Predicting Solubility of Oxides of Metals and Metalloids in Supercritical Water

Abstract

The solubility of oxides of metals and metalloids in water can be considered as a reaction of hydration with the formation of hydroxides species, like Al(OH) 3 •H 2 O, Si(OH) 4 , B(OH) 3 , etc. Calculation of solubility requires, along with the equilibrium constant of the dissolution reaction in the ideal gas state, knowledge of the fugacity coefficients, φ 2 ∞ , for aqueous species. This work describes simple ways of estimating fugacity coefficients for such species in water of various pressures/densities, based on the stoichiometry of hydroxides or the corresponding-states correlation. The method is verified by satisfactorily predicting the solubility of quartz, SiO 2 , at 647.1−773 K, and the pressure dependence of solubility of corundum, Al 2 O 3 , at 973 K in water up to 2000 MPa. A few experimental data points, if available, may significantly improve the accuracy of the proposed method.

Thermodynamic Modeling of the Solubility of Quartz in Water up to High Temperatures and Pressures

“…The current study uses methods of evaluation of solubility of oxides in water with the formation of hydroxides based on thermodynamics of nonideal fluid mixtures, as advocated earlier. 27 The essential points are the estimation of the fugacity coefficients of the silica monomer and the dimer, Si(OH) 4 and Si 2 O(OH) 6 , and computation with the quantum chemistry (QC) methods of the thermodynamic properties of these species in the ideal gas state. Like Gerya et al, 26 we found that to match the speciation data for aqueous silica at high temperatures, we have to consider the polymerization of silica beyond the dimer.…”

“…The thermodynamic properties of pure water throughout this work are calculated from the Wagner−Pruß equation of state. 29 The second approach, the density model, is consistent 27 with the following expression for A 12…”

“…Several methods of evaluation of fugacity coefficients of components of gaseous mixtures have been proposed in the literature; 37 however, they are not applicable to gaseous hydroxides. Therefore, for this specific group of compounds, we 27 proposed a way to estimate φ 2 ∞ . This method is a "hybrid" of two approaches.…”

“…It was proposed 27 to combine both approaches through the computation of the function A 12 ∞ , which is linearly related to the spatial integral of the molecular solute−water direct correlation function at infinite dilution 41 arising in the fluctuation solution theory. 42,43 The density dependence of A 12 ∞ allows calculation of φ 2 ∞ with the relation 41,44 ∫…”

“…where κ T = (1/ρ 1 *) (∂ρ 1 */∂P) T is the isothermal compressibility of the pure solvent. It can be shown 27 that the first approach gives where the function A 11 * is defined as…”