, except the treatments at 278 K where the differences are not statistically significant. The Table 8-4. Specific surface and point-of-zero charge (pzc) of the Mn dioxides and rate constants and energies of activation for the depletion of As(I1I) by the Mn dioxides (Oscarson et al., 1983a).

Mineral

Specific surface

Rate constant x 10 3 pzc

m2 g-l

Birnessite 277±5t 2.3±0.1 Cryptomelane 346±4 2.8±0.1 8±1 6.4±0.3 Pyrolusite t Mean ± SF"

278 K 298 K - - - - - h -1 126±13 54±10 0.12±0.02

267±6 189±8 0.44±0.03

318 K _

533±38 318±22 0.58±0.05

Energies of activation kJ mol " ! 26.0±0.2 32.3±6.7 29.0±9.8

HUANG

198

Table 8-5. Rate constants for the depletion of As(III) by untreated Mn02 and Mn02 coated with Fe and Al oxides and CaCO a (Oscarson et al., 1983b). Rate constants x lOa, h- 1 Treatment

278 K

Mn02 (no coating) CaCOa coating (Ca/Mn = 0.08) CaCOa coating (Ca/Mn = 0.32) Al oxide coating (AlIMn = 0.10) Al oxide coating (AlIMn = 0.40) Fe oxide coating (Fe/Mn = 0.42) Fe oxide coating (Fe/Mn = 1.58)

126 39 18 35 11 70 51

± ± ± ± ± ± ±

13ta* 2b 3b 2c 1c 9d 6d

298 K 267 188 39 257 119 318 100

± ± ± ± ± ± ±

6a 15b 5c lOa 5d 17e 4f

318 K 533 456 73 1265 376 844 172

± ± ± ± ± ± ±

38a 28a lOb 122c 13a 22d 2e

* For the coated Mn02'S, at a given temperature, values followed by "a" are not significantly different (P <0.05) from those of the untreated Mn02 according to Duncan's Multiple Range test; and within each mineral group (CaCOa, Al oxide, or Fe oxide) of two coating levels at a given temperature, the values followed by the same letter are not significantly different (P < 0.05). Columns are considered separately in the statistical treatments. t Rate constant ± SE.

decrease in the reaction rate with increasing levels of coatings is not simply reflecting a dilution of the MnOz by the oxides of Fe and Al or CaC03 , but rather indicates that the electron-accepting sites on MnOz are partially masked by the oxides and CaC0 3 • The corroborating evidence shows that Fe and Al oxides and CaC0 3 do not oxidize As(III) to As(V) (Oscarson et aI., 1981a,b). Therefore, the fraction of the depletion of As(III) caused by the oxidation of As(III) to As(V) by the coated MnOz is due solely to MnOz. On the other hand, Fe and Al oxides have a greater sorption capacity for As than does MnOz. Consequently, if the oxidation reaction did not occur and the depletion of As(III) was due solely to the sorption process, the rate constant would be greater for the MnOz coated with high levels of Fe and Al oxide than it would be for the untreated MnOz. However, the reverse trend is observed, indicating that the inhibition of the oxidation of As(III) overrides the enhancement in the sorption of As(III) when Fe and Al oxides are coated at the high levels on MnOz. Manganese oxide sorbs more As than does CaC0 3 • The decrease in the rate constant is approximately sevenfold for MnOz coated with high levels of CaC03 relative to the untreated MnOz. Therefore, the predominant effect of CaC03 is likely a masking of the electron-accepting sites on MnOz and the subsequent inhibition of the transfer of electrons from As(III) to MnOz. When As(III) (HAsO z) is added to untreated or coated MnOz, it can either be oxidized to As(V) (H 3As04) by MnOz (Oscarson et al., 1981a) or sorbed on the surface of the oxides or CaC0 3 • The oxidation of As(III) by MnOz is shown in the following equations HAsO z

+ MnOz

=

(MnOz) . HAsO z

[IJ [2J

KINETICS OF REDOX REACTIONS

H 3As04 H 2As04 (Mn02) . HAs0 2

199

= = +

H 2As04"

+

H+

[3]

HAsol-

+

H+

[4]

2H +

= H 3As04 +

Mn 2+ .

[5]

The first step in the process appears to be the formation of an adsorbed layer (Eq. [1]). With subsequent transfer, HAs02 is oxidized to H 3As04 (Eq. [2]). At pH 7 or less, the predominant As(III) species will be arsenious add (HAs0 2), but the oxidation product H 3As04 should dissociate (K1 = 5.62 x 10 -3; K 2 = 1.70 x 10 -7) to form about equal amounts of H 2As04- and HAsol- with little H 3AS04 present at equilibrium (Eq. [3] and [4]). Therefore, each mole of As(III) oxidized will release about 1.5 mole H + into the system. If no other reaction takes place, this will substantially lower the pH. The pH of the systems after the reaction periods, however, remains close to 7.0. This indicates that the H + produced as a result of the dissociation of H 3As04 react with the adsorbed HAS0 2 on Mn02' leading to the formation of H 3As04 and the reduction and dissolution of Mn (Eq, [5]). Consequently, when every mole of As(III) is oxidized to As(V), a mole of Mn(IV) in the solid phase is reduced to Mn(II) and partially dissolved in solution (Oscarson et aI., 198Ia). In addition to the reaction shown in Equation [5], H + dissociated from H 3As04 may attack coatings of Al and Fe oxides and CaC0 3. If surface coatings are partially dissolved by H + , fresh Lewis acid sites on Mn02 would be exposed and the oxidation process would be promoted. The extent of masking of the electron-accepting sites on the Mn02 for the oxidation of As(III) to As(V) significantly varies with the kinds and levels of coatings (Oscarson et aI., 1983b). Coatings of Fe and Al oxides and CaC03 on Mn02 distinctively affect the oxidation of the toxic As(III) to the less toxic As(V) and the sorption of As. Manganese oxide evidently catalyzes the sorption of As by Al oxide through oxidation of As(III) to As(V). The oxidation of As(III) to As(V) by uncoated and coated Mn oxides has important implications for the transport, fate and toxicity of As in terrestrial and aquatic environments. In some environments that have been contaminated with As(III), the addition of reactive Mn oxides, such as birnessite and cryptomelane, to the system may alleviate the toxicity of As(III) through converting As(III) to the less toxic and mobile As(V).

°

OXIDATION OF TRACE METALS

Besides oxidation of metalloids such as As(III), Mn oxides and oxyhydroxides (e.g., Mn304' MnOOH) can catalyze the oxidation of trace metals by disproportionation to Mn 2+ and Mn02. The disproportionation facilitates electron-transfer processes that can either greatly decrease or increase the equilibrium solubility of certain metals (Hem, 1978).

HUANG

200

Chromium and plutonium are similar in chemical behavior in aqueous environments (Rai and Serne, 1977; Bartlett and James, 1979). Both elements can exist in multiple oxidation states and as cationic and anionic species in aqueous environments. Chromium occurs in the II, III, and VI oxidation states in water. The divalent form is unstable, the trivalent state has broad stability, and hexavalent Cr occurs under strongly oxidizing condition. Chromium (III) exists as the cation Cr3+ and its hydrolysis products, or as the anion Cr02-' Chromium (VI) occurs as the dichromate Cr20?-, or chromate HCr04- and CrOl- anions. Hexavalent Cr is suspected of being a human carcinogen. Plutonium exists in the III to VI oxidation states as Pu 3 +, Pu 4+, Puot, and Puoi + in strong acid solutions. These states coexist under some conditions. Plutonium is an extremely toxic element of great environmental concern. The safe disposal of the long-lived isotopes, 242pU (half-life 3.8 x 105 yr) and 244pu (half-life, 7 x 107 yr), is one of the most difficult problems that faces the nuclear enterprise. Chromium (III) and Pu (III/IV) cations are sorbed to soil constituents and, thus, immobile in most aqueous and soil environments. On the other hand, Cr(VI) and Pu(VI) are quite mobile in soils and aqueous systems, because they are not sorbed by soil components to any extent. Therefore, in the hexavalent form, these elements are readily bioavailable (Amacher and Baker, 1982) and are of concern in food chain contamination. Chromium(III) and Pu(III/IV) can be oxidized to Cr(VI) and Pu(VI) by Mn(III/IV) oxides (Cleveland, 1970; Amacher and Baker, 1982). Manganese oxides can, thus, enhance the mobility and toxicity of Cr and Pu in soil and associated environments. The kinetics of Cr(III) oxidation by soil was studied by Amacher and Baker (1982). Most of the oxidation occurred during the 1st h. The oxida-

-!.J "0 E

. "E...

5.0

[Soil] =12.5g 1:' [er U1ll]o=192I1mol 1:'

~A

4.0

c:

~

3.0

If

--

....>... u

//

2.0

1.0

6

296K

1

~l /' ---7

::t Q)

/6

pH=5.5

301K

?

->

275K

,,

l

,....0,....0 °

..0

Time (min) Fig. 8-3. Effect of temperature on the kinetics of Cr(lll) oxidation in moist Hagerstown silt loam soil (Amacher and Baker. 1982).

201

KINETICS OF REDOX REACTIONS

tion of Cr(lll) increased with increasing temperature (Fig. 8-3). Kinetics of Cr(lll) oxidation on Mn(III/IV) oxides (Fig. 8-4) show a trend similar to that observed for soils (Fig. 8-3). The effect of temperature and the shape of the rate curves are similar. The rapid decrease in the reaction rate and lack of complete oxidation of Cr(lll) is attributed to part of the reduced Mn(lI) not being released to solution as Cr(lll) is oxidized. The 'Y-Mn02 has a high affinity for its own divalent metal ion (Morgan and Stumm, 1964). Manganese(lI) may be adsorbed on the oxide surface and hinders fresh Mn(lV) from being exposed to oxidize Cr(lll). Disproportionation of Mn oxides and oxyhydroxides also could catalyze the oxidation of other trace metals such as Co, Pb, Ni, and Cu (Hem, 1978). The Mn 2+ and Mn H in Mn oxides have similar physical dimensions as species Co H, C0 3 + , NiH, NiH, Cu H, and Pb 2+ , and where vacancies develop in the structure during the disproportionation of Mn oxides, such ions might enter and become a part of the structure. The behavior of these metal ions may be directly influenced by redox processes coupled to disproportionation of Mn mixed-valence oxide, to catalyzed oxidation by aqueous 02' or to other redox reactions involving changes from one Mn oxide species to another. When the oxidized form of the element has a lower solubility than the reduced form, this effect can be of major significance. If electron transfers from Mn species, in the disproportionation process, result in the formation of C0 304 from Co H, Ni304 from NiH, Pb02 from Pb H, and CuO from Cucli-, the following equations can be written (Hem, 1978)

-

~

20.0

(5

E

~

i

.

0

o~

[8-Mn02J =250mg L-l

E

-> -

275K

15.0 0

I-

&

0

10.0

[ Cr (III) Jo = 24.0 ,limo I 1: 1 pH=5.5

5.0

I-

0

Time (min) Fig. 8-4. Effect of temperature on the kinetics of Cr(lll) oxidation by o-Mn02 at pH 5.5 (Amacher and Baker, 1982).

202

HUANG

Table 8-6. Binding energy values for Co reference oxides and Co(ads)-Mn02' Precision of binding energies is ±0.1 eV (Murray and Dillard, 1979). Sample

pH

Co 2P1l2

Co 2PS/2

A B C D Mn02 Co20S CoOOH Co(OHb

3.4 4.5 5.2 7.0

NM:j: NM 795.4 795.3

780.1 780.2 780.2 780.2

15.2 15.1

794.4 794.9 797.0

779.2 779.9 780.9

15.2 15.0 16.1

t BE(Co 2Pl/2 - Co 2Ps/21. :j: Not measured due to low photopeak intensity. 2Mn304(C) + 3Co2+ + 4H + Mn02(C) 2Mn304(C)

+

[6]

+ NiP4 + 2H 20 + 5Mn2+

[7]

+ Pb 2+ + 8H + Mn02(C)

2Mn304(C)

+ 5Mn2+ + 2H 20

+ 3Ni2+ + 4H + Mn02(C)

2Mn304(C)

C0 30 i c)

+ Pb0 2(c) + 5Mn 2+ + 4H 20

[8]

+ 2CuCli- + 8H + 2CuO(c)

+

Mn02(C)

+ 5Mn2+ + 6CI- + 4H 20

[9]

where c stands for crystalline state. Based on thermodynamic data for the equilibrium constants (Naumov et al., 1971; Wagman et aI., 1968, 1969; Pourbaix, 1963), the following relationships are derived (Hem, 1978) [10] [11]

[Mn2+]5/[Pb 2+][H+]8

= 1029.53

[Mn2+]5[Cl-]6/[CuCli-]2[H+]8

=

[12]

°.

1047.2

[13]

X-ray photoelectron spectroscopy (XPS) measurements of Co adsorbed on Mn02 reveal strong evidence that Co(ll) is oxidized to Co(III) in the presence of the strong electric field at the MnOrsolution interface (Table 8-6; Fig. 8-5). The spectrum in Fig. 8-5 and the binding energy data in Table 8-6 show all three characteristic features of Co(III): (i) Co(2P 1d and Co(2P 3I2 ) binding energies; (ii) narrow Co(2P t d and CO(2P3d peak widths and the absence of intense satellite peaks, and (iii) the energy of separation

203

KINETICS OF REDOX REACTIONS

Co 2p

3/2

Co (n}-Mn0 2

800

790

780

Binding Energy (ev) Fig. 8-5. Cobalt 2-p spectra for Co(ll) adsorbed on Mn02 (Murray and Dillard, 1979).

of the Co(2Pl/z) and Co(2P3n) photopeaks. Nickel(II), however, cannot be oxidized at the interface except at very high concentrations (Murray and Dillard, 1979). Strong experimental evidence for the oxidation of other trace metals on Mn oxides still remains to be attained. Furthermore, little information is available on the kinetics and mechanisms of redox reductions of these trace metals on the surfaces of Mn oxides.

FORMATION OF IRON OXIDES AND OXYHYDROXIDES Iron oxide minerals playa significant role in pedogenesis and dynamics and fate of nutrients and pollutants in soil environments. The effect of pedogenic environments on the formation and transformation of Fe oxide was thoroughly reviewed by Schwertmann (1985). Postma (1985) reported that the surface of birnessite and possibly other Mn(IV) oxides can limit the rate of the solution Fe z+ -Mn(lV) oxide interactions. Krishnamurti and Huang (1987) found that birnessite promotes increased precipitation of Fe oxide (Table 8-7). The oxidation of Fe(II) by birnessite is thermodynamically feasible and is confirmed by the presence of Mn(II) in the solution using electron spin resonance (ESR) spectroscopic analysis. Birnessite also influences the crystallization processes of hydrolytic products of Fe that range from lepidocrocite (oy-Fe OOH). geothite (o-Fe OOH), akaganeite ({3-Fe OOH) to x-ray noncrystalline Fe oxides (Fig. 8-6). The rates of crystallization of these

HUANG

204

Table 8-7. Precipitation of Fe in the FeCI2-NH40H system as influenced by birnessite at different pH values (Krishnamurti and Huang, 1987). Mn/Fe molar ratio

Final Eh (mV)

%Fe precipitated from solution

0

+385

0.01 0.1 1.0

+470 +490 +770

5.0

0 0.01 0.1 1.0

+260 +290 +380 +650

6.0

0 0.01 0.1 1.0

+10 -30 -10 +570

No precipitate (30)t 2.0 (150) 12.8 (1220) 68.0 (15) 1.0 (65) 6.5 (200) 16.0 (1435) 91.6 (85) 8.0 (140) 12.0 (295) 30.0 (1495) 94.5

Final pH 4.0

In the precipitate, g kg- 1 Fe

Mn

372 476 311

79 179 298

372 558 447 357

0 16 142 199

526 479 568 353

0 8 52 211

t Amount of precipitate (mg).

Fe precipitates appear to be rapid, since these crystalline precipitation products of Fe are formed within 1 h. Manganese oxides, which have different structural and surface properties, vary in their ability to promote the precipitation and crystallization of Fe oxides and oxyhydroxides (Krishnamurti and Huang, 1988). The standard electrode potential (EO) of the redox pairs Fe 2+ -Mn02 and Fe2+_ Mn304 can be described by the following equations (Bricker, 1965) 2Fe2+ + Mn02 + 4H+

=

Mn2+ + 2Fe3+ + 2H 20 EO

2Fe2+ + Mn304 + 8H +

=

=

+0.438 V

[14]

3Mn 2+ + 2Fe 3+ + 4H 20 EO

=

+1.04 V

[15]

These EO values indicate that oxidation of Fe 2+ by Mn oxides is thermodynamically feasible. The Eh-pH diagram (Fig. 8-7) indicates the feasibility of Mn4+ and Mn3+ to Mn2+ reduction in Mn oxides in the Eh-pH ranges of the formation of Fe oxides. Furthermore, the ESR spectra of the filtrates (Fig. 8-8) after the reduction show significant amounts of Mn2+ in the filtrates. The reaction time of 1 h was too short to disproportionate the Mn 4+ and Mn3+ of the Mn oxides (Figs. 8-8b,d) to the large amounts of Mn2+ observed in the filtrates (Fig. 8-8a,c). The g (spectroscopic splitting factor) and Mn-hyperfine G (Breath in Gauss) values of Mn2+ in the filtrates (given in the respective figures) compare well with standard (2.007 and 95.2 G) for Mn2+ species in solution (Bielski and Gebicke, 1967). The data indicate that Mn 4+ or Mn3+ of the Mn oxides is partly dissolved by reduction to Mn 2+. Simultaneously, the oxidation of Fe2+ to Fe3+ by Mn

205

KINETICS OF REDOX REACTIONS

(c ) L O.625nm

L O.330nm

I

I 80

I

I

!

70

I

I

I

60

I

I

I

..

I 50

I

I

I

I

I 40

I

I

I

I

! 30

I

I

I 20

I

I

I 10

°28, Fe KO(

Fig. 8-6. The XRD patterns of the precipitation products formed in the FeClrNH40H system at different pH values both in the presence and absence of Mn02 (birnessite). B = birnessite; L = lepidocrocite; G = goethite; and A = akaganeite. At pH 6.0 with a Mn/Fe molar ratio of (a) 0, (b) 0.01, and (c) 1.0; at pH 5.0 with a Mn/Fe molar ratio of (d) 0.01 and (e) 1.0; and pH 4.0 with a Mn/Fe molar ratio of (f) 0.01 and (g) 1.0 (Krishnamurti and Huang, 1987).

oxides leads to subsequent hydrolysis of Fe 3 + to form the precipitation products of Fe. At the initial molar ratios of Mnsolid/Fesolution (Mn/Fe molar ratio) of 0.1 and 1, the Fe oxide precipitates formed at pH 5.0 in the presence of pyrolusite are x-ray noncrystalline, whereas the crystalline component of the precipitation products formed at pH 6.0 at the Mn/Fe molar ratios of 0.1 and 1.0 is lepidocrocite (Krlshnamurti and Huang, 1988). The Fe extractable in

HUANG

206

,°2

O

H

2

,

--

<, ,

+0.6

Mn02

>

s: W

+0.4

<,

2+

Mn

aq

+0.2

° ...

-0.2

- 0.4 '--_.........._ _ 2 4

....l-_----'L..-~___L _

°

6

8

__'___.L.___..J

10

12

pH

Fig. 8-7. Stability relations of different species of Mn at 298 K, 0.101 MPa, and aMn2+ = IO -6 M (Bricker, 1965). The Eh and pH ranges of the systems during the formation of Fe oxide precipitates in the presence of Mn oxides in the present study are shown as shaded region (Krishnamurti and Huang, 1988).

hydroxylamine hydrochloride, which reflects the amounts of noncrystalline Fe oxides present (Chao and Zhou, 1983), was 100 and 85% of the precipitate formed at pH's 5.0 and 6.0, respectively, at a Mn/Fe molar ratio of 1.0 (Table 8-8). The Fe oxides formed at all pH's and at a Mn/Fe molar ratio of 1.0 in the presence of cryptomelane are akaganeite ({3-Fe OOH) and feroxyhyte (0 '-Fe OOH) (Table 8-8). The Fe oxides formed at all pH's and at a Mn/Fe molar ratio of 1.0 are completely extractable by hydroxylamine hydrochloride. The reactivity of akaganeite towards the reducing agent (NHzOH . HCI) may be due to its tunnel structure (Holm, 1985) and/or its poorly crystalline nature (Krishnamurti and Huang, 1988). The Fe oxides formed at pH 4.0 and a Mn/Fe molar ratio of 1.0 in the presence of hausmannite are largely x-ray noncrystalline (Table 8-8). On the other hand, the Fe oxides formed at pH's of 5.0 and 6.0 and at a Mn/Fe molar ratio of 1.0 contain mainly magnetite. The Fe extractable by hydroxylamine hydrochloride in the Fe oxides formed at pH's of 4.0, 5.0, and 6.0 and at a Mn/Fe molar ratio of 1.0 was 91, 41, and 32%. respectively.

KINETICS OF REDOX REACTIONS

207

1'-9.6294

g-2.006

(0)

Mn hyperfine 95.6G Mn -10- 2 mol L- 1

r

3430G

( b)

--""-'--.--------

M n < 10 -!l mol L- 1

1'-9.6265

---..--- g-2.006 Mn hyperfine

(c)

95.4G Mn-5xlO- 2 mol L- 1

1

3428G

1'-9.6271

g"2.006

(d)

Mn hyperfine 95.2 G Mn- 10- 4 mol L- 1

Fig. 8-8. Electron spin resonance spectra of Mn(II) in the filtrates after reaction at pH 5.0 (a) cryptomelane-FeCI 2-NH40H system, Mn/Fe molar ratio = I, (b) cryptomelane-HjoNH 40H system, (c) Hausmannite-Fef.lj-HCl system, Mn/Fe molar ratio = I, and (d) Hausmannite-HyOc-H'Cl system (Krishnamurti and Huang, 1988).

During the oxidation of Fe2+ to Fe 3 + in solution, Mn 4 + and Mn3+ in the Mn oxides is partly reduced to Mn 2 + . Manganese (II) may significantly influence the formation and transformations of Fe oxides. Detourneyet al. (1975) studied the influence of Mn 2 + on the transformation of geothite in S04 medium at different temperatures. Cornell and Giovanoli (1987) reported that Mn2+ influences the transformation of ferrihydrate to Mngeothite and lacobsite in Fe3+-Mn 2 + nitrate systems at pH 11 to 13. Krishnamurti and Huang (1989) studied the influence of Mn2+ on the crystallization of the oxidation products of Fe 2 + in the presence of CI and S04 ions, which are common inorganic anions in natural systems, in the pH range of 6 to 8, typical of hydromorphic soils, in which Fe2+ and Mn 2 + coexist in solution.

208

HUANG

Table 8-8. X-ray powder diffraction identification and noncrystalline Fe content of Fe oxide precipitates formed in the FeCI2-NH 40H system in presence of different Mn oxide minerals (Krishnamurti and Huang, 1988).t pH:I:

Proportion of extractable Fe(%)§ Pyrolusite 100 85 Cryptomelane 100 100 100 100 Hausmannite 91 41 32

5.0 6.0 3.0 4.0 5.0 6.0 4.0 5.0 6.0

Minerals present' PCL L A,F A,F A,F A,F NC, F M,F M

t Mn/Fe molar ratio of 1.0 :I: pH of synthesis; pH was maintained for 1 h with 0.1 M NH 40H/0.1 M HCl. § Extractable in hydroxylamine hydrochloride. 1 Dominant constituent of the Fe oxide precipitate. PCL = poorly crystalline lepidocrocite; L = lepidrocrocite; A = !kaganeite; F = feroxyhyte; M = magnetite; NC = noncrystalline. The differential infrared data (not shown) are in accord with x-ray data. Table 8-9. Chemical analysis of the precipitates formed in the absence and presence of Mn2+ (Krishnamurti and Huang, 1989). pH of formation

Solution MniFe molar ratio

6.0 6.0 6.0 6.0 8.0 8.0 8.0 8.0

0 0.1 1.0 10.0 0 0.1 1.0 10.0

6.0 6.0 6.0 6.0 8.0 8.0 8.0 8.0

0 0.1 1.0 10.0 0 0.1 1.0 10.0

Mn, - MIlo:l: Products] (Mnt - MIlo) + (Fet - Feo) mol % FeCI2-NH40H system L 0 L 0.3 POL 1.3 POL 3.2 Mh 0 Mh 0.3 POL 2.0 NC 8.1 FeSOrNH40H system L,G 0 L 0.6 POL 1.6 POL 3.0 L 0 L 0.7 POL 2.1 HLM 15.0

t Dominant precipitation products identified by x-ray powder diffraction: L

Fe§

24.0 17.5 40.1 40.2 16.0 11.1 38.5 41.8 18.5 9.0 37.6 40.0 15.5 13.0 33.2 24.4

= lepidocrocite; POL = poorly ordered lepidocrocite; Mh = maghemite; NC = noncrystalline; G = goethite; and HLM = honessite-like mineral. :I: Mn, and Fe, = total Mn and Fe; MIlo and Feo = Mn and Fe extractable by hydroxylamine hydrochloride. § Average of duplicates: ±0.2%.

KINETICS OF REDOX REACTIONS

209

In the absence of Mn2+, lepidocrocite (v-Fe OOH) and maghemite ('Y. FeZ03) are the crystalline species formed at pH's of 6.0 and 8.0, respectively, in the FeClz system, whereas lepidocrocite + geothite (o-Fe OOH) and lepidocrocite alone are the crystalline species formed at pH 6.0 and 8.0, respectively, in the FeS04 system (Table 8-9). The amounts of Mn coprecipitated with Fe oxides increase with the increasing initial solution Mn/Fe molar ratios. The crystallization processes of the precipitation products of Fe are perturbed by increasing coprecipitation of Mn. At pH 6.0, the perturbation results in the formation of poorly ordered lepidocrocite in both chloride and sulfate systems. At pH 8.0, the perturbation results in the formation of poorly ordered lepidocrocite and a honessite-like species (Mn-Fe-S04-HzO) in the FeCl z and FeS04 systems, respectively (Fig. 8-9 and 8-10). The influence of Mn2+ on the formation of Fe oxides in both chloride and sulfate systems was observed in 1 h. Although the kinetics of formation of Fe oxide in the presence of Mn z+ remain to be critically studied, the reaction processes appear to be quite rapid. Various Mn oxides differ in their ability to promote the formation of Fe oxides and oxyhydroxides. The Mn oxide/solution Fe2+ ratio, pH, and anions such as CI- and 801- also substantially influence the promoting effect. Therefore, the role of Mn oxides in the formation of Fe oxides and oxyhydroxides under various ionic environments merits close attention.

OXIDATIVE POLYMERIZATION, POLYCONDENSATION, AND DEGRADATION OF ORGANICS The oxidative polymerization of polyphenols in soils is regarded as one of the main processes in the formation of humic substances (Scheffer and Ulrich, 1960; Felbeck, 1965; Kononova, 1966; Hurst and Burges, 1967; Martin and Haider, 1971; Schnitzer and Khan, 1972; Flaig et al., 1975; Wang et aI., 1986). The polymerization causes a darkening of polyphenols that can be accelerated nonenzymatically as well as enzymatically (Scheffer et aI., 1959; Scheffer and Ulrich, 1960; Kyuma and Kawaguchi, 1964; Kumada and Kato, 1970; Haider et al., 1975; Wang et al., 1978; Kumada, 1981). Shindo and Huang (1982) reported that, among the metal oxides studied, Mn(IV) oxide is most effective with respect to the abiotic oxidation of a hydroquinone solution over the pH range (4-8) common in soils. Table 8-10 shows the effects of Mn oxides on the oxidation of hydroquinone solution at different pH values at the end of the reaction period of 24 h. The control solution without the oxides becomes colored only when the initial pH of the solution is 7.0 or higher. The addition of Mn oxide greatly accelerates the oxidation over the pH range of 4 to 8. The high degree of the oxidation in the Mn oxide systems at the initial pH values of 6.0 or higher is attributed to the following processes: (i) the Mn oxide acts as a Lewis acid that accepts electrons from hydroquinone leading to its oxidative polymerization, and (ii) the acceleration of oxidative polymerization that is driven by an increase

210

HUANG

of pH that is in turn caused by the reduction of Mn oxide. To determine whether microorganisms influence the oxidation of hydroquinone solution, antiseptic or inoculum was added to the system. The hydroquinone solution in the absence of Mn oxide was colorless both in the absence and presence of toluene or inoculum (Table 8-11). The degree of oxidation in the Mn oxide M

0.253 nm

(a)

Mn/Fe- 0

M 0.296nm

M

M

0.210 nm

0.483 nm

M 0.171 nm

M M

(b)

M

Mn/Fe-O.I M

M

(d)

Mn/Fe-IO.O

0.25nm

70

60

50

0.70nm

40

30

20

10

Fig. 8-9. X-ray powder diffractograms of the precipitation products of Fe in the FeCI2-NH40H system at pH 8.0 and at initial solution Mn/Fe molar ratios of (a) O. (b) 0.1, (c) 1.0, and (d) 10.0; M = maghemite (Krishnamurti and Huang, 1989).

211

KINETICS OF REDOX REACTIONS

O.626nm L

(a) Mn/Fe-O L

L

O.330nm

O.247nm L

O.194nm L

O.173nm L L L

(b) Mn/Fe-O.1

L

L"

L

(el Mn/Fe-1.0

O.25nm

(d) Mn/Fe-IO.O

70

60

40

30

20

O.880nm

10

028, Fe Koo' Fig. 8-10. X-ray powder diffraclograms of tne precipitation products of Fe in the FeSO.-NH.OH Iyllern II pH H.O and al initial solution Mn/Fe molar ratios of (a) 0, (b) 0.1, (c) 1.0, and (d)IO,(); I. - lepldocroclte (Krishnamurti and Huang, 1989).

