Pitzer Approach

The statistical thermodynamic approach of Pitzer (14), involving specific interaction terms on the basis of the kinetic core effect, has provided coefficients which are a function of the ionic strength. The coefficients, as the stoichiometric association constants in our ion-pairing model, are obtained empirically in simple solutions and are then used to predict the activity coefficients in complex solutions. The Pitzer approach uses, however, a first term akin to the Debye-Huckel one to represent nonspecific effects at all concentrations. This weakens somewhat its theoretical foundation. 

As most other methods, Including our 1on-pairing model which was described earlier, the Pitzer approach 1s empirical in practice. The interaction coefficients in this case are determined by curve fitting in single electrolyte solutions. 

One may sometimes have access to the parameters required for the Pitzer approaches, e.g., for some hydrolysis equilibria and for some solubility product data, cf. Baes and Mesmer [3] and Pitzer [4]. In this case, the reviewer should perform a calculation using both the B-G-S and the P-B equations and the full virial coefficient methods and compare the results. 

From Tables 6.3 and 6.4 it seems that the size and charge correlations can be extended to complex ions. This observation is very important because it indicates a possibility to estimate the ion interaction coefficients for complexes by using such correlations. It is, of course, always preferable to use experimental ion interaction coefficient data. However, the efforts needed to obtain these data for complexes will be so great that it is unlikely that they will be available for more than a few complex species. It is even less likely that one will have data for the Pitzer parameters for these species. Hence, the specific ion interaction approach may have a practical advantage over the inherently more precise Pitzer approach. 

Implementation of the Pitzer approach is through the FREZCHEM (FREEZING CHEMISTRY) model, which is at the core of this work. This model was originally designed to simulate salt chemistries and freezing processes at low temperatures (—54 to 25 °C) and 1 atm pressure. Over the years, this model has been broadened to include more chemistries (from 16... 

The chemical equilibrium model, FREZCHEM, requires calculation of solute activity coefficients (7) and the osmotic coefficient ((f)) in concentrated solutions (Chap. 3). In this work, the Pitzer approach is used to calculate these quantities. 

Calculating the osmotic coefficient and activity coefficients of an aqueous solution using the Pitzer approach requires knowing the cation-anion parameters, Bi°J, Bii, and Cca the cation-cation (or anion-anion) parameter, Qcc> (or 9aa>) and the triple particle parameter, important constituents of a solution. If neutral solutes are present at significant concentrations, then the neutral-cation (or neutral-anion) parameter, nc (or Xna), and the triple particle parameter, Cnca, are also needed. Fortunately, there have been many studies using the Pitzer approach in the past 30 years. As a consequence, many of the most important parameters and their temperature dependence have been determined (see, for example, Harvie et al. 1984 Pitzer 1991, 1995 Appendix B). 

While the mathematics of calculating the osmotic coefficient and activity coefficients are complicated (Eqs. 2.39 to 2.69), the great virtue of the Pitzer approach is that it allows one to calculate these quantities at high solute concentrations (/ > 5 m) (Pitzer 1991, 1995 Marion and Farren 1999 Marion 2001, 2002 Marion et al. 2003a,b Marion et al. 2005, 2006). This is particularly important in characterizing the freezing process, which can concentrate solutes rapidly once ice begins to form. 

To our knowledge, no one has ever worked out the mathematics for directly estimating the pressure dependence of the osmotic coefficient (or aw) using the Pitzer approach. However, Monnin (1990) developed an alternative model based on the Pitzer approach that allows calculation of the pressure dependence for the activity of water (aw). The density of an aqueous solution (p) can be calculated with the equation... 

There are five reactions that deal with ion associations (numbers 8 to 12 in Table 3.3). There are, of course, many more such associations in concentrated electrolyte solutions. But the Pitzer approach allows one to either explicitly identify an ion association (Table 3.3) or to implicitly include the interaction effect in the interaction coefficients (B, C, minor components of the aqueous phase. 

The FREZCHEM model was basically designed for estimating the aqueous properties of concentrated electrolyte solutions, which is why we used the Pitzer approach. Nevertheless, it is still necessary that these models accurately describe dilute solutions. The comparisons in Table 3.5 demonstrate that the FREZCHEM model is reasonably accurate for both dilute and concentrated electrolyte solutions. 

One of the inherent limitations of the Pitzer approach is the necessity that all significant interactions among ions and neutral species must be quantified. In appendix Tables B.4 to B.6, we quantify 291 binary and ternary interaction... 

These pseudopotentials are inconvenient because the resulting pseudoorbitals are eigenfunctions to different Hamiltonians. We developed a more suitable scheme [44], [45] based on the Christiansen-Lee-Pitzer approach [9]. Let us consider first the construction of pseudopotentials, then their use for molecular systems, and, finally, for simulating surfaces and bulk of solids. 

The Kesler-Lee correlations for liquid and vapour phase heat capacities of petroleum fluids are used for estimating the respective enthalpies at temperatures of interest. The Lee-Kesler corresponding-states method is used for obtaining estimates of the heats of vaporization and for developing the saturation envelope enthalpies. This method uses the Curl and Pitzer approach and calculates various thermodynamic properties by representing the compressibility factor of any fluid in terms of a simple fluid and a reference fluid as follows ... 

