Solvation phenomena in dilute multicomponent solutions I. Formal results and molecular outlook

We derive second-order thermodynamically consistent truncated composition expansions for the species residual partial molar properties--including volume, enthalpy, entropy, and Gibbs free energy--of dilute ternary systems aimed at the molecular account of solvation phenomena in compressible media. Then, we provide explicit microscopic interpretation of the expansion coefficients in terms of direct and total correlation function integrals over the microstructure of the corresponding infinite dilution reference system, as well as their pressure and temperature derivatives, allowing for the direct prediction of the species partial molar properties from the knowledge of the effective intermolecular interactions. Finally, we apply these formal results (a) to derive consistent expressions for the corresponding properties of the binary system counterparts, (b) to illustrate how the formal expressions converge, at the zero density limit, to those for multicomponent mixtures of imperfect gases obeying the virial equation of state Z = 1 + BPkT, and (c) to discuss, and highlight with examples from the literature, the thermodynamic inconsistencies encountered in the currently available first-order truncated expansions, by pinpointing the mathematical origin and physical meaning of the inconsistencies that render the first-order truncated expansions invalid.