Quantifying ion–ion association in mixed electrolyte systems using bulk thermodynamic experimental data

For single electrolytes, it is already well established that the net affinities between salt-salt, salt-solvent, and solvent-solvent can be derived from bulk thermodynamic volumetric and chemical potential composition-derivative data via Kirkwood-Buff integrals (KBIs). In this simplest case, it is also widely known how to reinterpret those component-based KBIs to obtain the species-based KBIs (cation-cation, cation-anion, etc.). However, this process has never been performed for systems with more than one species of cation and/or anion-a severe restriction. Here, we show how to obtain the ion-ion KBIs for bulk mixed electrolyte solutions regardless of the ion concentration, valency, molecular complexity, degree of ion pairing, etc., assuming one has correlating equations for the bulk thermodynamic data and the system is miscible. This is achieved using a combination of Kirkwood-Buff theory and global and local electroneutrality constraints and is illustrated for mixtures of NaCl + KBr (aq) at 298 K and 1 bar and MgCl2 + KBr (aq) at 373 K and 1 bar. The single electrolyte and select common ion subsystems are also studied. A comparison of the experimental KBIs to those obtained from molecular dynamics simulations shows excellent agreement for the ambient NaCl + KBr (aq) system using the KBFF + SPC/E force field.