... N

N

Table 8-10. Effects of Mn, Fe, Al and Si oxides on the browning of hydroquinone solution at different pH values at the end of the reaction period of 24 h (Shindo and Huang, 1982). Initial pH of 4.0 Final Oxide

pH

Eh(V)

None Mn Fe AI Si

4.0 4.1 4.0 4.0 4.0

0.38 0.44 0.40 0.38 0.38

Initial pH of 5.0

Absorbancet 400 nm 600 nm <0.01:1: 1.64 0.06 <0.01 <0.01

<0.01 0.46 0.02 <0.01 <0.01

Final

Oxide

pH

Eh(V)

None Mn Fe AI Si

6.9 7.7 6.9 6.7 6.8

0.24 0.29 0.25 0.25 0.24

Eh(V)

400 nm

600 nm

pH

Eh(V)

5.0 5.3 5.0 5.0 5.0

0.32 0.38 0.33 0.32 0.32

<0.01 0.88 0.01 <0.01 <0.01

<0.01 0.20 <0.01 <0.01 <0.01

6.0 7.5 6.1 6.0 6.0

0.27 0.32 0.27 0.27 0.27

Absorbance 400 nm 600 nm <0.01 7.44 <0.01 <0.01 <0.01

<0.01 1.84 <0.01 <0.01 <0.01

Initial pH of 7.8

Absorbance 400nm 600 nm 0.30 8.62 0.10 0.10 0.20

Final

Absorbance

pH

Initial pH of 7.0 Final

Initial pH of 6.0

0.09 2.06 0.02 0.04 0.06

Final pH

Eh(V)

6.9 7.7 7.0 6.8 6.9

0.24 0.32 0.25 0.24 0.24

Absorbance 400 nm 600 nm 0.70 8.86 0.37 0.24 0.49

0.17 2.12 0.10 0.08 0.12

The absorbance of the supernatant was measured with a spectrophotometer directly or after dilution; the resulting absorbance was scaled by the dilution factor. :j: The supernatant is visibly colorless. t

:: e > Z o

213

KINETICS OF REDOX REACTIONS

Table 8-11. Effects of antiseptic and inoculum on the browning of hydroquinone solution both in the absence and presence of birnessite at the end of the reaction period of 24 h (Shindo and Huang, 1982).

No. 1 2 3 4 5 6 7 8

Mn oxide

Antiseptic

Inoculum']

HgCl2 Toluene

+ + + +

+ HgCl2 Toluene

+

Final pH 6.0 5.5 6.0 6.0 7.4 7.1 7.4 7.4

Growth of microorganisms:l:

Absorbance§ 400 nm

600 nm

<0.01' 0.23 <0.01 <0.01 6.70 5.00 6.70 6.70

<0.01 0.04 <0.01 <0.01 1.66 1.42 1.66 1.66

ND# ND ND

t Filtrate was obtained from the soil water suspension (soil/water ratio

= 1:10). The fresh soil sample was taken from the Ap horizon of the Unity Orthic soil (Typic Haploboroll) in Wilkie, Saskatchewan, Canada. :I: The growth of microorganisms in the solution at the end of the reaction period of 24 h was examined using agar plates which contained nutrient broth and agar. § The absorbance of the supernatant was measured with a spectrophotometer directly or after dilution; the resulting absorbance was scaled by the dilution factor. , The supernatant is visibly colorless. # ND = No colonies were observed on the plates even after 4 d.

system was not influenced by the presence of either toluene or inoculum. Agar plates, inoculated with the browning solution upon oxidation, did not show any growth of microorganisms. Therefore, the results clearly show that the oxidation of hydroquinone solution under the conditions studied occurs abiotically. In the nonsterilized systems in which abiotic and biotic processes were not differentiated, Larson and Hufnal (1980) also reported that the Mn(lV) oxides are the most efficient, among the metal oxides, in oxidative polymerization of dissolved phenols. Ono et al. (1977) investigated the rate of radical formation on Mn02 at high pH (pH 9) and proposed a mechanism that involves the removal of protons from hydroquinone before electron transfer. Stone and Morgan (1984a) reported that the reduction of Mn oxide by hydroquinone is a first-order reaction (with respect to oxide loading) and must occur on the oxide surface, i.e., phenols must form a surface complex prior to electron transfer. The factors affecting the oxidation of dihydroxybenzene by birnessite and the extent of Mn2+ solubilized were studied by McBride (1989a,b). A kinetic study of the oxidation of hydroquinone by hausmannite at pH 6 was conducted by Kung and McBride (1988). Electron transfer from hydroquinone to the oxide was clearly indicated by the release of Mn2+ accompanying the loss of hydroquinone from solution (Fig. 8-11). This observation indicates that electrons extracted from hydroquinone reduce surface Mn, releasing Mn 2+ into solution. The ESR spectroscopy detected, during the electron transfer process, a quintet of hyperfine lines arising from four equivalent protons (hyperfine coupling constant = 2.4 G, g value = 2.005), confirmed to be the p-benu}scmiquinone anion radical spectrum (Wertz and

HUANG

214

0-----------------...,1.5

--

c:

--... o e

"0

~­

o"eJ

c:

~

g

<5 01 E .

Q)

1.0

III III

"0

+

8 E o

:::c

<5 E E

N

c: ~

/0.0 lJ-L_L-~:E=::g:::~~::o::====od 0 .0 o 60 20 40

TIME (min) Fig. 8-11. Change in solution concentration of hydroquinone (HQ) and Mn 2 + due to the oxidation reaction. Initial concentrations were 2 x 10-4 M hydroquinone and 600 mg of hausmannite (Mn304) at pH 6 (Kung and McBride, 1988).

Vivo, 1955; Fukuzumi et al., 1975). Radical formation at pH 6 apparently depends on both the concentration of hydroquinone and the amount of oxide. This is in accord with the studies of Fukuzumi et al. (1975) and Ono et al. (1977) at pH 9, in which the formation of radicals obeys first-order kinetics with respect to both phenol concentration and the amount of Mn oxides. The presence of semiquinone radicals indicates that the reduction of hausmannite involves a one-electron transfer process. The radical concentration initially increases, but then decreases simultaneously with the consumption of dissolved O2 (Fig. 8-12). Once O2 is depleted, the concentration of free radical gradually increases again. The rapidly generated semiquinone anion radical is apparently slowly oxidized by dissolved O2 in solution. The radical becomes more abundant at relatively high concentrations of hydroquinone. Oxide suspensions containing high concentrations of hydroquinone have insufficient capacity to oxidize hydroquinone to quinone completely, resulting in the accumulation of the semiquinone radicals. Both evidence of the browning caused by the high-intensity absorption of conjugated chromophoric groups and upward shifts in the ultravioletvisible spectral baselines indicate that higher hydroquinone concentrations produce more polymers. Free radical coupling is probably involved in the polymerization since the existence of free radicals is correlated to hydroquinone concentration. The ultraviolet-visible absorption profiles of these polymers formed in the systems that are not sterilized (Kung and McBride, 1988) appear to be similar to those of phenol-derived polymers in the systems free

215

KINETICS OF REDOX REACTIONS 8

3.0

c:

- . - Radical --0-

0

O2

I..J

+-

+-

E

c: Q)

c: :::>

01

c:

... ... ... «

~

+-

u

0

L>

>-

-

~

2.0 5

0

(\I

0

+-

0

u

"0 0

0::

.0

"0

-

>

Q)

(5

1.0 3 0.0

en en 0

2 500

200

300 TIME (min)

Fig. 8-12. Concentration of p-benzosemiquinone radical (arbitrary units) and dissolved O 2 in solution as a function of time (Kung and McBride, 1988).

of microbial activities (Shindo and Huang, 1982, 1984b). However, it is essential that biotic processes should be eliminated by sterilization of the systems in future research on the kinetics and mechanisms of abiotic transformations of phenols on the surface of metal oxides. Shindo and Huang (1984b) reported that in sterilized systems, the rate and degree of the polymerization of phenolic compounds varies with the kinds of Mn oxides, the chemistry of the phenolic compounds, and the pH values of the systems. Figure 8-13 shows the influence of various oxides on changes in the degree of the darkening of hydroquinone solutions as a function of time at different pH values. In Fig. 8-13, the degree of the polymerization is expressed as the absorbance at 600 nm, since it is proportional to absorbance at 400 nm. The control system (without oxides) becomes noticeably colored only when the initial pH is 7.8 and the absorbance at 600 nm increases as time elapses. The addition of each Mn oxide greatly accelerated the darkening over the pH range of 4.0 to 7.8. The rate and degree of darkening varies with the Mn oxide and the pH values of the systems. The oxidative polymerization of hydroquinone in the Mn oxide systems is accelerated to a greater extent under near neutral conditions than under acidic conditions. The reduction of Mn02 consumes larger amounts of H + than that released by the oxidation of diphenols C6H4(OHh as indicated by the following reaction (Weast, 1978)

EO EO

=

1.208 V

[16]

= -0.6992 V

[17]

HUANG

216

LEGEND

E

c 0 0

CO

A. Initial pH of 4.0 2.0 1.~

a:s

Q)

o c

10

o Control x Birnessite <> Cryptomelane .. Pyrolusite o Fe oxide ~ AI oxide • 5i oxide

B. Initiol pH of 5.0

a:s

.D .... 0 U)

.D

«

C. Initial pH of 6.0

D. Initiol pH of 7.8

3.0

E

c

~:

2~

0 0

CO

a:s

2.0

Q)

o C

1~

a:s

.D 0

....

1.0

U)

.D

«

o.~

I

I

I

I

2

4

~

6

Reaction Period (d)

Reaction Period (d)

Fig. 8-13. Changes in the degree of the darkening of hydroquinone solution at different pH values as influenced by various oxides as a function of time (Shindo and Huang, 1984b).

The EO for the overall redox reaction is 0.509 V, indicating that the oxidation of diphenols by Mn02 is thermodynamically favorable. However, the existing literature (Schnitzer, 1982) indicates that the rate-determining step in the synthesis of humic substances, by oxidative polymerization of simple phenols and phenolic acids, is the formation of a semiquinone radical involving a one-electron transfer reaction. Some semiquinones, which are normally relatively unstable, will couple with each other to form stable humic acid polymers. In contrast to electron-transfer reactions, the coupling of radicals requires no activation energy (Chang and Allan, 1971). Therefore, coupling of semiquinones rather than the formation of Quinones appears to be kinetically the preferred reaction path for the conversion of diphenols to humic acid during the reduction of Mn oxides. When comparisons among the Mn oxide systems are made, the degree of hydroquinone darkening is higher in the presence of birnessite and cryptomelane than in the presence of pyrolusite at the early stages of the reaction period, whereas the reverse is true at the latter stages. Birnessite and

217

KINETICS OF REDOX REACTIONS

Table 8-12. The degree of the darkening of three phenolic compounds and dissolved Mn in the Mn oxide systems at the end of 6 h and 7 d (Shindo and Huang, 1984b). Reaction condition Phenolic Mn02t compoundt B C P B C P B C P B C P B C P B C P

Hy Hy Hy Hy Hy Hy Hy Hy Hy Hy Hy Hy Re Re Re

Ca Ca Ca

Initial Reaction pH period pH§ 4.0 4.0 4.0 4.0 4.0 4.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0

6h 6h 6h 7d 7d 7d 6h 6h 6h 7d 7d 7d 7d 7d 7d 7d 7d 7d

4.1 4.1 4.1 4.1 4.1 4.1 7.6 7.4 7.3 6.9 6.8 6.7 7.6 7.3 6.0 7.6 7.5 6.6

Final Eh(V)§

0.42 0.42 0.42

0.41 0.39 0.38 0.40 0.40 0.51 0.40 0.39 0.40

Dissolved Mn, JLg mL -1 in supernatant'

Absorbance at 600 nm#

425 432 355 430 470 570 138 115 100 275 258 230 225 235 12 213 250 178

0.16 0.17 0.07 0.54 0.54 0.68 1.24 0.36 0.16 2.26 2.52 2.80 1.64 1.40 0.02 0.44 0.22 0.11

t B, C, and P = birnessite, cryptomelane, and pyrolusite, respectively. tHy, Re, and Ca = hydroquinone, resorcinol, and cathechol, respectively. § The precision of the pH and Eh measurement is ±0.1 and ±0.01 V, respectively. , Mean of duplicates; the average of errors was ± 9 JLg mL -1. # Mean of duplicates; the average of errors was ±0.02. The absorbance of the supernatant was measured with a spectrophotometer directly or after dilution; the resulting absorbance was scaled by the dilution factor.

cryptomelane are short-range ordered Mn oxides; in contrast, pyrolusite is a longer-range ordered Mn oxide. The specific surface of both birnessite (277 m 2 g -I) and cryptomelane (346 m 2 g -I) is much higher than that of pyrolusite (8 m 2 g-I) (Oscarson et al., 1983a). The information described above suggests that the reaction between hydroquinone and birnessite or cryptomelane occurs more rapidly than that between hydroquinone and pyrolusite. At the end of 6 h, the same relationship exists for the amount of Mn dissolved at pH's of 4.0 and 6.0; the degree of the darkening increases with increasing amounts of Mn dissolved at both pH conditions (Table 8-12). However, at the latter stages, the degree of the darkening of hydroquinone in the pyrolusite system exceeds that of the birnessite and cryptomelane systems (Fig. 8-13 and Table 8-12). In these systems at the initial pH of 4.0, any Mn oxides added are almost dissolved due to the reduction at the end of 1 d. pyrolusite is a pure MnOb but cryptomelane and birnessite contain K in their structures (McKenzie, 1971). The content of Mn02 is thus higher in the pyrolusite system than in the cryptomelane and birnessite systems, accounting for the higher amount of Mn dissolved and the higher degree of the darkening in the former than in the latter at pH 4.0 at the end of 7 d. The amount of Mn dissolved at pH 6.0 is much lower than that at pH 4.0 (Table 8-12), and a portion of Mn oxides added is not dissolved at pH

218

HUANG

6.0. The darkening substances are likely adsorbed in larger amounts by shorter-range ordered Mn oxides, birnessite and cryptomelane, than by a longer-range ordered oxide, pyrolusite. Therefore, less adsorption of the darkening substances by pyrolusite of lower specific surface apparently accounts for the fact that the degree of hydroquinone darkening in the pyrolusite system exceeds that of the birnessite and cryptomelane systems at pH 6.0 at the end of 7 d, despite less dissolution of Mn (Table 8-12). Figure 8-14 shows the changes in the degree of darkening, (expressed as the absorbance at 600 nm) of resorcinol solution at the initial pH of 6.0 as influenced by various Mn oxides as a function of time. The addition of birnessite and cryptomelane greatly promotes the darkening of resorcinol.

LEGEND 0 x

.. o

3.0

Control Birnessite Cryptomelane Pyrolusite

0

Fe oxide

t:.

AI oxide

•

Si oxide

2.5

E c

0 0 to

-.,

2.0

0

1.5

u

c 0

.Q ~

0

III .Q

1.0


o

2

Reaction

3

4

Period

5

6

7

(d)

Fig. 8-14. Changes in the degree of the darkening of resorcinol solution at the initial pH of 6.0 as influenced by various oxides as a function of time (Shindo and Huang, 1984b).

KINETICS OF REDOX REACTIONS

219

But pyrolusite, which has a strong ability to darken hydroquinone (Fig. 8-13), only slightly promotes the darkening of resorcinol solution even at the end of 7 d (Fig. 8-14), and the amount of Mn dissolved in the pyrolusite system was extremely small (Table 8-12). This is attributed to: (i) a higher Eh value of the resorcinol solution (0.42 V) added, compared with the hydroquinone solution (0.3 V), and (ii) the differences in the surface chemistry of Mn oxides previously described. These factors retard the reduction of pyrolusite by resorcinol and the subsequent oxidative polymerization of resorcinol by pyrolusite. The higher the Eh value of the phenolic compound solution, the weaker is its reducing power since phenolic compounds act as electron donors. There is a great difference in the degree of the darkening and the amount of Mn dissolved between the birnessite and cryptomelane systems (Table 8-12). The degree of the darkening of catechol, which is expressed as the absorbances at 400 and 600 nm, is presented in Fig. 8-15. The presence of each Mn oxide substantially increases the absorbance at 400 nm. The degree of the darkening at 400 nm in the birnessite and cryptomelane systems shows a peak within 1 d, and then steadily increased as time elapses. At the end of 7 d, the degree of the darkening of catechol at 400 and 600 nm is higher in the birnessite and cryptomelane systems than in the pyrolusite system. The amount of Mn dissolved in catechol solution is also lowest in the pyrolusite system (Table 8-12). These results can be interpreted in the same way as for resorcinol, since the relationship between the degree of the darkening and Mn oxides or the amount of Mn dissolved for catechol is the same as that for resorcinol. The absorbance measured at 600 nm (initial pH of 6.0) at the end of 7 d in the Mn oxide systems generally follows the sequence: hydroquinone > resorcinol> catechol (Table 8-12). A generally much lower degree of darkening of catechol compared with hydroquinone and resorcinol in the Mn oxide systems is attributable to the retardation of the oxidative polymerization of catechol by the complexation of catechol with Mn of the Mn oxides. In the control systems (Table 8-13), humic acid formation was not detectable for any of the phenolic compounds studied. The addition of Mn oxides greatly accelerates the formation of humic acid. Like the degree of darkening, the yield of humic acid is significantly influenced by the kinds of Mn oxides and phenolic compounds, and the pH values. The yields of humic acids formed in the Mn02 systems are highly correlated (r 2 = 0.983) with the degree of darkening measured at 600 nm (Shindo and Huang, 1984b). Humic acids formed have a range of degrees of humification and are relatively highly humified. The nature of humic acids does not appear to be significantly influenced by the kinds of Mn oxides used and the pH of the system, but appears to be influenced by the kinds of phenolic compounds studied. Therefore, the results indicate that various Mn oxides can convert diphenols such as hydroquinone, resorcinol, and catechol to humic acids with a relatively high degree of humification by similar mechanisms over the pH range common in soil environments.

220

HUANG

LEGEND 0

Control

x

Birnessite

o

Cryptomelane

•

°

Fe oxide

t:.

AI oxide

•

Si oxide

2.0

E c:: 0

x

1.5

i

0

1.0

U

x

""()/

?~

•

c::

0

.a

en

x~

o

I»

... 0

Pyrolusite

0.5

.a

«

./

_____0

0-° -IQI.

»l

I

I

E c::

o o
e

1.0

0.5

=~?:: s -s;: I 2

lQl I

3

Reaction

I 4

I

5

===:~ I 6

~I 7

Period (d)

Fig. 8-15. Changes in the degree of the darkening of catechol solution at the initial pH of 6.0 as influenced by various oxides as a function of time (Shindo and Huang, I984b).

The effect of Mn oxides on the oxidative polymerization of hydroquinone is much greater than that of various other inorganic compounds such as short-range ordered Fe(III), AI, and Si oxides (Shindo and Huang, 1982), primary minerals (Shindo and Huang, 1985a), and clay minerals (Kumada, 1981; Shindo and Huang, 1985b). Furthermore, Mn oxide (birnessite), which is common in natural environments, greatly promotes the abiotic formation

221

KINETICS OF REDOX REACTIONS

Table 8-13. Effects of various oxides on the formation of humic acids at the end of the reaction period of 7 d (Shindo and Huang, 1984b). Reaction condition Oxidet No B C P Fe No B C P Fe No B C P Fe No B C P Fe

Initial pH 4.0 4.0 4.0 4.0 4.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0

Humic acid

Phenolic compoundr

Yield§

Hy Hy Hy Hy Hy Hy Hy Hy Hy Hy Re Re Re Re Re Ca Ca Ca Ca Ca

mg, C ND:j::j: 1.36 1.56 1.97 Trace ND 5.14 6.61 7.93 ND ND 4.00 3.58 ND ND ND 0.80 Trace Trace Trace

~log

K,

RF#

Conversion of phenolics added to humic acid tt %

--§§ 0.54 0.56 0.55

73 54 66

0.63 0.60 0.58

65 65 67

0.70 0.70

92 90

0.52

105

0 9.4 10.8 13.7 Trace 0 35.7 45.9 55.1 0 0 27.8 24.9 0 0 0 5.6 Trace Trace Trace

t No = none; B = birnessite; C = cryptomelane; and Fe = iron oxide. :j: Hy = hydroquinone; Re = resorcinol; and Ca = catechol. § 1 milliliter of 0.02 M KMn04 consumed was calculated as corresponding to 0.45 mg C (Kumada et al., 1967; Kumada, 1981). Mean of duplicates; the average of errors was ±0.09 mg. , The logarithm of the ratio of the absorbance at 400 nm to that at 600 nm. Mean of duplicates; the average of errors was ±0.01. # (Absorbance at 600 nmImL of 0.02 M KMn04 consumed by 30 mL of humic acid solution) x 1000. Mean of duplicates; the average of errors was ±3. tt Carbon content of phenolic compound added was 14.4 mg. Mean of duplicates; the average of errors was 0.6%. :j::j: Not detectable. §§ Not applicable because the yields were too small or not detectable.

of NHrN and nitrogenous polymers in hydroquinone-glycine systems in 24 h over the common pH range (4-8) of soils (Shindo and Huang, 1984a). Birnessite also catalyzes the polycondensation of pyrogallol and glycine and the subsequent formation of nitrogenous polymers that resemble natural humic substances in lR and ESR spectra (Wang and Huang, 1987). During the polycondensation, the decarboxylation of glycine is greatly promoted by birnessite especially in the presence of pyrogallol (Table 8-14). In an N2 atmosphere, the CO 2 release in the birnessite-glycine-pyrogallol systems is very drastically reduced. The amounts of NH 3 released from the birnessiteglycine-pyrogallol systems at pH 7.0 and 5.0 are 95.5 and 68.9 times, respectively, higher than those from the glycine-pyrogallol systems (Table 8-14). The presence of birnessite in the glycine-pyrogallol systems greatly enhances the formation of N-conlaining polymers at both pH 5.0 and 7.0 over a 90-h-

~

N

Table 8-14. The release of CO2 and the conversion of glycine-N to NH 4 , NH a, and N-polymers in the birnessite-glycine-pyrogallol systems at the end of a 90-h reaction period (Wang and Huang, 1987). Reaction condition t Birnessite

+§ + + +

Glycine

+ + + + + + + +

N in polymers:j:

Pyrogallol

+ +

-tt

-

+ +

-

CO2 release

Initial pH 7.0 5.0 7.0 5.0 7.0 5.0 7.0 5.0

1222 629 95.5 65 90 23

± ± ± ± ± ± 0 0

8' 3 0.4 1 2 2

(76 ± 31#

NH 4 + NH a

HA

FA

/lmol 840 ± 15 255 ± 3 72 ± 4 53.8 ± 0.5 8.8 ± 0.7 3.7 ± 0.4 ND ND

19.2 ± 0.3 9.2 ± 0.5 ND:j::j: ND 6.7 ± 0.2 2.2 ± 0.2 ND ND

75 ± 3 31 ± 1 ND ND 25.5 ± 0.7 7.3 ± 0.3 ND ND

t The experiment was conducted under air unless otherwise stated. The 100 mg of birnessite was suspended in 30 mL of aqueous solution that

contained 1.0 mmol of glycine and 0.5 mmol of pyrogallol. :j: Nitrogen in HA and FA formed in the supernatants of the reaction systems. In birnessite-glycine-pyrogallol systems, N in humic substances adsorbed on birnessite at pH 5.0 and 7.0 were 5.0 ± 0.4 and 2.1 ± 0.2 /lmol, respectively. § In the presence. , The average deviation from the mean. , The amount of CO2 released from the system under an N 2 atmosphere was in parenthesis. tt In the absence. :j::j: Not detectable.

:c e > Z

a'l

223

KINETICS OF REDOX REACTIONS

OH H 0 I II .)-yOH + NH 2 - C-C-OH lJ--OH I

1

MoO, H

.

o A-OH

U

OH

H 0 I II NH - C-C-OH 2 I

+

1

H

•

H 0 I I

NH -C-C-OH 2

I I H 0

h U I

OH

OH

I I

I

+

Polycondensoles

Fig. 8-16. Reaction of pyrogallol-derived free radicals with glycine (Wang and Huang, 1987).

reaction period. Birnessite is poorly crystalline and thus should have extensive exposed edge surfaces. These edges contain Mn of high oxidation numbers, e.g., Mn(III) and Mn(IV), which can serve as electron acceptors to promote the formation of pyrogallol-derived free radicals and the subsequent formation of polycondensates through their reaction with glycine (Fig. 8-16). Most of the released NH 3 can be attributed to deamination of glycine upon its reaction with pyrogallol-derived free radicals (Table 8-14). However, an appreciable amount of NH 3 released can also be directly derived from the deamination of glycine in the presence of birnessite. The edges of birnessite can adsorb and polarize O2 molecules that are a strong oxidant and promote the deamination and decarboxylation of glycine in the system (Fig. 8-17). More recent data reveal that birnessite greatly promotes the abiotic H I

H-C-COOH I

NH 2

Mn~

t

• co, + Nl~': other products NH+4

+

OH -

Fig. 8-17. Decarboxylation lind deamination of glycine as catalyzed by birnessite (Wang and Huang, 1987).

HUANG

224

Table 8-15. Recovery of 14C after reaction of ring-labeled 14C-ferulic acid (2.2 x 10- 4 mmol) with MnOz (11.5 mmol) (Lehmann and Cheng, 1988). Recovery of 14C Reaction time

By extraction t

min

O§ 2 5 10 30 60 120

By oxidationf

Total

% 88 54 28 23 20 17 14

2 35 61 62 70 77 76

90 89 89 85 90 94 90

t By solvent extraction with 82:15:2:1 ethyl acetate/methanollwater/l0% HCI solvent mixture.

:!: By dry combustion after solvent extraction. § For time 0, the ferulic acid was added to a mixture of MnOz and the extraction solution; and the mixture was then subjected to the same extraction procedure as others.

generation of CO 2 through its ability to cleave the ring of pyrogallol under ambient temperature and pressure (M.C. Wang and P.M. Huang's unpublished data). Besides polyphenolics, many organic compounds can solubilize Mn by reduction, including salicylic acid, pyruvic acid, and oxalic acids (Stone and Morgan, 1984a,b). Organics, such as malate (Jaurequi and Reisenauer, 1982) and glutamate (Traina and Doner, 1985) are oxidatively decomposed during the reduction of Mn oxides. Even monophenolic compounds, particularly those containing electron-donating substituent groups on the aromatic ring, can be oxidized by Mn oxides, releasing Mn 2+ (Lehmann et aI., 1987; Stone, 1987). Phenolic acids are shown to be oxidized rapidly in the presence of Mn02 to form a number of soluble products that were detectable by high pressure liquid chromatography (HPLC) (Lehmann and Cheng, 1988). Some of the soluble reaction products of oxidation have somewhat higher molecular weights than the parent compounds as shown by mass spectrometry. Unlike the products of enzymatic polymerization that range from dimers to hexamers found by Liu et aI. (1981) and Bollag et aI. (1982), the soluble products of chemical reaction of ferulic acid and Mn02 do not contain any ferulic acid-derived polymers. Evidently, the oxidized products of ferulic acid are rapidly sorbed to Mn02 surfaces and become less extractable with time, whereas the unextracted reaction products increase (Table 8-15). The 14C label recovered by extraction could not be identified by HPLC as ferulic acid. Thus, the 14C label that is sorbed on the Mn02 surface and not extracted by the solvent is probably also not ferulic acid, but reaction products of ferulic acid and Mn02. The reaction products of ferulic acid sorbed on the Mn02 surface are far more extractable after acid or base hydrolysis than without hydrolysis. The organic products sorbed on the Mn02 surface appear to exist as high surface-area polymers, similar to the humic polyers reported

225

KINETICS OF REDOX REACTIONS

Table 8-16. Kinetic constants for polyhydroxyphenolic acid oxidation by soil and manganese oxide suspensions (Pohlman and McColl, 1989lt. Challenge A horizon Compound

Rate constants L mol " !

2,3-dihydroxybenzoic 2,5-dihydroxybenzoic 2,6-dihydroxybenzoic 3,4-dihydroxybenzoic 3,5-dihydroxybenzoic Gallic acid Syringic acid Vanillic acid

acid acid acid acid acid

ND§ 0.06 0' 0.10 0 0.25 ND ND

oy2:j:

Mn02 Rate constants

oy2

Lmol- 1s- 1

s-1

ND 0.99 ND 0.96 ND 0.97 ND ND

0.03 0.04 ND 0.04 0 0.05 0.01 0

0.98 0.98 ND 0.99 ND 0.99 0.99 ND

t Oxidations were run using 10 g L -1 soil and 2.5 x 10 -4 M phenolic acid, or 0.19 g L -1 Mn02 and 5.0 x 10 -4 M phenolic acid at pH 4.5 and 30°C. :j: Correlation for regression equation of second-order kinetics of oxidation of polyhydroxyphenolic acid. § ND = not determined. , No oxidation of phenolic acid within 120 min of reaction.

by Shindo and Huang (1984b) following the reaction of diphenols with Mn oxides. The nature of the organic products sorbed on the MnOz surface needs to be investigated in detail. A kinetic model is presented by Pohlman and McColl (1989) to describe the initial and rapid redox processes between polyhydroxyphenolic acid and soil or Mn oxide suspensions. The oxidation process of polyhydroxybenzoic acid by soil and Mn oxides follows second-order kinetics. The rate constants derived from the model are similar in magnitude in both suspensions for the organic reductants studied (Table 8-16). Polyhydroxyphenolic acids with para- and ortho-OH groups are rapidly oxidized by Mn oxides with spectral evidence suggesting that the reaction leads to polymeric humic products probably via semiquinone or benzoquinone derivatives. By contrast, polyhydroxyphenolic acids with meta-oriented phenolic-OH groups are not oxidized by soil or Mn oxide suspensions within a 120-min reaction period. Presumably these compounds are not capable of being oxidized to semiquinone or benzoquinone intermediates. The rapid disappearance of polyhydroxyphenolic acids is accompanied by formation of Mn 2+ and colored humic products in both soil and Mn oxide suspensions. These results provide further evidence that abiotic oxidation of certain organics can lead to the formation of humic substances and the mobilization of Mn in nature. The existing information discussed above indicates that various Mn oxides differ in their ability to catalyze oxidative polymerization, polycondensation, and degradation of organics. Abiotic formation of humic substances, C turnover. and N transformations in nature as catalyzed by Mn oxides, thus, deserves in-depth research.