The thermodynamic data compiled in the present review (see Chapters III and IV and Appendix E) refer to the reference temperature of 298.15 K and to standard conditions, cf. Section II.3. For the modelling of real systems it is, in general, necessary to recalculate the standard thermodynamic data to non-standard state conditions. For aqueous species a procedure for the calculation of the activity factors is thus required. This review uses the approximate specific ion interaction method (SIT) for the extrapolation of experimental data to the standard state in the data evaluation process, and in some cases this requires the re-evaluation of original experimental values (solubilities, emf data, etc.). For maximum consistency, this method, as described in Appendix B, should always be used in conjunction with the selected data presented in this review. However, some solubility data for highly soluble selenates were evaluated in the original papers by the Pitzer approach. No attempt was made to re-evaluate these data by the SIT method. 

Ake Olin wants to thank Peter M. May, Murdoch University, for discussions, now and earlier, on the art of stability constant determinations in aqueous solution and for putting the selenium data in the JESS Thermodynamic Database at his disposal. His thanks also go to Christomir Christov, University of California at San Diego, for providing data prior to their publication and for generous information on the application of the Pitzer approach to these data. Help with the assessment of voltammetric work... 

Pitzer s equations can be used for mixtures of electrolyes. Thermodynamic functions are obtained in the usual way as the derivatives of the chemical potential with respect to temperature or pressure. However, a considerable number of empirically adjusted parameters is needed to obtain satisfactory data description. The Pitzer approach is used as a self-standing data-reduction method, but it is also embedded by engineers in the so-called NRTL (nonrandom two liquid) electfolyte models. 

Modern theories of solutions combine aspects of both approaches, and the theories of Pitzer and Helgeson et al. are no different in this respect. The Pitzer approach must take into account strong complex formation, and the HKF approach uses activity coefficients, based on generahzed electrostatic considerations, in addition to species information. 

Another way of summarizing the difference between the HKF and the Pitzer approaches to developing an EoS for solutes is that HKF equations are fit to experimental data after extrapolation to infinite dilution, whereas Pitzer equations are fit to the data themselves, extending to high concentrations. Therefore HKF equations are standard state, Pitzer equations are real life. The general topic of excess Gibbs functions for solutes is introduced in 10.4, but the details are discussed, along with the HKF equations, in Chapter 15. 

As to the ion-interaction model, it is a semiempirical statistical thermodynamics model. In this model, the Pitzer approach begins with a virial expansion of the excess free energy of the form to consider the three kinds of existed potential energies on the ion-interaction potential energy in solution. 

Nonelectrolyte G mcxlels only account for the short-range interaction among non-charged molecules (—One widely used G model is the Non-Random-Two-Liquid (NRTL) theory developed in 1968. To extend this to electrolyte solutions, it was combined with either the DH or the MSA theory to explicitly account for the Coulomb forces among the ions. Examples for electrolyte models are the electrolyte NRTL (eNRTL) [4] or the Pitzer model [5] which both include the Debye-Hiickel theory. Nasirzadeh et al. [6] used a MSA-NRTL model [7] (combination of NRTL with MSA) as well as an extended Pitzer model of Archer [8] which are excellent models for the description of activity coefficients in electrolyte solutions. Examples for electrolyte G models which were applied to solutions with more than one solvent or more than one solute are a modified Pitzer approach by Ye et al. [9] or the MSA-NRTL by Papaiconomou et al. [7]. However, both groups applied ternary mixture parameters to correlate activity coefficients. Salimi et al. [10] defined concentration-dependent and salt-dependent ion parameters which allows for correlations only but not for predictions or extrapolations. 

Runde, W., M.P. Neu, and D.L. Clark. 1996. Neptunium(V) hydrolysis and carbonate complexation Experimental and predicted neptunyl solubility in concentrated NaCl using the Pitzer Approach. Geochim. Cosmochim. Acta 60 2065-2073. 

Electromigration of carrier-free radionuclides. 5. Ion mobilities and hydrolysis of Np(V) in aqueous perchlorate solutions. Radiochim. Acta, 42, 43-46. Runde, W. and Kim, J.L (1994) Chemical Behaviour of Trivalent and Pentavalent Americium in Saline NaCl-Solutions. Studies of Transferability of Laboratory Data to Natural Conditions. Report RCM-01094, Technische Universitat Miinchen, 236 pp. Runde, W., Neu, M.P., and Clark, D.L. (1996) Neptunium(V) hydrolysis and carbonate complexation experimental and predicted neptunyl solubility in concentrated NaCl using Pitzer approach. Geochim. Cosmochim. Acta, 60, 2065-2073. 

Typical results with the Pitzer approach and the SRK EoS are presented in Table 9.1 and similar ones are obtained with the PR and vdW-711 EoS. For the latter t = tQ should be used to avoid the pronounced and distorting effect that dt/dT) has on enthalpy and entropy departure values close to the criticd point (Androulakis et al, 1989). 

At very high pressures the Pitzer approach should be preferred over the aforemention, and other, cubic EoS. 

---