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, Δ<i>X</i> = (Δ<i>G</i>, Δ<i>H</i>, Δ<i>S</i>, Δ<i>C</i>_<i>P</i>). The analysis has been performed within the framework of the Correlated States Theory of hydrophobic effect (<i>J. Phys. Chem. B</i>, <b>2025</b>, <i>129</i>(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 <i>g</i> → <i>w</i> hydration thermodynamics. It was shown that the 'three-dimensional' solvation task is completely solvable if the concept of correlated pairs is transferred to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>g</mml:mi><mml:mo>→</mml:mo><mml:mi>l</mml:mi></mml:math> 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.