The Structure and Dimensions of the Ethane Molecule

VOL. 14, 1928

PHYSICS: J. K. MORSE

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THE STRUCTURE AND DIMENSIONS OF THE ETHAAIE MOLECULE

BY JARED KIRTLAND MORSI DFPARTM8NT OF PHYSICS, UNIVERSITY OF CHICAGO

Communicated November 21, 1927

In a previous paper,' it was shown in detail that the crystal lattices of diamond and graphite could be built up of cubes having one corner shared in common between adjacent cubes. These structures showed that simple geometrical relations connected the lattice constants and the radii (half the body diagonal) of the cubes. In diamond, this radius computed from the X-ray data was found to be 0.77 A and in graphite 0.75 A. These results were interpreted to indicate (1) that carbon atoms in combination may be conveniently treated as cubes, (2) that the radius of the carbon atom over a wide range of conditions is approximately threequarters of an angstrom and (3) that a union between atoms, consisting of a single electron, is a possible type of atomic union. This paper is an account of the application of these ideas to the problem of the structure of the ethane molecule. A model of this molecule built up of cubes is first presented by giving the coordinates of the cube centers (carbon nuclei), the cube corners (electron positions) and the possible hydrogen positions referred to three axes of reference in terms of a parameter R (radius of the carbon atom). This is followed by a description of the construction of a three-dimensional scale model of the ethane molecule and after this there is a brief discussion of the properties of this model. A Model of the Ethane Molecule.-As is well known, ethane is a saturated hydrocarbon which contains eight valency electrons due to carbon and six due to hydrogen. Since it is saturated all the "possible electron positions" must be occupied by electrons. This can easily be accomplished in a cubic model by uniting the two carbon atoms by a double electron bond (two cubes having an edge in common). The union between the two carbon atoms being taken care of the next question to decide concerns the nature of the bond between the carbon and hydrogen atoms. It will be recalled that both diamond and graphite have adjacent atoms united by a single electron bond (cube corner in common). Since this is the simplest type of atomic union and since there is no definite evidence in favor of any other type of bond between the carbon and hydrogen atoms in ethane this union will be assumed in this model as a first approximation. In diamond the "electron position" uniting two adjacent atoms lies on the straight line connecting the nuclei. In graphite this is not the case. Since the former bond is simpler from a geometrical standpoint it will be assumed for this model of ethane and, consequently, the radius of the carbon

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PROC. N. A. S.

atom (half the body diagonal of the cube) will be taken as 0.77 A. And as a final approximation, it will be assumed that the "electron position" joining the hydrogen and carbon atoms is midway between the two nuclei. It should be noted that these assumptions are arbitrary. Their purpose is to enable us to set up a definite scale model of ethane which can be quantitatively tested by comparison with experiment. One of the most rigorous tests that such a model can undergo is to build it into a lattice structure and compare the diffraction effects computed from the model with those actually observed by means of X-ray analysis. As will be shown in detail in another paper, the model herewith presented can be so arranged in a hexagonal close-packed lattice that it accounts quantitatively for all the observed diffraction effects, not only in regard to their position but also as to whether they are present or absent in the powder photographs. In this paper a description of this model is all that is intended. Taking three rectangular axes through the nucleus of one of the carbon atoms the coordinates of all parts of this model can be expressed in terms CO6RDINATS or THE ETHANu MOLEcuLE iN TsRMs oF R, THs RADIUS or THE CARBON ATOM Cube Centers. (Carbon Nuclei) 0.000, 0.000 0.000, -0.817, +0.471, +1.333 Possible Hydrogen Positions 0.667 +1.633, 0.943,

-1.633, 0.000, 0.817, -0.817, +0.817, -2.450,

0.943, 4=0.667 1.886, w:0.667 1.414, +2.357, -0.471, +1.414, -0.471,

+2.000

+0.667 +0.667 +2.000 +0.667

-2.450, Cube Corners. (Electron Positions) 0.817, -0.471, -0.333 -0.817, +0.471, +0.333 0.000, 0.943, =FO.333 0.000, 0.000, =1=1.000 -0.817, +0.471, +2.333 -1.633, 0.000, +1.000 -1.633, +0.943, +1.667 -0.817, +1.414, +1.000 -0.817, -0.471, +1.667 -0.817, -0.471, +0.333

of a parameter R, that is to say, the radius of the carbon atom which should be equal from the considerations mentioned above to 0.77 X 10-8 cm. The Construction of a Scale Model of Ethane.-Figure 1 shows a scale

Vou. 14, 1928

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PHYSICS: J. K. MORSE

plan of this model of ethane. The projections of the electron positions are shown by small black circles, the carbon nuclei by large cross-hatched circles, the hydrogen positions occupied by large black circles and the possible hydrogen positions unoccupied by large white circles. For a model at a scale of 5.0 cm. to the angstrom, the radii of the two circles shown in the figure are 3.6 cm. and 7.3.cm., respectively. The vertical

0

Sca/e I4A

1

FIGURE 1

positions measured above (+) and below (-) the equatorial plane have the following values. Cube centers (carbon nuclei) H1 -2.6 cm., (F1) +2.6 cm., hydrogen positions occupied (A) -5.1 cm., (C) +5.1 cm., hydrogen positions unoccupied (B) 0.0 cm., (D) 0.0 cm., cube corners (electron positions) (E) -3.85 cm., (F) -1.3 cm., (H) +1.3 cm., (G) +3.85 cm., (H1) -6.4 cm. and +1.3 cm., (F1) +6.4 cm. and -1.3 cm.

PHYSICS: J. K. MORSE

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PROC. N. A. S.

Discussion.-The distance between the carbon atoms of this model is easily found from the coordinates given above to be 1.26 A. A study of the model indicates that there are twelve possible hydrogen positions and that only six hydrogen nuclei are available to fill them. This raises the question as to what six positions the hydrogen nuclei are to be assigned. A study of the cobrdinates indicates that six of the hydrogen positions lie in a plane. The remaining six are divided into two sets of three each and are located on the corners of two equilateral triangles lying in two parallel planes. Hence, at least two isomers are theoretically possible which can be expressed symbolically by the formulae I and II. H C/-\C

I.

\H/ \H

H\

/H H C-C-H

II. H H/ \H The chemical data seems -to be in accord with the second of these formulae and for this reason the hydrogen nuclei are distributed in this model in two equilateral triangles in two parallel planes. In conclusion, I wish to express my thanks to Professor Henry G. Gale

for his interest in this work. J. K. Morse, Proc. Nat. Acad. Sci., 13, 227-232, 1927.

THE LATTICE STRUCTURE OF ETHANE By JARED KIRTLAND MORSE DEPARTMUNT OF PHYSICS, UNIVERSITY OF CHICAGO Communicated November 21, 1927

In a preceding paper1 a scale model of the ethane molecule was presented which was based on three simplifying assumptions. (1) The bond between the carbon atoms consists of two electrons held in common. (2) The hydrogen atoms are united to their respective carbon atoms by a single electron bond similar to the type of union between adjacent carbon atoms in diamond2 so that the electron position lies on the straight line joining the carbon and hydrogen nuclei. (3) This electron position lies midway between the hydrogen and carbon nuclei. As was pointed out in the paper referred to, these assumptions, especially the last two, are somewhat arbitrary and their purpose is not only to simplify but also to make definite and concrete a model which can be quantitatively established or rejected by experiment.