An alternative formulation for the 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. Hydration is considered for both the cations and the anions and the hydration numbers are allowed to receive negative values, representing the effect of the ions on the structure of the solvent. 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 model is applied to an extensive database of uni-univalent and bi- and tri-valent electrolytes with considerable success.

Typically, the thermodynamic description of electrolyte solutions is performed by assuming that long-range (electrostatic) and short-range (molecular) interactions are responsible for the deviation from ideality and that these can be assumed as being additive. The main trends in the simulation of the long-range interactions can be categorized as the Debye-Hückel (DH) equation [1], and its many extensions [2,3], and the mean spherical approximation (MSA) [4,5]. The main trends in the description of the short-range interactions can be summarized as excess Gibbs free energy models based on the local composition concept, extensions on the basis of the virial equation, considerations of the hydration of ions and equations of state. A relatively new trend is to combine hydration chemistry with a local composition model. The rigorous approach would require six different phenomena to be modeled for the description of the deviation from ideality of electrolyte solutions:

• electrostatic interactions that can be described by some form of the primitive model, which will dominate at low concentrations,

• short-range interactions that become dominant at higher concentrations and can be described on the basis of the local composition concept or the virial equation,

• ionic hydration that is significant in the whole concentration range,

• the structure of the solvent and the effect of the ions on it,

• partial dissociation or ionic association, for which some kind of evidence should exist, as it does for acids,

• localized hydrolysis, an effect more profound in basic solutions.

The detailed, yet somewhat cumbersome, approach is to express each one of the above phenomena through a number of unknowns (usually adjustable parameters). Fortunately, most of these phenomena are interrelated, allowing for the grouping of electrolytes that obey some simplifying assumption, which leads to a smaller number of adjustable parameters. In the past, simplistic assumptions have been made in order to develop what can be called a “global” model for all electrolyte solutions. This has lead, for instance, to the prediction of activity coefficients of acids and bases under the complete-dissociation, zero-hydration and negligible-hydrolysis assumptions for the whole concentration range, despite the experimental evidence to the contrary. In the present work, the basic aim is to try to distinguish between these phenomena and develop models that will be capable of identifying and addressing the dominant phenomena of the above for groups of electrolytes.

In this work the NRTL model has been chosen for the description of the short-range interactions of the hydrated ions with water and with each other. Following the work of Chen et al. [6], hydration chemistry is considered to be important for the description of electrolyte solutions. Here, hydration is used to describe the effect of ions on the composition of the local neighborhoods of the NRTL formalism. The original Debye-Hückel expression is used to describe the long-range interactions of the unhydrated solution, which is consistent with the derivation of the Debye-Hückel theory, in which the solvent is described as a dielectric medium. Ionic hydration is used to explain the high values needed in the DH equation for the distance of closest approach, using an approximate equation for the volumetric effect of hydration on the ionic radii. In a semi-empirical way the structure of water and the effect of the nature of ions on it are modeled, by allowing the hydration numbers to receive negative values. The latter follows the experimental evidence discussed by Frank [7] and Samoilov [8]. As a second step, the constant hydration numbers of this approach are replaced by a stepwise hydration equilibria equation similar to what has been proposed in the literature [9-11], extending the applicability of the model to very concentrated solutions.

The refined model has been applied to an extensive database of electrolytes. For electrolytes of low and moderately hydrated ions a constant hydration index has been found to describe satisfactorily the activity and osmotic coefficients of aqueous electrolytes up to their solubility limit. For electrolytes composed of highly hydrated ions a model has been applied that makes use of the stepwise hydration equilibria theory of Stokes and Robinson [11] in a thermodynamically consistent way. It will be discussed that the additivity assumption for ionic hydration seems to break down for highly hydrated electrolytes at high concentrations. The models proposed in this presentation are very efficient and accurate in the description of electrolytes for their entire concentration range, up to their solubility limit, using a minimal number of adjustable parameters. For concentrated acidic and basic aqueous solutions, in which partial dissociation has to be taken into account, a chemistry model is used with considerable success.

References

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

2. Fowler RH, Guggenheim EA. Statistical thermodynamics. Univ. Press, 1952.

3. Pitzer KS. Electrolytes - from Dilute-Solutions to Fused-Salts. Journal of the American Chemical Society. 1980;102:2902-2906.

4. Blum L, Hoye JS. Mean Spherical Model for Asymmetric Electrolytes. 2. Thermodynamic Properties and Pair Correlation-Function. Journal of Physical Chemistry. 1977;81:1311-1317.

5. Simonin JP, Blum L, Turq P. Real ionic solutions in the mean spherical approximation. 1. Simple salts in the primitive model. Journal of Physical Chemistry. 1996;100:7704-7709.

6. Chen CC, Mathias PM, Orbey H. Use of hydration and dissociation chemistries with the electrolyte-NRTL model. AIChE Journal. 1999;45:1576-1586.

7. Frank HS. Ion-solvent interaction. Structural aspects of ion-solvent interaction in aqueous solutions: a suggested picture of water structure. Discussions of the Faraday Society. 1957;24:133-140.

8. Samoilov OY. A new approach to the study of hydration of ions in aqueous solutions. Discussions of the Faraday Society. 1957;24:141-146.

9. Schönert H. The Thermodynamic Model of Stepwise Hydration of Hydrophilic Solutes in Aqueous-Solutions. 1. General-Considerations. Zeitschrift Fur Physikalische Chemie Neue Folge. 1986;150:163-179.

10. Simonin JP, Bernard O, Krebs S, Kunz W. Modelling of the thermodynamic properties of ionic solutions using a stepwise solvation-equilibrium model. Fluid Phase Equilibria. 2006;242:176-188.

11. Stokes RH, Robinson RA. Solvation equilibria in very concentrated electrolyte solutions. Journal of Solution Chemistry. 1973;2:173-191.