A Test of the Third Law of Thermodynamics by Means of Two Crystalline Forms of Phosphine. The Heat Capacity, Heat of Vaporization and Vapor Pressure of Phosphine. Entropy of the Gas

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Abstract
The heat capacity of solid and liquid phosphine has been measured from 15°K to its boiling point, 185.38°K. Transitions were found at 30.29, 49.43 and 88.10°K. The heats of transition are 19.6, 185.7 and 115.8 cal./mole, respectively. The transition at 49.43°K had not previously been reported. In order to obtain complete conversion to the form of phosphine which is stable below 49.43°K it was necessary to keep the unstable form near 40°K for several days. A graph showing the rate of conversion to the stable form as a function of temperature has been given. The transition at 30.29°K occurs in the form of phosphine, unstable below 49.43°K. There is also a region of abnormally high heat capacity in the supercooled form between 30.29 and 35.66°K. At the latter temperature the heat capacity decreases abruptly by 15 percent without evidence of latent heat. The melting point was found to be 139.35°K and the heat of fusion 270.4 cal./mole. The heat of vaporization at the boiling point, 185.38°K, was determined calorimetrically. The value found was 3489 cal./mole. The vapor pressure of solid and liquid phosphine was measured and the results represented by the equations: Solid phosphine 128.67 to 139.35°K; log10 P(int. cm Hg)=—895.700/T+6.86434. Liquid phosphine 139.35 to 185.56°K; log10 P(int. cm Hg) = —1027.300/T—0.0178530T+0.000029135T 2+9. 73075. The entropy of the solid at 49.43°K may be obtained either from measurement on the stable or unstable form. The values are 8.14 and 8.13 cal./deg. per mole, respectively. While the extraordinarily close agreement is somewhat fortuitous, the measurements provide the most accurate existing verification of the third law of thermodynamics by means of two crystalline forms of a substance. The molal entropy of the ideal phosphine gas at the boiling point was found to be 46.39±0.1 cal./deg. per mole. The corresponding value at 298.1°K is 50.35 cal./deg. per mole. This may be compared with the value 50.5 calculated by Yost with the assistance of spectroscopic data and an estimated bond angle. The above entropy values neglect the nuclear spinentropy,R ln 16=5.509 cal./deg. per mole, which should be added to obtain the absolute entropy. The values given are the ones which should be used in ordinary thermodynamic calculations. Phosphine is known to be a symmetrical top and the two equal moments of inertia are known from its band spectrum. It has not been found possible to evaluate the other moment of inertia in this manner. However, it can be calculated from the accurate entropy determination given above. The value found is Ic =(7.9±0.8)×10‐40 gram cm2. The P–H distance was found to be 1.45±0.02A and the bond angle, 98±5°.

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