Concentration dependence of single-ion activity coefficients: An analysis

Single-ion activity coefficients reported in literature for 10 ternary common-ion liquid-junction systems with KCl(aq) in the reference solutions and MX(aq) electrolytes in the test solutions at 25 °C are reproduced in the present work numerically over wide MX molality ranges by functions of mean activity coefficients and transport numbers of ions in the liquid junction, the MX being BaCl2, CaCl2, CsCl, HCl, KF, K2SO4, LiCl, MgCl2, NaCl and SrCl2. The activity coefficients of solutes in the ternary systems are represented in the calculations by Scatchardʹs Neutral Electrolyte Model, and the transport numbers by a molality-based version of Van Rysselbergheʹs rule. An analysis is given of factors affecting the magnitudes of the functions, among them composition profiles in the liquid junction, formulation of Van Rysselbergheʹs rule, concentration dependence of ion mobilities, and non-ideality of electrolyte mixing. Most importantly, it is found that the exact functions can be approximated reasonably closely by a product of the mean activity coefficients in binary MX and KCl solutions, both at molality of the test solution, raised to powers that can be understood as related to effective transport numbers of the respective non-common ions in the liquid junction. Advantage is taken of the simple formulas to interpret the observed concentration dependences of single-ion activity coefficients in terms of the mean activity coefficients and effective transport numbers.