Parameters Pitzer ionic

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) ... 

About the same time Beutier and Renon (11) also proposed a similar model for the representation of the equilibria in aqueous solutions of weak electrolytes. The vapor was assumed to be an ideal gas and < >a was set equal to unity. Pitzer s method was used for the estimation of the activity coefficients, but, in contrast to Edwards et al. (j)), two ternary parameters in the activity coefficient expression were employed. These were obtained from data on the two-solute systems It was found that the equilibria in the systems NH3+ H2S+H20, NH3+C02+H20 and NH3+S02+H20 could be represented very well up to high concentrations of the ionic species. However, the model was unreliable at high concentrations of undissociated ammonia. Edwards et al. (1 2) have recently proposed a new expression for the representation of the activity coefficients in the NH3+H20 system, over the complete concentration range from pure water to pure NH3. it appears that this area will assume increasing importance and that one must be able to represent activity coefficients in the region of high concentrations of molecular species as well as in dilute solutions. Cruz and Renon (13) have proposed an expression which combines the equations for electrolytes with the non-random two-liquid (NRTL) model for non-electrolytes in order to represent the complete composition range. In a later publication, Cruz and Renon (J4J, this model was applied to the acetic acid-water system. 

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 ... 

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. 

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)... 

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. 

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). 

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]. 

In our earlier work (28.61 we demonstrated how Pitzer parameters can be generated from pK% measurements in various ionic media. Recently we have extended these calculations to higher ionic strengths from 0 to 50°C (2). 

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. 

Reactive absorption processes occur mostly in aqueous systems, with both molecular and electrolyte species. These systems demonstrate substantially non-ideal behavior. The electrolyte components represent reaction products of absorbed gases or dissociation products of dissolved salts. There are two basic models applied for the description of electrolyte-containing mixtures, namely the Electrolyte NRTL model and the Pitzer model. The Electrolyte NRTL model [37-39] is able to estimate the activity coefficients for both ionic and molecular species in aqueous and mixed solvent electrolyte systems based on the binary pair parameters. The model reduces to the well-known NRTL model when electrolyte concentrations in the liquid phase approach zero [40]. 

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). 

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. 

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. 

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. 

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. 

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... 

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