Pitzer parameter

Coefficients in Electrolyte Solutions, vol. 1, Ricardo M. Pytkowicz, ed., CRC Press, Boca Raton, Fla. (1979) 

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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. 

In this work the temperature dependencies of Pitzer parameters and equilibrium constants were largely determined from isothermal data sets that were then fit to the following equation ... 

So there is an underlying basis related to the standard enthalpy of reaction (or heat capacities, Eq. 2.26) for the equation form used in this work to characterize the temperature dependence of equilibrium constants and Pitzer parameters (cf. Eqs. 2.70 and 2.73). 

Note that the equations for estimating the pressure dependencies of 7 and aw (Eqs. 2.87 and 2.90) depend on the Pitzer equations (Eqs. 2.76, 2.80, and 2.81) but this is not the case for the pressure dependence of the equilibrium constants (Eq. 2.29) the latter equation is based entirely on partial molar volumes at infinite dilution, which are independent of concentration. Also, compared to the pressure-dependent equation for the equilibrium constant (Eq. 2.29), the pressure equations for activity coefficients (Eq. 2.87) and the activity of water (Eq. 2.90) do not contain compressibilities (K) because the database for these terms and the associated Pitzer parameters are lacking at present (Krumgalz et al. 1999). The consequences of truncating Eqs. 2.80 and 2.81 for ternary terms and Eqs. 2.87 and 2.90 for compressibilities will be discussed in Sect. 3.6 under limitations. 

Equations 2.87 (activity coefficient), 2.88 (density), and 2.90 (activity of water) are all indirectly dependent on the temperature and pressure dependence of B v, B v, BC2), and Cv (Eqs. 2.76, 2.80, and 2.81). Table B.10 (Appendix B) lists the temperature dependence of these volumetric Pitzer parameters. The pressure dependence of these parameters were evaluated with the density equation (Eq. 2.88). All three terms in the denominator of Eq. 2.88 are temperature and pressure dependent. The density of pure water (p°) as a function of temperature and pressure is evaluated with Eqs. 3.14-3.16 and 3.20. Similarly, the molar volume of ions as a function of temperature and pressure is calculated by... 

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 Pitzer parameters have been fitted as a function of temperature to the following equations... 

Further details for the method used for determining the Pitzer parameters are given by Pitzer (591. Millero (28311. Harvie and co-workers (30.60). 

In Equation 16, the Pitzer parameter 0 is truly independent of the common ion, and is equal to V2 (bAjB0,1) in the Scatchard treatment, or gM,x according to Friedman. Also, the Pitzer and Scatchard equations for uni-univalent, three-ion systems are of comparable forms, with bA,B0 2 =... 

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. 

G The ion interaction coefficient s(An, CP) for An = Am and Cm is assumed to equal to s(Nd , CP) which is calculated from trace activity coefficients of Nd ion in 0 to 4 m NaCl. These trace activity coefficients are based on the ion interaction Pitzer parameters evaluated in [97KON/FAN] from osmotic coefficients in aqueous NdCP-NaCl and NdCfr-CaCfr. 

Throughout the present review the SIT is used for ionic strength corrections. However, numerous computer codes for geochemical model calculations, in particular for calculations in concentrated chloride solutions, are based on the ion interaction equations of Pitzer [1991PIT]. Pitzer parameters reported in the literature to calculate activity coefficients for the Th" ion in chloride solutions are briefly discussed and summarised in Table VI-2. 

Figure VI-5 Trace activity coefficients of in NaCl solution at 25°C, calculated with the SIT coefficient 8(Th", Cr) = (0.25 + 0.03) kg-mol [1980CIA], [1992GRE/FUG] (A) and with the different sets of the Pitzer parameters reported by Pitzer and Mayorga [1973PIT/MAY] (B) and by Roy et al. [1992ROYA OG] and Rai et al. [1997RAI/FEL] (C).

As Th(IV) hydroxide complexes are not included in the models proposed in [1991FEL/RAI] and [1997RAI/FEL], the solubility and hydrolysis constants selected in this review must not be combined with the Pitzer parameters used by Rai et al. [1997RAI/FEL] for the Th" ion and vice versa -the solubihty constants given in [1997RAI/FEL], [2000RAI/MOO] must not be combined with the SIT coefficients and hydolysis constants evaluated in the present review. 

Table A-68 Ion interaction (Pitzer) parameters given in [1992FEL/RA1],...

It should be noted that the model of Felmy et al. is neither consistent with the complexes and equilibrium constants selected in the present review nor with the speci-ation calculated with the SIT approach. Therefore the equilibrium constants selected in the present review must not be used in combination with the Pitzer parameters of Felmy etal. [1997FEL/RAI], [1999FEL/RAI]. 

Neck, V., Fanghanel, T., Rudolph, G., Kim, J. I., Thermodynamics of neptunium(V) in concentrated salt solutions Chloride complexation and ion interaction (Pitzer) parameters for the Np02 ion, Radiochim. Acta, 69, (1995), 39-47. Cited on page 104. 

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