HUANG

226

SUMMARY AND CONCLUSIONS

Manganese oxides and oxyhydroxides are widely distributed in terrestrial and aquatic environments. They occur as coatings on other soil and sediment particles and as discrete particles and exist in close association with many other chemical species. The surfaces of Mn oxides and oxyhydroxides have the ability to promote a series of redox reactions in the environment. Among metalloids, the toxic As(llI) has been proven to be oxidized to the less toxic As(V) by Mn oxides. The ability of Mn oxides to oxidize As(III) varies with their structural and surface properties. The extent of masking of the electron-accepting sites on the Mn oxides for oxidation of As(lIl) to As(V) substantially varies with the kinds and levels of coatings. Reactive Mn oxides may be added to some environments, that have been contaminated with As(III), to alleviate the toxicity of As(III) through converting As(III) to the less toxic and mobile As(V). Trace metals such as Cr(III), Pu(III), and Co(Il) can be oxidized in the disproportionation process of Mn oxides and oxyhydroxides. Oxidation of trace metals can greatly influence their solubility and mobility. When Cr(IlI) and Pu(III/IV) are oxidized to Cr(VI) and Pu(VI), these elements are quite mobile, because they are not sorbed by soil components to any extent. Manganese oxide can thus enhance the mobility, toxicity, and food chain contamination of Cr and Pu. On the other hand, oxidation of Co(lI) to Co(III) by Mn oxides decreases its solubility and mobility in soil and aquatic environments. Manganese oxides, which have different structural and surface properties, vary substantially in their ability to promote the precipitation and crystallization of Fe oxides and oxyhydroxides. The Mn(lI) dissolved from Mn oxides in the presence of Fe(lI) also influences the crystallization of oxidation products of Fe(II). The Fe oxides formed as influenced by Mn oxides and dissolved Mn(lI) range from lepidocrocite, goethite, maghemite, Akaganeite, feroxyhyte, magnetite, honessite-like minerals, to noncrystalline Fe oxides. Therefore, Mn oxides deserve close attention in the genesis of Fe oxides. The surfaces of Mn oxides promote the oxidative polymerization of many polyphenolics, the polycondensation of pyrogallol and glycine, and the formation of humic substances. Many organics are oxidatively decomposed by Mn oxides during the reduction of Mn(III) or Mn(IV). The role of Mn oxides in C turnover and N transformations should, thus, be studied in depth. Besides natural organics, the kinetics of the degradation of certain xenobiotics by Mn oxides and oxyhydroxides in soils and related environments warrant investigation. ACKNOWLEDGMENTS

Contribution no. R658, Saskatchewan Institute of Pedology, University of Saskatchewan, Saskatoon, SK, Canada. Financial Support (Grant no. A2383-Huang) from the Natural Sciences and Engineering Research Council of Canada is appreciated.

KINETICS OF REDOX REACTIONS

227

REFERENCES Amacher, M.L., and D.E. Baker. 1982. Redox reactions involving chromium, plutonium, and manganese in soils, DOE/DP/OY515.1. Inst. Res. Land and Water Resour. Pennsylvania State Univ., University Park. Andreae, M.O. 1978. Distribution and speciation of arsenic in natural waters and some marine algae. Deep-Sea Res. 25:391-402. Arrhenius, G. 1963. Pelagic sediments. p. 655-727. In M. Hill (ed.) The sea, ideas and observations. Vol. 3, Interscience, John Wiley & Sons, New York. Bartlett, R.J., and B. James. 1979. Behavior of chromium in soils. III. Oxidation. J. Environ. Qual. 8:31-35. Bielski, B.H.J., and J .M. Gebicke. 1967. Atlas of electron spin resonance spectra. Academic Press, New York. Bollag, J.-M., S.Y. Liu, and R.D. Minard, 1982. Enzymatic oligomerization of vanillic acid. Soil BioI. Biochem. 14:157-163. Bramin, R.S., and C.C. Foreback. 1973. Methylated forms of arsenic in the environment. Science 182:1247-1249. Bricker, O. 1965. Some stability relations in the system Mn-OrHzO at 25 0 C and one atmosphere total pressure. Am. Mineral. 50:1296-1354. Chang, H.M., and G.G. Allan. 1971. Oxidation. p. 433-485. In K.V. Sarkanen and C.H. Ludwig (ed.) Lignins. Wiley Interscience, New York. Chao, T.T., and L. Zhou. 1983. Extraction technique for selective dissolution of amorphous iron oxides from soils and sediments. Soil Sci. Soc. Am. J. 47:225-232. Cleveland, J.M. 1970. The chemistry of plutonium. Gordon & Breach, New York. Cornell, R.M., and R. Giovanoli. 1987. Effect of manganese on the transformation of ferrihydrite into goethite and jacobsite in alkaline media. Clays Clay Miner. 35:11-20. Crerar, D.A., and H.L. Barnes. 1974. Deposition of deep-sea manganese nodules. Geochim. Cosmochim. Acta 38:279-300. Detourney, P.J., M. Ghodsi, and R. Derie. 1975. Influence de la temperature et de la presence des Ions strangers sur la cinetique et la presence des Ions strangers sur la cinetique et la mecanisme de formation de la goethite en milieu aquex. Z. Anorg. Allg, Chern. 412:184-192. Dillard, J.G., and C.N. Schenck. 1986. Interaction of Co(ll) and Co(I1I) complexes on synthetic birnessite: Surface characterization. p. 503-522. In J .A. Davis and K.F. Hayes (ed.) Geochemical processes at mineral surfaces. ACS Symp. Ser. 323. ACS., Washington DC. E1tantawy, I.M., and P.W. Arnold. 1973. Reappraisal of ethylene glycol mono-ethyl ether (EGME) method for surface area estimations of clays. J. Soil Sci. 24:232-238. Felbeck, G.T., Jr. 1965. Structural chemistry of soil humic substances. Adv. Agron. 17:327-368. Ferguson, J.F., and J. Gavis. 1972. A review of the arsenic cycle in natural waters. Water Res. 6:1259-1274. Flaig, W., H. Beutelspacher, and E. Rietz. 1975. Chemical composition and physical properties of humic substances. p. 1-211. In J.E. Gieseking (ed.) Soil components, Vol. 1. Organic components. Springer-Verlag, Berlin. Fordham, A.W., and K. Norrish. 1979. Arsenate-73 uptake by components of several acidic soils and its implications for phosphorus retention. Aust. J. Soil Res. 17:307-316. Fukuzumi, S., Y. Ono, and T. Keii. 1975. ESR studies on the formation of p-benzosemiquinone anion over manganese dioxide. Int. J. Chern. Kinetics 7:535-546. Haider, K., J.P. Martin, and Z. Filip. 1975. Humus biochemistry. p. 195-244. In E.A. Paul and A.D. McLaren (ed.) Soil biochemistry, Vol. 4. Marcel Dekker, Inc., New York. Hem, J.D. 1978. Redox processes at surfaces of manganese oxide and their effects on aqueous metal ions. Chern. Geol. 21:199-218. Hess, R.E. and R.W. Blanchar. 1976. Arsenic stability in contaminated soils. Soil Sci. Soc. Am. J.40:847-852. Holm, N.G. 1985. New evidence for tubular sturcutre of l3-iron (III) oxide hydroxide-akaganeite. Origin Life Evol. Biosphere 15:131-139. Huang, P.M. 1975. Retention of arsenic by hydroxy-aluminum on surfaces of micaceous mineral colloids. Soil Sci. Soc. Am. Proc. 39:271-274. Huang, P.M. 1980. Adsorption processes in soil. p. 47-59. In O. Hutzinger (ed.) Handbook of environmental chemistry . Springer-Verlag, Amsterdam. Hurst. H.M., and N.A, Burllcs. 1967. Lignin and humic acids. p. 260-286. In A.D. McLaren and G.H. Peterson (ed.) Soil biochemistry, Vol. I. Dekker, New York.

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Jaurequi, M.A., and H.M. Reisenauer. 1982. Dissolution of oxides of manganese and iron by root exudate components. Soil Sci. Soc. Am. J. 46:314-317. Jenne, E.A. 1968. Controls on Mn, Fe, Co, Ni, Cu, and Zn concentrations in soils and water: The significant role of hydrous Mn and Fe oxides. Adv. Chern. Ser. 73:337-387. Kolthoff, I.M. 1921. Iodometric studies. VII. Reactions between arsenic trioxide and iodine. Anal. Chern. 60:393-406. Kononova, M.M. 1966. Soil organic matter, its nature, its role in soil formation, and in soil fertility. 2nd ed. Pergamon, Oxford. Krishnamurti, G.S.R., and P.M. Huang. 1987. The catalytic role of birnessite in the transformation of iron. Can. J. Soil Sci. 67:533-543. Krishnamurti, G.S.R., and P.M. Huang. 1988. Influence of manganese oxide minerals on the formation of iron oxides. Clays Clay Miner. 36:467-475 Krishnamurti, G.S.R., and P.M. Huang. 1989. Influence of Mn2+ and pH on the formation of iron oxides from ferrous chloride and ferrous sulfate solutions. Clays Clay Miner. 37:451-458. Kumada, K. 1981. Chemistry of soil organic matter. 2nd ed. (In Japanese.) Japan Scientific Soc. Press, Tokyo. Kumada, K., and H. Kato. 1970. Browning of pyrogallol as affected by clay minerals. I. Classification of clay minerals based on their catalytic effects on the browning reaction of pyrogallol. Soil Sci. Plant Nutr. (Tokyo) 16:195-200. Kumada, K., O. Sato, Y. Ohsumi, and S. Ohta. 1967. Humus composition of mountain soils in central Japan with special reference to the distribution of P type humic acid. Soil Sci. Plant Nutr. (Tokyo) 13:151-158. Kung, K.-H., and M.B. McBride. 1988. Electron transfer processes between hydroquinone and hausmannite (Mn304)' Clays Clay Miner. 36:297-302. Kyuma, K., and K. Kawaguchi. 1964. Oxidative changes of polyphenols as influenced by allophane. Soil Sci. Soc. Am. Proc. 28:371-374. Larson, R.A., and J.M. Hufnal. 1980. Oxidative polymerization of dissolved phenols by soluble and insoluble inorganic species. Limnol. Oceanogr. 25:505-512. Lehmann, R.G., and H.H. Cheng. 1988. Reactivity of phenolic acids in soil and formation of oxidation products. Soil Sci. Soc. Am. J. 52:1304-1309. Lehmann, R.G., H.H. Cheng. and J.B. Harsh. 1987. Oxidation of phenolic acids by soil iron and manganese oxides. Soil Sci. Soc. Am. J. 51:352-356. Liu, S.-Y., R.D. Minard, and J.-M. Bollag. 1981. Oligomerization of syringic acid, a lignin derivative, by a phenoloxidase. Soil Sci. Soc. Am. J. 45:11oo-Il05. Martin, J.P., and K. Haider. 1971. Microbial activity in relation to soil humus formation. Soil Sci. III :54-63. McBride, M.B. 1989a. Oxidation of dihydroxybenzenes in aerated aqueous suspensions of birnessite. Clays Clay Miner. 37:341-347. McBride, M.B. 1989b. Oxidation of 1,2- and 1,4-dihydroxybenzene by birnessite in acidic aqueous suspension. Clays Clay Miner. 37:479-486. McKenzie, R.M. 1971. The synthesis of birnessite, cryptomelane, and some other oxides and hydroxides of manganese. Mineral. Mag. 38:493-502. McKenzie, R.M. 1981. The surface charge on manganese dioxides. Aust. J. Soil Res. 19:41-50. McKenzie, R.M. 1989. Manganese oxides and hydroxides. p. 439-465. In J.B. Dixon and S.B. Weed (ed.) Minerals in soil environments. 2nd ed. SSSA, Madison, WI. Morgan, J.J., and W. Stumm. 1964. Colloid-chemical properties of manganese dioxide. J. Colloid Sci. 19:347-359. Murray, J.W., and J.G. Dillard. 1979. The oxidation of cobalt(II) adsorbed on manganese dioxide. Geochim. Cosmochim. Acta 43:781-787. Naumov, G.B., B.N. Ryzhenko, and I.L. Khodakovsky. 1971. Handbook of thermodynamic data (translated by G.J. Soleimani, 1974) Rep. PB-266 722. U.S. Dep. Comm., Natl. Tech. Int. Serv., Springfield, VA. Ono, Y., T. Matsumura, and S. Fukuzumi. 1977. Electron spin resonance studies on the mechanism of the formation of p-benzosemiquinone anion over manganese dioxide. J. Chern. Soc. Trans. 2:1421-1424. Oscarson, D.W., P.M. Huang, and W.K. Liaw. 1980. The oxidation of arsenite by aquatic sediments. J. Environ. Qual. 9:700-703. Oscarson, D.W., P.M. Huang, C. Defosse, and A. Herbillon. 1981a. The oxidative power of Mn(lV) and Fe(I1I) oxides with respect to As(lII) in terrestrial and aquatic environments. Nature (London). 291:50-51.

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Oscarson, D.W., P.M. Huang, and W.K. Liaw. 1981b. The role of manganese in the oxidation of arsenite by freshwater lake sediments. Clays Clay Miner. 29:219-225. Oscarson, D.W., W.K. Liaw, and P.M. Huang. 1981c. The kinetics and components involved in the oxidation of arsenite by freshwater sediments. Verh. Int. Ver. Theor. Angew. Limnol. 21:181-186. Oscarson, D.W., P.M. Huang. W.K. Liaw and U.T. Hammer. 1983a. Kinetics of oxidation of arsenite by various manganese dioxides. Soil Sci. Soc. Am. J. 46:644-648. Oscarson, D.W., P.M. Huang, and U.T. Hammer. 1983b. Oxidation and sorption of arsenite by manganese dioxide as influenced by surface coatings of iron and aluminum oxides and calcium carbonate. Water, Air, Soil Pollut. 20:233-244. Parfitt, R.L. 1978. Anion adsorption by soils and soil materials. Adv. Agron. 30:1-51. Penrose, W.R. 1974. Arsenic in the marine and aquatic sediments: analysis, occurrence and significance. CRC Crit. Rev. Environ. Control 4:465-482. Pohlman, A.A., and J.G. McColl. 1989.Organic oxidation and manganese and aluminum mobilization in forest soils. Soil Sci. Soc. Am. J. 53:686-690. Postma, D. 1985. Concentration of Mn and separation from Fe in sediments. I. Kinetics and stoichiometry of the relation between birnessite and dissolved Fe(lI) at 10 0 C. Geochim. Cosmochim. Acta 49:1023-1033. Pourbaix, M.J.N. 1963. Atlas d'equllibres electrochimiques at 25 0 C. Gauthier-Villars, Paris. Rai, D., and R.J. Serne. 1977. Plutonium activities in soil solutions and the stability and formation of selected plutonium minerals. J. Environ. Qual. 6:89-95. Scheffer, F., B. Meyer, and E.A. Niederbudde. 1959. Huminstoffbildung unter Katalyischer Einwirkung naturlich vorkommender Eisenverbindungen im Modellversuch. Z. Pflanzenernaehr, Dueng. Bodenkd. 87:26-44. Scheffer, F., and B. Ulrich. 1960. Humus and Humusdungung. Ferdinand Enke Verlag, Stuttgart. Schnitzer, M. 1982. Quo vadis soil organic matter research. Panel discussion papers. In Whither soil research. Trans. Int. Congr, Soil Sci., 12th. 5:67-78. Schnitzer, M., and S.U. Khan. 1972. Humic substances in the environment. Marcel Dekker, Inc., New York. Schwertmann, U. 1985. The effect of pedogenetic environments on iron oxide minerals. Adv. Soil Sci. 1:171-200. Shindo, H., and P.M. Huang. 1982. Role of Mn(lV) oxide in abiotic formation of humic substances in the environment. Nature (London) 298:363-365. Shindo, H., and P.M. Huang. 1984a. Significance of Mn(lV) oxide in abiotic formation of organic nitrogen complexes in natural environments. Nature (London) 308:57-58. Shindo, H., and P.M. Huang. 1984b. Catalytic effects of manganese(lV), lron(III), aluminum, and silicon oxides on the formation of humic polymers. Soil Sci. Soc. Am. J. 48:927-934. Shindo, H., and P.M. Huang. 1985a. Catalytic polymerization of hydroquinone by primary metals. Soil Sci. 139:505-511. Shindo, H., and P.M. Huang. 1985b. The catalytic power of inorganic components in the abiotic synthesis of hydroquinone-derived humic polymers. Appl. Clay Sci. 1:71-81. Stone, A.T. 1987. Reductive dissolution of manganese (1I1)/(IV) oxides by substituted phenols. Environ. Sci. Technol. 21:979-988. Stone, A.T., and J.J. Morgan. 1984a. Reduction and dissolution of manganese (III) and manganese (IV) oxides by organics. 1. Reaction with hydroquinone. Environ. Sci. Technol. 18:450-456. Stone, A.T., and J.J. Morgan. 1984b. Reduction and dissolution of manganese (III) and manganese (IV) oxides by organics. 2. Survey of the reactivity of organics, Environ. Sci. Technol. 18:617-624. Stumm, W., and J.J. Morgan. 1980. Aquatic chemistry. 2nd ed. Wiley-Interscience, New York. Taylor, R.M., and R.M. McKenzie. 1966. The association of trace elements with manganese minerals in Australian soils. Aust. J. Soil Res. 4:29-39. Taylor, R.M., R.M. Mckenzie, and K. Norrish. 1964. The mineralogy and chemistry of manganese in some Australian soils. Aust. J. Soil Res. 2:235-248. Traina, S.J., and H .E. Doner. 1985. Copper-manganese (II) exchange on a chemically reduced birnessite. Soil Sci. Soc. Am. J. 49:307-313. Wagman, D.O., W.H. Evans, V.B. Parker, I. Halow, S.M. Bailey, and R.H. Schumm. 1968. Selected values of chemical thermodynamic properties. National Bureau Standards, Tech. Note 270-3. Nltl. Rur. Stund., Washington, DC.

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Wagman, D.O., W.H. Evans, V.B. Parker, I. Halow, S.M. Bailey, and R.H. Schumm. 1969. Selected values of chemical thermodynamic properties. National Bureau Standards, Tech. Note 270-4. Nat!. Bur. Stand., Washington, DC. Walsh, L.M., and D.R. Kenney. 1975. Behavior and phytotoxicity of inorganic arsenicals in soils. p. 35-52. In E.A. Woolson (ed.) Arsenical pesticides. ACS, Washington, DC. Wang, M.C., and P.M. Huang. 1987. Polycondensation of pyrogallol and glycine and the associated reactions as catalyzed by birnessite. Sci. Total Environ. 62:435-442. Wang, T.S.C., P.M. Huang, C.H. Chou, and J.H. Chen. 1986. The role of soil minerals in the abiotic polymerization of phenolic compounds and formation of humic substances. p. 251-258. In P.M. Huang and M. Schnitzer (ed.) Interactions of soil minerals with natural organics and microbes. SSSA Spec. Pub!. 17. SSSA, Madison, WI. Wang, T.S.C., S.W. Li, and Y.L. Ferng. 1978. Catalytic polymerization of phenolic compounds by clay minerals. Soil Sci. 126:15-21. Wang, T.S.C., M.M. Kao, and P.M. Huang. 1980. The effect of pH on the catalytic synthesis of humic substances by illite. Soil Sci. 129:333-338. Weast, R.C. (ed.) 1978. CRC handbook of chemistry and physics. 58th ed. CRC Press, Inc., West Palm Beach, FL. Webb. J.L. 1966. Enzyme and metabolic inhibitors. Vo!. III. Academic Press, Inc., New York. Wertz, J.E., and J.L. Vivo. 1955. Electron spin resonance of semiquinone. J. Chern. Physics 23:2441-2442.

9

Oxidation and Hydrolysis of Ionizable Organic Pollutants at Hydrous Metal Oxide Surfaces Alan T. Stone

Department of Geography and Environmental Engineering Johns Hopkins University Baltimore, Maryland

ABSTRACT Adsorption of ionizable organic pollutants onto hydrous metal oxide surfaces in soils, sediments, and aquifers can have an important impact on pathways and rates of chemical transformations. In some instances, a particular degradative pathway can only occur at the oxide/water interface, for example, because of the low solubility of these higher-valent metals in most natural waters. In other instances, the unique chemical microenvironment of the oxide/water interface may catalyze transformations that otherwise would have occurred in solution. Hydrolysis of two carboxylic acid esters catalyzed by hydrous metal oxides is discussed. A detailed understanding of adsorption phenomena provides the basis for assessing the nature and importance of surface chemical transformations.

Adsorption and partitioning are of central importance in determining transformation rates and pathways of organic pollutants in the environment. This is particularly true for soils, sediments, and aquifers where the solids fraction is high. Pollutants that remain predominantly in the aqueous phase are the most mobile, spreading contamination over a wide area. Sorption of pollutants by mineral surfaces and by organic aggregates retards or prevents migration, and exposes them to chemical microenvironments that may modify rates of chemical transformations (Zepp and Wolfe, 1987). Our goal is to understand and predict pathways and rates of chemical transformations under these complex heterogeneous conditions. In order to meet this goal, (i) adsorption and partitioning of organic pollutants must be understood, (ii) the nature and reactivity of solids-bound metals and organic functional groups must be determined, and (iii) unique or unusual characteristics of surface Copyright (C) 1991 Soil Science Society of America, 677 S. Segoe Rd., Madison, WI 53711, USA. Rates of Soli Chrmtcat Processes. SSSA Special Publication no. 27. 231

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chemical reactions must be identified. It is quite evident that surface chemical reactions are a necessary and integral part of models that accurately describe the dynamics of important pollutants.

SURFACE CHEMICAL REACTIONS: AN OVERVIEW

The following physical and chemical steps are involved in all surface chemical reactions: 1. Movement of reactant molecules into the interfacial region by convection, diffusion, or electrical migration. 2. Diffusion of reactant molecules within the interfacial region. 3. Surface chemical reaction: ligand replacement, electron and group transfer reactions, addition or elimination reactions. 4. Outward movement of product molecules from the interfacial region out to bulk solution. Overall rates of reaction may depend upon rates of one or several of the steps listed above. Many of the more important and unique qualities of interfacial reactions arise from strong interconnections between surface chemical reactions and mass transport.

PROPERTIES OF THE HYDROUS METAL OXIDE SURFACE

Our examination of reactions at hydrous metal oxide surfaces must take length scales and dimensionality into account. On a macroscopic scale, sediment size and packing affect the flow of water; fine-grained sediments are less permeable to groundwater than coarse-grained sediments. A contaminant plume, for example, may be diverted around fine-grained sediments through neighboring coarse-grained sediments. On a microscopic scale, the contact of soil water and groundwater with particle surfaces is important; the presence or absence of interior pores and the total available surface area influences transport of reactants to mineral surfaces and the outward flux of products. The atomic scale introduces a new level of complexity. The nature, density, and arrangement of lattice-bound atoms in three-dimensional space defines the geometry of solute adsorption. Our discussion of mineral surfaces will be restricted to simple oxide and hydroxide minerals that are widely used in adsorption studies (Table 9-1). Under strong weathering conditions, these minerals may comprise a substantial fraction of the available surface area in soils and aquifers. More complex minerals, including parent material and partially weathered products (especially aluminosilicates), are of equal or greater importance in most other subsurface environments. Excellent reviews of the equilibrium and reaction chemistry of aluminosilicate surfaces are available (Voudrias and Reinhard, 1986; Mortland, 1970).

233

ORGANIC POLLUTANT OXIDATION

Table 9-1. Oxide minerals important in soils are listed below, along with their mineral stoichiometry and crystal system. Oxide

Crystal system

Hematite (Fe203) Corundum (AI20 3) Geothite (FeOOH) Diaspore (AIOOH)

Trigonal (rhombohderal) Trigonal (rhombohedral) Orthorhombic Orthorhombic Orthorhombic Orthorhombic Tetragonal Tetragonal Tetragonal Orthorhombic Trigonal (rhombohedral)

Lepidocrocite (FeOOH) Boehmite (AIOOH) Pyrolusite (Mn02) Rutile (Ti0 2) Anatase (Ti0 2) Brookite (Ti0 2) Quartz (Si0 2 )

The simple oxide and hydroxide minerals exhibit important characteristics common to all minerals. The relative numbers of various component atoms are given by chemical stoichiometry. These atoms may be arranged in three-dimensional space in different ways. Geothite and lepidocrocite, for example, share the same stoichiometry (FeOOH), but Fe-O and Fe-OH bond lengths and geometric relationships between octahedrally coordinated Fe atoms are different. As a consequence, the coordinative environment and accessibility of Fe atoms to incoming adsorbate molecules are different for the two minerals. In other situations, minerals comprised of different metals, such as hematite (Fez03) and corundum (Alz0 3) , have similar threedimensional structures. In situations where surface structure is more important than the nature of the incorporated metal, hematite and corundum should exhibit similar behavior. It is very likely that structural characteristics of hydrous metal oxide surfaces influence adsorption, since the surface structure must play some role in determining the conformation and "footprint" of adsorbed molecules. In reactions where net growth (precipitation) or depletion (dissolution) of a surface takes place, structural characteristics determine the accessibility of underlying lattice-bound atoms and ways that the structure can be built upon or broken apart. Although a tremendous amount is already known about the adsorption of gases onto solids, considerably less is known about adsorption onto solids from aqueous solution. Each mineral possesses cleavage planes that define the faces in contact with solution. The distances and arrangement of lattice-bound atoms are different for each cleavage plane. Crystallographic information can be used to calculate atomic arrangements on each crystal face. Recently Hiemstra et al. (l989a,b) used this information to estimate pKa values for surface groups on various lattice planes of important hydrous metal oxide minerals. Unless individual faces are examined in isolation (by blocking off other faces present on macroscopic crystals), adsorption measurements reflect the combined contribution from all faces exposed to solution.

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One last levelof detail remains for the description of hydrous metal oxide surfaces: an electronic or "bonding" level for lattice-bound metals and ligands. Although hematite and corundum have similar geometric structure, the nature of the surface-bound metal is quite different; Fe(III) is a transition metal with a partially filled d-orbital (d 5) , while AI(III) is a nontransition metal, binding ligands through s- and p-orbitals. The effects of electronic structure on the formation of coordination complexes in solution are wellunderstood, providing a basis for understanding analogous complexes on mineral surfaces (Stumm et aI., 1980). In fact, strong correlations have been found between equilibrium constants for complex formation in solution and for complex formation on hydrous metal oxide surfaces (Kummert and Stumm, 1980; Stumm et al., 1980). It should always be kept in mind, however, that surface metal centers have one or more bonds to lattice-bound ligands, which influence the stability of surface complexes (equilibrium constants) and the lability of surface sites (rates of ligand replacement). The next section will describe how other forces, in addition to surface complex formation, influence the adsorption of organic compounds onto hydrous metal oxide surfaces.

ADSORPTION OF ORGANIC COMPOUNDS

Adsorption of low molecular weight (MW < 500) organic compounds at the oxide/water interface is driven by the combined effects of (i) innerand outer-sphere complex formation and direct chemical bonding (specific adsorption), (ii) electrostatic interaction involving association with the diffuse double layer, (iii) exclusion from aqueous solution due to hydrophobic effects, and (iv) interactions with coadsorbed species. For larger molecules, entropy changes of adsorbed molecules and associated waters of hydration also become important. Recent advances in our understanding of Types 1 and 2 phenomena have improved predictions concerning effects of adsorbate concentration, ionic strength, and pH on the extent of organic compound adsorption (Davis and Leckie, 1978; Kummert and Stumm, 1980). Type 3 phenomena have been extensively studied with fully hydrophobic molecules and with well-behaved surfactant compounds (See, for example, Karickhoff et aI., 1979). Each of the phenomena listed above will now be examined in greater detail. Surface Complex Formation

As mentioned earlier, complex formation reactions at hydrous metal oxide surfaces can be treated as an extension of classic coordination chemistry; metal centers on mineral surfaces participate in inner-sphere and outersphere coordination reactions with molecules adsorbed from overlying solution, including H2 0 , OH -, 0 2 - , and solute molecules (Schindler, 1981; Schindler and Stumm, 1987). A variety of protonation/deprotonation and complex-formation reactions determine the speciation of surface sites. A few

ORGANIC POLLUTANT OXIDATION

235

examples are given below, illustrating reactions on an Fe oxide surface (Schindler, 1981; Schindler and Stumm, 1987) Protonation/Deprotonation: > Fe-OH 2+ - > Fe-OH

+ H+

[1]

>Fe-OH - >Fe-O-

+ H+

[2]

Adsorption of Metal Ions: > Fe-OH

+ Pb

(H 20)g+

=

> Fe-O-Pb (H 20)/

+ H 30 +

[3]

Inner-Sphere Adsorption of Ligands: > Fe-OHt + s01- - > Fe-OS03- + H 20,

[4]

> Fe-OH

+ H 2A - > Fe-AH + H 20

[5]

> Fe-OH

+ H 2A - > Fe-A - + H 30 +

[6]

Outer-Sphere Surface Complex Formation: > Fe-OH2+

+ CI04- = (> FeOHt, CI04- )

> Fe-OH >Fe-OH

+ H 2A - (> FeOH, H 2A)

+ Pb(H20)g+ - [>Fe-OH, Pb(H 20)g+].

