Electrolyte solutions, thermodynamics Pitzer equations

In this appendix, we summarize the coefficients needed to calculate the thermodynamic properties for a number of solutes in an electrolyte solution from Pitzer s equations.3 Table A7.1 summarizes the Debye-Huckel parameters for water solutions as a function of temperature. They provide the leading terms for Pitzer s equations, and can also be used to calculate the Debye-Huckel limiting law values from the equations... 

Recently, there have been a number of significant developments in the modeling of electrolyte systems. Bromley (1), Meissner and Tester (2), Meissner and Kusik (2), Pitzer and co-workers (4, ,j5), and" Cruz and Renon (7j, presented models for calculating the mean ionic activity coefficients of many types of aqueous electrolytes. In addition, Edwards, et al. (8) proposed a thermodynamic framework to calculate equilibrium vapor-liquid compositions for aqueous solutions of one or more volatile weak electrolytes which involved activity coefficients of ionic species. Most recently, Beutier and Renon (9) and Edwards, et al.(10) used simplified forms of the Pitzer equation to represent ionic activity coefficients. 

However, in most aqueous electrolyte systems of industrial interest, not only strong electrolytes but also weak electrolytes and molecular nonelectrolytes are present. While the modified Pitzer equation appears to be a useful tool for the representation of aqueous strong electrolytes including mixed electrolytes, it cannot be used in the form just presented to represent the important case of systems containing molecular solutes. A unified thermodynamic model for both ionic solutes and molecular solutes is required to model these kinds of systems. 

The semi-empirical Pitzer equation for modeling equilibrium in aqueous electrolyte systems has been extended in a thermodynamically consistent manner to allow for molecular as well as ionic solutes. Under limiting conditions, the extended model reduces to the well-known Setschenow equation for the salting out effect of molecular solutes. To test the validity of the model, correlations of vapor-liquid equilibrium data were carried out for three systems the hydrochloric acid aqueous solution at 298.15°K and concentrations up to 18 molal the NH3-CO2 aqueous solution studied by van Krevelen, et al. 

Numerous studies on the thermodynamics of calcium chloride solutions were published in the 1980s. Many of these were oriented toward verifying and expanding the Pitzer equations for determination of activity coefficients and other parameters in electrolyte solutions of high ionic strength. A review article covering much of this work is available (7). Application of Pitzer equations to the modeling of brine density as a function of composition, temperature, and pressure has been successfully carried out (8). 

K. S. Pitzer and L. Brewer used equation (18.12) as the base for tabulating a summary of the thermodynamic properties of aqueous electrolyte solutions at 298.15 K. They wrote equation (18.12) in the form that involves base 10 logarithms... 

Pitzer s solution to the problem was the development of a set of analytical equations that are thermodynamically consistent after transformations through the Gibbs-Duhem equation. These equations are known as the Pitzer equations, in recognition of the major role that he played in developing them and the major contributions he made in the understanding of electrolyte solutions through a lifetime of work. We will now summarize these equations and describe their usefulness. For details of the derivation we refer the reader to Pitzer s original paper.6... 

K. S. Pitzer, Ion Interaction Approach Theory and Data Correlation , Chapter 3 of Activity Coefficients in Electrolyte Solutions, 2nd Edition, K. S. Pitzer, Editor, CRC Press, Boca Raton, 1991. Parameters for many electrolytes are summarized in this reference. The equations and parameters can also be found in K. S. Pitzer, Thermodynamics, Third Edition, McGraw-Hill, Inc., New York, 1995. 

Chapter 18 describes electrolyte solutions that are too concentrated for the Debye-Hiickel theory to apply. Gugenheim s equations are presented and the Pitzer and Brewer tabulations, as a method for obtaining the thermodynamic properties of electrolyte solutions, are described. Next, the complete set of Pitzer s equations from which all the thermodynamic properties can be calculated, are presented. This discussion ends with an example of the extension of Pitzer s equations to high temperatures and high pressures. Three-dimensional figures show the change in the thermo-... 

The three appendices in this volume give selected sets of thermodynamic data (Appendix 5), review the statistical calculations covered in Principles and Applications (Appendix 6), and summarize the equations and parameters required to calculate the properties of electrolyte solutions, principally from Pitzer s equations (Appendix 7). 

This work and others (5, 51) have shown how the Pitzer model, together with appropriate Henry s law constants, can be used to calculate the solubility of volatile strong electrolytes in multicomponent solutions. The treatment of NH3 summarized above shows that Pitzer formalism can also be used to describe the solubility of weak and non-electrolytes. We have noted how, for low concentrations of NH3, the Pitzer equations reduce to a series of binary interaction terms similar in form to those of the well known Setchenow equations. However, the thermodynamically based approach constitutes a significant improvement over the use of purely empirical equations to predict individual thermodynamic properties because it is equally applicable to both electrolytes and uncharged species, and provides a unified description of a number of important solution properties. 

Pitzer (1973) developed a semi-empirical equation (ion-interaction model) to reproduce accurately the volumetric properties of aqueous electrolyte solutions. This model has been used to calculate accurately other thermodynamic properties such as expansivity, compressibility, free energy, enthalpy, and heat capacity. The ion-interaction model... 

The derivative equations for osmotic and activity coefficients, which are presented below, were applied to the experimental data for wide variety of pure aqueous electrolytes at 25°C by Pitzer and Mayorga (23) and to mixtures by Pitzer and Kim (11). Later work (24-28) considered special groups of solutes and cases where an association equilibrium was present (H PO and SO ). While there was no attempt in these papers to include all solutes for which experimental data exist, nearly 300 pure electrolytes and 70 mixed systems were considered and the resulting parameters reported. This represents the most extensive survey of aqueous electrolyte thermodynamics, although it was not as thorough in some respects as the earlier evaluation of Robinson and Stokes (3). In some cases where data from several sources are of comparable accuracy, a new critical evaluation was made, but in other cases the tables of Robinson and Stokes were accepted. 

Pitzer KS (1973) Thermodynamics of electrolytes. I Theoretical basis and general equations.-Jour.of Physical Chemistry, 77 pp 268-277 Pitzer KS (1981) Chemistry and Geochemistry of Solutions at high T and P -In RICKARD WICKMANN, 295, V 13-14... 

Clegg, S.L. Pitzer, K.S. 1992, Thermodynamics of Multicomponent, Miscible, Ionic Solutions Generalized Equations for Symmetrical Electrolytes. J. Phys. Chem., 96,3513. 

The ionic interaction theories of Brrfnsted-Guggenheim (48) and Pitzer (49,50) have been conspicuously successful in accounting for the mean activity coefficients and other thermodynamic properties of electrolytes, singly and in mixtures of ionic solutes. They have proved especially useful in salt mixtures such as seawater (51,52). Unfortunately, specific parameters characteristic of single ions do not appear in the theory. For a single 1 1 electrolyte, the equations lead to equality of the activity coefficients of cation and anion, as in Equation 7. 

Clegg SL, Pitzer KS (1992) Thermodynamics of multicomponent, miscible, ionic solutions generalized equations for symmetrical electrolytes. J Phys Chem 96 3513-3520... 

Dolar D, Kozak D (1970) Osmotic coefficients of polyelectrolyte solutions with mono and divalent counterions. Proc Leiden Symp 11 363 366 Katchalsky A (1971) Polyelectrolytes. Pure Appl Chem 26 327 374 Pitzer KS (1973) Thermodynamics of electrolytes I. Theoretical basis and general equations. J Phys Chem 77 268 277... 

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