Pitzer Based Method

Theoretical relationships for activity coefficients. The Setschenow equation is used to calculate the activity coefficients of aqueous molecular species in salt solutions. The Pitzer based methods may be used for binary or multicomponent solution activity coefflcient calculations for all species in the solution. 

Edifsrds. Maurer. Newman and Prausnitz Pitzer Based Method... 

This work was supported in part by the National Science Foundation under Grant Nos. CHE-8214689 and CHE-8214665 and also by the Research Corporation. We gratefully acknowledge our collaborators, Professor Kenneth S. Pitzer and Professor Yoon S. Lee, who were intimately involved in the development of the formalism and methods presented herein. In addition, Professor K. Balasubramanian has applied the REP-based method to a wide variety of molecular systems containing heavy atoms and has kindly kept us informed of the progress of his studies. 

Based on the cluster integral method [27], Pitzer [19] divided the difference terms 0mn into two parts... 

The LCM is a semi-theoretical model with a minimum number of adjustable parameters and is based on the Non-Random Two Liquid (NRTL) model for nonelectrolytes (20). The LCM does not have the inherent drawbacks of virial-expansion type equations as the modified Pitzer, and it proved to be more accurate than the Bromley method. Some advantages of the LCM are that the binary parameters are well defined, have weak temperature dependence, and can be regressed from various thermodynamic data sources. Additionally, the LCM does not require ion-pair equilibria to correct for activity coefficient prediction at higher ionic strengths. Thus, the LCM avoids defining, and ultimately solving, ion-pair activity coefficients and equilibrium expressions necessary in the Davies technique. Overall, the LCM appears to be the most suitable activity coefficient technique for aqueous solutions used in FGD hence, a data base and methods to use the LCM were developed. 

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... 

The field of relativistic quantum chemistry has been reviewed by Pitzer (1.) and by Pyykko (Z ). The results presented here are based on the relativistic Hartree-Fock-Slater method due to Snijders and Baerends (A), augmented in some cases by the recently proposed density functional method by Becke ( ). Our analysis will build on previous studies ( ) due to Ziegler,Snijders and Baerends. 

It would be difficult to find more comprehensive or more detailed studies on the physical chemistry of seawater than those done at the University of Miami (Millero, 2001). Several programs were developed for calculation of activity coefficients and speciation of both major ions and trace elements in seawater. The activity coefficient models have been influenced strongly by the Pitzer method but are best described as hybrid because of the need to use ion-pair formation constants (Millero and Schreiber, 1982). The current model is based on Quick Basic computes activity coefficients for 12 major cations and anions, 7 neutral solutes, and more than 36 minor or trace ions. At 25 °C the ionic strength range is 0-6 m. For major components, the temperature range has been extended to 0-50 °C, and in many cases the temperature dependence is reasonably estimated to 75 °C. Details of the model and the parameters and their sources can be found in Millero and Roy (1997) and Millero and Pierrot (1998). Comparison of some individual-ion activity coefficients and some speciation for seawater computed with the Miami model is shown in Section 5.02.8.6 on model reliability. 

Plans also include means to estimate and develop predictive schemes to obtain data where no measurements have been made and to develop methods to handle the properties of mixtures based on the Pitzer equations, particularly for the activity coefficients. 

This leads one to the question of methods to estimate Pitzer-equation parameters for binary ion pairs. The parameters to be estimated, 3 ) and 3, depend upon short-range interactions and are not independent of each other, following generally parallel trends Cl (The 3 ) term describes additional attractive interactions unique to 2-2 and higher electrolytes at low concentrations and has only a small constant effect at concentrations above 0.1 M). Thus, if one estimates 3 °), one can obtainCil) 3 ) from 3(0) 3 ) ratios for similar ion-pairs, or from plots of 3 vs. g(l) presented by Pitzer and MayorgaQ., or from an empirical equationQA) based upon those plots. 

The individual-ion activity coefficients for the free ions were based on the Macinnis (18) convention, which defines the activity of Cl to be equal to the mean activity coefficient of KCl in a KCl solution of equivalent ionic strength. From this starting point, individual-ion activity coefficients for the free ions of other elements were derived from single-salt solutions. The method of Millero and Schreiber (14) was used to calculate the individual-ion, activity-coefficient parameters (Equation 5) from the parameters given by Pitzer (19). However, several different sets of salts could be used to derive the individual-ion activity coefficient for a free ion. For example, the individual-ion activity coefficient for OH could be calculated using mean activity-coefficient data for KOH and KCl, or from CsOH, CsCl, and KCl, and so forth. 

Table 3.2 presents a selection of the most used thermodynamic options for phase equilibrium with suitable enthalpy and entropy methods. The accuracy of both phase equilibrium and enthalpy/entropy computation must be examined when using EOS models. For example, often a cubic EOS underestimates the enthalpy of vaporisation. In this case other methods are more accurate, as those based on three-parameters corresponding states law (Lee-Kesler, Curl-Pitzer, etc.). Mixtures rich in components with particular behaviour, as or CH, need special methods for accurate simulation. When binary interaction parameters for liquid activity models are absent, the UNI FAC predictive method may be employed. It is worth to note that UNIFAC is suitable only for exploratory purposes, but not for final design. When high non-ideal mixtures are involved at higher pressure then the combination of EOS with liquid activity models is recommended (see Chapter 6). 

A useful empirical correlation for the second virial coefficient is based on the Pitzer method. In this method, the dimensionless ratio, BPc/RT, is expressed in the form... 

Alekseyev et al. [9] have also developed code based on the SOCI method according to Pitzer and Winter [10] for which calculations of up to 1,000,000 double-group symmetry-adapted configurations have been reported. These authors concluded that the SOCI method is capable of accurate predictions of structures and spectra of heavy-element-containing molecules. 

Ab initio methods for lanthanide and actinide molecules are mostly based on the effective core potential (ECP) method, especially if the molecules in question have several heavy atoms. The philosophy of the ECP method is to replace the chemically unimportant core electrons by an effective core potential and treat the remaining valence electrons explicitly. There are several techniques to derive RECPs which we now briefly describe and refer to the reviews by Christiansen et al. (1985), Krauss and Stevens (1984), Balasubramanian and Pitzer (1987) for further details. 

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