Pitzer equation extension

In this paper, two new models for the activity coefficients of ionic and molecular species in electrolyte systems are presented. The first is an extension of the Pitzer equation and is covered in more detail in Chen, et al. (11). 

Two activity coefficient models have been developed for vapor-liquid equilibrium of electrolyte systems. The first model is an extension of the Pitzer equation and is applicable to aqueous electrolyte systems containing any number of molecular and ionic solutes. The validity of the model has been shown by data correlation studies on three aqueous electrolyte systems of industrial interest. The second model is based on the local composition concept and is designed to be applicable to all kinds of electrolyte systems. Preliminary data correlation results on many binary and ternary electrolyte systems suggest the validity of the local composition model. 

Chen, C., H. I. Britt, J. F. Boston, and L. B. Evans, "Extension and Application of the Pitzer equation for Vapor-Liquid Equilibrium of Aqueous Electrolyte Systems with Molecular Solutes," AIChE J., 1979, 25, 820. 

The Pitzer-equation computations for Figures 3 and 4 are based upon experimentally derived 25°C ion-pair and interaction coefficients taken from the literature. From the extensive prior work validating the theory and parameters, these curves should deviate from experiment by less than 20%. However, as Figures 1-4 show, solubility calculations are very sensitive to variations in activity coefficients and the approximations made in eqs. (l)-(9) limit the accuracy of the solubility curves which can be calculated. When higher-order terms are included, Pitzer s equations accurately oredict solubility in the CaSO -MgSO system up to... 

P2. a. Chen, C-C H.I. Britt, J.F. Boston, L.B. Evans, "Extension and application of the Pitzer equation for vapor-liquid equilibrium of aqueous electrolyte systems with molecular solutes", AIChE J, v25, 5, pp820-831 (1979)... 

Pessoa Filho PA, Maurer G (2008) An extension of the Pitzer equation to aqueous polyelec trolyte solutions. Fluid Phase Equilibr 269 25 35... 

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. 

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 generalized correlations of Pitzer provide an alternative to the use of a cubic equation of state for the calculation of thermodynamic properties. However, no adequate general method is yet known for the extension of the Pitzer correlations based on the compressibility factor to mixtures. Nevertheless, Z, as given by... 

Models are often developed to explain certain kinds of data, ignoring other kinds that also might be pertinent. The initial development of Pitzer s equations (33.34) for activity coefficients in concentrated solutions was focused on explaining measurements of vapor pressure equilibrium and of electromotive force (emf). The data could be explained by assuming that the electrolytes examined were, at least in a formal sense, fully dissociated. Later work using these equations to explain solubility data required the formal adoption of a few ion pair species (30). Even so, no speciation/activity coefficient model based on Pitzer s equations is presently consistent with the picture of much more extensive ion-pairing based on other sources, such as Smith and Martell s (35) compilation of association constants. This compilation is a collective attempt to explain other kinds of data, such as electrical conductance, spectrophotometry, and acoustic absorption. 

Activity Coefficients of Aqueous Species. The original version of EQ3/6 followed Helgeson et al. (1) in using the "B-dot" equation to describe the activity coefficients of aqueous solutes and a recommended approximation for the activity of water. The "B-dot" equation represents a simple extension of the Debye-Huckel equation and is only useful in relatively dilute solutions (deviations from precise measurements can be seen at ionic strengths below 0.1 molal, and become severe above 1.0 m). Beginning with version 3245, EQ3/6 offers two alternatives, the Davies (40) equation and Pitzer s equations (21,24,20,29). 

The Chao-Seader method12 is an example of the use of multiple equations of state for the calculation of K values. The Redlich-Kwong equation of state is used to compute the vapor-phase fugacity coefficient the Hildebrand equation for the calculation of the liquid-phase activity coefficient y/% and an extension of Pitzer s modified form of the principle of corresponding states for the calculation of the liquid-phase fugacity coefficient 4> ... 

Among a variety of extensions of the Guggenheim equation, those of Pitzer are the most successful ones. For a single electrolyte in solution they read... 

The first virial coefficient /(/) is some function of the ionic strength and is not 0 as it would be for an ideal solution, but is in fact a version of the Debye-Htickel equation, which represents departure from ideality in very dilute solutions. The following term is a function of the interactions of all pairs of ions, and the third term a function of the interactions of ions taken three at a time. The second coefficient. Ay, is a function of ionic strength, but the third coefficient ju-y - is considered to be independent of ionic strength and equals zero if /, j, and k are all anions or cations. Later extensions to the model published by Pitzer and co-workers allow for an ionic strength dependence to the third coefficient. Pitzer (1987) and Harvie and Weare (1980) note that higher virial coefficients are required only for extremely concentrated solutions, so the series is stopped at the third coefficient. 

The theoretical equations given by Setschinow and Pitzer can be evaluated based upon an extensive body of published data on a large number of binary and ternary systems involving weak electrolytes. The systems chosen for evaluation and illustration are ... 

This series of papers contains an extensive array of correlated data on aqueous electrolyte solutions, much of It having been calculated using the system of equations given In paper I In this series. The contents of these papers have been summarized by Pitzer In a chapter in the book edited by Pytkowicz (see Item [123]). The data Include activity and osmotic coefficients, relative apparent molar enthalpies and heat capacities, excess Gibbs energies, entropies, heat capacities, volumes, and some equilibrium constants and enthalpies. Systems of Interest Include both binary solutions and multi-component mixtures. While most of the data pertain to 25 °C, the papers on sodium chloride, calcium chloride, and sodium carbonate cover the data at the temperatures for which experiments have been performed. Also see Items [48], [104], and [124]. 

Ah initio relativistic effective core potentials can be derived from the relativi.stic all-electron Dirac-Fock solution of the atom the.se potentials are called the relativistic effective core potentials (RECP). and have been extensively used by several investigators to study the electronic structure of polyatomics containing very heavy atoms. The shape-consistent RECP method formulated by Christiansen, Lee, and Pitzer differs from the Phillips-Kleinman method in the representation of the nodeless pseudo-orbital in the inner region. The one-electron valence equation in an effective potential Vq of the core electrons can be expressed as... 

Note the differing equation for the ion interaction coefficients because of the 2 1 electrolyte. Also, for this electrolyte, the ionic strength / is three times the medium concentration. In Eq. (5.17), the expression for D needs to include the Pitzer extension as given in Eq. (5.25) ... 

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