A one-term extrapolation method for estimating equilibrium constants of aqueous reactions at elevated temperatures

Abstract

A one-term method for extrapolating equilibrium constants for aqueous reactions is proposed which is based on the observation that the change in free energy of a well-balanced isocoulombic reaction is nearly independent of temperature. The current practice in extrapolating log K values for isocoulombic reactions is to omit the ΔCp term but include a ΔS term (i.e., the two-term extrapolation equation of Lindsay, 1980). However, we observe that the ΔCp and ΔS terms for many isocoulombic reactions are not only small, but are often opposite in sign, and therefore tend to cancel one another. Thus, inclusion of an entropy term often yields estimates which are less accurate than omission of both terms.The one-term extrapolation technique is tested with literature data for a large number of isocoulombic reactions involving ion-ligand exchange, cation hydrolysis, acid-base neutralization, redox, and selected reactions involving solids. In most cases the extrapolated values are in excellent agreement with the experimental measurements, especially at higher temperatures where they are often more accurate than those obtained using the two-term equation of Lindsay (1980). The results are also comparable to estimates obtained using the modified HKF model of Tanger and Helgeson (1988) and the density model of Anderson et al. (1991). It is also found to produce reasonable estimates for isocoulombic reactions at elevated pressure (up to P = 2 kb) and ionic strength (up to I = 1.0).The principal advantage of the one-term method is that accurate estimates of high temperature equilibrium constants may be obtained using only free energy data for the reaction of interest at one reference temperature. The principal disadvantage is that the accuracies of the estimates are somewhat dependent on the model reaction selected to balance the isocoulombic reaction. Satisfactory results are obtained for reactions that have minimal energetic, electrostatic, structural, and volumetric differences between reactants and products. With careful choice of model reaction, the one-term isocoulombic extrapolation makes it possible to extend the vast amount of low temperature free energy data for aqueous reactions to higher temperatures, and therefore has important applications to the study of aqueous equilibria in geochemical systems.