The electrolyte NRTL model [1] has been extensively applied to represent thermodynamic properties of various electrolyte systems. Examples include mean ionic activity coefficients of aqueous strong electrolytes [1, 2] and aqueous organic electrolytes [3], phase behavior of weak electrolytes [1], strong acids [4], mixed-solvent electrolytes [5] and so forth. The main reasons of its wide acceptance and application are the incorporation of semi-fundamental chemical theories such as the NRTL model for the simulation of local neighborhoods in a solution, its applicability to a large variety of systems without any restrictions on the number of electrolytes and solvents or on the molality range, its ability to predict the effect of temperature on the solution behavior and its algebraic simplicity. The electrolyte NRTL model provides a solid thermodynamic framework for computing various electrolyte thermodynamic properties, including mean ionic activity coefficients, osmotic coefficients, and solute and solvent fugacities. The rigorous and accurate computation of electrolyte thermodynamic properties forms a sound foundation for phase equilibrium calculations (that is, vapor-liquid equilibrium, liquid-liquid equilibrium and salt solubilities) and for the simulation of chemical processes involving electrolytes.

Nowadays, with the advent of novel electrolyte processes such as thermochemical cycles for hydrogen production, the demand for accurate electrolyte models is higher than ever. Specifically, models are needed for the description of electrolyte systems at extremely high temperatures and concentrations, while the prediction of speciation has become more important. The electrolyte NRTL has been able to address these new challenges broadly [6] and is expected to be a useful tool in the analysis of these cycles. In view of these challenges it becomes important to examine the accuracy of the model and its assumptions when applied to multi-electrolyte, mixed-solvent systems. Furthermore, the effects of hydration and complex formation, which play an important role in the predictive accuracy of local composition models, such as the electrolyte NRTL, have to be comprehensively studied and appropriately incorporated in the model. Hydration chemistry, and its incorporation into the Gibbs free energy function and into the derived activity coefficients, has been demonstrated years ago [7, 8]. Typically in these studies, hydration of the proton is considered and an average-constant hydration number is usually assumed. In more recent studies [9] hydration equilibria were studied and a new remarkably simple equation was proposed to represent the relation of hydration with water activity. It is generally accepted that the inclusion of hydration equilibria will increase both the accuracy and the fundamental nature of electrolyte models.

In the electrolyte NRTL model the existence of different ions of the same charge sign is modeled with the use of mixing rules for the reference states and the interaction parameters. The effect of these mixing rules is not always evident, because ultimately the model is fitted against experimental data. But, when the accurate prediction of detailed speciation is important, these mixing rules become of higher significance. In this work, a new version of the electrolyte NRTL is developed, in which different and more consistent assumptions are used for the mixing rules of the reference states and the interaction parameters. Moreover, the effect of hydration equilibria on the predictive accuracy of the model is examined. The results are in agreement with previous work [2] for low molalities, where an average hydration number of 3 was found to represent many electrolyte systems accurately, but the decline of the hydration number with increasing molality, because of the decrease in water activity, is shown to be important.  This study has resulted in a new versatile model, in which the mixing rules are consistent and the hydration number can be considered constant, or the recently proposed hydration equilibrium methods can be used.  

As a demonstration of this new model, results for the aqueous solution of sulfuric acid will be presented. The aqueous sulfuric acid, even at ambient conditions, poses great challenges for the existing electrolyte models. Reasons include the partial dissociation of the bisulfate ion, the hydronium and bisulfate complex formation, the different extents of proton hydration (with respect to the initial H₂SO₄ molality) and the partial dissociation of the sulfuric acid at high concentrations (because of the elimination of free water). Attempts to model the sulfuric acid system have led to accurate representations of the system [10-13], but in many cases are deficient in the prediction of speciation. Considering the complexity of the aqueous sulfuric acid system and the large number of proton hydrates that can exist in this solution [14], it is indeed an intriguing problem to predict the speciation. At low molalities, hydration can be neglected or considered of constant extent, but with increasing molality the decreasing extent of hydration can be the dominating factor in the accuracy of model predictions. Furthermore, the sulfuric acid water mixture (although a binary system) is in fact a multi-electrolyte (because of the coexistence of the bisulfate and sulfate anions) and mixed-solvent (because of the formation of complexes and the partial dissociation of the sulfuric acid at high concentrations) system.

