Theoretical analysis of aqueous solutions of mixed strong electrolytes by a smaller-ion shell electrostatic model

In spite of the great importance of mixed electrolytes in science and technology, no compelling theoretical explanation has been offered yet for the thermodynamic behavior of such systems, such as their deviation from ideality and the variation of their excess functions with ionic composition and concentration. Using the newly introduced Smaller-ion Shell treatment - an extension of the Debye-Hückel theory to ions of dissimilar size (hence DH-SiS) - simple analytic mathematical expressions can be derived for the mean and single-ion activity coefficients of binary electrolyte components of ternary ionic systems. Such expressions are based on modifying the parallel DH-SiS equations for pure binary ionic systems, by adding to the three ion-size parameters - a (of counterions), b+ (of positive coions), and b- (of negative coions) - a fourth parameter. For the (+ + -) system, this is "b++," the contact distance between non-coion cations. b++ is derived from fits with experiment and, like the other b's, is constant at varying ion concentration and combination. Four case studies are presented: (1) HCl-NaCl-H2O, (2) HCl-NH4Cl-H2O, (3) (0.01 M HX)-MX-H2O with X = Cl, Br, and with M = Li, Na, K, Cs, and (4) HCl-MCln-H2O with n = 2, M = Sr, Ba; and n = 3, M = Al, Ce. In all cases, theory is fully consistent with experiment when using a of the measured binary electrolyte as the sole fitting parameter. DH-SiS is thus shown to explain known "mysteries" in the behavior of ternary electrolytes, including Harned rule, and to adequately predict the pH of acid solutions in which ionized salts are present at different concentrations.