Statistical Mechanics of Isotope Effects on the Thermodynamic Properties of Condensed Systems

Abstract

Evidence for the role of molecular structure on the difference in the thermodynamic properties of isotopic molecules in the liquid and solid states is summarized. The properties considered are vapor pressure, heats of vaporization, molal volume, and transition temperatures. It is shown that the molecular structure must be taken into consideration even for small quantum effects. In the approximation of the first quantum correction the difference in thermodynamic properties of isotopic molecules in the condensed state depends upon the atomic masses and an energy parameter associated with each atom in the molecule. The results are extended to higher-order quantum corrections for a harmonic potential. The rules of the mean are obtained directly. Various frequency distributions for the lattice modes are considered. For the case where the internal frequencies in the condensed phase are similar to the free molecule, the ordered quantum corrections can be used for T>(hvmax/12(2)½k)mol; T>(hvlattice/2πk). The role of the gas imperfection and the molal volume of the condensed phase is discussed for equilibria between gaseous and condensed phases. It is shown that the difference in molal volumes of isotopic molecules is a second-order effect. The difference in molal volumes of isotopic molecules is evaluated by an extension of Gruneisen's equation of state to molecular lattices. The results are in good agreement with available experimental data.