the equilibrium constatns of reactions involving hydroxyl

VOL,. 15, 1929

CHEMISTRY: D. S. VILLARS

705

of carbon monoxide, which corresponds very closely with the results of the gas analysis made by Hinsheiwood and Hutchinson.' 5. Conclusion.-The decomposition of acetone has been followed by an analytical method and it has been found that about 60% of the acetone decomposed can be recovered as ketene. Methods in which rate of change of pressure are used for following the course of the reaction are therefore unreliable. * Du PONT FELLOW. 1 Hinshelwood and Hutchinson, Proc. Roy. Soc., 111A, 245 (1926). 2 See Hurd, The Pyrolysis of Carbon Compounds, p. 247. Chemical Catalog Co., 1929. 3Taylor, J. Phys. Chem., 30, 1433 (1926); book review. 4Meyer, Lehrbuch der Organisch-Chemischen AMethodik, p. 846. Springer, 1922. 6 Goodwin, J. Am. Chem. Soc., 42, 39 (1920). 6 Slagle, Dissertation, "Decomposition of Aliphatic Ketones in the Gas Phase," Johns Hopkins University, 1929. 7Hurd and Tallyn, J. Am. Chem. Soc., 47, 1427 (1925).

THE EQUILIBRIUM CONSTANTS OF REACTIONS INVOLVING HYDROXYL By DONALD STATLR VILLARS CHEMICAL LABORATORY, UNIVZRSITY OF ILLINOIS Communicated July 26, 1929

A recent interpolation of band spectra data has indicated that the heat of dissociation of OH should be 138 k. cal.' An accurate value for the heat required in this dissociation would enable one to calculate the equilibrium constants of reactions involving this molecule.2 Thus Bonhoeffer3 and Reichardt have calculated the equilibrium constant of the following reaction, using their value for the heat of dissociation of water into H and OH: 2H20 = H2 + 20H KOH = [H2] [OH]2

[H20]12

As my value for the heat of dissociation of OH is some 14 k. cal. larger than that corresponding to Bonhoeffer and Reichardt's data, I have recalculated their constants and contributed some additional ones. In order to calculate the free energies of these reactions, use was made of the familiar equations:

F=H-TS AF= A - TAS = -RTinK

CHEMISTRY: D. S. VILLARS

706

AH

=

Evi (

Do +

RT + Erot + vibr. +, etc.)

Do

AF T

PRoc. N. A. S.

T+-

A

So

where

-Do

=

Qo = heat of reaction at absolute zero and S

=

S, +

TR + E

The entropies were obtained from an application of the method of Gibson and Heitler.4 In these methods involving the statistical interpretation of the third law of thermodynamics, the entropy of the molecule is considered to be the sum of its translational entropy, St

=

R In

(2rmkt) /2V 6/2 h3

N

its rotational entropy, its vibrational entropy, and that due to all its different possible kinds of orientation. The latter may be expressed' in short by

Sm

=

E + R In E p /en n

where p,, is the a priori probability of the state n. This applies equally well to entropy of vibration and rotation, and, in these cases, Em is the total amount of the corresponding energy, i.e., Evibration Erotation Eorientation (= 0 for a degenerate state). As a further check on the reliability of this method, beyond that already shown by Gibson and Heitler, the entropies of oxygen and hydrogen at 250C. were calculated. The count of the rotational entropy is simplified in the case of oxygen because there is only one kind present (symmetric or antisymmetric), as is shown by the fact that its band spectrum consists of alternately missing lines. Its theoretical entropy comes out to be 50.7, whereas the thermal values range from 45.6 to 49.2.6 This high value comes from the inclusion of the IS spectroscopic state of the oxygen molecule.7 If it were not for its triplet character, the calculated entropy would be 48.5. If the discrepancy is not due to calorimetric errors, this value predicts a fourth allotropic form of solid oxygen to be found with a transition temperature below 17'K. The count of the rotational entropy of hydrogen is complicated by the presence of the symmetric and antisymmetric kinds in a one to three ratio. The question has been raised by Giauque8 whether the entropy of mixing of these two kinds should not be included, especially as the

