Ionic Solutions in the Binding Mean Spherical Approximation. Thermodynamics of Associating Electrolytes up to Very High Concentrations

Abstract

A previous model, developed to describe the thermodynamic properties of associating electrolytes within the binding mean spherical approximation (BIMSA), is modified on the basis of a better representation of the pair. The ions are represented as charged hard spheres interacting through a sticky point potential, leading to the creation of pairs. In this version of the model, the species constituting the pair are allowed to have charges and sizes different from those of the free ions. New expressions for the osmotic and activity coefficients are proposed that account for these features. The equations were applied to fit the parameters in the model to osmotic data for a variety of aqueous solutions of inorganic acids, and for a base, NaOH, at 25°C up to the highest concentrations for which data are available. In all cases, accurate representations could be obtained up to very high concentrations, such as 28 mol kg -1 for nitric acid, 45 mol kg -1 for hydrochloric acid, and 29 mol kg -1 for NaOH. The case of sulfuric acid could be treated consistently in the concentration range 0-27.7 mol kg -1 by considering the equilibrium between sulfate and bisulfate ions. In all cases, the new model represents an improvement over the previous BIMSA model.

Description of the Thermodynamic Properties of Aqueous Ionic Solutions within the Mean Spherical Approximation

“…This new model was applied to solutions of acids and one base up to very high concentration (Vilariño et al, 2004) and to the modeling of the speciation in solutions of NaOH containing small amounts of hydrogen peroxide H 2 O 2 which produces HO 2 -in that medium (Chlistunoff and Simonin, 2006). Figures 7 and 8 show the results for HCl (to 45 mol/kg) and H 2 SO 4 (to 28 mol/kg) aqueous solutions, respectively.…”

Aqueous solutions of ionic liquids. Description of osmotic coefficients within the Binding Mean Spherical Approximation

“…[18][19][20][21][22]26 For clarity, we will recall only the main relations. The BiMSA model provides an expression for the excess Helmholtz energy of solution per volume unit (∆Α BiMSA ) at the Mac-Millan Mayer (MM) level, on molarity scale.…”

“…with η and Γ the classical MSA parameters [18][19][20][21][22][23] , β = 1/kT, ε 0 the permittivity of a vacuum, and ε the relative permittivity of solution. Expressions for η and Γ are given in eqs 7 to 11 of Ref.…”

“…Note that in this study, the variation of ε W with temperature is taken into account. Eqs 10 and 11 have been used in several papers dealing with MSA and BiMSA [18][19][20][21][22]28 and are used here to provide a set of parameters compatible with those previously obtained. In eq 10, σ + (0) is the diameter of cation at infinite dilution.…”

“…Within the Binding MSA (BiMSA) version of the model 20,21 , an effective association constant is introduced, taking into account the association of unlike ions yielding neutral pairs. This model has shown to provide very good description of the thermodynamic coefficients of aqueous solutions of salts such as alkali halide, nitrate, perchlorate, sulfate [20][21][22] , mixtures of salts [23][24][25] or complex electrolyte systems 26 and recently, lanthanide salts 25,27 and concentrated solutions of bulky ions such as alkymammonium or alkylsulfate ions. 28 Besides, the MSA model uses a few parameters that have some physical meaning.…”