On converting from the McMillan-Mayer framework I. Single-solvent system

Abstract

This paper presents a thermodynamic framework for transforming models derived in the McMillan-Mayer framework into the Gibbs framework G( T, P, n i ). Historically, the McMillan-Mayer theory has been used to develop the thermodynamics of dilute solutions of electrolytes, polymers and other solutes. The appropriate independent variables for the McMillan-Mayer dilute-solution theory are temperature, volume, chemical potential of the solvent, and number of moles of solutes. Hence, the proper thermodynamic potential is not the Helmholtz energy A( T, V, n j ) but a modified Helmholtz energy A′( T, V, μ 0, n j ( j # 0)) where A′ = A - n 0 μ 0. The most common theoretical developments for electrolyte solutions (e.g., Debye-Hückel theory, mean-spherical approximation) and many dilute polymer solution theories (e.g., osmotic virial expansion) yield excess values of A′, not A. As a result, the chemical potential of the solute, or its activity coefficient, should include a term −P Ex V j θ , whose presence has apparently not been explicitly recognized or discussed clearly ( P Ex is an excess pressure, and V j θ is the partial molar volume of solute j). The origin and influence of this additional term are explored.