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

Abstract

Recently, in an attempt to refine the chemical interpretation of the free energy 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 solvent have different molar volumes and is identical in form to the Flory−Huggins configurational entropy term. The need for any such correction has been 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 interpretation of the standard free energy of transfer of an infinitely dilute solute from one nonideal phase to a second, absolutely immiscible nonideal phase. This approach also provides a clear explanation of the effect of the choice of standard states, and especially of concentration scales, on the interpretation of transfer free energies. The principle virtue of the present work lies in the conceptually simple but qualitatively complete description inherent in the van der Waals treatment of a fluid mixture, as it incorporates both attractive and repulsive interactions. It is shown that the free energy of transfer of a solute between two immiscible van der Waals fluids will be nonzero even for an “ideal point solute” (here defined as an infinitely 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 fluids (solvents) and is true for transfer free energies based on both mole fraction and molar concentration scales, meaning that neither of these scales provides standard free energies of transfer that purely reflect attractive solute/solvent interactions free from volume entropy effects.