Calculation of dissociation constants and the relative stabilities of polynuclear clusters of 1:1 electrolytes in hydrothermal solutions at supercritical pressures and temperatures

Abstract

Monte Carlo calculations ( Pitzer and Schreiber, 1987), electrostatic theory ( Oelkers and Helgeson, 1990), and revised interpretation of the concentration dependence of conductance data ( Oelkers and Helgeson, 1991) indicate that monatomic ions and neutral ion pairs predominate in single 1:1 electrolyte solutions only in the dilute concentration range at supercritical pressures and temperatures where the dielectric constant of H 2O (ϵ) is ≲ 15. To assess geologically realistic degrees of formation of polynuclear clusters at higher concentrations, the logarithms of overall dissociation constants (log β) for triple, quadruple, quintuple, and sextuple complexes of monatomic ions in 16 single 1:1 electrolyte solutions at pressures from 500 to 4000 bars and temperatures from 400 to 800°C were generated from the results of Monte Carlo calculations reported by Gillan (1983) for the restricted primitive model using hard sphere diameters ( δ H ) obtained by regression of the logarithms of dissociation constants (log K) for diatomic neutral ion pairs reported by Quist and Marshall (1968), Frantz and Marshall (1984), and Oelkers and Helgeson (1988). In addition, the logarithms of dissociation constants for polynuclear clusters involving more than one type of cation in the system NaCl-KCl-HCl were estimated by assuming a linear dependence of δ H on cluster stoichiometry. The calculated and estimated values of log β typically decrease monotonically with increasing cluster size at a given pressure and temperature. Speciation calculations generated from the logβ and log K values using activity coefficients for both charged and neutral aqueous species ( Oelkers and Helgeson, 1990, 1991) indicate that polyatomic clusters of monovalent ions are major solute species in supercritical aqueous solutions with 1:1 solute concentrations > 0.5 m at low pressures and high temperatures where the dielectric constant of H 2O is low, which is in general agreement with conclusions reached by Pitzer and Schreiber (1987). It follows by analogy that polyatomic clusters involving Si, Al, Ag, Cu, Fe, S, and other elements in geologic systems may increase substantially the solubilities of rock- and ore-forming minerals in concentrated hydrothermal solutions at supercritical temperatures and pressures.