Predictive models for the phase behaviour and solution properties of weak electrolytes: nitric, sulphuric, and carbonic acids

Abstract

The distribution of ionic species in electrolyte systems is important in many fields of science and engineering, ranging from the study of degradation mechanisms to the design of systems for electrochemical energy storage. Often, other phenomena closely related to ionic speciation, such as ion pairing, clustering and hydrogen bonding, which are difficult to investigate experimentally, are also of interest. Here, we develop an accurate molecular approach, accounting for reactions as well as association and ion pairing, to deliver a predictive framework that helps validate experiment and guides future modelling of speciation phenomena of weak electrolytes. We extend the SAFT-VRE Mie equation of state [D. K. Eriksen et al., Mol. Phys., 2016, 114, 2724–2749] to study aqueous solutions of nitric, sulphuric, and carbonic acids, considering complete and partially dissociated models. In order to incorporate the dissociation equilibria, correlations to experimental data for the relevant thermodynamic equilibrium constants of the dissociation reactions are taken from the literature and are imposed as a boundary condition in the calculations. The models for water, the hydronium ion, and carbon dioxide are treated as transferable and are taken from our previous work. We present new molecular models for nitric acid, and the nitrate, bisulfate, sulfate, and bicarbonate anions. The resulting framework is used to predict a range of phase behaviour and solution properties of the aqueous acids over wide ranges of concentration and temperature, including the degree of dissociation, as well as the activity coefficients of the ionic species, and the activity of water and osmotic coefficient, density, and vapour pressure of the solutions. The SAFT-VRE Mie models obtained in this manner provide a means of elucidating the mechanisms of association and ion pairing in the systems studied, complementing the experimental observations reported in the literature.

Further reflections about the “Born” term used in thermodynamic models for electrolytes

“…It has often been claimed that the "Born" term accounts for the change in ion-solvent interactions [4,[15][16][17][18]40] when an ion is transferred from the reference state (infinite dilution) to a solution of some finite salt concentration. Then, in the expression of the chemical potential of an ion, this term was introduced as a supposedly natural complement to the contribution for ion-ion interactions, which is usually a Debye-Hückel (DH) or MSA term at the McMillan-Mayer level.…”

“…Firstly, in these explicit-solvent models, it has played the role of accounting for ion-solvent interactions (as claimed, e.g., in Refs. 4,16,17) and, as such, it has been used in conjunction with a term for ion-ion interactions that was either a Debye-Hückel (DH) or a mean spherical approximation (MSA) term, both of which being theories regarding the solvent as a dielectric continuum. The latter feature contrasts with the type of models (with explicitsolvent) in which the "Born" term is usually employed.…”