Simultaneous Description of Activity Coefficients and Solubility with eCPA

Theoretical and practical investigation of ion-ion association in electrolyte solutions

In this study, we present a new equation of state for electrolyte solutions, integrating the statistical associating fluid theory for variable range interactions utilizing the generic Mie form and binding Debye-Hückel theories. This equation of state underscores the pivotal role of ion-ion association in determining the properties of electrolyte solutions. We propose a unified framework that simultaneously examines the thermodynamic properties of electrolyte solutions and their electrical conductivity, given the profound impact of ion pairing on this transport property. Using this equation of state, we predict the liquid density, mean ionic activity coefficient, and osmotic coefficient for binary NaCl, Na2SO4, and MgSO4 aqueous solutions at 298.15 K. Additionally, we evaluate the molar conductivity of these systems by considering the fraction of free ions derived from our equation of state in conjunction with two advanced electrical conductivity models. Our results reveal that, while ion-ion association has a minimal influence on the modification of the predicted properties of sodium chloride solutions, their impact on sodium and magnesium sulfate solutions is considerably more noticeable.

The Contribution of the Ion-Ion and Ion-Solvent Interactions in a Molecular Thermodynamic Treatment of Electrolyte Solutions

Developing molecular equations of state to treat electrolyte solutions is challenging due to the long-range nature of the Coulombic interactions. Seminal approaches commonly used are the mean spherical approximation (MSA) and the Debye-Hückel (DH) theory to account for ion-ion interactions and, often, the Born theory of solvation for ion-solvent interactions. We investigate the accuracy of the MSA and DH approaches using each to calculate the contribution of the ion-ion interactions to the chemical potential of NaCl in water, comparing these with newly computer-generated simulation data; the ion-ion contribution is isolated by selecting an appropriate primitive model with a Lennard-Jones force field to describe the solvent. A study of mixtures with different concentrations and ionic strengths reveals that the calculations from both MSA and DH theories are of similar accuracy, with the MSA approach resulting in marginally better agreement with the simulation data. We also demonstrate that the Born theory provides a good qualitative description of the contribution of the ion-solvent interactions; we employ an explicitly polar water model in these simulations. Quantitative agreement up to moderate salt concentrations and across the relevant range of temperature is achieved by adjusting the Born radius using simulation data of the free energy of solvation. We compute the radial and orientational distribution functions of the systems, thereby providing further insight on the differences observed between the theory and simulation. We thus provide rigorous benchmarks for use of the MSA, DH, and Born theories as perturbation approaches, which will be of value for improving existing models of electrolyte solutions, especially in the context of equations of state.