CHEMISTR Y: D. S. VILLARS

VOL. 15, 1929

707

two forms do not intercombine spectroscopically. Rodebush9 has answered that there really is only one hydrogen and that although the two forms do not intercombine in their spectral relations, they do so by collision when given a sufficient length of time to reach equilibrium. It is comforting to know that it really makes no difference in the final result which method of counting is used. The entropy of hydrogen at 250C. comes out to be 34.010, whether we consider it two kinds and include the entropy of mixing or one substance which will reach equilibrium if given time 'enough. This, in fact, must be," as can be seen from the following:

Srt

=

R In 44

rIkT

(3 + 1) + Erot

(one substance Gibson and Heitler count) or Srot

= Santi

+ Ssym + Smixing

1 1 4X2IkT _ -RlIn 3 1 47r2IkT 3+ -RlIn =-RlIn h h2 4 4 4 4

-34 R In 43 + ErotT =R n 4ir2Ik T 4 +

Rr01ot

The entropy of hydrogen was also calculated by a summation process to check against possible inaccuracies introduced by the integration of the rotational sum. The results were identical. The entropy of OH was next computed. As this molecule does not give rise to nuclear degeneracy the number of rotational terms is not halved as in the case of hydrogen and oxygen and the rotational entropy is expressed by the formula: Srof = R ln 87r2 IkT/h2 + Erot/T. In addition to this rotational entropy comes entropy to account for the electronic states in the 2p inverted ground term, which was incorrectly accounted for by Bonhoeffer and Reichardt. This should be as follows:

Selec

=

R In

(4 + 2e-hA1/k) + Eelec

The upper doublet term is not negligible in the case of the OH molecule, nor is it of full weight. Table 1 gives the numerical data used to calculate the entropy formulas given on the following page.

708

CHEMISTRY: D. S. VILLARS TABLE

Hydrogen Oxygen Hydroxyl

SO2

=

4.67 X 10-41 19.2 X 10-40 1.43 X 10-40

13.70 + 11.52

g.

log

PROC. N. A. S.

1

Cm.2

4415.2 cm.1565.4 3570

T -4.61

log

(1

-

137.9 cm.-

e-7475/T)

2

-4.61 1Og

SH2

=

-1.51 + 11.52 log T

4.61 log (1

-

-

e6

SOH

=

5.77 + 11.52 log T + 4.61 log (4 +

From these values and the free

AF0H2O gas

AF0H202 gas

=

=

-

-

4.61 log (1

2e-1975/T) energy

-

e

Palm +E02 T

/) +

4.61

R

+

log

R 2

Patm +

T

5112/T)

5R - 4.61 log Palm + EOH 2T

+

formulas from Lewis and Randall,

-57410 + 0.94 T

31200 + 5.5 T ln T

T + 0.00165 T2 -0.00000037 T3 + 3.92 T (Lewis and Randall, 485)

ln

-

0.00115 T2

-

9.3 T

(Lewis and Randall, 496) the equilibrium constants of the following reactions were calculated: (1) K1

[H21 [02] [OH]2

20H

=

H2 +

2 H20

=

2H2 + 02-114 k. cal.

(2) K02

2 H20

=

H2 + 20H

[H2] [OH]2 (3) KOH =- [H202

201H

=

02

]2

[H20

[H20O1]

H202

(4) K4

[H2°2]2I [OH

The results are given in table 2, in which the subscripts B denote that Bonhoeffer and Reichardt's values of the heat of dissociation of water were used and the subscripts V denote that my value was used.

CHEMISTRY: L. PA ULING

VOL. 15, 1929

TABLE 2 LOG KON B AND R, KOHB p. 96 LOG

ATURS ABS.

