The statistical mechanical local composition theory: The balance equations and concentration effects in nonideal mixtures

Abstract

The statistical mechanical local composition theory proposed in a previous paper (Lee et al.) is here applied to the study of the ‘number conservation’ conditions on the local compositions. It is demonstrated that detailed balances in molecule numbers using the rigorous statistical mechanical definitions for local compositions yield relations consistent with the Flemr and McDermott—Ashton conditions when well-defined assumptions are utilized. With the assumption that the nearest neighbor coordination numbers z a and z b for each component in a binary mixture are equal, the Flemr conditions are obtained. This assumption is implicit in Wilson's formulation. Allowing z a and z b to differ corresponds to a two-fluid theory. Calculations demonstrate that the detailed balance is satisfied by statistical mechanical calculations using the Percus—Yevick equation for argon—nitrogen mixtures in both the gas and liquid states. It is shown that formulations of two-fluid local composition methods, such as that of Renon and Prausnitz, which assume that the ratio z a / z b is constant, are consistent with the statistical mechanical local composition theory only in the limit of dilute solutions. The Percus—Yevick calculations show that there are wide variations in nearest neighbor numbers and the ratio z a / z b varies with composition even for simple mixtures such as the argon and nitrogen fluids studied here.