The chemical meaning of the standard free energy of transfer: Use of van der Waals' equation of state to unravel the interplay between free volume, volume entropy, and the role of standard states

Recently, in an attempt to refine the chemical interpretation of the free e nergy of transfer of a solute between two phases, Honig et al. introduced a "volume entropy" term into the canonical particle density-based expression for the free energy of transfer. This term is used when the solute and sol vent have different molar volumes and is identical in form to the Flory-Hug gins configurational entropy term. The need for any such correction has bee n denied by Ben-Naim and others on the basis of thermodynamic, conceptual, and empirical arguments. The purpose of the present work, based on the van der Waals model of a binary mixture, is to provide a simple, chemical inter pretation of the standard free energy of transfer of an infinitely dilute s olute from one nonideal phase to a second, absolutely immiscible nonideal p hase. This approach also provides a clear explanation of the effect of the choice of standard states, and especially of concentration scales, on the i nterpretation of transfer free energies. The principle virtue of the presen t work lies in the conceptually simple but qualitatively complete descripti on inherent in the van der Waals treatment of a fluid mixture, as it incorp orates both attractive and repulsive interactions. It is shown that the fre e energy of transfer of a solute between two immiscible van der Waals fluid s will be nonzero even for an "ideal point solute " (here defined as an inf initely hard, nonattractive but potentially repulsive particle of zero size at, or acting as if it is at, infinite dilution). This result arises from differences in the molar volumes and hard core diameters of the two bulk fl uids (solvents) and is true for transfer free energies based on both mole f raction and molar concentration scales, meaning that neither of these scale s provides standard free energies of transfer that purely reflect attractiv e solute/solvent interactions free from volume entropy effects.