(742g) Revisiting Theories and Conventions of Electrolyte Thermodynamic Models

An alternative formulation for the refined electrolyte-NRTL model will be presented. The changes can be summarized as the substitution of the Pitzer-Debye-Hückel equation with a detailed form of the original Debye-Hückel model and the inclusion of hydration chemistry in the model in a way that reflects the effect of hydration on the structure of the solution.

The Debye-Hückel model has had tremendous success for almost a century in the prediction of the electrostatic contribution of the deviation from ideality of electrolyte solutions. ^[1] However, the model has been criticized much on the validity and accuracy of the fundamental equation of Debye and Hückel because of its inherent assumptions about the role of solvents and the ensemble in which it has been developed. In Debye’s original model, solvents are assumed to be continuous medium with their dielectric constants being independent of temperature, pressure, and the presence of the ions. ^[2] Therefore, the Debye-Hückel model was developed under a framework with independent variables of temperature, volume, the number of electrolytes, and dielectric constants. However, on the one hand, dielectric constants of solvents are in fact a function of temperature, pressure and the number of electrolytes. On the other hand, the electrolyte-NRTL model describing the short-range contribution of excess Gibbs free energy of electrolyte solution systems were developed under Lewis-Randall ensemble where temperature, pressure, and the number of molecules are independent variables. Therefore, the combination of Debye’s long-range contribution with electrolyte-NRTL model requires conversion of Debye-Hückel’s framework to the Lewis-Randall framework in which experimental measurements are typically taken. The details of the assumptions and the ensemble in which the Debye-Hückel theory was developed and the rigorous extensions of the Debye-Hückel theory to the Lewis-Randall ensemble will be shown. Relative considerations will be accounted for the so-called Born equation which transfers the reference state of ions infinitely diluted in an aqueous solution to that of mixed solvents. On the basis of common engineering assumptions regarding the dependence of the volume of the solution and of the dielectric constant of the solvent on composition, the activity coefficients converted to the Lewis-Randall ensemble will be criticized and conclusions of the effect of the various treatments will be drawn.

For the short-range contribution to the excess Gibbs free energy of an electrolyte solution system, the electrolyte-NRTL model has had great success.^[3] This model was improved by the inclusion of hydration chemistry.^[4] In this presentation we will show how hydration should be considered for both the cations and the anions with hydration numbers allowed to receive negative values, representing the forming or breaking effect of the ions on the solvent structure. The distance of closest approach of the ions that is inherent as an adjustable parameter in the Debye-Hückel theory is expressed as a function of the radii of the ions and their hydration layer. Two different assumptions are considered for the hydration numbers of the ions: i) that they are independent of the concentration and the activity of the solvent and ii) that they are function of the short-range activity of the solvent (water). The second model is applied to electrolytes consisting of ions that are known to bind with water molecules and show extensive hydration.

The electrolyte-NTRL model, revised to include the conversion between thermodynamic frameworks, impact of solvent composition and structure, and hydration was applied to an extensive database of uni-univalent and bi- and tri-valent electrolytes and showing considerable success.

References

[1] P. Debye, E. Hückel, Zur Theorie der Elektrolyte. I. “Gefrierpunktserniedrigung und verwandte Erscheinungen”, Physikalische Zeitschrift, 24 (1923) 185-206.

[2] R.H. Fowler, E.A. Guggenheim, Statistical thermodynamics, Univ. Press, 1939.

[3] C.C. Chen, H.I. Britt, J.F. Boston, L.B. Evans, AIChE J. 28 (1982) 588-596.

[4] G.M. Bollas, C.C. Chen, P.I. Barton, AIChE J. 54-6 (2008) 1608-1624.