[7] [8] [9]

Each reaction has a corresponding equilibrium constant, which is used to find the abundance of various surface species at equilibrium. The symbol " > " denotes bonds between surface metal centers and lattice donor groups, and H 2A represents an organic compound containing two donor groups. Reactions [1] to [9] are generalizations; additional information that may be important to understanding surface speciation include bond lengths and structures of adsorbed species (Hayes et al., 1987) and heterogeneities on hydrous metal oxide surfaces (Benjamin and Leckie, 1981). Adsorption of organic ligands is represented by Reactions [5], [6], and [8] (see Sigg and Stumm, 1981; Stumm et al., 1980). A variety of functional groups can participate in complex formation: carboxylate, carbonyl, phenolate, alcoholic, amino, and heterocyclic (N, S, and 0) groups are among the important participating groups. Organic compounds may bind directly to the metal center via inner-sphere surface complex formation (Reactions [5] and [6]), or indirectly, via outer-sphere surface complex formation (Reaction [8]). In outer-sphere coordination, one or more layers of molecules separates the adsorbate from the surface metal center. Rates of inner-sphere complex formation are limited by the lability, or ligand replacement rate, of the surface metal center. Outer-sphere complex formation can occur more quickly, since the energies of bonds being made and broken are substantially weaker.

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The inner coordination sphere of surface metal centers may be occupied by more than one adsorbed donor group, depending upon whether the metal center is at a plane, step, or corner site on the mineral surface. Solute molecules with two or more donor groups can chelate individual surface metal centers, or bind to two adjacent surface metal centers (when surface geometry is favorable). Stability constants for surface-coordination complexes can be predicted from stability constants for analogous metal ion complexes in solution (Stumm et aI., 1980). Catechol (H 2A), for example, forms complexes with Al 3 + in solution and with Al(III) sites on oxide surfaces (Kummert and Stumm, 1980)

+ H 2A = Al(H20)iA)+(aq) + 2H 30+ >Al( -OHh + H 2A = >AI-A + 2H 20.

AI(H20)~+ (aq)

[10] [11]

Reaction [11] is written for a surface site with two coordinative positions available for exchange with overlying solution. Although ligands with single donor groups can form complexes in solution and on oxide surfaces, ligands with two or more groups form complexes with much higher stability, because of chelation. Thus, salicylic acid forms complexes in solution and on oxide surfaces that are more than an order of magnitude more stable than complexes formed from benzoic acid or phenol alone (Kummert and Stumm, 1980). Electrostatic Interaction An electrical potential gradient develops in the vicinity of charged surfaces. Ions of opposite charge (counter ions) experience an attractive force towards a charged surface, while ions of the same charge as the surface (coions) experience a repulsive force. An equilibrium concentration gradient of ions near charged surfaces is defined by the balance of this electrostatic force with the diffusive force (Fick's law of diffusion). The concentration of species i with charge Zi at a distance x from a charged surface is a function of the electrical potential (1{;x) relative to bulk solution (Bard and Faulkner, 1980) [llx

=

[lhulk . exp( -z;F1{;x/R 1)

[12]

(where F, R, and T are the Faraday constant, the gas constant, and temperature, respectively). Integration of Eq. [12] over the thickness of the oxide/water interface yields the amount of ion adsorption that can be attributed to electrostatic interaction. Clearly, this effect is more dramatic as the ionic charge is increased; divalent or trivalent species experience a steeper concentration gradient near charged surfaces than monovalent ions. The electrical double layer consisting of a charged surface and the layer of counter ions in neighboring solution has been the subject of extensive research. Our knowledge of electrostatic interactions relies upon an under-

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237

standing of surface charge and surface potential, and their relationship to pH, ionic strength, and medium composition. Westall and Hohl (1980) provide an excellent review of alternative models for the electrical double layer, and James and Parks (1982) provide a detailed description and explanation of the surface chemistry and electrostatics of hydrous metal oxides. Hayes et al. (1988) present an excellent discussion of the effect of the electrical double layer on the adsorption of inorganic anions. A similar approach is used by Zachara et al. (1990) to model the adsorption of aminonaphthalene and quinoline onto amorphous silica. Hydrophobic Exclusion from Bulk Water

Solute adsorption is strongly influenced by the relative energies of solvent-solvent, solvent-solute, solvent-surface, and solute-surface interactions. Hydrogen bonding, dipole interactions, and other interactions between water molecules in bulk solution provide a driving force for excluding hydrophobic organic molecules. This hydrophobic effect (Tanford, 1980) occurs with both fully hydrophobic molecules and with molecules that contain both hydrophobic and hydrophilic portions. The relationship between the structure of organic molecules and hydrophilic/hydrophobic interactions with solvent water molecules is the subject of an excellent review by Wolfenden (1983). Adsorption of purely hydrophobic compounds onto soils and sediments has been successfully modeled and predicted by treating the organic matter fraction as a separate phase in equilibrium with the aqueous phase (see Karickhoff et aI., 1979). Morel (1983) succinctly summarizes findings from the considerable amount of work that has been completed in this area: (i) within a typical range of concentrations, sorption isotherms are linear, (ii) the extent of partitioning is proportional to the sediment organic C content, and (iii) for a given sediment, the extent of partitioning is proportional to the octanol-water partition coefficient (Kow) of the organic compound, which is a measure of its hydrophobicity. This approach has been tremendously successful in describing the sorption of neutral, hydrophobic organic compounds, but has been somewhat less successful in describing the ionic and ionizable organic compounds containing both strongly hydrophilic and hydrophobic regions. Many of these compounds are surface active, molecules are aligned with hydrophobic regions directed away from water and with hydrophilic regions directed towards water. Adsorption of organic compounds onto hydrous metal oxides is influenced by the degree of surface hydration. Charged, polar, or hydrogenbonding surface groups have a strong hydrophilic character. On such surfaces, interaction with water is more favorable than interaction with hydrophobic portions of organic molecules, suppressing adsorption. The hydrophilic character of hydrous oxide surfaces is poorly understood, but should be affected by the composition and crystal structure of the surface, and by the adsorption of protons, hydroxide ions, inorganic anions, inorganic cations, and natural organic matter.

238

STONE

Favorable Interaction with Coadsorbed Species Three spatial patterns for the adsorption of organic molecules to hydrous metal oxide surfaces can be postulated. If organic molecules experience neither favorable nor unfavorable interaction with coadsorbed molecules, they may occupy surface sites in a purely random fashion. If molecules repel one another, as would be the case for ions of like charge, molecules would be expected to space themselves apart on the surface. If, however, coadsorbed molecules favorably interact, adsorption may occur in "patches" on the surface. Within such a patch, hydrophobic portions of molecules could align themselves in such a way that their hydrophobic portions are in contact with each other and no longer in contact with solvent water. Through this interaction, the driving force for adsorption becomes greater than if individual molecules were adsorbed in isolation. The optimal patch may contain only two or three coadsorbed molecules, or may include hundreds or thousands of molecules. Favorable interaction between dissimilar organic molecules may be an important phenomenon in natural waters, where the amount of adsorbed natural organic-matter (NOM) may far exceed the amount of adsorbed pollutant m6lecules. Adsorption Dominated by Chemical and Electrostatic Interaction The coordination chemistry model has been successfully combined with models of electrostatic phenomena at charged surfaces in order to explain the adsorption behavior of low molecular weight, ionizable organic compounds. Adsorption of benzoate, salicylate, phthalate, and catechol onto aluminum oxide surfaces has been examined by Kummert and Stumm (1980). In order to model the effect of pH on the extent of adsorption, the protonation level of the surface (> AIOHl, > AIOH, and > AIO -) and of the organic compound (HzA, HA -, A z-) under examination must be known. Acid/base titrations can be used to determine the surface protonation level and surface charge. The protonation level of organic compounds in solution is readily calculated from their pKa values. The protonation levels of organic compounds adsorbed onto the surface are not, however, directly known. Most typically, several protonation levels and stoichiometries can be postulated for adsorbed organic compounds (Kummert and Stumm, 1980) > AI-OH > AI-OH

+ HzA = > AI-AH + + HzA = > AI-A - +

2>AI-OH

+

HzA

HzO

Kf

[11]

H 30 +

K~

[12]

Kj.

[13]

= (>AI-)zA +

2H zO

Experimental measurements yield the actual effect of pH upon the extent of organic compound adsorption. The model is defined by choosing values of Ki, K~, and Kj (s = surface complex formation) that best represent the

239

ORGANIC POLLUTANT OXIDATION

experimental measurements. In some cases, one or more of the postulated protonation levels and stoichiometries may be left out entirely. The set of equilibrium constants and mass balance equations are then solved by appropriate computer programs for calculating aqueous equilibria such as SURFEQL (Westall and Hohl, 1980) or HYDRAQL (Papelis et al., 1988). In order to be true constants, surface equilibrium constants must be written in terms of dissolved species concentrations at the oxide surface; constants written in terms of bulk solution concentrations require an electrostatic correction for the effects of the electrical double layer

Kl = K~

(>AI-A -)(H+)x=o / (>AIOH)(H 2A)

= (>AI-A -)(H+hulk exp( -F1/;o/RT)

/ (>AIOH)(H 2A)

[16]

[17]

In the example given above, the proton activity at the oxide surface was replaced by the bulk proton activity, using a conversion factor based upon Eq. [12]. This specific adsorption model successfully accounts for experimental observations concerning the adsorption of carboxylate compounds and other anionic organic compounds onto hydrous metal oxide surfaces. At high pH, OH - displaces carboxylate species and other anions on the surface, forming > AIO - . As the pH is decreased, OH - adsorption is less pronounced and the adsorption of anions increases to a maximum value. Eventually, at sufficiently low pH, protonation of ligand donor groups lessens their affinity for surface sites, and adsorption decreases (Kummert and Stumm, 1980). More recently, Balistrieri and Murray (1987) examined the adsorption of oxalate, phthalate, salicylate, and lactate onto geothite (FeOOH). Adsorption was depressed in major ion seawater (containing Na, Ca, Mg, CI, and S04) when compared to equimolar NaCl solution. This depression arises from (i) competition of divalent inorganic ions for oxide surface sites and (ii) complexation of organic anions by Ca and Mg in bulk solution (Balistrieri and Murray, 1987). The investigators were able to account for the first phenomenon using equilibrium constants for the adsorption of Ca, Mg, and S04 onto geothite that had been measured in earlier work. Much less is known about the adsorption of anilines, phenols, and other ionic or ionizable compounds that do not contain carboxylate groups. Adsorption of phenol on geothite (FeOOH) was examined by Yost and Anderson (1984). Under the experimental conditions examined (pH 5.8, 2 x 10- 5 to 5 x 10-4 M phenol, 1.28 x 10-4 mol L - I FeOOH), adsorption of phenol was below the detection limit of a 14C radiotracer technique. Radiolabelled phenol has also been used to examine the adsorption of phenol to Al oxides (Ballion and Jaffrezic-Renault, 1985). Experimental conditions in this case were much more favorable for adsorption (3 < pH < 9, 1.0 x 10 -2 M phenol, and 0.98 mol L -I AI203) . Phenol adsorption was found to be nearly constant from pH 3 to 7, then decreased as the pH increased from 7 to 9. These data, along with the observation that the Al oxide surface charge becomes more negative in the presence of phenol, indicate that

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weak specific adsorption of phenol is taking place (Ballion and JaffrezicRenault, 1985). More recently, Ulrich and Stone (1989) have examined the adsorption and oxidation of phenol and chioro-substituted phenols on Mn oxides. In agreement with Yost and Anderson (1984), measurable adsorption of phenol and 2-chlorophenol was not observed. Low (but measurable) amounts of adsorbed 3,4-dichlorophenol, 2,4,6-trichlorophenol, 2,3,4,5-tetrachlorophenol, and pentachlorophenol were, however, observed. The extent of adsorption increases dramatically with increasing number of chloro-substituents, because of increased hydrophobic interactions that favor adsorption. The extent of adsorption decreases as the pH is increased above the pKa of the chlorophenol. Adsorption when Hydrophobic Interactions are Important The organic molecules used in adsorption experiments described in the last section were strongly hydrophilic, and of low molecular weight. As hydrophobic portions of molecules are increased in size, hydrophobic interactions play an increasingly dominant ole in determining the extent of adsorption. One recent study examin d the adsorption of linear alkyl carboxylic-acids by AI oxide surfaces in olution (Ulrich et al., 1988). Specific interaction between carboxylic acid g oups and Al oxide surface sites is an important driving force for adsorpti , especially for short chain-length carboxylic acids. As the alkyl chain I ngth is increased, the contribution of hydrophobic interactions towards verall driving force for adsorption increases, eventually becoming the d minant force. For linear alkyl carboxylic acids, the contribution of hydrophobic interactions equals the contribution from specific adsorption when the alkyl chain is eight C atoms in length (Ulrich et al., 1988). In longer chain-length molecules, self aggregation may also become important; coadsorbed carboxylic acids may orient their alkyl chains adjacent to each other to minimize unfavorable hydrophobic interactions with solvent water molecules. At present, our understanding of how hydrophobic forces influence adsorption of other classes of organic compounds is surprisingly limited.

OXIDATION BY IRON AND MANGANESE-CONTAINING HYDROUS OXIDE MINERALS In the presence of molecular oxygen (02), oxidation of organic compounds to CO 2 and H 20 is thermodynamically favorable. Direct reaction with O2 is, however, exceedingly slow for many organic compounds. This is particularly true for organic pollutants that persist in the environment. Transition metals are potentially important participants in the abiotic oxidation of organic compounds. Higher-valent transition metals may participate directly, by oxidizing a stoichiometric amount of organic substrate, or indirectly, by catalyzing reactions of 02' Iron is the most abundant and

241

ORGANIC POLLUTANT OXIDATION

most widely distributed transition metal capable of multiple oxidation states. Manganese, although less abundant, is enriched in some locations, often in association with Fe. As we shall see, Mn(III, IV) and Fe(III) exhibit important differences in both thermodynamics and kinetics, which affect the nature of their participation in environmental redox transformations. The solubility of higher-valent forms of Fe and Mn is exceedingly low within the pH domain of natural systems because of the formation of sparingly soluble oxide/hydroxide solids. Comparison of the solubility of Fe(II) and Fe(III) at pH 7.0 illustrates this point At pH 7.0

Solubility-limiting phase:

Fe(II)

Fe(lIl)

Fe(OHMs) (Amakinite)

Fe203(S)

Fe 2 + , FeOH +, Fe(O )~

Major dissolved species: Total dissolved cotfentration: (saturated solution)

(Hematite) FeOH2+, Fe(OH)t, Fe(OH)~

8.2

X

10- 17 M

[solubility calculations were made using th rmodynamic data quoted in Stumm and Morgan (1981) and Morel (198 »). Unless strong inorganic or organic ligands are added, the solubilities f Fe(III), Mn(III), and Mn(IV) are all below I oM. As a consequence, ost higher-valent forms of Fe and Mn are mineral-bound, and reactions involving them must take place at interfaces. The next few sections will (i) address whether oxidation by Fe and Mn oxides is thermodynamically favorable, (ii) characterize mechanisms for surface chemical oxidation, (iii) identify characteristics of organic pollutants that favor or discourage reaction, and (iv) examine prior research on the oxidation of xenobiotic and natural organic compounds by Fe and Mn oxides. Thermodynamics

Table 9-2 lists standard potentials (EO) for representative oxide/hydroxide minerals containing Mn(III), Mn(lV), Fe(III), and Co(III). Potentials (EO') are also calculated for a set of chemical conditions that are more representative of the environment: pH 7.0, 1.0 x 10- 6 M reduced metal ion concentration. Oxidant strength decreases in the following order: Mn(III,IV) oxides> Co(III) oxides ~ Fe(III) oxides. Thus, according to thermodynamics, Fe(III) oxides are substantially harder to reduce than Mn(III,IV) oxides. On the other hand, Fe2+ is substantially easier to oxidize than Mn2+. It is more difficult to assign thermodynamic quantities to half-reactions involving the oxldation of most organic compounds. Very often, two or more

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242

Table 9-2. Mineral phases containing Mn(IV), Mn(III), Fe(III), and Co(lll) can be reduced by organic matter and other reducing agents in soils. Half-reactions are listed below, along with standard reduction potentials (EO) and reduction potentials calculated under more realistic environmental conditions (EO'). Eot V Vernadite (Bricker, 1986) 1I2MnIV02(s) + 2H+ + e : = 1I2Mn 2+ + H 20

+1.29

+0.64

Manganite (Bricker, 1986) Mn IIIOOH(s) + 3H + + e -

+1.50

+0.61

+0.67

-0.22

+0.66

-0.23

+0.90

-0.23

+l.48

+0.23

= Mn 2+

+ 2H 20

Geothite (Robie et al., 1978) FeIIIOOH(s) + 3H+ + e- = Fe 2+ + 2H 20 Hematite (Robie et al., 1978) 1I2FeJIl03(s) + 3H+ + e- = Fe 2+ + 3/2H 20 Magnetite (Robie et al., 1978) 1/2FeJIlFeIl04(s) + 4H+ e- = 3/2Fe 2 + + 2H 20 Cobalt hydroxide oxide (crystalline) (Hem et al., 1985) CoIIIOOH(s) + 3H+ + e- = Co 2+ + 2H 20 tEO = Standard reduction potential ([i] = 1.0 M).

:I: EO' = Reduction potential under the following conditions, [H +]

= 1.0

x 10 -7 M; [Me 2+]

= 1.0

x 10 -6 M.

competitive oxidation pathways occur concurrently, generati a mixture of reaction intermediates and products. Single, well-characterized p oducts arise in special instances where competitive pathways are sterical y blocked or retarded in some fashion relative to the dominant pathway. Sev ral of these well-characterized organic half-reactions are presented in Tab e 9-3, along with the half-reaction for oxidation of bisulfide to elemental S. When the potentials of the oxidant half-reaction are higher than that of the reductant Table 9-3. Natural organic matter contains several types of functional groups capable of reducing metals. Reactions are listed below for a few representative compounds, along with their reduction potentials. t EO:j:

----V----

Hydroquinone p-Benzoquinone + 2H+ + 2e- = hydroquinone

0.699

0.196

Ascorbate Dehydroascorbate + 2H + + 2e - = ascorbate

0.40

-0.103

-0.062

-0.17

Hydrogen sulfide SOls) + H+ + e : = HS-

Oxalate 2HCOi + 2H+ + 2e- = -OOC-COO- + 2H 20 -0.18 -0.69 t Using thermodynamic data compiled in Latimer (1952) and Stone and Morgan (1984). :I: EO = Standard reduction potential ([i] = 1.0 M). § EO' = reduction potential under the following conditions: [H +] = 1.0 x 10 -7 M; reductants concentration = 1.0 x 10 -3 M; oxidant concentration = 1.0 x 10 -6 M; CT (total dissolved carbonate) = 1.0 x 10 - 3 M.

243

ORGANIC POLLUTANT OXIDATION

half-reaction, overall reaction is thermodynamically favorable. Thus, by comparing EO , values in Tables 9-2 and 9-3, it can be seen that Mn(III,IV) oxides are capable of oxidizing hydroquinone, ascorbate, bisulfide, and oxalate under the conditions specified. The Fe(III) oxides, in contrast, can only oxidize oxalate; under the stated conditions, Fe(III) oxides are not strong enough oxidants to oxidize bisulfide, ascorbate, or hydroquinone. Reactions do, however, become more favorable as the pH is decreased. At pH 4.0, for example, Fe(III) oxides can oxidize all the reductants listed in Table 9-3. To generalize, reaction of Mn(III,IV) oxides with a wide variety of organic compounds is thermodynamically favorable over a wide pH range. Reactions of Fe(III) oxides, in contrast, are limited by unfavorable thermodynamics, particularly at neutral and alkaline pH and with organic compounds that are only weakly reducing.

Mechanism of Surface Chemical Oxidation In order for an organic compound to be oxidized by a metal center, a precursor complex must first form within which electron transfer can take place. When the reaction occurs at the mineral/water interface, the nature of this precursor complex is clear; the organic compound is adsorbed to the surface through a combination of specific interac ions (inner- and outersphere bond formation) and nonspecific interactions (e trostatic, hydrophobic, and coadsorbed species interactions). Rates of electr transfer within the precursor complex are related to the characteristics of the underlying metal center and the adsorbed organic compound, and to the nature of the encounter complex. The successor complex generated by electron transfer undergoes further transformation; bonds between participating groups are formed and broken, and reaction products are released.jnio overlying solution. Desorption and dissolution are potentially important processes involved in the breakdown of the successor complex. The following mechanism has been postulated for the oxidation of phenolic compounds (ArOH) by Mn(III) surface sites (denoted as >MnIIl-OH) (Stone, 1987; Ulrich and Stone, 1989) Precursor complex formation:

>MnIII-OH

Electron transfer: Release of phenoxy radical:

+

k1 ...... >MnIII-OAr ArOH ..k_ 1

+

H 2O

k2 ...... > MnIII-OAr ..- (>Mn Il , ·OAr) k_ 2

(> Mn

Il

,

.OAr) + H 20

k3 ...... ..- > Mn Il-OH 2 + ·OAr k_ 3

[18]

[19]

[20]

244

Release of reduced Mn(II): Coupling and further oxidation:

STONE

> Mn lI-OH 2

k4 ¢

«.,

ArO· -

Mn2+ (+ free underlying site)

[21]

Quinones, dimers, and [22] polymeric oxidation products

A rate constant k is assigned to each surface chemical reaction. This is a schematic representation of the mechanism based upon analogous reactions of metal ion complexes in solution (see Purcell and Kotz, 1977, p. 659-669). Experimental determination of dissolved reactant and product concentrations [ArOH(aq), Mn2+(aq), etc.] can provide indirect information about the surface reaction [discussed in Stone (1986), Stone and Morgan (1987), and Stone (1987)]. Additional detail concerning the stoichiometry and structure of surface species will require the use of spectroscopic or other surface-analytical techniques. The mechanism outlined in Eq. [18] to [22] can be used to illustrate important attributes of surface chemical redox reactions: 1. Although electron transfer between a dissolved reductant and a surface-bound metal can occur over distances slightly more than 1 nm, this is still within the interfacial region. The "characteristic thickness" of electrostatic disturbance arising from charged surfaces is referred to as the double layer thickness, 11k. At an ionic strength of 1.0 X 10 -3 M, this thickness is equal to 8.9 nm, while at 1.0 x 10 -I M, this thickness is equal to 0.89 nm (p. 617, Stumm and Morgan, 1981). 2. Inner- or outer-sphere surface complex formation is ~ necessary prerequisite for most surface chemical redox reactions. (ESR may-provide important information regarding the nature ofthe precursor complex.) When electron transfer is fast (k2 ~ kl[ArOHD, overall rates of reaction are influenced by rates of organic reductant adsorption. When electron transfer is slow (k2 ~ kl[ArOHD, Eq. [18] can be modeled as a pseudoequilibrium reaction, using the equilibrium constant K 1 [23] [24]

Ligand-donor molecules generally adsorb more strongly to oxide surfaces as the pH is decreased. Since the rate of electron transfer is proportional to (> Mn 1I1-0Ar), a decrease in pH generally favors higher rates of redox reaction (Stone, 1987). 3. Susceptibility of a particular organic compound towards oxidation depends upon both surface coverage and upon rates of electron transfer within the surface precursor complex. Some organic compounds (such as phthalate)

OR(,ANJ(' 1'01.1 ,lilA NI OXIUATION

245

are readily adsorbed by Mn oxide surfaces, but are resistant to oxidation. Other organic compounds (such as hydroquinone) are only weakly adsorbed, but are quickly oxidized once the precursor complex is formed. The importance of adsorption characteristics and redox lability in the oxidation of mono-, di-, tri-, tetra- and pentachlorophenols has recently been explored (Ulrich and Stone, 1989). 4. Manganese(III,IV) oxides are reduced by phenolic compounds an order of magnitude more quickly than Co(III) oxides, and several orders of magnitude more quickly than Fe(III) oxides. This apparent relationship between reaction-free energy and reaction rate is not likely to arise from differences in adsorption phenomena alone. Instead, it probably arises from differences in electron-transfer rate within the surface precursor complex. 5. Although electron transfer might occur at appreciable rates, the appearance of reaction products in solution may be delayed or suppressed by slow (or thermodynamically unfavorable) desorption. The affinity of metal ions for hydrous metal oxide surfaces increases as the pH is increased, often increasing dramatically within a narrow pH range. This "adsorption edge" behavior is responsible for the retention of Mn(II) onto Mn02(S) and of Co(II) onto CoOOH(s) during reduction of hydrous metal oxide surfaces by hydroquinone (Stone and Ulrich, 1989). Thus, net dissolution of hydrous metal oxide surfaces accompanies surface chemical redox reactions in some cases (particularly at low pH and in the presence of ligands), but may be delayed or suppressed under other conditions (such as at high pH). 6. Equations [18] to [22] represent a homolytic pathway for the oxidation of phenolic compounds, in which a collection of reactive free radical intermediates are produced. Several reactions in parallel eventually consume the phenoxy radical ArO', possibly involving readsorption and additional oxidation by the mineral surface. Dimers, trimers, etc., produced by oxidative coupling are less soluble and more likely to adsorb to the mineral surface. Partitioning phenomena are therefore important in determining the nature and final distribution of reaction products. Structure-Reactivity Relationships Small structural modifications can be made to an organic substrate in order to examine how chemical characteristics influence reaction rate. It has been observed that alkyl, alkoxy, and other electron-donating substituents promote oxidation of phenolic compounds by Mn oxides, while carboxyl, aceto, nitro, chloro, and other electron-withdrawing substituents retard oxidation (Stone, 1987). This observation may arise from (i) the increased basicity of phenolic compounds containing electron-donating substituents, favoring adsorption, and (ii) the increased electron density of the phenolic OH group in compounds containing electron-donating substituents, facilitating electron transfer. Hydrophobic contributions to adsorption are also important, as illustrated by related research examining oxidation of chlorophenols. As the number of hydrophobic chloro-substituents is increased, adsorption density increases, favoring reaction (Ulrich and Stone, 1989). Additional general-

STONE

246

izations can be made: bidentate organic reductants react more quickly than monodentate reductants, because of increased adsorption density; bulky, nonreactive substituents retard reaction, through steric hindrance. Additional Surface Chemical Oxidation Studies It is particularly important that reactions of Fe(III) oxides with organic

compounds be addressed, because of the widespread abundance of Fe in terrestrial environments. In one recent study (LaKind and Stone, 1989), goethite was shown to oxidize hydroquinones, catechols, and pyrogallol under weakly acidic conditions. Rates of reaction diminished substantially as the pH was increased above pH 4.0, becoming negligible above a pH of 6.0. The inability of goethite [and other Fe(III) oxides] to oxidize phenolic compounds in neutral and alkaline solution may arise from reaction thermodynamics; since the potential of the Fe(III) oxide/Fe(II) half-reaction diminishes as the pH is increased, free energy for reaction becomes progressivelyless favorable. Above a pH of 6.0, most mono- and dihydroxybenzenes are not strong enough reductants for the reaction with geothite to take place. Thermal and photochemical reactions of other, stronger reductantswith Fe(III) oxides, including oxalate (Baumgartner et al., 1983; Blesa et al., 1987), ascorbate (Zinder et aI., 1986), and citrate (Waite and Morel, 1984b) have been studied. The oxidation of mercaptans by Fe(III) oxides has been examined (Baumgartner et aI., 1982; Waite et aI., 1986; Waite and Torikov, 1987) in order to understand chemical transformations of mercaptans in the environment, and to improve formulations for rust and scale removal. Fulvic acids, an important, intermediate size fraction of natural organic matter, are believed to play an important role in the reduction of metals and organic pollutants. Reduction of Mn(III,IV) oxides (Sunda et al., 1983; Waite et aI., 1988) and Fe(III) oxides (Waite and Morel, 1984a; Waite and Morel, 1984c; Finden et al., 1984) by fulvic acid has been examined extensively, under chemical conditions resembling those in the environment. Recently, electron spin resonance (ESR) and other spectroscopic techniques have been applied to the study of redox reactions of Fe and Mn oxides (Kung and McBride, 1988; McBride, 1989a,b). Identification and quantification of adsorbed reactants, intermediates, and products by spectroscopic techniques could substantially improve our understanding of surface chemical reaction mechanisms.

