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

This paper presents a thermodynamic framework for transforming models derived in the McMillan-Mayer framework into the Gibbs framework G(T, P, ni). 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, nj) but a modified Helmholtz energy A′(T, V, μ0, nj (j # 0)) where A′ = A - n0μ0. 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 −PExVjθ, whose presence has apparently not been explicitly recognized or discussed clearly (PEx is an excess pressure, and Vjθ is the partial molar volume of solute j). The origin and influence of this additional term are explored.