Fractional Ion Contributions to Mixed Electrolyte Ion Atmospheres from Experimental Thermodynamic Data

The ion atmosphere that develops around a central ion in solution results in neutralization of the central charge together with additional changes in ion distributions that contribute to the thermodynamics of the solution mixture. The nature of these changes is poorly understood beyond the limiting Debye-Hückel behavior, with mixed electrolyte solutions being particularly challenging to study. Recently, we developed a combined Kirkwood-Buff (KB) inversion and electroneutrality based approach for bulk mixed electrolyte solutions that provide the experimentally derived ion-ion KB integrals (KBIs), which quantify the relative affinity between all the possible ion pairs. Here, we use the resulting experimental KBIs to obtain the fractional contributions from all ions to the ion atmosphere of a central ion for two mixed electrolyte solutions and their single and common ion subsystems, namely NaCl + KBr (aq) at 298.15 K and 1 bar and MgCl2 + KBr (aq) at 373.45 K and 1 bar. These quantities are further decomposed into two contributions. One term contributes to the neutralization of the central charge but not to the thermodynamic properties of closed electrolyte solutions, and the other term gives rise to the thermodynamic properties of the electrolyte solution but does not contribute to the neutralization of the central charge. The results suggest that the thermodynamics of these solutions are dominated by the net thermodynamic enrichment of all ions at low concentrations which, for the systems studied here, typically changes to net thermodynamic depletion of all ions at higher total concentrations. For mixed electrolytes, the switch between behaviors passes through an intermediate concentration range where some ions are thermodynamically enriched and others thermodynamically depleted. Furthermore, we illustrate how to study the competition between two different ions in a particular ion atmosphere for the simpler case of the common ion subsystems, and detail how this relates to the solution thermodynamics.