THE SURFACE AS A CATALYST: HYDROLYSIS AT THE HYDROUS METAL OXIDE SURFACE Hydrous metal oxide surfaces can also participate in interfacial reactions without undergoing any net change; they can act as catalysts for reactions of organic compounds. Catalysis by surfaces is observed when (i) all participating reactants partition into the interfacial region to a significant degree, and (ii) rates constants for reaction in the interfacial region are

ORGANIC POLLUTANT OXIDATION

247

comparable to or exceed rate constants for reaction in homogeneous solution (Stone, 1989a). Adsorption and partitioning into the interfacial region have already been discussed. For some potential reactants, our knowledge concerning adsorption phenomena is sufficient to predict interfacial concentration and mode of association with the surface. Assessing reaction rates in the interfacial region presents a greater challenge. We can postulate several different ways in which hydrous metal oxide surfaces can influence reaction rates: 1. In some instances, hydrous metal oxide surfaces may simply concentrate reactants in a small space, leading to increased encounter frequency. Adsorbed species diffuse in two dimensions along the surface, while dissolved species diffuse in three dimensions. For comparable diffusion coefficients, encounter frequencies between reactants are increased when the dimensions of the system are reduced (Hardt, 1979; Adam and Delbruck, 1968). 2. The conformation of adsorbed molecules may be different from that of molecules in solution. Constraints imposed by the nature of bonding to the surface and the geometric arrangement of mineral surface sites may introduce strain. These changes may elevate or lessen the reactivity of adsorbed species. 3. Hydrous metal surface sites may act as general catalysts or as specific catalysts. Weak acidic sites and weak basic sites are found on surfaces that can promote reactions by donating protons (general acid catalysis) or hydroxide ions (general base catalysts). Surface sites may also exhibit nucleophilic or electrophilic character. 4. Chemical reactions are sensitive to medium effects. Near surfaces, medium characteristics are perturbed by the accumulation of charge and by the accumulation and selected orientation of solvent and solute molecules. The dielectric constant of aqueous solutions decreases as a charged surface is approached because the fraction of water molecules bound by the hydration of counter ions is increased and because increases in electrical potential exert a stronger effect in dipole moments of free water molecules (Nurnberg and Wolff, 1969; Nurnberg, 1974). Activation energies of reaction may be lowered in the interfacial region by the dissociation field effect, discussed in detail by Nurnberg and Wolff (1969). Dissociation reactions frequently pass through an ion pair stage. The polarized medium of the interfacial region can promote separation of ion pairs (Nurnberg and Wolff, 1969). Our knowledge of these factors influencing reaction rates is quite elementary in many respects. Direct study is difficult in many instances, because of the complex nature of the hydrous metal oxide surface. Much of our current understanding comes from using indirect methods. One useful approach is to make small changes in reactant structure, then examine the effect on reaction rate. Another approach is to systematically examine how reactant concentration, medium composition (pH and ionic strength), and the presence of other adsorbing solutes influence reaction rate. In order to illustrate various aspects of surface catalysis, results from research with two hydrolyzable carboxylic acid esters, monophenyl terephtha-

248

STONE

late (MPT -) and phenyl picolinate (PHP) will now be summarized. Within the pH range of natural waters, both esters are subject to base-catalyzed hydrolysis in particle-free solution kb

+ OH - -

MPT PHp

o

+

= 0.241

L mol-I S-I

terephthalate

+ phenol

[25]

k b = 7.15 L mol " ! S-I OH - - picolinate + phenol.

[26]

Below pH 3.5, acid-catalyzed hydrolysis of PHP also becomes important. Structure and chemical properties of the two esters are listed in Table 9-4, as well as a summary of the experimental findings. Monophenyl Terephthalate

Positive-charged oxide surfaces such as Al oxide (below pH 8.6) and Ti oxide (below pH 6.4) accelerate the hydrolysis of MPT - by an order of magnitude or more. Detailed examination of the reaction in the presence of Al oxide (Stone, 1989a) provides substantial evidence for the following mechanism of catalysis

> AIOHt + MPT -

~

> AI-MPT + H 20

> AI-MPT + OHct-

fast

[27]

k2 -

products.

[28]

A rate constant k is assigned to each surface chemical reaction. In Reaction [28], the concentration of hydroxide ion in the plane of closest approach (the diffuse layer) is denoted by the subscript d. An important aspect of this reaction is the way in which reactants are concentrated near the oxide surface. The free, ionized carboxylate group of MPT - provides a basis for specific adsorption, through complex formation with surface Al centers. Monophenyl terephthalate also experiences favorable electrostatic attraction towards the positive-charged oxide surface. The positive Al oxide surface charge and extent of MPT - adsorption both diminish as the pH is decreased (Stone, 1989a). The extent of MPTadsorption also decreases as the ionic strength is increased, an indication that the surface complex is outer sphere rather than inner sphere (Hayes et aI., 1988). Accumulation of the nucleophile OH - at the Al oxide/water interface is an important component of the observed surface catalytic effect. The OH - concentration at the plane of closest approach to the surface (at the diffuse layer, [OH ct ]) , is higher than the concentration in bulk solution, because of favorable electrostatic interaction.

..~ Z

n

"'CI

ot"" t"" c:: ... Table 9-4. Monophenyl terephthalate (MPT-) and phenyl picolinate (PHP) are subject to mineral surface-catalyzed hydrolysis. Observations concerning the behavior of these two compounds in suspensions containing various mineral surfaces are summarized. MPTStructure

-o-cROW ~ II c-o pKa

Surface Si0 2 (pHzpc 2.4) Ti0 2 (pHzpc 6.4)

~

J

= 3.4 (-COOH/-COO-) No effect observed

(}8-

0

...

o

il<

PHP

-0

> Z

-o

..~...

~

pKa < 3.0 (NH + ,N)

No effect observed Surface promotes hydrolysis

Al20 a (pH zpc 8.6)

Surface promotes hydrolysis Surface promotes hydrolysis

FeOOH (pH zpc 704)

(Not examined)

Surface promotes hydrolysis

Effect of increased ionic strength on surface catalysis

Dramatic decrease

Slight decrease

No effect observed

~

250

STONE

Thus, the surface serves to accumulate both the ester (by complex formation and electrostatic attraction) and the nucleophile (by electrostatic attraction alone), facilitating reaction. In fact, the overall first-order rate constant for hydrolysis (kh ) reflects this concentration effect; k h reaches its highest value at the pH where the product [> AI-MPT][OH -ld is at a maximum. No other role of the oxide surface in promoting hydrolysis need be postulated. As expected, both the extent of reactant adsorption and hydrolysis rate decrease substantially as the ionic strength is increased. At high ionic strength, counter ions of the supporting electrolyte accumulate in the diffuse layer, shielding the oxide surface charge and lessening the accumulation of MPT and OH - at the Al oxide/water interface. Specifically adsorbing anionic species (such as maleate) and natural organic matter lower the extent of MPT - adsorption and overall rates of hydrolysis by blocking surface sites and by lowering the oxide surface charge (Stone, 1989b). Phenyl Picolinate A comprehensive study of PHP hydrolysis in the presence of various hydrous metal oxides has been completed (Torrents and Stone, 1991). Surface catalytic effects observed with PHP are in many ways distinct from those observed with MPT - . Oxide surfaces can be neutral or negatively charged and still catalyze PHP hydrolysis. The Ti oxide suspensions, for example, can accelerate PHP hydrolysis at pH values at and above the pH zpc ' Iron oxides catalyze hydrolysis while Al oxides do not, despite very similar surface charge and surface proton level characteristics. Phenyl picolinate is subject to metal ion catalysis in homogeneous solution. Appropriate metal ions chelate the heterocyclic N and the carbonyl 0, increasing the partial positive charge at the carbonyl C and facilitating nucleophilic attack (Fife and Przystas, 1985). Chelation by surface metal centers can also be postulated

h

Oe"o~

.r.1'---8 V ~~

chelation by dissolved metal ions

chelation by surface metal centers

The extent of PHP adsorption is too low to be measured by loss from bulk solution. The catalysis of PHP hydrolysis by various metal oxides must come from their ability to chelate the ester and polarize the carbonyl C-O bond. Apparently Ti oxides and Fe oxides are capable of doing this, while Al oxides are not. Ionic strength effects on PHP surface-catalyzed hydrolysis are small; electrostatics apparently have a minor role in ester chelation and subsequent attack by OH - (Torrents and Stone, 1991).

ORGANIC POLLUTANT OXIDAnON

251

Other Surface-Catalyzed Nucleophilic Substitution Reactions Chemical heterogeneities present in soils, sediments, and aquifers undoubtedly have an effect on rates of pollutant degradation. Other sources of surface catalysis not discussed here include Bronsted acidity of surface sites, that become apparent as surfaces become dehydrated (El-Amamy and Mill, 1984). Surface and pore structure may playa role in the catalysis of phosmet hydrolysis by montmorillonite (Sanchez-Camazano and SanchezMartin, 1983) and in the catalysis of ethyl acetate hydrolysis by zeolites (Namba et al., 1981).

CONCLUSIONS In order to predict rates and mechanisms of reactions at hydrous metal oxide surfaces, adsorption phenomena must be understood in greater detail. Although forces contributing to the adsorption of organic compounds have been identified, their relative importance and interdependence have not been determined on a quantitative level. In addition, more must be learned about the nature of chemical transformations at interfaces. Changes in medium composition and the close vicinity of other adsorbed species are potentially of great importance in determining rates of interfacial reactions. Reactions of Mn(III,IV) and Fe(III) must necessarilytake place at mineral/water interfaces, because of the exceedingly low solubility of these metals. Whether or not surface chemical oxidation is important for a particular organic pollutant depends upon relative rates of other, competitive degradation processes. Similarly, surface-catalyzed hydrolysis is only important when the relative rate of the surface reaction is high relative to the corresponding reaction in overlying solution.

ACKNOWLEDGMENTS This work was supported by the Environmental Engineering Program of the National Science Foundation (ECE-8519793), the Office of Exploratory Research of the Environmental Protection Agency (R812944-01-0), and the Water Resources Research Division of the U.S. Geological Survey (14-08-ooo1-G1647).

REFERENCES Adam, G., and M. Delbruck. 1968. Reduction of dimensionality in biological diffusion processes, p. 198-215. In A. Rich and N. Davidson (ed.) Structural chemistry and molecular biology. W.H. Freeman, San Francisco. Balistrieri, L.S., and J.W. Murray. 1987. The influence of the major ions of seawater on the adsorption of simple orllollic acids by goethite. Geochim. Cosmochim. Acta 51: 1151-1160.

252

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Ballion, D., and N. Jaffrezic-Renault. 1985. Study of the uptake of inorganic ions and organic acids at the alpha-alumina-electrolyte interface in a colloid system by radiochemical techniques and microelectrophoresis. J. Radioanal. Nucl. Chern. 92:133-150. Bard, A.J., and L.R. Faulkner. 1980. Electrochemical methods. Wiley, NY. Baumgartner, E., M.A. Blesa, and A.J.G. Maroto. 1982. Kinetics of the dissolution of magnetite in thioglycolic acid solutions. J. Chern. Soc. Dalton Trans. 1982:1649-1654. Baumgartner, E., M.A. Blesa, H.A. Marinovich, and A.J.G. Maroto. 1983. Heterogeneous electron transfer as a pathway in the dissolution of magnetite in oxalic acid solutions. Inorg. Chern. 22:2224-2226. Benjamin, M.M., and J.O. Leckie. 1981. Multiple-site adsorption of Cd, Cu, Zn, and Pb on amorphous iron oxyhydroxide. J. Colloid Interface Sci. 79:209-221. Blesa, M.A., H.A. Morinovich, E.C. Baumgartner, and A.J.G. Maroto. 1987. Mechanism of dissolution of magnetite by oxalic acid-ferrous ion solutions. Inorg. Chern. 26:3713-3717. Bricker, O.P. 1965. Some stability relationships in the system Mn-OrHzO at 25 0 C and 1 atm total pressure. Am. Mineral. 50:1296-1354. Davis, J.A., and J.O. Leckie. 1978. Effect of adsorbed complexing ligands on trace metal uptake by hydrous oxides. Environ. Sci. Technol. 12:1309-1315. El-Amamy, M.M., and T. Mill. 1984. Hydrolysis kinetics of organic chemicals on montmorillonite and kaolinite surfaces as related to moisture content. Clays Clay Miner. 32:67-72. Fife, T.H., and T.J. Przystas. 1985. Divalent metal ion catalysis in the hydrolysis of esters of picolinic acid. Metal ion promoted hydroxide ion and water catalyzed reactions. J. Am. Chern. Soc. 107:1041-1047. Finden, D.A.S., E. Tipping, G.H.M. Jaworski, and C.S. Reynolds. 1984.Light-induced reduction of natural iron(lII) oxide and its relevance to phytoplankton. Nature 309:783-784. Fleischer, M. 1980. Glossary of mineral species. 3rd ed. Mineralogical Record, Tucson, AZ. Hardt, S.L. 1979. Rates of diffusion-controlled reactions in one, two, and three dimensions. Biophys. Chern. 10:239-243. Hayes, K.F., A.L. Roe, G.E. Brown, K.O. Hodgson, J.O. Leckie, and G.A. Parks. 1987. In situ X-ray adsorption study of surface complexes: Selenium Oxyanions on alpha-FeOOH. Science 238:783-786. Hayes, K.F., C. Papelis, and J.O. Leckie. 1988. Modeling ionic strength effects on anion adsorption at hydrous oxide/solution interfaces. J. Colloid Interface Sci. 125:717-726. Hem, J.D., C.E. Roberson, and C.J. Lind. 1985. Thermodynamic stability of CoOOH and its coprecipitation with manganese. Geochim. Cosmochim. Acta 49:801-810. Hiemstra, T., W.H. van Reimsdijk, and G.H. Bolt. 1989a. Multisite proton adsorption modeling at the solid/solution interface of (hydr)oxides: A new approach. I, Model description and evaluation of intrinsic reaction constants. J. Colloid Interface Sci. 133:91-104. Hiemstra, T., J.C.M. de Wit, and W.H. van Riemsdijk. 1989b. Multisite proton adsorption modeling at the solid/solution interface of (hydr)oxides: A new approach. II. Application to various important (hydr)oxides. J. Colloid Interface Sci. 133:105-117. James, R.O., and G.A. Parks. 1982. Characterization of aqueous colloids by their electrical double-layer and intrinsic surface chemical properties. Surface Colloid Sci. 12:119-216. Karickhoff, S.M., D.S. Brown, and T.A. Scott. 1979. Sorption of hydrophobic pollutants on natural sediments. Water Res. 13:241-248. Kummert, R., and W. Stumm. 1980. The surface complexation of organic acids on hydrous delta-AlP3' J. Colloid Interface Sci. 75:373-385. Kung, K.-H., and M.B. McBride. 1988. Electron transfer processes between hydroquinone and hausmannite (Mn304)' Clays Clay Miner. 36:297-302. LaKind, J .S., and A.T. Stone. 1989. Reductive dissolution of geothite by phenolic reductants. Geochim. Cosmochim. Acta 53:961-971. Latimer, W.M. 1952. Oxidation potentials, 2nd ed. Prentice-Hall, Englewood Cliffs, NJ. McBride, M.B. 1989a. Oxidation of dihydroxybenzenes in aerated aqueous suspensions of birnessite. Clays Clay Miner. 37:341-347. McBride, M.B. 1989b. Oxidation of 1,2- and 1,4-dihydroxybenzene by birnessite in acidic aqueous suspension. Clays Clay Miner. 37:479-486. Morel, F.M.M. 1983. Principles of aquatic chemistry. p. 427. Wiley-Interscience, NY. Mortland, M.M. 1970. Clay-organic complexes and interactions. Advan. Agron. 22:75-117. Namba, S., N. Hosonuma, and T. Yashima. 1981. Catalytic application of hydrophobic properties of high-silica zeolites. J. Catal. 72:16-20.

ORGANIC POLLUTANT OXIDATION

253

Nurnberg, H.W. 1974. The influence of double layer effects on chemical reactions at charge interfaces. p, 48-53. In U. Zimmerman and J. Dainty (ed.) Membrane transport in plants. Springer-Verlag, New York. Nurnberg, H.W., and G. Wolff. 1969. Influences on homogeneous chemical reactions in the diffuse double layer. J. Electroana!. Chern. Interfacial Electrochem. 21:99-122. Papelis, C., K.F. Hayes, and J .0. Leckie. 1988. HYDRAQL: A program for the computation of chemical equilibrium composition of aqueous batch systems including surfacecomplexation modeling of ion adsorption at the oxide/solution interface. Department of Civil Engineering Technical Report no. 306, Stanford Univ. Menlo Park, CA. Purcell, K.F., and J.C. Kotz. 1977. Inorganic chemistry. W.B. Saunders, Philadelphia, PA. Robie, R.A., B.S. Hemingway, and J.R. Fisher. 1978. Thermodynamic properties of minerals and related substances at 298.15 K and I Bar (10 5 Pascals) pressure and at higher temperatures. Geo!. Surv. Bull. 1452, U.S. Gov. Print. Office, Washington, DC. Sanchez-Camazano, M., and M.J. Sanchez-Martin. 1983. Montmorillonite-catalyzed hydrolysis of phosmet. Soi!. Sci. 136:89-93. Schindler, P.W. 1981. Surface complexes at oxide-water interfaces. p. 83-110. In M.A. Anderson and A.J. Rubin (ed.) Adsorption of inorganics at solid-liquid interfaces, Ann Arbor Science, Ann Arbor, MI. Schindler, P.W., and W. Stumm. 1987. The surface chemistry of oxides, hydroxides, and oxide minerals. p. 83-110. In W. Stumm (ed.) Aquatic surface chemistry. Wiley-Interscience, New York. Sigg, L., and W. Stumm. 1981. The interaction of anions and weak acids with the hydrous goethite (alpha-FeOOH) surface. Colloids Surf. 2: 101-117. Stone, A.T. 1986. Adsorption of organic reductants and subsequent electron transfer on metal oxide surfaces. p. 446-461. In J.A. Davis and K.F. Hayes (ed.) Geochemical processes at mineral surfaces, ACS Symposium Series 323. ACS, Washington, DC. Stone, A.T. 1987. Reductive dissolution of manganese (III,IV) oxides by substituted phenols. Environ. Sci. Techno!. 21:979-988. Stone, A.T., 1989a. Enhanced rates of monophenyl terephthalate hydrolysis in aluminum oxide suspensions. J. Colloid Interface Sci. 127:429-441. Stone, A.T. 1989b. The effect of Dismal Swamp dissolved organic matter on the adsorption and surface-enhanced hydrolysis of monophenyl terephthalate in aluminum oxide suspensions. J. Colloid Interface Sci. 132:81-87. Stone, A.T., and J.J. Morgan. 1984. Reduction and dissolution of manganese(lII) and manganese(lV) oxides by organics: 2. Survey of the reactivity of organics. Environ. Sci. Techno!. 18:617-624. Stone, A.T., and J.J. Morgan. 1987. Reductive dissolution of metal oxides. p. 221-254. In W. Stumm (ed.) Aquatic surface chemistry. Wiley-Interscience, New York. Stone, A.T., and H.-J. Ulrich. 1989. Kinetics and reaction stoichiometry in the reductive dissolution of manganese(lV) dioxide and Co(III) oxide by hydroquinone. J. Colloid Interf. Sci. 132:509-522. Stumm, W., R. Kummert, and L. Sigg. 1980. A ligand exchange model for the adsorption of inorganic and organic ligands at hydrous oxide interfaces. Croat. Chern. Acta 53:291-312. Stumm, W., and J.J. Morgan. 1981. Aquatic chemistry, 2nd ed. Wiley-Interscience, New York. Sunda, W.G., S.A. Huntsman, and G.R. Harvey. 1983. Photoreduction of manganese oxides in seawater and its geochemical and biological implications. Nature 301:234-236. Tanford, C. 1980. The hydrophobic effect. Wiley, New York. Torrents, A., and A.T. Stone. 1991. Hydrolysis of phenyl picolinate (PHP) at the mineral/water interface. Environ. Sci. Techno!. 25:143-149. Ulrich, H.-J., B. Cosovic, and W. Stumm. 1988. Adsorption of aliphatic fatty acids on aquatic interfaces. Comparison between two model surfaces: The mercury electrode and deltaAI203 colloids. Environ. Sci. Techno!. 22:37-41. Ulrich, H.-J., and A. T. Stone. 1989. Oxidation of chlorophenols adsorbed to manganese oxide surfaces. Environ. Sci. Technol, 23:421-428. Voudrias, E.A., and M. Reinhard. 1986. Abiotic organic reactions at surfaces of minerals. p, 462-486. In J.A. Davis and K.F. Hayes (ed.) Geochemical processes at mineral surfaces. ACS Symposium Series 323. ACS, Washington, DC. Waite, T.D., and F.M.M. Morel. 1984a. Coulometric study of the redox dynamics of iron in seawater. Anal. Chern. 56:787-792. Waite, T.D., and "'.M.M. Morel. 1984b. Photoreductive dissolution of colloidal iron oxide: Effect of curate. J. Colloid Interface Sci. 102:121-137.

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Waite, T.O., and F.M.M. More!. 1984c. Photoreductive dissolution of colloidal iron oxides in natural waters. Environ. Sci. Techno!. 18:860-868. Waite, T.O., A. Torikov, and J.D. Smith. 1986. Photoassisted dissolution of colloidal iron oxides by thiol-containing compounds. J. Colloid Interface Sci. 112:412-420. Waite, T.D., and A. Torikov. 1987. Photoassisted dissolution of colloidal iron oxides by thiolcontaining compounds. 2. Comparison of lepidocrocite (gamma-FeOOH) and hematite (alpha-Fe203) dissolution. J. Colloid Interface Sci. 119:228-235. Waite, T.O., I.C. Wrigley, and R. Szymczak. 1988. Photoassisted dissolution of a colloidal manganese oxide in the presence of fulvic acid. Environ. Sci. Techno!' 22:778-785. Westall, J., and H. Hohl. 1980. A comparison of electrostatic models for the oxide/solution interface. Adv. Colloid Interface Sci. 12:265-294. Wolfenden, R., 1983. Waterlogged molecules. Science 222:1087-1093. Yost, E.C., and M.A. Anderson. 1984. Absence of phenol adsorption on geothite. Environ. Sci. Techno!. 18:101-106. Zachara, J .M., C.C. Ainsworth, C.E. Cowan, and R.L. Schmidt. 1990. Sorption of aminonaphthalene and quinoline on amorphous silica. Environ. Sci. Techno!. 24:118-126. Zepp, R.G., and N.L. Wolfe. 1987. Abiotic transformation of organic chemicals at the particlewater interface. p. 423-455. In W. Stumm (ed.) Aquatic surface chemistry. WileyInterscience, New York. Zinder, B., G. Furrer, and W. Stumm. 1986. The coordination chemistry of weathering: II. Dissolution of Fe(III) oxides. Geochim. Cosmochim. Acta 50:1861-1869.

10

Modeling Nonequilibrium Reactions of Inorganic Solutes in Soil Columns P. M. Jardine

Environmental Sciences Division Oak Ridge National Laboratory Oak Ridge, Tennessee

ABSTRACT Modeling techniques are discussed that are appropriate for describing timedependent adsorption, transformation, diffusional mass exchange, and precipitation reactions of inorganic cations and anions with soil. Included are the inorganic cations NH 4 , K, Ca, Mg, Cr, and Al as well as the inorganic anions N0 3 , F, and H ZP04 • Experimental column breakthrough curves (BTC) for various types of inorganic reactions in soil are presented where the local equilibrium assumption is not valid and tracer migration is controlled by physical, chemical, and/or biological nonequilibrium. Such processesrequire that the reaction pathway be modeled during the approach to equilibrium. Proposed reaction schemes based on empirical expressions and the microscopic properties of the porous media are discussed. The effect of nonlinear adsorption and dispersion on the interpretation of time-dependent transport reactions are stressed, since these very different phenomena may lead to similar experimental BTC.

VALIDITY OF THE LOCAL EQUILIBRIUM ASSUMPTION The assumption of local equilibrium during solute transport suggests that the chemical, physical, and biological interactions of the solute with the porous media are instantaneous, or that the solute resident time in the media is sufficiently large to achieve negligible concentration differences between pore classes. Valocchi (1985) suggests that the validity of the local equilibrium assumption (LEA) depends on the degree of interaction between macroscopic transport properties (i.e., water flow velocity and hydrodynamic dispersion) and microscopic sorption properties (i.e., diffusional mass transfer, aggregate size and sorbed solute distribution). When the rate of change of solute mass during microscopic sorption processes is fast relative to the Copyright (el 1991 Soil Science Society of America, 677 S. Segoe Rd., Madison, WI 53711, USA. Rates of .'illil Ch"m/cu/I'rocesses. SSSA Special Publication no. 27.

255

JARDINE

256

bulk fluid flow, the interaction is generally considered instantaneous thereby conforming to the LEA. Also for observations far from the source the LEA is appropriate. Deviations from local equilibrium occur as the interactions of the solute with the porous media become increasingly time-dependent. Parker and Valocchi (1986) have shown that divergence from local equilibrium occurs as soil aggregates increase in size and the pore-class heterogeneity increases. James and Rubin (1979) also suggest that nonequilibrium considerations are necessary as the ratio of the hydrodynamic dispersion coefficient to the molecular diffusion coefficient of the solute deviates significantly from unity. Kinetic limitations during solute transport have been shown by Jennings and Kirkner (1984) to become significant as the dimensionless reaction rate coefficients (i.e., Damkohler numbers) decrease below::::: 10. In the sections that follow, modeling techniques are discussed that are appropriate for describing time-dependent solute interactions during transport in soil. Experimental column BTC are presented for various types of inorganic reactions in soil where the LEA is not valid and tracer migration is controlled by physical, chemical, and/or biological nonequilibrium processes.

PHYSICAL NONEQUILIBRIUM REACTIONS Diffusional Mass Exchange The occurrence of physical nonequilibrium during solute transport in soil suggests that the rate of solute movement is controlled by diffusive mass exchange between pores of varying size and shape. The interaction of solutes between the various pore classes is usually described by deterministic mathematical models that partition soil water into mobile macro- and mesopores (flowing region) and immobile rnicropores (stagnant region). The two domains are linked by an interaction term that considers the diffusional mass exchange of water and solutes from one pore class to another (Villermaux, 1974; van Genuchten and Wierenga, 1976; Parker and van Genuchten, 1984a). Both macroscopic and microscopic descriptions of intrapore solute transfer have been formulated. The latter description considers water and solute distributions at the pore scale or even the molecular scale, whereas a macroscopic description of solute transport treats the system as a continuum for which extensive properties may be represented by continuous functions. Macroscopic Approach The interaction of solute between mobile and immobile pore domains has been described by empirical first-order kinetic expressions (van Genuchten, 1981; Parker and van Genuchten, 1984a). A diffusional interpretation of the rate expression is strictly valid only for the case of very thin films. However, Parker and Valocchi (1986) have shown that under certain

257

MODELING NON EQUILIBRIUM REACTIONS

conditions, the first-order expression can be used to describe stagnant porediffusion limitations. The macroscopic approach differs from a microscopic analysis of solute transfer since knowledge of the system geometry is not necessary. Because of this, the physical significance of the rate coefficient is lost in the macroscopic approach; however, the time dependency of the solute interaction with the soil is known. The governing transport equations that describe this scenario, may be expressed as (Parker and van Genuchten, 1984a; van Genuchten and Shulin, 1986)

[1]

ll.

U1m

R.

rm

aqm at _

01

(C

m -

C) im

[2]

where subscripts m and im denote mobile and immobile domains, respectively; C denotes the solution concentration of the solute; D is the hydrodynamic dispersion coefficient; v is the average pore water velocity; R = R m + Rim is the retardation factor; 01 is the first-order mass-transfer coefficient; 0 = Om + 0im is the volumetric water content; x is soil distance; and t is time. As written, Eq. [1] assumes a linear isotherm of the form s = kC, where s is the adsorbed solute concentration and k is the equilibrium distribution coefficient. Therefore, R = 1 + (Pk/O) where p is the porous media bulk density. The partitioning of solutes into mobile and immobile domains is frequently distinguished with a parameter denoted as F = sm/S that represents the mass fraction of adsorbed solutes that are in direct contact with the mobile liquid phase. The transport model described by Eq. [1] and [2] is commonly referred to as the two-region or mobile-immobile model. Investigating K transport in repacked soil columns, Jensen (1984) utilized the two-region model to describe nonequilibrium mass transfer of K in sandy loam and loamy sand soils (Fig. 10-1). His model combined the effects of hydrodynamic dispersion and first-order mass transfer between mobile and immobile regions with instantaneous, nonlinear cation exchange in both regions that was described by the modified Kiellard equation. The model was found to describe observed K effluent with optimization of parameters F and 01 (Fig. 10-1). Jensen (1984) found that a model that assumed only one region (F = 1; 01 = 0) in local equilibrium with the solid phase was an inadequate description of the observed K effluent concentrations (Fig. 10-1). The tworegion model fitted parameter F was less for the high velocity experiment relative to the low velocity experiment indicating a greater proportion of immobile water in the former and an increased importance of time-dependent mass transfer from mobile to immobile regions (Fig. 10-1). The results of Jensen (1984) also showed the dependence of 01 on the mean pore water velocity, with larger values of 01 expected at higher flow velocities (Nkedi-Kizza et al., 1983).

258

JARDINE

SANDY LOAM

0.2

z

0

!;(

F=1 cx= 0

------f-- --

F = 0.74 ex = 0.06 h-1

0.1

a:

I-

Z

W

U Z

---- ----

0

0

U 0

w 0.2

U

:::>

0

w a:

F=1

.. - - -.. /.. ..cx= -.. -0

-.. -

0.1

0 0

4

8

12

16

20

24

28

32

PORE VOLUMES Fig. 10-1. Observed K effluent concentrations from a sandy loam soil at low and high flow velocities (v = 7.2 and 27 cm h - I, respectively) with model-predicted curves assuming equilibrium (F = I; a = 0) and nonequilibrium, two-site, diffusive mass transfer (F < 1; a > 0 h -I) [from Jensen (1984), with permission].

Selim et al. (1987) also found that a two-region model was more appropriate for describing Mg-Ca transport through an aggregated soil relative to a one-region model (Fig. 10-2). Predicted curves using the two-region model were determined independently of observed BTC data, with D calculated from nonreactive tracers, R determined from batch adsorption isotherms, F predicted by assuming mobile water was drained under 20-cm suction, and 01 approximated by [3] where D = Iv + 0.0005; and D m = aVm + 0.0005. Parameter I is the longitudinal dipersivity, a is the approximate diameter of the aggregate size used in the soil columns and the value 0.0005 m 2 d -1 was regarded as the value for the solute diffusion term. The two-region model was better able to describe observed data at long times where BTC tailing occurred because of significant diffusive mass transfer (Fig. 10-2). The model also became increasingly necessary at higher fluxes where nonequilibrium conditions were more prevalent. Mansell et al. (1988) also utilized the two-region model to simulate the transport of multiple cations (Na, Mg, Ca) through soil columns. They found that although the use of variable selectivity coefficients for each binary com-

MODELING NONEQUILlBRIUM REACTIONS

8

259

ONE-REGION MODEL

t1JII"------

5

.... ....• ~

"

"

I

I6

3

6 6 6

ca

6 6

2

z

0

1

Mg

l-

-e

a::

0

w

8

IZ

0

5

10

15

20

25

30

TWO-REGION MODEL

0

z

...... ----

0

/~66 Ca

0 I-

/,. /Ii.

