Thermodynamic properties of aqueous solutions of mixed electrolytes: A new mixing rule

Abstract

The prediction of several thermodynamic properties of mixed aqueous electrolyte solutions has been considered earlier (Patwardhan and Kumar, 1986a,b). A unified set of predictive equations for several properties was presented by them and was tested against experimental data. These predictive equations require knowledge of properties of corresponding single electrolyte solutions. No further system-specific empirical constants are involved. The experimental data used for testing these equations involved mixed systems having a common ion in most cases, with only a few exceptions. It is thus clear that the equations developed earlier can be used with confidence for common ion systems. We consider here the application of these equations to mixed systems having no common ion, as well as several properties for which reliable data are available for different systems involving four ions. Process of MixingLet us consider the mixing of single electrolyte solutions of equal ionic strength which do not have any common ion, for example, mixing of NaCl solution and KBr solution. In the final solution, interactions of sodium ions with both chloride and bromide ions are present and may be important. A similar statement can be made about the potassium ions. If an equation involving only these two electrolytes were used for predicting the vapor pressure of the final mixture, then it would account for only the Na-Cl and K-Br interactions, leaving out the other two interactions, namely Na-Br and K-Cl. Therefore, even though the final mixed electrolyte solution has been actually prepared by mixing NaCl solution with KBr solution, it should be considered as obtained by conceptually mixing four single electrolyte solutions: NaC1, KCl, NaBr, and KBr. The amounts of these solutions have to be so selected that each mixing process involves a common ion or a common ionic atmosphere (cationic or anionic). These amounts can be calculated in the following manner. Consider a mixed electrolyte solution containing several species of cations and anions. Let i refer to cations and j refer to anions. The total anionic charge, ( C H ) , which is also equal to the total cationic charge, is given by:Correspondence concerning this work should be addressed to V. S. Patwardhan. I jThe cationic strength is:Z,=O.S c rnd 1 and the anionic strength is: Z,=O.S c m dThe total ionic strength is given by:Let the cationic strength fraction and the anionic strength fractions be defined as:and Let us consider a quantity of the mixed electrolyte solution which contains 1, OOO g of water. Consider a process whereby cation i in the solution is conceptually separated from other cations into a region containing (l,OOOyi) g water, keeping the anions well mixed where yi is unknown at present. The cationic strength in this region is XJc/Yi and the anionic strength in the same region is [mgi/( CH)]Z,/yi. We now select yi such that the total ionic strength in this region is equal to Z. Z=

Ionizable side chains at catalytic active sites of enzymes

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Interacting Ions in Biophysics: Real is not Ideal

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