Three-Dimensional Case in Solvation Thermodynamics: Variation of Temperature, Transfer Route, and Thermodynamic Function

In this work, we considered a complex case in solvation thermodynamics, referred to as the 'three-dimensional solvation' where the three 'dimensions' are being varied, viz., (1) the solute transfer is described between three phases (gas-to-liquid, gas-to-water, and liquid-to-water), (2) the transfer is accomplished in a wide temperature range at constant pressure, and (3) the solvation thermodynamics is given by four thermodynamic functions, ΔX = (ΔG, ΔH, ΔS, ΔCP). The analysis has been performed within the framework of the Correlated States Theory of hydrophobic effect (J. Phys. Chem. B, 2025, 129(21), 5245-5267), which introduces the new physical entity, i.e., the correlated/uncorrelated state of solute-water pair, enabling us to fully quantify the g → w hydration thermodynamics. It was shown that the 'three-dimensional' solvation task is completely solvable if the concept of correlated pairs is transferred to the g→l route. Interrelations between the heat capacity changes and enthalpy/entropy convergence temperatures for different transfer routes, known previously from empirical thermodynamic studies, have been derived as a general consequence of solvation theory.