Z

~

W

::J ..J

U. U.

W

5

10

15

V I

20

25

30

v;

Fig. 10-2. Observed Mg and Ca effluent concentrations for 1- to 2-mm aggregates at a flux q = v(J of 1.19 em h -1 with model-predicted curves assuming one-region (equilibrium) and two-regions (nonequilibrium). The vivo on the x-axis is synonymous with pore volumes [from Selim et al. (1987), with permission].

bination of cation species gave improved descriptions of BTC tails in their ternary soil-water system, incorporation of two-region flow was also required (Fig. 10-3). By assuming local equilibrium during transport with variable selectivity coefficients, solute retardation was dramatically overestimated. Assuming two-region flow where 5 % of the total soil water was immobile provided an adequate description of multiple cation effluent concentrations (Fig. 10-3).

Microscopic Approach Interchange of solute between mobile and immobile zones can also be specified by Fick's second law of diffusion. This approach requires knowledge of the geometry of the sorbent material and assumes that solute transport occurs through a single-sized pore of known geometry. Assuming a uniformly sized spherical aggregate of radius 0, Eq. [1] remains valid for mobile phase transport, while Eq. [2] is replaced by the spherical diffusion equation (Rao et al., 1980; van Genuchten and Schulin, 1986)

JARDINE

260

0.5

z

0

l-

VARIABLE SELECTIVITY COEFFICIENT

0.4

ex = 0.008 h-1

e(

a: Izw 0.3 o z

0

Na

• Mg

0

o 0.2 0

w

o

::J

0

w

0.1

a: 0 234

0

5

6

PORE VOLUMES Fig. 10-3. Observed Na and Mg effluent concentrations from soil column at an average flow velocity of v = 6.3 em h -1 with model-predicted curves assuming (){ = 0.008 h -I, variable selectivity coefficients, and one-region (F = 1.0) or two-regions (F = 0.95) [from Mansell et al. (1988), with permission).

(0

<

r

<

a)

[4]

where C; is the solute concentration in the aggregate; r is the radial coordinate; and D; is the effective matrix diffusion coefficient. The average immobile solute concentration qm in Eq. [1] and [2] is now the average solute concentration of the intra-aggregate liquid phase (van Genuchten and Schulin, 1986)

qm

(x, t)

=

3

ja

a

0

-2

r 2 Ca (x, r, t)dr.

[5]

Nkedi-Kizza et al. (1982) utilized this approach to describe Ca mobility through an aggregated Oxisol (Fig. 10-4). Mobile pore water was assumed to be that water that drained under tensions < 80 em and estimates of Dela 2 [related to the nonequilibrium index, 'Y = 3De L(1 - 8)/a 2v] and P = vLID, where De is the effective diffusion coefficient within the aggregates; P is mobile-phase Peelet number; and L is the column length, were obtained by curve fitting 3H 20 BTC. Agreement between calculated and observed Ca BTC at two fluxes suggested that a distribution of soil aggregate sizes may be adequately represented by a single-sized equivalent spherical aggregate (Fig. 10-4). Rao et al. (1982) also indicated that diffusion within aggregates of mixed sizes and shapes could be represented by a single equivalent spherical aggregate whose radius was computed on a volume-weighted basis. Similarly, van Genuchten (1985) showed that solute diffusion within soil aggre-

261

MODELING NONEQUILIBRIUM REACTIONS

"Ca

8=0.61

P a2.1 R -3.03

. a.a

u

z

-

s cs]

,I' 'Y = /> / VM =

10.1

> ;: 0.4 « oJ 10.1 a::

/"

02 •

•

'Y

·

1.31 • 3.2 em h - 1 • ••

= 0.03

VM = 127.5 em h- 1

,(

2

3

Calculated

4

5

•

6

7

B

9

10

11

12

PORE VOLUMES Fig. 10-4. Observed Ca effluent concentrations from an aggregated Oxisol at low- and highflow velocities in the mobile region (Yrn = 3.2 and 127.5 em h -I, respectively) with modelfitted curves assuming two-region diffusive mass transfer where l' = 3D"L (I-O)/a 2y is an index of nonequilibrium [from Nkedi-Kizza et aI. (1982), with permission].

gates of varying geometry, could be represented by a shape factor specific to a particular pore geometry of interest. The results of Nkedi-Kizza et a1. (1982) suggest that an increased level of detail at the pore scale is valuable for practical predictions of observed macroscopic solute transport processes.

CHEMICAL AND BIOLOGICAL NONEQUILIBRIUM REACTIONS

Adsorption Nonequilibrium conditions during solute transport may be caused by kinetically limited adsorption reactions. Frequently, biphasic ion adsorption on soils is encountered (Sawhney, 1966; Griffin and Burau, 1974; Jardine and Sparks, 1984; Selim and Amacher, 1988) where rapid reactions on readily accessible sites occur simultaneously with slow reactions on less accessible sites. The energetics of adsorption may differ on these two types of sites depending on their location within the structure of the soil mineralogy. Certain locations exhibit structural constraints and increased charge densities (i.e., interlayer spaces) that influence the rate of chemical reaction during solute transport. Often, the more restrictive interlayer spaces of clay minerals exhibit larger solute adsorption energetics relative to easily accessible external mineral surfaces. Disequilibrium due to chemical kinetic limitations on heterogeneous soil surfaces have been modeled by Selim et al. (1976a) and Cameron and Klute (1977). These transport models are commonly known as two-site nonequilibriurn models, which assume solute adsorption on the two types of sites occur at different rates. Generally, empirical first-order and second-order expressions are utilized to describe the nonequilibrium adsorption process.

262

JARDINE

First-Order Ion Exchange The governing transport equation that describes solute adsorption on two different types of sites may be expressed as (Selim et al., 1976a; Cameron and Klute, 1977)

ac ax

ac + e (as! + as2) at () at at where parameter definitions are analogous S2 are the adsorbed solute concentrations for tively. The rate of solute interaction with described by first-order kinetic expressions

v-

[6]

to those in Eq. [I] and s! and type-I and type-2 sites, respecthe two different sites can be of the form [7]

where st and s, are the concentrations of adsorbed solute at equilibrium and any time t for type-i sites, respectively, and af and ab are forward (adsorption) and backward (desorption) first-order rate coefficients for type-r sites, with t = I and i = 2 for type-I and type-2 sites, respectively. Since type-I sites are readily accessible for ion adsorption, they frequently exhibit instantaneous adsorption reactions in local equilibrium with the solution phase. For such conditions, linear adsorption on type-I sites may be expressed as

as!/at = /k (oc/at)

[8]

where k = k! + k 2 is the net distribution coefficient for type-I and type-2 sites, and/ = k-/k is the fraction of type-I sites present. Under conditions of linear adsorption, = (1-f)kC and for type-2 sites, Eq. [7] becomes

s;

[9] where a is the rate coefficient for solute adsorption-desorption interactions with the soil assuming the adsorption and desorption rate coefficients are numerically equivalent. Investigating the transport of inorganic cations through undisturbed soil columns, Jardine et a1. (1988) found that reactive tracer effluent concentrations were well-described by a two-site, linear nonequilibrium model (Fig. 10-5). The observed BTC for the reactive tracers exhibited a retarded initial concentration increase relative to nonreactive tracers, followed by extensive tailing that continued to long times. In the context of the two-site model, the initial concentration increase reflected saturation of type-I sites while the duration of tailing was governed by the rate coefficient, a, for type-2 sites. The authors justified the use of a two-site model relative to a two-region model by illustrating that the physical heterogeneities of the soil system could be described by the classical convection-dispersion (CD) equation. This justifi-

263

MODELING NON EQUILIBRIUM REACTIONS 1.0

z

-r-----------------------,

0.8

0

....... E-<

a: a:::: E-< z

Mg MELTON COLUMN 1 0.6

w u

OBSERVED

z

0

0

u

MODEL

0.4

0

F'I TTED

w u

:::l 0 W

a::::

0.2

0.0 .....---___,r__---"""T"----~---___,r__---_t B 10 4 6 o 2

PORE VOLUMES

Fig. 10-5. Observed Mg effluent concentrations from undisturbed soil columns with a modelfitted curve determined using a two-site, nonequilibrium model where R = 2.11 was determined from a dynamic isotherm and f and IX were best-fit (O.ll ± 0.04 and 1.89 ± 0.17 h -I, respectively) [from Jardine et al, (1988), with permission].

cation may be erroneous, however, if the adsorption capacity of the less accessible, type-2 sites is relatively large and the fraction of immobile water is very small. For this situation, reactive tracer BTC could tail relative to nonreactive tracer BTC because of physical heterogeneities within the soil. Often, it becomes conceptually difficult to distinguish adsorption reactions that are controlled by two-sites or by two-regions (chemical vs. physical heterogeneity). Fortunately, these operationally distinct models are mathematically identical. Jardine et al. (1988) suggested that the observed time-dependent kinetic reactions of the inorganic cations with the soils was attributed to the chemical diffusion of these solutes into the interlayers of 2:1 nonexpandable clays (Fig. 10-5). Adsorption on these sites was believed to be energetically different than adsorption on external mineral surfaces. Fluhler and Selim (1986) investigating F adsorption on an acid loam soil, found that a two-site Langmuir isotherm was required to describe observed F BTC. The transport model used by these authors considered nonlinear adsorption on two types of sites with chemical reactions on these sites governed by first-order kinetic expressions (Fluhler and Jury, 1983). The various ionic species of F (i.e., F -, AI-F, etc.) were thought to exhibit different adsorption/desorption kinetics due to differences in their abilities to penetrate the varlouN layers of mineral surfaces.

JARDINE

264

Second-Order Ion Exchange Time-dependent ionic adsorption reactions on solids that exhibit two sites may also be described by empirical second-order expressions of the form (Selim and Amacher, 1988) [IOJ

where Vti and s, are the amounts of vacant and full sites of type-i, respectively, where i = 1 and i = 2 for type-l and type-2 sites, respectively. Equation [10J is first-order with respect to the adsorbed solute concentration and first-order with respect to the solute solution concentration, thus it is secondorder overall. Parameters eYf and eYb now reflect the adsorption and desorption of solutes via a second-order process. Selim and Amacher (1988) argue that first-order kinetic expressions imply that the soil has infinite solute retention since maximum solute sorption is not attained as the solution concentration increases. Their proposed second-order expression, however, achieves maximum sorption when all unfilled sites become occupied during solute transport. Using independently measured parameters for Cr, Selim and Amacher (1988) showed fair agreement between the second-order, two-site model and experimental Cr BTC (Fig. 10-6). Adsorption isotherms obtained from batch studies were modeled with the two-site Langmuir expression to provide model parameters, f (fraction of type-l sites) and ST (maximum number of sites).

WINDSOR -SOTS 1.0 .,----CUAVE

B

, ...

.8

C

/

I o

o

I

8

I

tJ

....

A

E

I

I

I

,

I

I

.2

I

o

2

..

-. .. .. 10

.....

.....--- .....

....

....

12

14

18

Fig. 10-6. Observed Cr effluent concentrations from the Windsor soil with predicted curves A, B, C, D, and E determined with a two-site, second-order nonequilibrium model (SOTS) using batch-rate coefficients for initial Cr concentrations of 25, 10, 5, 2, and I rng L -I, respectively. X-axis vivo and y-axis cleo represent pore volumns and reduced concentrations, respectively [from Selim and Amacher (1988), with permlNNlolIl.

MODELING NONEQUILIBRIUM REACTIONS

265

Batch kinetic studies at various initial Cr concentrations were also used to obtain adsorption and desorption second-order rate coefficients. A strong dependence of the rate coefficients on the initial input concentration was observed, thus Cr BTC were difficult to model because of transient Cr concentrations during transport (Fig. 10-6). Fluhler and Selim (1986) suggested that physically controlled processes were unlikely to be responsible for Cr retention since this soil has little, if any, aggregation. Low peak concentrations and extensive tailing during Cr desorption were believed to be the result of slow chemical reactions of Cr on soil surfaces exhibiting multiple types of reaction sites. Transformations Nonequilibrium behavior during solute transport in soil may also result from time-dependent chemical and biological transformation reactions. Consideration of chemical fixation, dissolution, hydrolysis, and polymerization reactions in mathematical models are often necessary to correctly describe the transport of certain solutes in soil. Time-dependent biological reactions that transform solutes into a variety of chemical species may also need consideration during solute transport in some soils. Aluminum Polymerization The significance of Al transport through subsurface soil environments is of great concern to agriculturalist and environmentalist. Soil solution Al is known to adversely effect terrestrial and aquatic ecosystems by severely limiting plant and fish production (Lewis, 1989; Sposito, 1989). It has also been linked to several human health disorders such as Alzheimer's disease and senile dementia. Therefore, the biogeochemical and hydrologic processes controlling the transport and cycling of Al are of considerable economic and scientific interest. The transport of Al through columns of Ca-saturated kaolinite was shown by Jardine et al. (1985) to involve instantaneous Ca-Al exchange and time-dependent Al polymerization reactions. The authors modeled the phenomena as a two-site nonequilibrium transport process (Fig. 10-7a) that assumed type-l sites were in local equilibrium with the solution phase and type-2 sites were governed by first-order kinetics (Eq. [6-9]). Independent estimation of fitted parameter f (fraction of type-l sites) was possible by assuming negative surface charge sites of kaolinite were in local equilibrium with the solution phase. This analysis supported a mechanism of instantaneous, electrostatic exchange of Al for Ca on the kaolinite surface. Further support is given by the simultaneous termination of Ca desorption with the change in slope ofthe Al BTC (Fig. 1O-7a). Recall that the initial concentration increase of the AI BTC reflects saturation of type-I sites. Jardine et al. (1985) suggested that the extended tailing of the Al BTC to long times was governed by time-dependent Al polymerization reactions (Fig. 1O-7a) that was modeled with the first-order rate coefficient Q. They

Fig. 10-7. a) Breakthrough curve for 0.73 rng L -1 AI at pH 4.29 on kaolinite with corresponding desorbed Ca. Solid line is the fitted curve from a two-site, nonequilibrium model [from Jardine et al. (1985), with permission], b) Breakthrough curve for 1.50 mg L -I Al at pH 3.97 on kaolinite with corresponding desorbed Ca. Solid line is the fitted curve from the onesite, equilibrium model. Note scales of abscissa for Fig. 1O-7a,b differ [from Jardine et al. (1985), with permission].

found that 0: was unaffected by variations in column length (Table 10-1) but was slightly affected by variations in influent Al concentration (Table 10-2), with the latter effect suggesting that the kinetic reactions of Al with kaolinite were not strictly first-order. The mechanism of time-dependent Al polymerization was supported through a series of studies examining the effect of influent pH on Al transport. The authors found that by lowering the

267

MODELING NON EQUILIBRIUM REACTIONS

Table 10-1. The effect of column length on the first-order rate coefficient. t Column length (mm)

ex (h -1)

3.2 22.0 42.5 64.3

0.147 0.256 0.262 0.198

t From Jardine et al.

(1985), with permission.

Table 10-2. The effect of influent Al concentration on the first-order rate coefficient. t Influent cone, (mg L -1) 0.73 1.51 2.37 4.85 7.75

0.132 0.124 0.127 0.262 0.330

t From Jardine et al. (1985), with permission.

influent pH, the slower kinetic reaction was eliminated and the observed Al BTC was well predicted by a one-site equilibrium model (Fig. 1O-7b). Nitrification/Denitrification The application of N fertilizer sources to soils frequently results in numerous chemical and microbiological mediated N transformation reactions. One of the more common N fertilizers is urea that, upon application to soil systems is rapidly hydrolyzed by the enzyme urease to form NH 4 • The ammonium ion is both a reactive cation in soils, which can become fixed within interlamellar spaces of certain 2: 1 phyllosilicates (Mengel and Scherer, 1981), and is subject to microbial oxidation resulting in the formation of N0 3 • This oxidation reaction is known as nitrification and is typically governed by either zero-order or first-order kinetics (McLaren, 1976; Starr, 1983). The microbial-mediated reduction of N0 3 (denitrification) also occurs in soils resulting in time-dependent formation of N 2 and N 20 gases (Reddy et aI., 1978). Numerous transport models have been adapted to consider nonequilibrium N transformation reactions in soil during one- and threedimensional flux of soil water (Starr and Parlange, 1975; Juryet al., 1976; Mironenko and Pachepsky, 1984; Clothier et aI., 1986). In a classic study performed by Wagenet et al. (1977), the unsaturated transport and transformations of urea, NH 4 , and N0 3 in soil were assumed to be described by the following equations (Cho, 1971)

[lla]

268

JARDINE

( 1

ec;

+ Pk - Z) ec; -- = D azczz ()

at

v- +

ax

aC3 at

ax

zc 3 z ax

(}:I

C1

-

(}:Z

aC ax

=D a

v -3 + (}:z Cz -

(}:3

Cz

[lIb]

C3

[lIe]

where parameter definitions are analogous to those in Eq. [1] and k and (}: are the linear distribution coefficient and first-order rate coefficient, respectively. Subscripts 1, 2, and 3 represent urea, NH 4 , and N0 3 , respectively, with (}:h (}:z, and (}:3 being the rate coefficients describing the processes of urea hydrolysis, NH 4 oxidation, and N0 3 reduction, respectively. Wagenet et al. (1977) found excellent agreement between observed urea, NH 4 , and N0 3 effluent concentrations and theoretical curves determined from Eq. [l la.b.c] (Fig. 10-8). Adsorption of urea and NH 4 by the soil was assumed to be instantaneous, with parameters k, and k z estimated independently of the transport model. Urea hydrolysis, nitrification, and denitrification were assumed to be governed by first-order kinetics with (}:I determined independently of the transport model and (}:z and (}:3 estimated by curve fitting Eq. [l Ib.c] to observed N0 3 and NH4 effluent concentrations. The magnitude of the rate coefficients was in the order (}:I > (}:z ~ (}:3, with single model-fitted values of (}:z and (}:3 (i.e., (}:z = 0.01 h -I and (}:3 = 0.001 h -I) sufficing for all soil columns.

•

r-:

o

C,.IOOO I

I

:

C~.500

....I

z

I

I

-

~200

0:'3

V

\

...

\ •

= 0.016 h= 0.010 n" = 0.001 h= 0.26 em h-

o = 0.09

1

1

1

ern" h- 1

\

/

...

I

o z

.

<{ w

I

/

II

/.

"'.,, .

N03

a: ::l

0:'2

I • •\ I • \

C;.o

r

0:'1

100

/

NH4

-

I

I

8....1

I

Z

I

Cl

I

,

E

I

4...

I

:r::

I

z

I I

•

40

80

120

0

TIME (h) Fig. 10-8. Observed urea, NH4 , and N03 effluent concentrations from soil pulsed with 1000 mg L -I urea (CPl, 500 mg L -I N0 3 (Cj), and 0 rna L - I NH 4 (q') with model-predicted curves determined using Eq, [I la-c) [from Waaenet el Ill. (1\177), with permission],

MODELING NONEQUILIBRIUM REACTIONS

269

The time-dependent transformation of N compounds by microbial oxidation and reduction reactions can also be described by Michaelis-Menten rate expression [12]

where A and B are constants, m is a constant biomass of microbes, and C, is a particular N substrate concentration (Starr, 1983). Since the rate limiting substrates for microbial growth are difficult to identify, parameters A and m are typically lumped into a single constant. For situations where B~ C, or B ~ C;, Eq. [12] reduces to zero- and first-order kinetic expressions, respectively.

Potassium Fixation/Release Potassium transformation reactions in soil are assumed to occur between solution, exchangeable, nonexchangeable ("fixed"), and primary mineral phases. Transformation of K from one phase to another is induced by transient soil conditions that promote K mineral weathering, leaching losses of soil solution K, and plant uptake of soil solution and exchangeable K. Exchangeable K is largely bound on readily accessible soil sites that mayor may not be in local equilibrium with the solution phase. Several studies have shown that the adsorption and release of exchangeable K may be kinetically limited in the presence of 2:1 nonexpanding clay minerals (Sparks et al., 1980a,b; Sparks and Jardine, 1981, 1984; Jardine and Sparks, 1984). Nonexchangeable and mineral K retention and release reactions in soil are typically very time dependent relative to transformations between solution and exchangeable K phases (Chute and Quirk, 1967; Feigenbaum et al., 1981; Helgeson et al., 1984; Martin and Sparks, 1983, 1985). Modeling K transport in soils, therefore, requires consideration of the nonequilibrium transformation reactions that occur between the various K phases. Selim et al. (l976b) formulated a mathematical model describing the kinetics of K transformation during transport. Transformations in the exchangeable phase (denoted by subscript ex) were represented by

where parameter definitions are synonymous with Eq. [1] and [6]; O:f and O:b are the forward (adsorption) and backward (desorption) rate coefficients for reactions between the solution and exchangeable phases; 0:1 and 0:2 are the nonexchangeable fixation and release rate coefficients, respectively; and N is the order of the reaction for adsorption of K from solution to the exchangeable phase. Transformations in the nonexchangeable phase (denoted by subscript nex) were defined by [14]

270

JARDINE

where CX3 and CX4 are the immobilization and the mineralization rate coefficients describing time-dependent K reactions between nonexchangeable and mineral phases, and Smin is the amount of K in the mineral phase. Finally, transformations in the mineral phase were represented by [15] Based on Eq. [13-15], Selim et al. (l976b) assumed the reactions between exchangeable and nonexchangeable as well as those between nonexchangeable and primary minerals were first-order kinetic reactions. The authors coupled Eq. [13-15] with the one-dimensional convective-dispersive equation (one-site version of Eq. [6]) to describe the transformation kinetics of K during transport in soil. To the author's knowledge, validation of this model with experimental data has not been attempted; however, Selim et al. (1976b) provide numerous simulations of K transport and transformation in sandy and loamy soils. The distribution of exchangeable, nonexchangeable, and mineral phases of K in a sandy soil as a function of time are presented in Fig. 10-9. These simulations showed that a continuous transformation of exchangeable K to nonexchangeable and mineral phases occurred with time at all profile depths. At any particular time, the distributions of nonexchangeable and mineral K lagged in the soil profile relative to the distribution of exchangeable K, which indicated nonequilibrium adsorption reactions. The simulations presented by Selim et al. (l976b) illustrate the dependence of leaching losses, plant uptake, and mineral weathering on the kinetics of K transformation reactions

E u

I LAKELAND I 30

40

ONE APPLICATION

Fig. 10-9. Simulations of exchangeable, nonexchangeable. and mineral phases of K distributions in a Lakeland soil profile where Ilf = Ilb ~ III > (~2 = (~4 > 113 [from Selim er al. (l976b), with permission).

271

MODELING NONEQUILIBRIUM REACTIONS

in soil. The significance of these transformation reactions will affect the quantity and timing of K fertilization and thus plant growth. Chemical Precipitation

Solute transport in soils may be complicated by precipitation reactions that act as kinetic sinks for chemicals. Because of its agronomic and environmental significance, P precipitation reactions during transport in soil have been most frequently studied. Often P is a severely limited nutrient in terrestrial and aquatic ecosystems which adversely affects plant and fish production. Because of the significance of P precipitation reactions in soil, the biogeochemical and hydrologic processes controlling P transport must be clearly understood. Many of the principles to be discussed for P reactions, may in some instances be applicable to other types of precipitation reactions (i.e., AI, Fe, etc.) Mansell et al. (l977a), investigating the transport of orthophosphate through saturated and unsaturated columns of a sandy soil, found that reversible, equilibrium adsorption-desorption relationships were inadequate for describing observed data. By coupling a reversible, first-order kinetic expression with the classical CD equation and considering nonlinear exchange, these authors substantially improved the prediction of orthophosphate transport through soil (Fig. 10-10). Mansell et al. (l977a) noted, however, that this model overpredicted the peak concentration and tailing response of observed P effluent concentrations. The authors further modified their model by considering first-order irreversible precipitation described by

Q

= a c (OC)

[16]

and first-order irreversible chemical immobilization via physical adsorption described by 1.0r-----------------, .'1

.

NoSink,../ : .::

0.8

v=42.46 cmjh • •

0.2 4

8

Sink Term

";,.

.

..

...

.... ( 0 • ..... , 0 •••••••• 12

16

-1

= Ire C; Ire =0.2 h = Ir.S;Ir. =0.2h24

28

1

32

v/v. Fig. 10-10. Observed P effluent concentrations from the Al horizon of a sandy soil with predicted curves determined 1111111111 nne-site, nonlinear, nonequilibrium model with and without a sink term for lrrevenlble IKJrpllllll IIl1d immobilization [from Mansell et al. (l977a), with permission).

JARDINE

272

Q

=

<X s

[17]

(ps)

where <Xc and <x s are the rate coefficients for precipitation and chemical immobilization, respectively; and Q is the rate of solute consumption (sink). Incorporating an irreversible sink for chemical immobilization or precipitation into the kinetic CD equation provided significantly better agreement between the observed data and the model-predicted curve (Fig. 10-10). Raats et al. (1982) developed a model for simulating one-dimensional convective-dispersive transport of P in soil, with nonlinear, reversible adsorption and irreversible fixation. The rate of fixation was assumed proportional to the amount of mobile phosphate in solution and to the amount of Al and Fe available for binding P. Therefore the fixation capacity was finite and first-order that differed from traditional first-order expressions assuming an infinite sink for immobilized P (Larsen et al., 1965; Fitter, 1974). Investigating orthophosphate transport through undisturbed cores of an acid, sandy soil (Fig. 10-11), Gerritse et al. (1982) found fair agreement between observed P concentration distributions in the columns and predicted curves using the model developed by Raats et al. (1982). In general the model predicted greater vertical mobility of P than was observed experimentally (Fig. 10-11). Because of the long-term nature of these experiments AP inorganic

1000 (mg or---'r-T~r--~r--~r---T""'"""""~r---r--~r---r--"':"":" 500 ~~.

15 20

25

P kg -1)

A --~ L.-_---,

,,--.~

,.------ .. ---~

-- .... '

35 ' depth (em)

Fig. 10-11. Profile distribution of inorganic P after adding 80 g (A) and 20 g (B) of freezedried pig slurry to the upper 2 em of undisturbed soil columns and simulating rainfall of 2150 mm over 1.3 yr (A) or 3600 mm in 1 yr (B). Solid lines represent the observed data and dashed lines are model-predicted assuming inorganic P only (from Gerritse et al. (1982), with permission].

MODELING NONEQUILIBRIUM REACTIONS

273

(i.e., 1-1.3 yr), various chemical factors such as pH and Eh may have affected P adsorption equilibria and kinetics causing deviations between observed and predicted P transport. Another important consideration was the possible large fixation of P in microbial biomass that was not quantified in these leaching experiments. The transport and transformations of P in soil have also been modeled by Mansell et al. (1977b), Enfield et ai. (1981), and Staunes and Enfield (1984). The former authors developed a multistep model describing the kinetic interactions between four phases of P during one-dimensional vertical transport. Staunes and Enfield (1984) used a one-dimensional CD model with irreversible precipitation kinetics and linear adsorption. These authors suggested that minimal error was introduced during model simulation of observed data by assuming a linear P adsorption isotherm. DeCamargo et al. (1979) used the model of Selim et al. (1976a) to describe orthophosphate transport in soil columns from an Alfisol. Adsorption was assumed to occur on two types of sites, with type-1 sites being in local equilibrium with the solution phase and type-2 sites exhibiting nonequilibrium first-order kinetic reactions with P (Eq. [6-9]). Fair agreement between observed P effluent concentrations and model-predicted curves were noted when the leading and tailing sections of the BTC were simulated separately. Enfield and Ellis (1983) further suggested that the dominant factor controlling the reaction kinetics of P retention by soil was the rate of nucleation and crystal growth based on solubility product theory considerations.

EFFECT OF NONLINEAR ADSORPTION AND DISPERSION ON THE INTERPRETATION OF NONEQUILIBRIUM REACTIONS The effects of nonlinear adsorption and dispersion on the interpretation of time-dependent transport reactions are very important considerations since these very different phenomena can behave with similar experimental BTC. The extent of solute dispersion in a soil depends on pore water velocity heterogeneity that will affect both the leading and tailing sections of the BTC. Soil systems having large dispersion characteristics (extensive distribution of pore classes) will exhibit rapid solute breakthrough followed by extended tailing to long times (Elrick and French, 1966; Nkedi-Kizza et al., 1983; Seyfried and Rao, 1987; Jardine et al., 1988). Breakthrough-curve tailing caused by solute dispersion is very similar in appearance to tailing caused by nonequilibrium kinetic reactions. Nonlinear exchange reactions, which are typical of heterovalent competitive adsorption (i.e., K-Ca), also affect the leading and tailing sections of the BTC (Schweich and Sardin, 1981). Simulating K-Ca transport through soil columns, Parker and Jardine (1986) utilized two-site, nonequilibrium models with linear exchange and nonlinear exchange described by the Vanselow selectivity coefficient (kv ) , to illustrate the effect of nonlinear adsorption during nonequilibrium and equilibrium adsorption reactions (Fig. 1O-12a,b). AssumhlK low solute dispersion (i.e., P = vL/D = 50) and local

JARDINE

274

Z J.O 0

... ...-.. .>:------

A.

..... I-

.;-

'/

~ 0.8

"'"

--

--

I-

Z

W

u 0.6

z

0

VARIABLE K. - -

u

B0.4

CONSTANT k, _ _

U ::J

LINEAR -

--

0 ~ 0.2

0.0

J

.

0

2

Z J.O

/ f

8.

0

.....

I

. / ..... • I Y' ,,V I

l-

~ 0.8

.

4

.

