The Vapor Pressure Isotope Effect, Separated Isotopes

3 The Vapor Pressure Isotope Effect, Separated Isotopes 

Thermodynamic analysis of VPIE data for separated isotopes (see, e.g., Figs. 7.18a and b) proceeds by equating partial molar free energies in condensed and vapor phases for each isotope. Using Equations 5.1, 5.5 and 5.6 one obtains 

This is a simple and important result. It equates VPIE to the isotopic difference of standard state free energies on phase change, plus a small correction for vapor phase nonideality, here approximated through the second virial coefficient. Therefore Equation 5.8 is limited to relatively low pressure. As T and P increase third and higher virial corrections may be needed, and at even higher pressures the virial expansion must be abandoned for a more accurate equation of state. 

In Equation 5.10 and subsequently we have dropped the superscript ° s from the Q s in order to simplify the notation. 

Equation 5.11 is important. It relates the experimentally observed vapor pressure ratio to the theoretically important isotope effects on the free energy differences and/or partition function ratios. This equation encapsulates the essential physics of the vapor pressure isotope effect and, as we shall see, provides a path for its theoretical interpretation in terms of molecular structure and dynamics via the partition function ratios. 

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