A novel method for correlating/predicting the thermodynamic properties of aqueous ions at high T and P

Calculation of the molar standard state Gibbs energies of aqueous ions, $G_2^o$, at supercritical temperatures and pressures is a prerequisite for thermodynamic modeling of hydrothermal processes. Currently, such calculation is performed only with the well-known HKF model, and the development of alternative methods is highly desirable to avoid any possible bias. As a step in this direction, the author presents a novel “isochoric” method for predicting the Gibbs energies of aqueous ions up to high temperatures and pressures. The method is based on the analysis of the temperature dependence of the partial molar isochoric heat capacity of aqueous ions, $C_{v,2}^o$. Knowing $C_{v,2}^o$, one can compute the partial molar isobaric heat capacity $C_{p,2}^o$, provided that $V_2^o$ is known as a function of T and P. Then the calculation of $G_2^o$ can be performed by the traditional methods. The test of this method was performed using two literature formulations (Arcis et al., 2024; Marshall and Franck, 1981) for the ionization constant of water over wide ranges of temperature (273–1273 K) and water density ρ (up to ρ = 1.25 g cm⁻³), which allow computing all thermodynamic properties of a hypothetical HOH electrolyte. Using 4 parameters at most, it is possible to reproduce the water ionization constants recommended by either Arcis et al. (2024) or Marshall and Franck (1981) formulations at supercritical temperatures with deviations less than those of these formulations. It is expected that the proposed “isochoric” method deserves further investigation.