LOG K02 L AND R, p. 485

LOG KO0 B AND R, p. 96

LOG

1000 1300 1500 1705 1900

-19.8 -13.9 -11.2 - 9.13 - 7.55

-20.1 -14.01 -11.42 - 9.28 - 7.6

-21.8 -15.2 -12.24 - 9.95 - 8.21

2155 2505

-

TUMPER-

709

-21.1 -14.3 -11.4 - 9.0 - 7.2

KOHV LOG KiB LOG KV LOG K4B LOG K4V -15.5 +1.95 -4.35 +2.74 -3.55 -10.34 +1.31 -3.53 +0.30 -4.54 - 8.05 +1.03 -3.16 -0.79 -4.98 - 6.26 +0.81 -2.87 -1.66 -5.35 - 4.90 +0.65 -2.66 -2.29 -5.60

interp. 5.94 4.27

- 6.08 - 4.31

6.42 4.59

5.5 - 3.50 +0.48 -2.43 -2.99 -5.91 3.5 - 2.08 +0.32 -2.19 -3.67 -6.18 > H2 + 02 + 14,000 cal. (B) 20H 20H - 11 + 02 - 15,000 cal. (V) 1 Villars, J. Am. Chem. Soc., 51, 2374-7 (1929). 2 Dr. Langmuir has kindly pointed out that the knowledge of such equilibrium constants will be extremely useful in investigating the possibility of the direct formation of hydroxyl during the combustion of hydrogen and oxygen at high temperatures, an investigation which he is at present carrying on. Z. physik. Chem., 139A, 75-97 (1928). 4 Z. Physik, 49, 465. 5 Cf. Rodebush's chapter XVII, p. 1202, in Taylor, A Treatise on Physical Chemistry, D. Van Nostrand, 1925. 6 Lewis and Gibson, J. Am. Chem. Soc., 39, 2554 (1917). 7 Mulliken, Phys. Rev., 32, 186. 8 J. Am. Chem. Soc., 50, 3221. s These PROcEgDINGS, 15, 678-680 (1929). 10 Rodebush, loc. cit., obtained this value and showed that the experimental method used to determine the entropy of hydrogen is theoretically unsound. "Prof. Rodebush has shown independently that this relation must obtain. -

-

-

ON THE CRYSTAL STRUCTURE OF THE CHLORIDES OF CERTAIN BIVALENT ELEMENTS By LINUS PAULING GATES CHEMIcAL LABORATORY, CALIFORNIA INSTITUTE OF TECHNOLOGY Communicated August 6, 1929

In 1925 Bruni and Ferrari' reported that the lines on a powder photograph of the hexagonal crystal MgCl2 could be accounted for on the basis of a rhombohedral (pseudocubic) unit of structure with a = 5.08 A and a = 90. containing 2 MgCl2. Later they announced2 that ZnCl2, CdCI2, and MnCl2 have the same structure, with values of a a few degrees larger than 90 . Ferrari3 then added CoC12 and NiCl2 to the group; certain weak lines occurring on the powder photographs of these substances require the value of a to be doubled, giving a rhombohedral unit with a = 900

396396TCHEMISTRYY: D. S. VILLARS

PROC. N. A. S.'

tern of their own, which never changed in detail. Flat-fishes control the mottling of their skins through their nervous system; apparently this type of control is entirely absent from the tree toad. The total pattern of the toad becomes sharper or fainter but without local modification of its detail. In the tree toad not the least evidence of differential mottling could be discovered. When these animals were injected with very weak adrenalin they became extremely light and remained so for some hours. On injecting them with pituitrin they became dark and remained so for some time. These two drugs call forth the total natural range of the animal. Such results suggest the conclusion that the tree toad suffers a change of color through internal secretions and not by direct nervous action as in the flat-fishes. Notwithstanding the success with which the tree toad imitates its surroundings, its capacity in this respect must be much more limited than that of the flat-fish and involves merely a lightening or a darkening of its total pattern without local changes in the details. This conclusion supports the general view advanced by Hogben to the effect that the color changes in amphibians are brought about by humoral rather than by nervous control.

