Partial molar volumes of 1–1 electrolytes at high T and P: correlations and predictions

Abstract

Knowledge of the partial molar volumes of aqueous ions allows accurate calculation of the pressure dependence of equilibrium constants, solubility of minerals, etc., thus being useful for thermodynamic modeling of hydrothermal processes. This study analyzed methods to correlate and predict the values of the partial molar volumes at infinite dilution, $V_2^o$, for 1–1 electrolytes and singly charged ions at elevated T and P. Since the precise experimental values of the dielectric constant of water are measured only up to 873 K, we were interested only in non-electrostatic ways to correlate $V_2^o$ data. First of all, we compiled the $V_2^o$ values at T > 373 K for the following 1–1 electrolytes: HCl, LiCl, LiI, LiNO₃, LiOH, NaF, NaCl, NaBr, NaI, NaNO₃, NaOH, NaHCO₃, NaClO₄, NaH₂PO₄, NaTr (Tr stands for triflate), KF, KCl, KBr, KI, KNO₃, KOH, CsBr, and NH₄Cl. Relations, following from the “density” model and from the Fluctuation Solution Theory (FST) were employed to analyze data. It was concluded that at the current state of knowledge of $V_2^o$ the FST-relations for electrolytes are recommended mainly to reject strongly deviating experimental outliers. However, the “density” model provides a simple and fairly accurate way to describe the compiled set of data with only two parameters for each ion, $n$ and $V_{\text{hc}}$, values of which were evaluated for the following singly-charged ions: H⁺, Li⁺, Na⁺, K⁺, Cs⁺, NH₄⁺, F^-, Cl^-, Br^-, I^-, OH^–, NO₃^–, H₂PO₄^-, HCO₃^–, ClO₄^-, Tr^- (Tr = triflate). Following Mesmer et al. (1988), we consider the fitting parameters $V_{\text{hc}}$ and $n$ to be related to the intrinsic volume of the ion and to the number of water molecules transferred from the bulk water to a hydration shell around the ion, respectively.

Although the values of $n$ and $V_{\text{hc}}$ were fitted from data at temperatures from 373 to 673 K and water densities, $d_o$, from 0.5 to 1.1 g cm⁻³, apparently, they predict realistic $V_2^o$ values at temperatures up to 1600 K and $d_o$ ranges from 0.2 to 1.6 g cm⁻³.