6

PORE VOLUMES

8

10

8

10

-

I

I

l-

Z

W

u 0.6

z

0 U

VARIABLE k. - -

004 W .

CONSTANT

I

I I I

u

LINEAR -

I

,

::J

0

~ 0.2

kv -

--

I

J

0.0

j,' 0

2

.

4

6

PORE VOLUMES

Fig. 10-12. Simulated K breakthrough curves for P = 50, and WI _ 00 using two-site, nonlinear variable and constant k; models and a two-site, linear model for (A) W2 = 1.0 and (B) W2 _ 00. (wI and W2 are dimensionless forms of ex for type-I and type-2 sites, respectively) [from Parker and Jardine (1986), with permission].

equilibrium of type-I sites with the solution phase (i.e., WI - 00, where WI is a dimensionless form of the first-order rate coefficient a on type-1 sites; Parker and Jardine, 1986), simulated BTC in Fig. 1O-12a illustrate that both the linear model and nonlinear model (with constant or variable kv) exhibit pronounced tailing when nonequilibrium conditions are imparted on type-2 sites (i.e., W2 = 1.0, where W2 represents dimensionless (2)' Breakthrough-curve tailing for K transport assuming linear exchange is due solely to time-dependent kinetic reactions. Tailing during K transport assum-

MODELING NONEQUILIBRIUM REACTIONS

275

ing nonlinear exchange, is due to time-dependent reactions on type-2 sites and the nonlinear features of the adsorption isotherm (Fig. 1O-12a). If equilibrium reactions are assumed for both type-l and type-2 sites (i.e., WI = W2 _ 00), the simulated K BTC using the linear model exhibits no tailing while those using the nonlinear model maintain the tailing response to long times (Fig. 1O-12b). Thus, in the absence of time-dependent reactions, extensive BTC tailing may result from nonlinear exchange processes. By just looking at the variable k; BTC (Fig. 1O-12b), it is difficult to decide whether tailing is due to kinetic reactions or nonlinear adsorption without knowledge of the adsorption isotherm. Since solute dispersion, nonlinear adsorption, and time-dependent kinetic reactions may result in experimental BTC that are similar in appearance, independent measurements of two or more of these phenomena should be performed whenever possible. Solute dispersion may be obtained with nonreactive tracers and assuming similar dispersion characteristics for the corresponding reactive tracer (Nkedi-Kizza et aI., 1982; Jensen, 1984; Selim et aI., 1987). It is important when obtaining dispersion parameters by modeling nonreactive tracer BTC, that appropriate boundary conditions are used (Parker and van Genuchten, 1984b; van Genuchten and Wierenga, 1986; Barry and Sposito, 1988; Jardine et aI., 1988). By using correct boundary conditions, not only will correct dispersion characteristics be obtained, but the possible presence of diffusive mass transfer nonequilibrium processes can be detected. Determination of equilibrium adsorption isotherms using batch (van Genuchten, 1981; Jensen, 1984; Southworth, 1987) or transient techniques (Lai and Jurinak, 1971; Jardine et al., 1988) will indicate whether a nonlinear (k varies as a function of solution concentration) or linear (k is constant with solution concentration) transport model should be used. Batch techniques can also be used to verify if time-dependent kinetic reactions exist during solute transport. By obtaining independent measurements of solute dispersion, adsorption characteristics, and nonequilibrium kinetic reactions, correct interpretation of complex solute transport phenomena is possible.

CONCLUSIONS Techniques for modeling time-dependent adsorption, transformation, diffusional mass exchange, and precipitation reactions of inorganic ions with soil have been reviewed. The models discussed in this chapter are all based on the convective-dispersive equation and assume steady-state fluid flow through a homogeneous soil column. The models are useful from a mechanistic standpoint for the study of mass transfer kinetics when the effects of nonlinear adsorption and dispersion are considered. Application of these models to field scale solute transport studies is questionable, however, because of the vast continuum of soil pore sizes resulting in spatially variable fluid flow (Beven and Germann, 1982; Quisenberry and Phillips, 1976; Van de Pol et al., 1977; Shuford ct al., 1977; Wilson and Luxmoore, 1988; Wilson et al.,

276

JARDINE

1989; Jardine et aI., 1989, 1990). More complex conceptual models are being developed to describe solute transport in extremely heterogeneous soil systems dominated by preferential flow (Steenhuis et at, 1988; Luxmoore et aI., 1990). However, at present, these models lack numerical expressions that consider the possible time-dependent kinetic reactions of ions with the soil.

ACKNOWLEDGMENTS

This research was funded by the Subsurface Science Program of the Ecological Research Division; Office of Health and Environmental Research, U.S. Dep. of Energy under contract DE-AC05-840R2l400 with Martin Marietta Energy Systems Inc. Publication no. 3692. I appreciate the efforts of Dr. Frank Wobber, the contract officer for Dep. of Energy, who has supported this work.

REFERENCES Barry, D.A., and G. Sposito. 1988. Application of the convection-dispersion model to solute transport in finite soil columns. Soil Sci. Soc. Am. J. 52:3-9. Beven, K., and P. Germann. 1982. Macropores and water flow in soils. Water Resour. Res. 18:1311-1325. Cameron, D.R., and A. Klute. 1977. Convective-dispersive solute transport with combined equilibrium and kinetic adsorption model. Water Resour. Res. 13:183-188. Cho, C.M. 1971. Convective transport of ammonium with nitrification in soil. Can. J. Soil Sci. 51:339-350. Chute, J.H., and J.P. Quirk. 1967. Diffusion of potassium from mica-like minerals. Nature 213:1156-1157. Clothier, B.E., T.J. Sauer, and S.R. Green. 1986. Nitrogen movement in soil during fertilization with urea. p. 516-522. In D.R. Nelson (ed.) Trans. Int. Congr, Soil Sci. 13th. Vol. 6. Int. Soil Sci. Soc., Hamburg, Germany. DeCamargo, a.A., J.W. Biggar, and D.R. Nielsen. 1979. Transport of inorganic phosphorous in an Alfisol. Soil Sci. Soc. Am. J. 43:884-890. Elrick, D.E., and L.K. French. 1966.Miscibledisplacement patterns on disturbed and undisturbed soil cores. Soil Sci. Soc. Am. Proc. 30:153-156. Enfield, C.G., T. Phan, D.M. Walters, and R. Ellis, Jr. 1981. Kinetic model for phosphate transport and transformation in calcareous soils: I. Kinetics of transformations. Soil Sci. Soc. Am. J. 45:1059-1064. Enfield, C.G., and R. Ellis, Jr. 1983. The movement of phosphorus in soil. p. 93-107. In D.W. Nelson et al. (ed.) Chemical mobility and reactivity in soil systems. SSSA Spec. Publ. II. SSSA, Madison, WI. Feigenbaum, S., R. Edelstein, and I. Shainberg. 1981. Release rate of potassium and structural cations from micas to ion exchangers in dilute solutions. Soil Sci. Soc. Am. J. 45:501-506. Fitter, A.H. 1974. A relationship between phosphorus requirement, the immobilization of added phosphate and the phosphate buffering capacity of colliery shales. J. Soil Sci. 25:41-50. Fluhler, H., and W.A. Jury. 1983. Estimating solute transport using nonlinear, rate dependent, two-site adsorption models. Rep. 245. Swiss Federal Inst. of For. Res., Zurich. Fluhler, H., and H.M. Selim, 1986. Ion exchange and ion transport in soils. p. 541-547. In D.R. Nielson (ed.) Trans. Int. Congr. Soil Sci. 13th. Vol. 6. Int. Soil Sci. Soc., Hamburg, Germany. Gerritse, R.G., P. De Willigen, and P.A.C. Raats. 1982. Transport and fixation of phosphate in acid, homogeneous soils. III. Experimental case study of acid, Nandy mil columns heavily treated with pig slurry. Agric, Environ. 7: 175-185.

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Griffin, R.A., and R.G. Burau. 1974. Kinetic and equilibrium studies of boron desorption from soil. Soil Sci. Soc. Am. Proc. 38:894-897. Helgeson, H.C., W.M. Murphy, and P. Aagaard. 1984. Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions. II. Rate constants, effective surface area, and the hydrolysis of feldspar. Geochim. Cosmochim. Acta 48:2405-2432. James, R.V., and J. Rubin. 1979. Applicability of local equilibrium assumptions to transport through soil of solutes affected by ion exchange. p. 225-235. In E.A. Jenne (ed.) Chemical modeling in aqueous systems. Symp, Ser. Vol. 93. ACS, Washington, DC. Jardine, P.M., and D.L. Sparks. 1984. Potassium-calcium exchange in a multireactive soil system. I. Kinetics. Soil Sci. Soc. Am. J. 48:39-45. Jardine, P.M., J .C. Parker, and L. W. Zelazny. 1985. Kinetics and mechanisms of aluminum adsorption on kaolinite using a two-site nonequilibrium transport model. Soil Sci. Soc. Am. J. 49:867-873. Jardine, P.M., G.V. Wilson, and R.J. Luxmoore. 1988. Modeling the transport of inorganic ions through undisturbed soil columns from two contrasting watersheds. Soil Sci. Soc. Am. J. 52:1252-1259. Jardine, P.M., G.V. Wilson, and R.J. Luxmoore. 1990. Unsaturated solute transport through a forest soil during rain storm events. Geoderma 46:103-118. Jardine, P.M., G.V. Wilson, R.J. Luxmoore, and J.F. McCarthy. 1989. Transport of inorganic and natural organic tracers through an isolated pedon in a forest watershed. Soil Sci. Soc. Am. J. 53:317-323. Jennings, A.A., and D.J. Kirkner. 1984. Instantaneous equilibrium approximation analysis. J. Hydraul. Eng. 110:1700-1717. Jensen, J.R., 1984. Potassium dynamics in soil during steady flow. Soil Sci. 138:285-293. Jury, W.A., W.R. Gardner, P.G. Saffigna, and C.B. Tanner. 1976. Model for predicting simultaneous movement of nitrate and water through a loamy sand. Soil Sci. 122:36-43. Lai, Sang-He, and J .J. Jurinak. 1971. Numerical approximation of cation exchange in miscible displacement through soil columns. Soil Sci. Soc. Am. Proc. 35:894-899. Larsen, S., D. Gunary, and C.D. Sutton. 1965. The rate of immobilization of applied phosphate in relation to soil properties. J. Soil Sci. 16:141-149. Lewis, T.E. 1989. Environmental chemistry and toxicology of aluminum. Lewis Publ. Inc., Chelsea, MI. Luxrnoore, R.J., G. V. Wilson, P.M. Jardine, and R.H. Gardner. 1990. Use of percolation theory and latin hypercube sampling in field-scale solute transport investigations. p. 437-439. In D.-Q. Lin (ed.) Proc. 1st Int. Symp. For. Soils, Harbin, People's Republic of China. 22-27 July. Northeast Forestry Univ., Harbin, People's Republic of China. Mansell, R.S., H.M. Selim, P. Kanchanast, J.M. Davidson, and J.G.A. Fiskell. 1977a. Experimental and simulated transport of phosphorus through sandy soils. Water Resour. Res. 13:189-194. Mansell, R.S., H.M. Selim, and J.G.A. Fiskell. 1977b. Simulated transformations and transport of phosphorus in soil. Soil Sci. 124:102-109. Mansell, R.S., S.A. Bloom, H.M. Selim, and R.D. Rhue, 1988. Simulating transport of multiple cations in soil using variable selectivity coefficients. Soil Sci. Soc. Am. J. 52:1533-1540. Martin, H.W., and D.L. Sparks. 1983. Kinetics of nonexchangeable potassium release from two Coastal Plain soils. Soil Sci. Soc. Am. J. 47:88~-887. Martin, H. W., and D.L. Sparks. 1985. On the behavior of nonexchangeable potassium in soils. Commun. Soil Sci. Plant Anal. 16:133-162. McLaren, A.D. 1976. Rate constants for nitrification and denitrification in soils. Radiat. Environ. Biophys. 13:294-299. Mengel, K., and H.W. Scherer. 1981. Release of nonexchangeable (fixed) soil ammonium under field conditions during the growing season. Soil Sci. 131:226-232. Mironenko. E. V., and Ya.A. Pachepsky. 1984. Analytical solution for chemical transport with nonequilibrium mass transfer, adsorption and biological transformation. J. Hydrol. 70:167-175. Nkedi-Kizza, P., P.S.C. Rao, R.E. Jessup, and J.M. Davidson. 1982. Ion exchange and diffusive mass transfer during miscible displacement through an aggregated Oxisol. Soil Sci. Soc. Am. J. 46:471-476. Nkedi-Kizza, P., J .M. Uillllar, M.Th. van Genuchten, P.J. Wierenga, H.M. Selirn, J.D. Davidson, and D.R. Nielsen. IIIH3. Modeling tritium and chloride 36 transport through an aggregated O~INClI. Wlllrr NrMlIllr. Res, 19:691-700.

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Parker, J.C., and P.M. Jardine. 1986. Effects of heterogeneous adsorption behavior on ion transport. Water Resour. Res. 22:1334-1340. Parker, J.C., and A.J. Valocchi. 1986. Constraints on the validity of equilibrium and firstorder kinetic transport models in structured soils. Water Resour. Res. 22:399-407. Parker, J.C., and M.Th. van Genuchten. 1984a. Determining transport parameters from laboratory and field tracer experiments. Virginia Agric. Exp. Stn. Bull. 84-3. Parker, J.C., and M.Th. van Genuchten. 1984b. Flux-averaged and volume-averaged concentrations in continuum approaches to solute transport. Water Resour. Res. 20:866-872. Quisenberry, V.L., and R.E. Phillips. 1976. Percolation of simulated rainfall under field conditions. Soil Sci. Soc. Am. J. 40:484-489. Raats, P.A.C., P. De Willigen, and R.G. Gerritse. 1982. Transport and fixation of phosphorus in acid, homogeneous soils. I. Physico-mathematical models. Agric, Environ. 7:149Q60. Rao, P.S.C., D.E. Rolston, R.E. Jessup, and J.M. Davidson. 1980. Solute transport in aggregated porous media: Theoretical and experimental evaluation. Soil. Sci. Soc. Am. J. 44:1139-1146. Rao, P.S.C., R.E. Jessup, and T.M. Addiscott. 1982. Experimental and theoretical aspects of diffusion in spherical and nonspherical aggregates. Soil Sci. 133:342-249. Reddy, K.R., W.H. Patrick, Jr., and R.E. Phillips. 1978. The role of nitrate diffusion in determining the order and rate of denitrification in flooded soil: I. Experimental results. Soil Sci. Soc. Am. J. 42:268-272. Sawhney, B.L. 1966. Kinetics of cesium sorption by clay minerals. Soil Sci. Soc. Am. Proc. 30:565-569. Schweich, D., and M. Sardin. 1981. Adsorption, partition, ion exchange and chemical reaction in batch reactors or in columns - A review. J. Hydrol. 50:1-33. Selim, H.M., and M.e. Amacher. 1988. A second-order kinetic approach for modeling solute retention and transport in soils. Water Resour. Res. 24:2061-2075. Selim, H.M., J.M. Davidson, and R.S. Mansell. 1976a. Evaluation of a two-site adsorptiondesorption model for describing solute transport in soils. p. 444-448. In Proc. Summer Computer Simulation Conf., Washington, DC. 12-14 July. Selim, H.M., R.S. Mansell, and L.W. Zelazny. 1976b. Modeling reactions and transport of potassium in soils. Soil Sci. 122:77-84. Selim, H.M., R. Schulin, and H. Fluhler. 1987. Transport and ion exchange of calcium and magnesium in an aggregated soil. Soil Sci. Soc. Am. 1. 51:876-884. Seyfried, M.S., and P.S.C. Rao. 1987. Solute transport in undisturbed columns of an aggregated tropical soil: Preferential flow effects. Soil Sci. Soc. Am. J. 51:1434-1444. Shuford, J. W., D.D. Fritton, and D.E. Baker. 1977. Nitrate-nitrogen and chloride movement through undisturbed field soil. J. Environ. Qual. 6:255-259. Southworth, G. 1987. Movement of radiotracer metal cations through a forest soil column. Environ. Int. 13:197-201. Sparks, D.L., and P.M. Jardine. 1981. Thermodynamics of potassium exchange in soil using a kinetic approach. Soil Sci. Soc. Am. J. 45:1094-1099. Sparks, D.L., and P .M. Jardine. 1984. Comparison of kinetic equations to describe potassiumcalcium exchange in pure and in mixed systems. Soil Sci. 138:115-122. Sparks, D.L., L.W. Zelazny, and D.C. Martens. 1980a. Kinetics of potassium exchange in a Paleudult from the Coastal Plain of Virginia. Soil Sci. Soc. Am. J. 44:37-40. Sparks, D.L., L.W. Zelazny, and D.C. Martens. 1980b. Kinetics of potassium desorption in soil using miscible displacement. Soil Sci. Soc. Am. J. 44:1205-1208. Sposito, G. 1989. The environmental chemistry of aluminum. CRC Press, Inc., Boca Raton, FL. Starr, J.L. 1983. Assessing nitrogen movement in field. p. 76-92. In D.W. Nelson et al. (ed.) Chemical mobility and reactivity in soil systems. SSSA Spec. Publ. 11. SSSA, Madison, WI. Starr, J.L., and J.Y. Parlange. 1975. Nonlinear denitrification kinetics with continuous flow in soil columns. Soil Sci. Soc. Am. Proc. 39:875-880. Steenhuis, T.S., M.S. Andreini, and J. Parlange, 1988. A numerical model for preferential solute movement. p. 1-21. In Proc. ASAE Meet., Chicago. 13-16 December. Paper No. 88-2631. Stuanes, A.a., and C.G. Enfield. 1984. Prediction of phosphate movement through some selected soils. J. Environ. Qual. 13:317-320. Valocchi, A.J. 1985. Validity of the local equilibrium assumption for modeling sorbing solute transport through homogeneous soils. Water Resour. Res. 21 :808-820.

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Van de Pol. R.M., P.J. Wierenga, and D.R. Nielsen. 1977. Solute movement in a field soil. Soil Sci. Soc. Am. J. 41:10-13. van Genuchten, M.Th. 1981. Non-equilibrium transport parameters from miscible displacement experiments. Res. Rep. no. 119. U.S. Salinity Lab., Riverside, CA. van Genuchten, M.Th. 1985. A general approach for modeling solute transport in structured soils. Mem. Int. Assoc. Hydrogeol. 17:513-526. van Genuchten, M.Th., and R. Schulin. 1986. Modeling solute transport processes in the unsaturated zone. p. 523-532. In D.R. Nielsen (ed.) Trans. Int. Congr. Soil Sci. 13th. Vol. 6. Int. Soil Sci. Soc., Hamburg, Germany. van Genuchten, M.Th., and P.J. Wierenga. 1976. Mass transfer studies in sorbing porous media. I. Analytical solutions. Soil Sci. Soc. Am. J. 40:473-480. van Genuchten, M.Th., and P.J. Wierenga. 1986. Solute dispersion coefficients and retardation factors. p. 1025-1054. In A. Klute (ed.) Methods of soil analysis. Part 1. 2nd ed. Agron. Monogr. 9. ASA, Madison, WI. Villermaux, J. 1974. Deformation of chromatography peaks under the influence of mass transfer phenomena. J. Chromotogr. Sci. 12:822-831. Wagenet, R.J., J.W. Biggar, and D.R. Nielsen. 1977. Tracing the transformations of urea fertilizer during leaching. Soil Sci. Soc. Am. J. 41:896-902. Wilson, G. V., and R.J. Luxmoore. 1988. Infiltration, macroporosity, and mesoporosity distributions on two forested watersheds. Soil Sci. Soc. Am. J. 52:329-335. Wilson, G.V., J .M. Alfonsi, and P.M. Jardine. 1989. Spatial variability of saturated hydraulic conductivity of the subsoil of two forested watersheds. Soil Sci. Soc. Am. J. 53:679-685.

11

Sorption Kinetics of Organic Chemicals: Methods, Models and Mechanisms Mark L. Brusseau

Soil and Water Science Department University of Arizona Tucson, Arizona P. S. C. Rao

Soil Science Department University of Florida Gainesville, Florida

ABSTRACT Rate-limited or, nonequilibrium, sorption of organic chemicals by natural sorbents (i.e., soils, sediments, and aquifer materials) has been a topic of interest for quite some time. The impact of nonequilibrium sorption on transport of organic chemicals in the subsurface has recently come under increased scrutiny as groundwater contamination has become a major issue. The purpose of this paper is to provide a brief review of the rate-limited sorption of organic chemicals by natural sorbents. The proposed processes held responsible for nonequilibrium sorption will be presented, as will a discussion of recent experiments whose results provide elucidation of rate-limiting mechanisms. Several models have been proposed to simulate sorption kinetics, and the transport of solutes influenced by nonequilibrium sorption; these will be reviewed. A large array of techniques are available for the study of sorption kinetics. However, much of this work has been oriented towards the study of inorganic chemicals. We will discuss two techniques that, in addition to the standard batch time study, have received the greatest amount of use in investigating nonequilibrium sorption of organic chemicals.

Rate-limited or, nonequilibrium, sorption of organic chemicals by natural sorbents (i.e., soils, sediments, and aquifer materials) has been a topic of interest for quite some time. Early work in this area was performed by soil scientists (e.g., Hamaker et aI., 1966; Hance, 1967; Kay and Elrick, 1967; Copyright

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Davidson et aI., 1968; Davidson and Chang, 1972; Green et al., 1968, 1972), many of whom were investigating the effects of rate-limited sorption and/or soil structure on transport of pesticides in soils. The impact of nonequilibriurn sorption on transport of organic chemicals in the subsurface has recently come under increased scrutiny (e.g., Schwarzenbach and Westall, 1981; Goltz and Roberts, 1986; Hutzler et aI., 1986; Bouchard et aI., 1988; Lee et aI., 1988; Brusseau et al. 1989c, 1991c; Brusseau and Rao, 1989a,b; NkediKizza et aI., 1989) as groundwater contamination has become a major issue. The first to recognize the effect of nonequilibrium sorption on solute transport was Wilson (1940), who stated "the width of a band (chromatographic pulse) may increase because the leading edge of the band migrates too rapidlyon account of a low rate of adsorption, or because the trailing edge of the band migrates too slowly on account of a low rate of desorption." Since then, research on the impact of nonequilibrium sorption on transport of solutes has been carried out in several disciplines, including chemical engineering, chromatography, petroleum engineering, soil science, hydrology, and environmental science. The purpose of this paper is to provide a brief review of the rate-limited sorption of organic chemicals by natural sorbents. The processes that have been proposed as being responsible for nonequilibrium sorption will be presented, as will a discussion of recent experiments whose results allow elucidation of rate-limiting mechanisms. Several models have been proposed to simulate sorption kinetics and the transport of solutes influenced by nonequilibrium sorption. These will be briefly reviewed. As evidenced by other talks in this symposium and by the material presented by Sparks (1989), a large array of techniques are available for the study of sorption kinetics. However, much of this work has been oriented towards the study of inorganic chemicals. We will discuss two techniques that, in addition to the standard batch-time study, have received the greatest amount of use in investigating nonequilibrium sorption of organic chemicals.

EXPERIMENTAL METHODS

The primary technique that has been used to investigate the sorption kinetics of organic chemicals is the batch-sorption rate method. Several methods have been developed that may be used as alternatives to the batchrate method. The two that have received the greatest use are the gas-purge (GP) and the miscible-displacement (MD) techniques. These two techniques will be briefly reviewed. The GP technique was first applied to sorption by Karickhoff (1980), who investigated the rate-limited desorption of polynuclear aromatics from freshwater sediments. The GP technique has since been used by others to investigate sorption dynamics of sediment/water (Karickhoff and Morris, 1985; Oliver, 1985; Coates and Elzerman, 1986; Wu and Gschwend, 1986) and soil/water (Buxton and Green, 1987; Brusseau et al., 1990a) systems. To employ the GP technique, a reactor containing a heads pace lind a pre-

SORPTION KINETICS

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equilibrated slurry of sorbent, solute, and water is purged with a gas such as air or N z• The gas stream strips the solute from the water phase, thus inducing desorption of the sorbate from the sorbent. The gas stream is trapped upon exiting the reactor to allow determination of the mass flux of solute. This method as described above allows performance of only desorption experiments. A modified approach was utilized by Wu and Gschwend (1986) to perform both adsorption and desorption experiments. The apparatus was designed to operate under closed conditions to prevent mass loss. To operate in such a manner, a nondestructive detector, such as a photoionization detector (PIO), is required. A limitation of the Karickhoff apparatus is that it can only be operated in the desorption mode. A limitation of the design used by Wu and Gschwend is that desorption can only be studied with the dilution approach (i.e., a given volume of soil-water solute slurry in a condition of equilibrium is diluted by adding a given volume of "clean" water, which induces desorption). A disadvantage of a design using a PIO detector is the relatively high detection limit associated with the PIO. This is of special concern for solutes with very low solubilities and/or Henry's constants, where small changes at minute concentration levels may not be discernable. In such cases the preferred design is that used by Karickhoff (1980), where a trapping device is employed. The apparatus employed by Brusseau et al. (1990a) (Fig. 11-1) was designed to combine the advantageous features of the Karickhoff (1980) and Wu and Gschwend (1986) designs.

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Miscible displacement techniques have been widely used in chemical engineering, petroleum engineering, and soil science to investigate various aspects of solute dispersion, sorption, and transport. Use of the MD technique to investigate the nonequilibrium sorption or sorption kinetics of organic solutes was initiated by soil scientists (e.g., Kay and Elrick, 1967; Davidson et al., 1968; Green et aI., 1968; Davidson and Chang, 1972; Green et aI., 1972), who were evaluating the transport of pesticides in soils. The MD technique has since been used to investigate nonequilibrium sorption of other types of organic chemicals, such as chlorinated aromatics and ethenes, alkylbenzenes, and polynuclear aromatics, as well as other pesticides, in soils and aquifer materials (e.g., Schwarzenbach and Westall, 1981; Southworth et aI., 1987; Bouchard et al., 1988; Lee et aI., 1988; Brusseau and Rao, 1990b; Brusseau et aI., 1989a,b; 1990a, 1991a,c; Nkedi-Kizza et aI., 1989). An evaluation of the general applicability and the equivalency of these two techniques was presented by Brusseau et al. (1990a). A brief review of some of their findings is presented below. Gas-purge experiments have been performed for chlorobenzenes by Brusseau et al. (1990a), Karickhoff and Morris (1985), Oliver (1985), and Wu and Gschwend (1986). To compare the results obtained by these researchers, values for k 2 (first-order desorption rate constant) and K p (equilibrium sorption constant) are plotted in log form in Fig. 11-2 (taken from Brusseau et aI., 1990a). A regression of the combined data yields an r 2 = 0.99, suggesting that the experimental results obtained by the different authors are comparable. The GP technique therefore, seems to have associated with it a high degree of reproducibility. To have confidence in the kinetic parameters determined from a GP experiment, there must be a significant difference between the desorption and gas-stripping (i.e., removal of solute from system devoid of sorbent) curves. In other words, the characteristic time of the desorption reaction (Td ) must be greater than the characteristic time for gas-liquid mass trans(1) Brusseau etal., 1990a

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SORPTION KINETICS

fer (Tg\ ) . The condition under which Td ~ Tgh and thus under which the GP technique is viable, is dependent on the magnitude of the desorption rate constant. Given the inverse relationship that appears to exist between k 2 and K p (Brusseau and Rao, 1989c; Brusseau et al., 1990a, 1991a) as illustrated in Fig. 11-2, the Td conditionality is a function of the sorptive character of the specific solute/sorbent pair. Based on the results presented in Brusseau et al. (l990a), it appears that the GP technique is viable for systems having K, values ranging from> 100 000 to < 10, and becomes unreliable for K p values in the vicinity of 0.1 to 1 L kg -I. Values for k 2 and K p obtained by Brusseau et al. (l990a) from miscible displacement experiments performed using benzene (BNZ), chlorobenzene (CB), 1,3-dichlorobenzene (DCB), and 1,2,4-trichlorobenzene (TCB) are plotted in Fig. 11-3, along with the values for the same chemicals presented in Fig. 11-2 that were obtained from gas-purge experiments (note that different soils were used). The apparatus used for the MD experiments is shown in Fig. 11-4. The similarity between the two data sets suggests that the two experimental techniques produced comparable results. The comparability of the two methods was further tested by attempting to use kinetic-parameter values determined by gas purge to predict breakthrough curves (BTC) obtained from the same soil/solute pairs. A BTC obtained from miscible displacement of PCE through the Eustis soil column is presented in Fig. 11-5. The values for k 2 and F (fraction of sorbent for which sorption is instantaneous) determined from the Eustis/PCE gas-purge experiment were used to calculate values for (3 (fraction of "instantaneous" retardation) and w (ratio of hydrodynamic residence time to reaction time). The simulation produced by a first-order bicontinuum model (Brusseau and Rao, 1989a) with these independently determined kinetic parameters is shown in Fig. 11-5. The model simulation compares extremely well with the experimental BTC. Such predictions for organic chemicals, where values for

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all model parameters were obtained independent of the column experiment (the K p value was determined from a batch isotherm and the dispersion coefficient was obtained from a tracer), are scarce. It appears that the gas-purge and miscible-displacement techniques yield comparable results. In addition, the miscible-displacement technique has been shown to yield results similar to those of batch-rate studies when similar time scales are used (Brusseau et aI., 1991c). This would suggest that the three methods are measuring the same physicochemical process. This also suggests that the bicontinuum model, since it was used successfully in data analysis

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287

for all methods, provides a valid representation of the process responsible for the observed nonequilibrium, whatever it may be. The parameter k 2 , rather than being just a "fitting" function, may thus be considered as having a mechanistic basis. It is apparent from inspection of Fig. 11-4 that a flow-through analytical technique was employed by Brusseau et al. (1990a) in their MD studies. Previous MD studies have usually employed a collection of effluent fractions, which would then be analyzed using chromatographic or radioassay methods. Flow-through analysis provides a continuous form of data, whereas fraction collection provides data for discrete points. For volatile chemicals, fraction collection suffers from potential losses resulting from volatilization during the fraction collection and analysis steps. This problem is eliminated using flow-through analysis. The analytical process is significantly simplified with the flow-through approach. The chemicals that may be used will, however, be constrained by the use of detectors that are suitable for flowthrough operation. In addition, this technique, unless modified (e.g., two detectors), is generally limited to single-solute solutions. The miscible displacement technique is especially useful for low-sorptivity systems. Its efficacy, however, is greatly reduced for systems comprised of highly sorptive chemicals or of soils containing high levels of clay and/or organic matter. As the sorptivity of the solute increases, both time constraints and problems such as sorption to the apparatus become of increasing concern. These problems can be ameliorated through modification of the experimental method. One such approach involves the use of miscible organic cosolvents. The presence of cosolvent results in reduced values of K p (Rao et aI., 1985; Nkedi-Kizza et al., 1985; Fu and Luthy, 1986; Nkedi-Kizza et aI., 1987) and in increased values of k 2 (Brusseau et al., 1989b, 1991b; Nkedi-Kizza et al., 1989). With these effects, the use of cosolvent can significantly reduce the experiment time and the occurrence of other problems associated with the use of highly sorptive chemicals. For example, Brusseau et al. (1989b, 1991b) have shown that values of k 2 in aqueous systems can be estimated successfully by extrapolation from experiments performed with mixed-solvent systems. The determination of kinetic parameter values from column experiments is predicated upon the ability of the mathematical model to successfully simulate the experimental data. Confidence in the robustness of the parameter values so determined is attained only with a unique solution (i.e., when one suite of parameter values provides a solution that is significantly better than all others). For cases wherein a system is near equilibrium or under extreme nonequilibrium, attainment of a unique solution may prove difficult. A modified miscible-displacement technique, involving flow interruption, that enhances the potential for achieving unique solutions, and thus increases the robustness of optimized values of kinetic parameters, was presented by Brusseau et al. (1989a). In addition, the method has increased sensitivity to nonequilibrium, making it useful for process-level investigation of sorption kinetics. Thill method would appear to be especially useful for systems com-

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prised of aquifer materials, which require enhanced sensitivity because of their relatively low sorptivity. In planning to use any experimental method it is important to consider its range of applicability. The useful range of the gas-purge technique is controlled by the Henry's constant of the chemical and the sorptivity of the solute/sorbent combination. The method will obviously be applicable only for chemicals whose Henry's constant is such that gas-phase concentrations are of sufficient magnitude to be detected. The useful range of the GP method can be extended for compounds with low values of Henry's constants through the use of trapping devices. The efficacy of the technique becomes questionable when K p values are less than approximately 0.5 L kg -I. Below this K p value, the characteristic time of sorption may be indistinguishable from that of gas-liquid mass transfer. The gas-purge technique would appear to be the method of choice for systems comprised of highly sorptive chemicals and especially those with soils containing high clay or organic matter contents. The efficacy of the miscible displacement technique is controlled by the sorptivity of the solute/sorbent combination and by the texture of the sorbent. The useful range may be extended with modifications such as mixed-solvent solutions or flow interruption. This technique is especially useful for systems comprised of chemicals of low to moderate sorptivity and of sandy soils or aquifer materials.

