Statistical Thermodynamics of Solutions

Abstract

A new approach to the statistical problem of solutions is presented, which combines the main ideas of the cell method and of the theorem of corresponding states. The basic assumption is that the cell partition function of a molecule in the solution may be formally expressed by the same function as in pure liquid, but with other well-defined values of the reduced temperature and volume. For pure liquids this theory reduces to the usual theorem of corresponding states. The excess properties of the mixture are expressed in terms of molecular parameters related to the interaction energies between pairs of molecules. All the macroscopic coefficients appearing in the excess functions are expressed by experimental properties of the pure compounds, just as in the theory of conformal solutions of Longuet-Higgins. The present model correctly gives the ``first-order contributions'' to the excess functions like the theory of conformal solutions; it gives also an approximative estimate of the higher order terms. Explicit expressions for the excess functions have been calculated up to the second-order terms. The relations between intermolecular forces and excess functions is discussed in detail for some typical cases. All the conclusions drawn from this model confirm those obtained previously by Prigogine and his collaborators; however the present model permits a much more direct derivation of the main results without the introduction of subsidiary simplifying hypotheses (like simplified cell models).