In conclusion the combination of a representative chemistry model and thermodynamically consistent mixing rules with the virtues of the electrolyte NRTL leads to a very accurate representation of the sulfuric acid system. Furthermore, the proposed representation possesses better extrapolation capabilities for the case of high temperatures and concentrations.

References

1.         Chen, C. C. & Evans, L. B. (1986) A Local Composition Model for the Excess Gibbs Energy of Aqueous-Electrolyte Systems. AIChE Journal, 32, 444-454.
2.         Chen, C. C., Mathias, P. M. & Orbey, H. (1999) Use of hydration and dissociation chemistries with the electrolyte-NRTL model. AIChE Journal, 45, 1576-1586.
3.         Chen, C. C., Bokis, C. P. & Mathias, P. (2001) Segment-based excess Gibbs energy model for aqueous organic electrolytes. AIChE Journal, 47, 2593-2602.
4.         Chen, C. C. (1987) Some Recent Developments in Process Simulation for Reactive Chemical-Systems. Pure and Applied Chemistry, 59, 1177-1188.
5.         Mock, B., Evans, L. B. & Chen, C. C. (1986) Thermodynamic Representation of Phase-Equilibria of Mixed-Solvent Electrolyte Systems. AIChE Journal, 32, 1655-1664.
6.         Mathias, P. M. (2005) Applied thermodynamics in chemical technology: current practice and future challenges. Fluid Phase Equilibria, 228, 49-57.
7.         Conway, B. E. (1981) Ionic hydration in chemistry and biophysics, Amsterdam, Elsevier Scientific Pub. Co.
8.         Robinson, R. A. & Stokes, R. H. (1959) Electrolyte Solutions, London, Butterworth.
9.         Simonin, J. P., Bernard, O., Krebs, S. & Kunz, W. (2006) Modelling of the thermodynamic properties of ionic solutions using a stepwise solvation-equilibrium model. Fluid Phase Equilibria, 242, 176-188.
10.       Cherif, M., Mgaidi, A., Ammar, M. N., Abderrabba, M. & Furst, W. (2002) Representation of VLE and liquid phase composition with an electrolyte model: application to H3PO4-H2O and H2SO4-H2O. Fluid Phase Equilibria, 194, 729-738.
11.       Clegg, S. L. & Brimblecombe, P. (1995) Application of a Multicomponent Thermodynamic Model to Activities and Thermal-Properties of 0-40-Mol Kg(-1) Aqueous Sulfuric-Acid from Less-Than-200-K to 328-K. Journal of Chemical and Engineering Data, 40, 43-64.
12.       Clegg, S. L., Rard, J. A. & Pitzer, K. S. (1994) Thermodynamic Properties of 0-6 Mol Kg-1 Aqueous Sulfuric-Acid from 273.15 to 328.15-K. Journal of the Chemical Society-Faraday Transactions, 90, 1875-1894.
13.       Wang, P., Anderko, A., Springer, R. D. & Young, R. D. (2006) Modeling phase equilibria and speciation in mixed-solvent electrolyte systems: II. Liquid-liquid equilibria and properties of associating electrolyte solutions. Journal of Molecular Liquids, 125, 37-44.
14.       Walrafen, G. E., Yang, W. H. & Chu, Y. C. (2002) High-temperature Raman investigation of concentrated sulfuric acid mixtures: Measurement of H-bond Delta H values between H3O+ or H5O2+ and HSO4. Journal of Physical Chemistry A, 106, 10162-10173.