Calculation of Interaction Virial Coefficients

A number of empirical rules have been proposed for calculating an interaction virial coefficient from the virial coefficients of pure components at the same temperature. None is very satisfactory, but the best of the combinations appear 

More reliable procedures are based on the principle of corresponding states. As noted in the earlier section, it is possible to define reduced virial coefficients that are universal functions of the reduced temperature. Pitzer has shown that this corresponding states principle is strictly valid for substances that interact with a potential of the form 

Ahlert and L. A. Wenzel, Amer. Inst. Chem. Engineers J., 1969,15, 256. 

The results just cited seem to demonstrate that the potentials of the rare gases have the same forms, yet crossed molecular beam studies show that the potentials are not strictly conformal. To put these results into perspective it is useful to make a distinction between utility and validity employed by Hanley and Klein in a discussion of the m—6—8 potential. They define utility as the ability to correlate particular kinds of data and validity as the ability. . . to fit all possible kinds of data and, at the same time, to be compatible with independent fundamental ideas on the nature of the forces between molecules.. The principle of corresponding states has very great utility even if its validity may in some sense be challengeable. 

For substances that follow simple corresponding states, the interaction virial coefficients can be calculated at any temperature once the potential parameters 12 and ai2 have been specified. Obviously it would be advantageous to be able to calculate the parameters for the unlike interaction from the potential parameters for the pure components, although there is no fundamental reason why this should be possible. 

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