Vapor Pressures of the Deuterated Ethanes

Abstract

The vapor pressures of all 10 deutero—protio-ethane isomers C2HiD6—i (0≤i≤6) have been measured over the temperature range 115° to 200°K [∼1 mm C2H6 to 1600 mm C2H6] by direct manometry. The isotope effects are inverse and go through maxima between 125° and 140°K. At the maxima they are on the order of 1.2% per D atom. Deviations from the law of the mean are small, but for the three sets of equivalent isomers 1,1- and 1,2-C2H4D2; 1,1,1- and 1,1,2-C2H3D3; and 1,1,1,2- and 1,1,2,2-C2H2D4 significant differences in vapor pressure are observed. The more unsymmetrically substituted compound has the higher vapor pressure in all cases. The data are interpreted in the light of the statistical theory of isotope effects in condensed systems. A model calculation is made within the framework of this theory in its harmonic-cell approximation using reasonable force fields. It is necessary to invoke temperature-dependent force constants for the low-energy (u=hv/kT<2π) modes in order to rationalize the temperature dependency below 140°K. The agreement between the model calculation and experiment is excellent. The calculations reveal that the torsional motion, which must be blue shifted on condensation, is the single most important contributor to the isotope effects between equivalent isomers. The results constitute the second independent confirmation of the statistical theory of isotope effects in condensed systems as applied to molecules exhibiting higher-order quantum effects.