Theory of Multi-Component Fluid Mixtures. II. A Corresponding States Treatment

Abstract

The theoretical basis for a theorem of corresponding states for mixtures is examined in a rigorous manner by the use of statistical mechanics. With the aid of the general theory of mixtures presented in a previous paper, the theorem of corresponding states is found to be a consequence of the following assumptions: (a) the internal molecular partition functions depend only on the temperature, (b) the system is in a condition of random mixing, and (c) the several intermolecular interactions can be described by a set of pair-potentials of the same analytical form. In addition to providing a firm theoretical foundation for the corresponding states treatments of Prigogine et al. and Scott, several new approaches to the use of corresponding states in the statistical thermodynamics of mixtures are also presented. In particular, the chemical potentials in binary mixtures of molecules of equal size, and of unequal sizes, are developed. The coefficients in the Margules expansion of the activity coefficients are found to be expressible as functions of the intermolecular interaction parameters and certain experimentally determined thermodynamic properties of the pure components. The relationships of the Regular solution and Conformal solution theories to the present development are also demonstrated.