Third Virial Coefficients of Mixtures

Reliable methods for estimating and correlating third virial coefficients of mixtures have not yet been developed. Even for pure substances, the extent of our knowledge concerning C is very limited. In part this ignorance is due to a lack of reliable data. No techniques for the direct determination of C have been devised, and third virial coefficients can be extracted from p, K, T-data only if they are extensive and highly precise. The temperature dependence of the third virial coefficient has been determined for relatively few pure substances interaction virial coefficients are known for only a handfiil of mixtures. 

Theoretical treatments of the third virial coefficient must deal with an effect not encountered in calculations of B. The interaction between three molecules is not strictly additive, that is, it is not the sum of the pair interactions. In recent years the effect of non-additive contributions to the attractive forces has received considerable attention and it is clear that for simple molecules such as Ar the non-additive portion of C can be as large as 10 to 15 per cent of the total. The contribution of any non-additive repulsive force has not yet been ascertained. Crude quantum mechanical estimates indicate that it is of opposite sign to the 

The exact calculation of interaction third virial coefficients is very complicated. It was not until 1968 that Stogryn obtained C s for mixtures of molecules that interact with a Lennard-Jones potential. In later work, he extended the calculations to include multipolar interactions and also treated non-additivity in the multipolar terms.  

A semi-empirical method for calculating the additive portion of the interaction third virial coefficient from a knowledge of the reduced third virial coefficient of a pure substance was proposed by Rowlinson, Sumner, and Sutton. Their equation can be written in the form 

Chueh and J. M. Prausnitz, Amer. Inst. Chem. Engineers J., 1967,13, 896. 

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