Molecular-Based Description of the Osmotic Second Virial Coefficients of Electrolytes: Rigorous Formal Links to Solute-Solvent Interaction Asymmetry, Virial Expansion Paths, and Experimental Evidence

Abstract

We introduce a molecular-based route to the evaluation of the osmotic second virial coefficients of dissociative solutes in dilute binary solutions, according to a general molecular thermodynamic solvation formalism of electrolyte solutions. We discuss the underlying solvation fundamentals and derive rigorous expressions leading to (i) the functional relationship among the osmotic second virial coefficients and the limiting composition behavior of the non-Coulombic contribution to the Kirkwood-Buff integral of the solute-solute interactions, the corresponding composition slope of the mean activity coefficient of the electrolyte solute, and a precisely defined solute-solvent intermolecular interaction asymmetry that characterizes unambiguously the solution non-ideality; (ii) the self-consistent calculation of the osmotic second virial coefficients of electrolytes as defined by the composition expansion along different thermodynamic paths and/or composition variables; (iii) the microstructural interpretation of Hill's isobaric-isothermal osmotic second virial coefficient in terms of Kirkwood-Buff correlation function integrals and its relationships to other osmotic coefficients from composition expansions along alternative thermodynamic paths; and (iv) the identification of drawbacks in the implementation of previous methods, originally intended for non-electrolyte systems, to systems involving dissociative solutes. The proposed formalism provides the fundamentally based foundations to the determination of the osmotic second virial coefficients of any type of electrolyte solute, whose thermodynamic expressions converge naturally to the non-electrolyte ones by setting to unity the solute stoichiometric coefficient ν. Following the formal results, we illustrate the formalism with the calculation of a variety of osmotic second virial coefficients involving a wide selection of aqueous solutions at ambient conditions and comprising a wide range of anion-cation type combinations characterized by 2 ≤ ν ≤ 6. Finally, we interpret the behavior of the resulting osmotic virial coefficients in terms of the solute-solvent intermolecular interaction asymmetry, discuss the experimental data requirements for the accurate evaluation of the osmotic second virial coefficients, and provide some observations as well as their modeling implications.