Pitzer ionic interaction parameters

Q Combination of PITZER binary ionic interaction parameter q = g(0)/(g(0)+ gO))... 

S sum of PITZER binary ionic interaction parameters Q=8V +p T temperature (K)... 

In applying this equation to multi-solute systems, the ionic concentrations are of sufficient magnitude that molecule-ion and ion-ion interactions must be considered. Edwards et al. (6) used a method proposed by Bromley (J7) for the estimation of the B parameters. The model was found to be useful for the calculation of multi-solute equilibria in the NH3+H5S+H2O and NH3+CO2+H2O systems. However, because of the assumptions regarding the activity of the water and the use of only two-body interaction parameters, the model is suitable only up to molecular concentrations of about 2 molal. As well the temperature was restricted to the range 0° to 100 oc because of the equations used for the Henry1s constants and the dissociation constants. In a later study, Edwards et al. (8) extended the correlation to higher concentrations (up to 10 - 20 molal) and higher temperatures (0° to 170 °C). In this work the activity coefficients of the electrolytes were calculated from an expression due to Pitzer (9) ... 

A is a Debye-Hiickel parameter (cf. Appendix II) and I is the ionic strength. Pitzer found that binary interaction parameter Xdepends on ionic strength and may conveniently be expressed as ... 

An important series of papers by Professor Pitzer and colleagues (26, 27, 28, 29), beginning in 1912, has laid the ground work for what appears to be the "most comprehensive and theoretically founded treatment to date. This treatment is based on the ion interaction model using the Debye-Huckel ion distribution and establishes the concept that the effect of short range forces, that is the second virial coefficient, should also depend on the ionic strength. Interaction parameters for a large number of electrolytes have been determined. 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

Because of the high ionic strength of the brines, the calculations were carried out using a Pitzer ion interaction model (US DOE, 1996) for the activity coefficients of the aqueous species (Pitzer, 1987, 2000). Pitzer parameters for the dominant non-radioactive species present in WIPP brines are summarized in Harvie and Weare (1980), Harvie et al. (1984), Felmy and Weare (1986), and Pitzer (1987, 2000). For the actinide species, the Pitzer parameters that were used are summarized in the WIPP Compliance Certification Application (CCA) (US DOE, 1996). Actinide interactions with the inorganic ions H, Na, K, Mg, CU, and HCO /COa were considered. 

DH-type, low ionic-strength term. Because the DH-type term lacks an ion size parameter, the Pitzer model is also less accurate than the extended DH equation in dilute solutions. However, a.ssuming the necessary interaction parameters (virial coefficients) have been measured in concentrated salt solutions, the model can accurately model ion activity coefficients and thus mineral solubilities in the most concentrated of brines. 

Alternatively, water activities can be taken from Table B-1. These have been calculated for the most common ionic media at various concentrations applying Pitzer s ion interaction approach and the interaction parameters given in [91 PIT]. Data in italics have been calculated for concentrations beyond the validity of the parameter set applied. These data are therefore extrapolations and should be used with care. 

Water activities for the most common ionic media at various concentrations applying Pitzer s ion interaction approach and the interaction parameters given in [91 PIT].362... 

These two models present the two main approaches to modeling solutions, which have been in evidence since the beginning, as discussed on page 304. Pitzer stands back, as it were, from the details of ionic interactions, and builds up an empirical model of complex solutions from data on the simpler binary systems of which they are composed. All aspects of ionic interaction are buried in the magnitudes of the parameters. This empirical model works very well at predicting the macroscopic properties of complex solutions, apparently because the form of the equations he has chosen to use suits the problem very well. 

Bromley was led to believe that the Interaction parameters are linear in ionic strength, particularly at low molalities, after viewing Figure 22-8 in the Pitzer and Brewer revision of Thermodynamics (B2). Consequently, he presented a method for calculating activity coefficients that takes this dependence into account (B3). He found that the best correlation to experimental data for strong electrolytes was ... 

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. 

In equations (15), (16) and (17), y is an adjustable parameter for each pair of anions or cations for each cation-cation and anion-anion pair, called triplet-ion-interaction parameter. The functions, 0 and 0 are fxmctions only of ionic strength and the electrolyte p>air type. Pitzer (1975) derived equations for calculating these effects, and Harvie and Weare (1981) summarized Pitzer s equations in a convenient form as following ... 

The ion-ion electrostatic interaction contribution is kept as proposed by PITZER. BEUTIER estimates the ion - undissociated molecules interactions from BORN - DEBYE - MAC. AULAY electric work contribution, he correlates 8 and 8 parameters in PITZER S treatment with ionic standard entropies following BROMLEY S (9) approach and finally he fits a very limited (one or two) number of ternary parameters on ternary vapor-liquid equilibrium data. 

Table II summarizes the existing studies of ionic criticality and lists the critical parameters. In the following, we will focus on results for immis-cibilities which seem to be primarily driven by Coulombic interactions, as exemplified by Pitzer s system n-hexyl-triethylammonium n-hexyl-triethyl-borate (HexEt3N+HexEt3B ) + diphenylether [35], solutions of Bu4NPic in alcohols [87], and solutions of Na in NH3 [46],...

A careful investigation of the picrate systems yields a substantial diameter anomaly [87] observed with all reasonable choices of the order parameter (see, however, somewhat contradicting results in Ref. 89). The data are consistent with the predicted (1 — a) anomaly. Large diameter anomalies are expected, when the intermolecular interactions depend on the density, as expected in these cases The dilute phase is essentially nonconducting and mainly composed of neutral ion pairs, while the concentrated phase is a highly conducting ionic melt [68]. However, any general conclusion is weakened by the fact that with Pitzer s system no such anomaly was observed [96]. 

The knowledge of both thermodynamic constants at zero ionic strength and of the specific interaction coefficients will allow the speciation diagram of the element in the considered medium to be established. At higher electrolyte concentrations, more sophisticated theories (Pitzer, MSA,. .. [29,31]) have been developed. However, they involve a larger number of characteristic parameters, which unfortunately are unknown for the majority of chemical elements. 

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