A new method for multicomponent activity coefficients of electrolytes in aqueous atmospheric aerosols

Abstract

Three‐dimensional models of atmospheric inorganic aerosols need accurate and computationally efficient parameterizations of activity coefficients of various electrolytes in multicomponent aqueous solutions. In this paper, we extend the Taylor's series expansion mixing rule used by C. Wagner in 1952 for estimating activity coefficients in dilute alloy solutions to aqueous electrolyte solutions at any concentration. The resulting method, called the multicomponent Taylor expansion method (MTEM), estimates the mean activity coefficient of an electrolyte in a multicomponent solution on the basis of its values in binary solutions of all the electrolytes present in the mixture at the solution water activity aw, assuming aw is equal to the ambient relative humidity. MTEM is applied here for atmospheric aerosol systems containing H+, NH4+, Na+, Ca2+, SO42−, HSO4−, NO3−, and Cl− ions. The aerosol water content is calculated using the Zdanovskii‐Stokes‐Robinson (ZSR) method. For self‐consistency, most of the MTEM and ZSR parameters are derived using the comprehensive Pitzer‐Simonson‐Clegg model at 298.15 K and are valid for an aw range of 0.2–0.97. Because CaSO4 is sparingly soluble, it is treated as a solid in the model over the entire aw range. MTEM is evaluated for several multicomponent systems representing various continental and marine aerosols and is contrasted against the mixing rule of C. L. Kusik and H. P. Meissner and of L. A. Bromley and the newer approach of S. Metzger and colleagues. Predictions of MTEM are found to be generally within a factor of 0.8–1.25 of the comprehensive Pitzer‐Simonson‐Clegg model and are shown to be significantly more accurate than predictions of the other three methods. MTEM also yields a noniterative solution of the bisulfate ion dissociation in sulfate‐rich systems: a major computational advantage over other ionic‐strength‐based methods that require an iterative solution. CPU time requirements of MTEM relative to other methods for sulfate‐poor and sulfate‐rich systems are also discussed.