RATE-LIMITING PROCESSES Potential Rate- Limiting Processes

Several processes have been proposed as being responsible for nonequilibrium sorption; these will be briefly reviewed. Rate-limiting processes have been grouped into two general classes: transport related and sorption related (Brusseau and Rao, 1989a; Brusseau et al., 1991a). Transport-related Nonequilibrium

This type of nonequilibrium results from the existence of a heterogeneous flow domain. Spatial (or temporal) heterogeneities in such properties as hydraulic conductivity or sorption capacity can result in nonuniform velocity fields. Conditions for diffusive mass transfer of solute may develop because of concentration gradients created by the nonuniform velocities. If this diffusive mass transfer is rate limited, nonequilibrium behavior (e.g., asymmetrical BTC) results. The influence of macroscopic heterogeneities (e.g., aggregates, macropores) on solute transport in soil has been welldocumented [see Brusseau and Rao, (1990) for a recent review]. It should be noted that transport-related nonequilibrium (TNE) affects both sorbing and nonsorbing solute. Behavior attributable to TNE has been observed in aggregated, macroporous, heterogeneous (with respect to hydraulic conductivity), and fractured

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289

porous media. Some of the earliest work on solute transport in aggregated soils, where the nonideality observed in experimentally derived BTC was attributed to TNE, was performed by Biggar and Nielsen (1962) for nonsorbing solutes (Cl), by Biggar and Nielsen (1963) for sorbing inorganic solutes (Mg), and by Elrick et aI. (1966), Kay and Elrick (1967), Davidson et aI. (1968), Davidson and Chang (1972), and Green et al. (1968, 1972) for organic compounds [pesticides atrazine (2-chloro-4-ethylamino-6-isopropylamino-s-triazine), lindane (hexachlorocyclohexane), fluometuron (3-mtrifluromethylphenyl-1, l-dimethyl-urea), and picloram (4-amino-3,5,6-trichloropicolinic acid)]. Several field studies of solute transport under controlled conditions, where observed nonideality was attributed to TNE, have been performed for inorganics (cf., Balasubramanian et aI., 1973; Wild and Babiker, 1976). An early study of TNE during field-scale transport of an organic solute (picloram) was performed by Rao et aI. (1974). Other field studies for organic chemicals (Bowman and Rice, 1986; Jury et aI., 1986) have since been reported. The occurrence of TNE during solute transport in structured soils is welldocumented, as discussed above. There exists, however, a significant amount of published data where nonideal behavior is exhibited in the absence of TNE; for example, nonsorbing solutes exhibiting symmetrical BTC whereas sorbing solutes do not (cf., Elrick et al., 1966; Davidson and Chang, 1972; Rao et aI., 1979; Nkedi-Kizza et aI., 1987; Bouchard et aI., 1988; Lee et aI., 1988; Brusseau et aI., 1989a,b; 1990a; 1991a,b). Such behavior suggests that the nonequilibrium is a result of some sorption-related mechanism (Brusseau and Rao, 1989a). Sorption-related Nonequilibrium This type of nonequilibrium may result from chemical nonequilibrium (CNE) or from rate-limited diffusive mass transfer within the sorbent matrix. Chemical nonequilibrium is caused by rate-limited interactions between the sorbate and sorbent. Such rate-limited interactions are usually characteristic of activated processes such as "chemisorption." Conversely, physical adsorption (e.g., van der Waals interactions) is generally considered to be rapid. Sorption of hydrophobic organic chemicals (HOC) by natural sorbents is generally thought to involve a partitioning between the solution and organic matter components of the sorbent (Choiu et al., 1979, 1983; Karickhoff, 1981; Mackay and Powers, 1987). Thus, specific, activated sorbate-sorbent interactions are usually unimportant and CNE may be eliminated as a probable nonequilibrium mechanism for HOC (Brusseau and Rao, 1989a,c; Brusseau et aI., 1991a). It must be stressed that while CNE may be unimportant for nonpolar organic chemicals, it may well be important for ionic or highly polar organic chemicals such as some pesticides (Brusseau and Rao, 1989a,c; 1991). Three different diffusive mass-transfer related mechanisms can cause sorption-related nonequilibrium: film diffusion, retarded intraparticle diffusion (RIPD), and intrasorbent diffusion. Film diffusion will not be

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considered further, as many researchers have shown that this mechanism is generally insignificant in comparison to other mechanisms for the uptake/release of organic chemicals [see Brusseau and Rao (l989a) and references cited therein]. Retarded intraparticle diffusion involves diffusion of solute within pores of microporous particles (e.g., sand grains) and retardation occurring by instantaneous sorption to pore walls. Such a mechanism was proposed for the rate-limited uptake/release of HOC by sediments (Wu and Gschwend, 1986) and by aquifer materials (Ball and Roberts, 1991). This model is based on the radial diffusion models that have been developed in chemical engineering. Two of the most important assumptions associated with this model are: the existenceof microporous particles and, for HOC, whose sorption is generally controlled by organic matter, that most, if not all, organic matter resides inside the particles. Furthermore, it is usually assumed that the organic matter exists as surface coatings on the pore walls. These assumptions, especially the later two, have not been substantiated to any extent for natural sorbents. Note that for the RIPD model, aqueous-phase diffusion in a fixed-pore network is assumed, and that rate-limited behavior is due only to retardation occurring by instantaneous sorption to pore walls. This conceptualization, in essence, means that hindered diffusion is assumed to not be a factor for RIPD. However, it has been suggested, based upon analyses of applications of the RIPD model to experimental observations, that this model can not describe all aspects of the data without calling upon the concept of hindered diffusion (Steinberg et al., 1987; Brusseau and Rao, 1989a; Brusseau et al., 1991a). Retarded intraparticle diffusion has also been classified as a type of physical nonequilibrium. While it is true that, in pore diffusion, RIPD shares with TNE a similar diffusion mechanism, several reasons have been proposed (Brusseau et al., 1991a) as to why RIPD may be better classified under sorption-related nonequilibrium. First, TNE is the result of macroscopic, or larger, heterogeneities in the flow domain, in comparison to RIPD, which results from the presence of microporous particles. Second, TNE influences both sorbing and nonsorbing solutes, whereas RIPD affects only sorbing solutes. Third, as mentioned above, the RIPD model has been found inadequate without using the hindered-diffusion concept. Hindered diffusion is sufficiently different from simple pore diffusion such that processes involving hindrance may be operationally differentiated from TNE. Confusion and discord surrounding the classification of rate-limiting mechanisms may be reduced if the term TNE is used, rather than the more general physical nonequilibrium. Intrasorbent diffusion involves the mass transfer of sorbate within the matrix of the sorbent. Given organic matter as the predominant sorbent for HOC, intrasorbent diffusion is usually considered to involve diffusive mass transfer within the matrix of organic matter (intraorganic matter diffusion, or IOMD). Intraorganic matter diffusion was proposed as the rate-limiting mechanism for sorption of organic chemicals as early as 1966 by Hamaker

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291

et al., and has since been proposed by several others (see Brusseau and Rao, 1989a,c, and references cited therein). While IOMD is the most likely intrasorbent diffusion-related mechanism for HOC, diffusion within, for example, matrices of expanding clay minerals (e.g., intercalation) may be important for other organic chemicals. For the IOMD model, the primary assumption is that sorbent organic matter is a polymeric-type substance within which sorbate can diffuse. The organic matter associated with natural sorbents has been reported to be a flexible, cross-linked, branched, amorphous (noncrystalline), polyelectrolytic polymeric substance (Choudhry, 1983; Hamaker and Thompson, 1972; Hayes and Swift, 1978; Schnitzer, 1978; Stevenson, 1982; Wershaw, 1986). Direct confirmation of the "porous" nature of organic matter has been reported (Degens and Mopper, 1976; Schnitzer, 1978). Two major physical differences between organic matter and porous particles are readily apparent. First, the size of the "pores" associated with organic matter is similar to the size of the sorbate molecules, whereas for porous particles the pores are much larger than the diffusing molecule (except for the case of extreme hindrance). Second, while the pore networks for porous particles are fixed and comprised of rigid pores, the "pore network" associated with the organic matter is dynamic and comprised of nonrigid pores. In fact, it is inaccurate to regard the free volume in organic matter as being a pore network in the conventional sense; rather the system should be considered as a flexible "mesh," a term utilized in polymer science (Brusseau et al., 1991a). Elucidation of Rate-Limiting Processes There exists a significant amount of research suggesting that nonequilibrium sorption is caused by the presence of heterogeneities in the flow domain (i.e., TNE). The mechanisms responsible for TNE are relatively wellunderstood and the resultant conceptual model is well-established. Such has not been the case, however, for sorption-related nonequilibrium. Only recently have attempts been made to identify the process(es) responsible for this type of nonequilibrium (cf., Karickhoff and Morris, 1985; Wu and Gschwend, 1986; Steinberg et al., 1987; Bouchard et al., 1988; Brusseau and Rao, 1989c, 1991; Brusseau et al., 1989a, 1991a,b; Nkedi-Kizza et al., 1989; Pignatello, 1990; Ball and Roberts, 1991). The conclusion reached by most investigators is that some type of diffusive mass-transfer mechanism is involved. In terms of the definition scheme presented above, this would be either RIPD or IOMD. Few experiments have allowed discrimination between these two processes. Brusseau et al. (l991a) presented an analysis, both of their results and those of others reported in the literature, that provides strong evidence that IOMD, rather than RIPD, is the process most probably responsible for the sorption-related nonequilibrium observed for HOC. It must be stressed that this conclusion was for nonionic, low-polarity organic chemicals. Chemicals of a more polar nature with "reactive" functional groups, such as some

292

BRUSSEAU & RAO

pesticides, may be affected by CNE in addition to IOMD. Thus, these chemicals may have a greater degree of kinetic constraint in comparison to HOC. The results of MD experiments using several pesticides (atrazine (2-chloro4-ethylamino-6-isopropylamino-s-triazine), cyanazine {2-[[4-chloro-6-(ethylamino )-1 ,3,5-triazine-2-yl]amino] -2-methylpropanenitrile}, trietazine (6chloro-N,N,N' -triethyl-l ,3,5-triazine-2,4-diamine), simazine (6-chloro-N,N /diethyl-l ,3,5-triazine-2,4-diamine), alachlor [2-chloro-N-(2,6-diethylphenyl)N-(methoxymethyl)acetamide]) reported by Brusseau and Rao (1991), revealed significantly smaller rate constants for the pesticides in comparison to HOC. However, this difference was shown to result primarily from the greater size (and thus increased diffusional constraint) of the pesticide molecules.

MODELING NONEQUILIBRIUM SORPTION Nonequilibrium Models

Early attempts to model the rate-limited uptake/release of organic chemicals by natural sorbents employed a "one-site" model where all sorption was rate-limited; this approach, however, has failed to adequately represent experimental data (Rao and Jessup, 1983; Wu and Gschwend, 1986; Boesten and Van Der Pas, 1988). Organic chemicals have been found to exhibit a two-stage approach to equilibrium: a short initial phase of fast uptake or release, where roughly 30 to 50% of the total sorption occurs within minutes to hours, followed by an extended period of much slower uptake/release occurring over periods of days or months (Hamaker and Thompson, 1972; Kaarickhoff, 1980; Karickhoff and Morris, 1985; McCall and Agin, 1985; Oliver, 1985; Coates and Elzerman, 1986; Wu and Gschwend, 1986; Ball and Roberts, 1991). This type of behavior is readily approximated using a bicontinuum conceptualization. Such a conceptualization can be effected through use of diffusion equations based on Fick's law (e.g., Wu and Gschwend, 1986; Ball and Roberts, 1991) or using first-order mass-transfer equations (e.g., Selim et al., 1976; Cameron and Klute, 1977; Karickhoff, 1980) based on the linear driving force approximation of Glueckauf and Coates (1947). The conceptual basis for, and the performance of, these two approaches has been discussed by several researchers [see Brusseau and Rao (1989a) and references cited therein]. A major disadvantage associated with the diffusion-based models is that detailed information on the structure of the porous medium is required; such detailed information is not required for the mass-transfer model. In addition, use of diffusion-based models assumes a priori knowledge of the nonequilibrium mechanism; a commitment to a particular mechanism is required in designing/selecting the model to be used. Such a requirement is desirable for situations where the mechanism is fully understood. However, for situations where the mechanism involved is not fully elucidated, the use of a model that is not mechanism-unique, such as the first-order mass-transfer model,

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293

is preferable. The first-order bicontinuum model can represent each of the major processes responsible for nonequilibrium [(i.e., TNE, eNE, RIPD, IOMD) (Brusseau and Rao, 1989a)]. Models based on first-order mass transfer have been shown to provide results similar to those obtained with diffusion-based models [see Brusseau and Rao (1989a) and references cited therein]. Hence, because of its simplicity and greater versatility, the firstorder mass transfer bicontinuum model receives the greatest amount of use. Models formulated using the first-order bicontinuum conceptualization have been variously called "two-site," "two-compartment," or "two-box" models. In these models, nonequilibrium is assumed to be the result of a time-dependent interaction between the solute and the sorbent. Sorption may be represented by two "reactions," occurring either in series or in parallel. The former is appropriate for the case of diffusive mass-transfer limited sorption, while the latter is used for the case of two types of sorption mechanisms. The sorbent is hypothesized as having two sorption domains, where sorption is essentially instantaneous for one and is rate-limited for the other. Sorption for the kinetically controlled domain is described by a first-order rate equation, whereas the other domain is represented by an equilibrium isotherm equation. It should be noted that, as long as one of the domains is equilibrium controlled, the series and parallel conceptualizations are mathematically indistinguishable (Karickhoff, 1980; Karickhoff and Morris, 1985). Also, the equilibrium-controlled domain can be replaced such that both domains are kinetically controlled (cf., Selim et al., 1976; Karickhoff, 1980). The suggestion that the existence of a second, rate-limited class of sorption sites may be responsible for nonequilibrium was first made by Giddings and Eyring (1955). Although the first-order model has met with widespread success, there are conditions under which this model may fail. For example, a more continuous distribution, rather than the extreme duality in reaction rates assumed by the bicontinuum models, may be a more accurate representation of true conditions. Accordingly, the separation of the sorbent into two parallel domains differing in reaction time may be extended to accommodate any number of domains, each with its own unique rate constant. For example, Boesten et al. (1989) have presented a "three-site" model. The limiting case would be a continuous distribution of domains and associated rate constants. A model describing this case has been developed by Villermaux (1974), where the site population is represented by the transfer-time distribution (i.e., the rate-constant distribution). However, the number of parameters associated with such a model greatly exceeds our present capability to independently evaluate the processes represented by those parameters. Such models would, therefore, be constrained to operation in a calibration mode. Modeling the influence of rate-limited sorption on the transport of organic chemicals has been a topic of interest for some time. Initial attempts incorporated the one-site sorption kinetics model into the advective-dispersive transport equation (cf., Oddson et aI., 1970). This approach was based on that taken by researchers in chemical engineering (i.e., Lapidus and Amund-

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son, 1952). However, models using the one-site formulation have not been able to predict observed behavior (Davidson and McDougal, 1973; Hornsby and Davidson, 1973; Schwarzenbach and Westall, 1981; Rao and Jessup, 1983). Transport models employing the bicontinuum-sorption formulation, with one domain equilibrium controlled, were presented by Selim et al. (1976) and Cameron and Klute (1977), while Selim et al. (1976) also presented a model where both domains were rate limited. The one-site model mentioned previously is a special case of the two-site model, where all sorption sites are assumed to be of the time-dependent class (Selim et aI., 1976; van Genuchten, 1981). The bicontinuum-based model has generally been able to represent nonequilibrium data much better than has the one-site model. It should be noted that the bicontinuum models presented by Selim et al. (1976) and Cameron and Klute (1977), which were developed to represent sorption nonequilibrium, are mathematically equivalent in nondimensional form, for the case of linear isotherms, to the first-order mass-transfer bicontinuum model presented by van Genuchten and Wierenga (1976), which was developed to represent transport-related nonequilibrium. This equivalency is beneficial in that it lends a large degree of versatility to the first-order bicontinuum model. However, this equivalency also means that elucidation of nonequilibrium mechanisms is not possible using modeling-based analysis alone. With the first-order model, sorption is conceptualized to occur in two domains ' [1]

[2]

where C is the solution-phase solute concentrations (M L -3); 8 1 and 8 2 are the sorbed-phase concentrations in the "instantaneous" and rate-limited domains, respectively (M M- I ) ; K p is the equilibrium sorption constant (L 3 M- I ) ; F is the fraction of sorbent for which sorption is instantaneous; t is time; and k l and k 2 are forward and reverse first-order rate constants (T- \ respectively. At equilibrium, Eq. [2] reduces to [3]

Thus, we obtain (1 - F)/F

[4]

for the ratio of rate constants. The following equations describe the transport of rate-limited sorbing solute during one-dimensional, steady-water flow in a homogeneous porous medium

SORPTION KINETICS

iJC*liJp

+

295

({3R-l) iJC*liJp

+

(l-{3)R iJS*liJp

(lIP) iJ 2C*liJX2

iJC*liJX

[5]

(C* - S*)

[6]

-

=w

(l-{3)R iJS*liJp

=

where

=

C*

P

=

CICo

[7a]

vLID

[7b] [7c]

R

= p

{3 -

(l

1

+

= +

(P1()Kp

vtlL

F(PI()Kp] / R

X= xlL

[7d] [7e]

[7f] [7g] [7h]

and where Co is the solute concentration of the influent solution (M L -3); D is the dispersion coefficient (L 2 T- 1) ; v is the average pore-water velocity (L T- 1) ; x is distance (L); L is column length (L); p is dimensionless time in pore volumes; p is bulk density (M L -3); () is volumetric soil-water content; P is the Peclet number, which represents the dispersive-flux contribution to transport; R is the retardation factor, which represents the effect of sorption on transport; {3 is the fraction of instantaneous retardation; and w is the Damkohler number, which is a ratio of hydrodynamic residence time to characteristic time of the sorption "reaction." Interpretation of the Bicontinuum Model in Mechanistic Terms Retarded Intraparticle Diffusion The first-order mass transfer model can be readily interpreted in terms of the various diffusion-based models and several researchers have done so [see Brusseau and Rao (l989a) and references cited therein]. A straightforward means of equating the two models is to define the mass transfer constant in terms of the aqueous diffusion coefficient, shape factor, and diffusion path length characterizing the porous medium. Ball (l989) reported the following equation, equating k 2 from the first-order bicontinuum model to the RIPD model

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296

where D p is the pore diffusion coefficient (L 2 r- I ) ; which can be related to the aqueous diffusion coefficient (Do) through a tortuosity factor (r); Rim is the retardation factor for sorption occurring inside the particle; 8im is the volume fraction of internal porosity, and a is particle radius (L). The equation on the right-hand side is exact when all sorption occurs inside the particles, which is the usual assumption for the RIPD model. Several researchers have presented similar equations relating the first-order model to diffusionbased models for TNE. Intraorganic Matter Diffusion

The manner in which the first-order bicontinuum model can be interpreted in terms of IOMD has been qualitatively discussed (Brusseau and Rao, 1989a). A quantitative treatment has been presented by Brusseau et al. (1991a) and is reviewed below. The two sorptive domains of the bicontinuum model are represented by volume fractions VI and V2, which are the volumes of the respective domains per total sorbent mass. The macroscopic sorbed-phase concentrations, SI and S2' may be defined in terms of microscopic concentrations

[9] where Si = sorbate mass in Region i/volume of Region i. At equilibrium the following relationships are derived between F and ~ using Eq. [1] and [3]

The change in the sorbed-phase concentration of Domain 2 is [11 ] where k, is a mass-transfer coefficient (L r- I ) and A is the cross-sectional area through which mass transfer is occurring. In cases where it is difficult to explicitly define A and V, a mass transfer constant (a, r- I ) may be used. The mass transfer constant is defined as [12] Equation [11] may be rewritten in terms of the macroscopic sorbed-phase concentrations and rate constants using Eq. [9], [11], and [12]

where and

[14a] [14b]

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SORPTION KINETICS

For diffusion in polymeric materials, a can be related to the polymer diffusivity of the sorbate [15]

where c is a shape factor, D py is the diffusion coefficient (L 2 T- 1) for the specific sorbate/polymer pair, and I is the characteristic diffusion length (L). Diffusion in polymers is dependent upon the physicochemical properties of the polymer, the diffusing molecule, and the solvating medium. In general, the diffusion coefficient decreases exponentially with increasing molecular weight (MW) or size of the diffusant for a given polymer. This is especially true for systems where the size of the diffusant is similar to the size of the mesh, as would be the case for IOMD. It is interesting to note that this dependency, given by (MW) -n, where n ranges from 1.33 to 5 (Brusseau et aI., 1991a), is much stronger than that observed for aqueous diffusion coefficients, which is generally described by (MW) -0.5. Multiprocess Nonequilibrium A great deal of data have been reported in the literature that suggest that the transport of solutes can be influenced by transport-related and by sorption-related nonequilibrium processes. It is logical to assume that, in some cases, and especially for field-scale problems, solute transport will be constrained by both of these nonequilibrium processes. When investigating solute transport it is imperative that the potential for multiple sources of nonequilibrium be recognized and evaluated. A new model that explicitly accounts for multiple sources of nonequilibriurn influencing solute transport in porous media was presented by Brusseau et aI. (l989c, 1990b). The multiprocess nonequilibrium (MPNE) model was designed to simulate solute transport in porous media where both transportrelated and sorption-related nonequilibrium processes contribute to the observed nonequilibrium. The sorption dynamics of such systems was represented by two serially arranged bicontinuums coupled in parallel. A schematic of the model conceptualization is shown in Fig. 11-6, taken from Brusseau et al. (1989c). This conceptualization results in discretization of the porous medium into four sorption domains, where instantaneous sorption occurs in the first domain and rate-limited sorption occurs in the other three. An example system, where nonequilibrium may be caused by both TNE and rate-limited sorbate-organic matter interaction, would be an aggregated soil with an appreciable organic C content. In this system, instantaneous transfer of solute occurs between the interaggregate (or "mobile") region and the surface of organic matter situated on external surfaces of the aggregates (Sorption Domain 1). Sorption Domain 1 and 2 are coupled by diffusive mass transfer within the matrix of the organic matter. The mobile and immobile (intra-aggregate) regions are in turn coupled by diffusive mass transfer within the intra-aggregate pores (i.e., TNE). Transfer between the immobile region and Sorption Domain 3 is instantaneous, as it was between the mo-

298

BRUSSEAU & RAO MODEL CONCEPTUALIZATION 1 "Mobile" Solution Phase

"Immobile" Solution

Km

-.

K. .,m

Phase

2

"Instantaneous"

"Rate-LImited"

Sorbed-Phase

Sorbed-Phase

"Instantaneous"

"Rate-Limited"

Sorbed-Phase

Sorbed-Phase

3

4

Fig. 11-6. Conceptualization of sorption and transport dynamics used in the multiprocess nonequilibrium model developed by Brusseau et aI., (1989c). Figure was taken from Brusseau et aI., 1989c.

bile region and Domain 1. The coupling between Sorption Domain 3 and 4 is similar to that between Domain 1 and 2. Note that, although sorption in Domain 3 is instantaneous, accessibility to sorption "sites" is rate limited by mobile-immobile mass transfer. Also, note that sorption in Domain 4 is constrained by two mechanisms, TNE and IOMD.

.--_ .. -- ... , ,

1

,,

--. 2-reglon model

0

..IV

c

CD

•• •• •• •• •

(J= 0.44

:0::

, = 0.93

0.6

Exp. 1-4

~ '----------------'1

R = 2.23

c

c

I

0

I

•• •• ,,

U CD

>

- - MPNE model

I

u

:0::

2,4,5-T/Glendale loam (van Ganuchten at al., 1977)

••,

P = 95

0.8

•

,

0.4

IV

'ii ~

P = 95

't

0.674

R = 2.23

, = 0.256

(J =0.44

, = 0.051

k'= 1.84

, = 0.019

2

3

4

0.2

o

o

2

4

6

8

Pore Volumes

Fig. 11-7. Comparison of model predictions to data for 2,4,5- T transport in an aggregated soil (data from van Genuchten et aI., 1977). A prediction produced with a two-region model (van Genuchten and Wierenga, 1976) is compared to a prediction produced with the MPNE model of Brusseau et al, (1989c). Figure was taken from Brusseau et 81.. 19H9c.

SORPTION KINETICS

299

To evaluate the MPNE model and the validity of its conceptualization, Brusseau et al. (1989c) applied the model to several published data sets. One set to which it was applied was that of van Genuchten et al. (1977), who presented BTC obtained from miscible displacement of the herbicide 2,4,5-T (2,4,5-trichlorophenoxyacetic acid) through columns packed with an aggregated soil. The performances of the bicontinuum and MPNE models were tested by comparing independent predictions of the experimental BTC. It is stressed that values for all model parameters were obtained from independent sources. The predictions produced by the two models are provided in Fig. 11-7 (taken from Brusseau et al., 1989c) along with the experimental BTC. It is evident that the MPNE model provides a better prediction of the data than does the bicontinuum model. The MPNE model has also been used successfully to simulate miscible displacement of Sr through a laboratory model of a stratified aquifer (Brusseau, 1991), where transport was influenced by hydraulic-conductivity heterogeneity, sorption-capacity heterogeneity, and chemical nonequilibrium, and to analyze BTC obtained from a small-scale field experiment involving natural-gradient transport of several organic solutes (Brusseau and Rao, 1989b).

CONCLUSIONS It is important to recognize that "nonideal" transport can be caused

by factors other than sorption nonequilibrium. In fact, several factors may cause nonideal solute transport, including nonhomogeneous soil physical properties (e.g., hydraulic conductivity, soil-water content, bulk density), physical nonequilibrium, nonhomogeneous soil chemical properties (e.g., sorption equilibrium constant), sorption nonequilibrium, sorption isotherm nonlinearity, and sorption-desorption nonsingularity. Factors related to the physical nature ofthe porous medium, such as structure (i.e., nonhomogeneous soil physical properties and physical nonequilibrium), will obviously control nonideality for the transport of nonsorbing solutes and of water. It has been suggested that the primary factors causing nonideal transport for organic solutes are nonhomogeneous soil properties (both physical and chemical), and nonequilibrium, both transport-related (TNE) and sorption-related (SNE). Hence, the potential for multiprocess nonideality must be considered when investigating the impacts of rate-limited sorption on transport and fate of chemicals in the subsurface.

ACKNOWLEDGMENTS

Approved for publication as Florida Agricultural Experiment Station Journal Series no. Roo737. This work was supported, in part, by Florida Department Environmental Reg. Contract no. WM-254.

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