EQUILIBRIUM CONSTANTS OF REACTIONS INVOL VING HYDROXYL: A CORRECTION By DONALD STATLER VILLARS SCHOOL OF CHUMISTRY, UNIVERSITY OF MINNESOTA

Communicated April 18, 1930

In a communication of the above title,' two mistakes have come to light which the author wishes to correct in this note. The first is an arithmetical error in the formula, top of p. 708, for the entropy of oxygen. It should read

SO, = 13.70 + 11.52 log T - 4.61 log (1 -e22436/T + 5R/2 - 4.61 log Pat±+ E o1/T. The wrong formula led to a false value for the entropy of oxygen at 2980K. The corrected value, SO, - 298 = 49.2 cal. degrees-', is in approximate agreement with the more accurate value of Giauque and Johnston,2 namely, 49.03, and hence the expectation of a fourth allotropic form of solid oxygen is uncalled for. The second error is more fundamental and was due to the neglect of the nuclear degeneracy of the hydrogen atom in hydroxyl. It was originally thought by the author that this was automatically taken care of when

VOL. 16, 1930

397

CHEMISTR Y: D. S. VILLARS

one includes all of the rotational terms in the formula for rotational entropy. This is not true, however, and the formula for the entropy of hydroxyl3 should read

7.15 + 11.52 log T - 4.61 log (1 - e /5112T) + 4.61 log (4 + 2e-197.5/T) + 5R/2 - 4.61 log P1,,, + EoH/T. (2) In order for the free energy calculations to be consistent, therefore, one must add an entropy of R In 2 for each gram molecule of hydroxyl taking part in those reactions which involve theoretical entropies of hydrogen. Thus, the common logarithms of the equilibrium constants of reactions (1), (3) and (4) of the article cited must be corrected by the corresponding amounts 2 log 2 or 0.6. That no error is introduced by the use of the free energy equations involving calorimetric data is due to the fact that the same correction for nuclear entropy must be added to both sides of the equation, with the result that they cancel out in the difference. This is in agreement with the-ideas of Gibson and Heitler,4 Giauque and Johnston5 and Rodebush.6 The corrected equilibrium constants are given in the following table: EQUILIBRIUM CONSTANTS

SOH

=

LOG KOH B & R,

TSMP.

LOG Ko2 L & R, P. 485

1000 1300 1500 1705 1900

-19.8 -13.9 -11.2 - 9.13 -7.55

-14.7 - 9.5 - 7.15 - 5.35 -3.97

2155 2505

-

- 2.55 -0.47 - 1.12 -0.56

20H 20H

LOG Ko2 B & R, P. 96 LOG

KOHB P. 96

LOG

-20.1 -21.0 -21.1 -14.01 -14.3 -14.3 -11.42 -11.3 -11.4 - 9.28 - 9.04 - 9.0 -7.6 -7.28 -7.2 Interp. 5.94-- 6.08 - 5.47 - 5.5 4.27 - 4.31 - 3.63 - 3.5 -H2 + 02 + 14,000 cal. (B) -H2 +02 -15,000 cal. (y)

1 These PROCE}3DINGS, 15,

705-709

KOHV LOGK1B LOG KIV +1.12 -5.18

LOG KB4 LOG

+1.91 +0.43 -4.41 -0.58 +0.13 -4.06 -1.69 -0.10 -3.78 -2.57 -0.28 -3.59 -3.22

K4V

-4.38

-5.42 -5.88 -6.26 -6.53

-3.38 -3.94 -6.86 -3.15 -4.63 -7.14

(1929).

Giauque and Johnston, J. Am. Chem. Soc., 51, 2300-2321 (1929). 3The correct calculated value for the entropy of hydroxyl at 298°K. is 45.9 cal. degrees-' mole-'. Owing to our inability to measure calorimetrically the nuclear entropy, the experimentally observed entropy should be less than this amount by 1.4 E. U. 4 Gibson and Heitler, Z. Physik, 49, 465 (1928). 5 Private communication. The author wishes to thank Prof. Johnston for his friendly cooperation in locating the arithmetical error which was the cause of the lack of agreement between the two calculated values of the entropy of oxygen and for his communications in which he emphasized the necessity of including the nuclear entropies of the other hydrogen compounds involved in the reactions which were considered. Cf. also Giauque, J. Am. Chem. Soc., 51, 1150 (1929) and Ind. Eng. Chem., 21, 353 2

(1929). 6

Rodebush, Phys. Rev., 35, 210 (1930).