Pitzer model parameters

Equilibrium constants calculated from the composition of saturated solutions are dependent on the accuracy of the thermodynamic model for the aqueous solution. The thermodynamics of single salt solutions of KC1 or KBr are very well known and have been modeled using the virial approach of Pitzer (13-15). The thermodynamics of aqueous mixtures of KC1 and KBr have also been well studied (16-17) and may be reliably modeled using the Pitzer equations. The Pitzer equations used here to calculate the solid phase equilibrium constants from the compositions of saturated aqueous solutions are given elsewhere (13-15, 18, 19). The Pitzer model parameters applicable to KCl-KBr-l O solutions are summarized in Table II. 

Table I. Pitzer Model Parameters for the HNO3, MSA and the Hydrohalic Acids, Valid to 6 mol kg ...

Pitzer s Model Parameters for Aqueous NajSiOj Solutions... 

Osmotic coefficient data measured by Park (Park and Englezos, 1998 Park, 1999) are used for the estimation of the model parameters. There are 16 osmotic coefficient data available for the Na2Si03 aqueous solution. The data are given in Table 15.1. Based on these measurements the following parameters in Pitzer s... 

Using the model parameters of Table II the calculated osmotic coefficient is within 0.15% or better for all solutions investigated. Agreement with the experimental results (17) is within 0.02% or better if ( ci.Br.K = 0.0003 (Table III) instead of zero (Table II). We may conclude from this comparison that the thermodynamic model of Pitzer (Table II) is very realistic. An uncertainty of 0.0003 in i(ic Br K leads to uncertainties of less than 0.4% in log K(x). The largest uncertainty in equilibrium constants may thus be attributed to the original analytical data (j3). 

The species concentrations are formulated in activities using the Pitzer model (207) for the aqueous phase and the Hildebrand-Scott solubility parameter (208) for the organic phase. 

The only compounds in Table 3.2 that do not form solid phases within our model are Mg(NOs)2 and Ca(NOs)2. On Earth, common nitrate salts such an NaNC>3 and KNO3 typically form in arid, alkaline environments. Under these environmental conditions, Mg and Ca concentrations are low because of the insolubility of their respective carbonate minerals. Mg(N03)2 and Ca(N03)2 Pitzer-equation parameters were added to the model to account for trace concentrations of Mg and Ca in such nitrate environments. It would be a serious misuse of the model to calculate solution properties in systems where Mg(NC>3)2 and Ca(N03)2 are present at high concentrations. 

Table B.l lists all the chemical reactions and their temperature dependence. Table B.2 lists the Debye-Hiickel constants A,p and Av) as a function of temperature and pressure. Table B.3 lists the numerical arrays used for calculating unsymmetrical interactions (Equations 2.62 and 2.66). Table B.4 lists binary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.5 lists ternary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.6 lists binary and ternary Pitzer-equation parameters for soluble gases as a function of temperature. Table B.7 lists equations used to estimate the molar volume of liquid water and water ice as a function of temperature at 1.01 bar pressure and their compressibilities. Table B.8 lists equations for the molar volume and the compressibilities of soluble ions and gases as a function of temperature. Table B.9 lists the molar volumes of solid phases. Table B.10 lists volumetric Pitzer-equation parameters for ion interactions as a function of temperature. Table B.ll lists pressure-dependent coefficients for volumetric Pitzer-equation parameters. Table B.12 lists parameters used to estimate gas fugacities using the Duan et al. (1992b) model.

Table B.4. Binary Pitzer-equation parameters for cations and anions used in the FREZCHEM model.a (Numbers are in computer scientific notation, where e xx stands for 10 xx)... 

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 Pitzer model requires so-called interaction parameters involving the aqueous species of interest and major species in the water. Such parameters have been measured for major ions, but are often unavailable for trace species, including strong complexes. Sometimes the missing parameters can be reasonably assumed to be equal to those for similar species, however (cf. Langmuir and Melchior 1985). 

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. 

The strongest interactions in an electrolyte solution occur between ions of opposite sign. Within the Pitzer model these are accounted for by the B a and Cca functions, which are known for most solutes. The mixing parameters By and /yk, while having relatively small effect in dilute solutions such as seawater, are important in the much more concentrated mixtures typical of the atmospheric aerosol. Further examples of the effects of individual ions on partial pressures can be seen in partial pressure measurements, e.g. (6.50L... 

The Pitzer treatment of the aqueous model is based largely on the equations and data as presented by (8-9). A data base of Pitzer interaction parameters is provided that is identical to the data base of (9) at 25 °C for the system Na-K-Mg-Ca-H-Cl-S04-0H-HC03-C0q-C02 H20. This data base has been partially validated (8-9) using previously published laboratory solubility measurements for evaporite minerals in water... 

Extensions beyond the data base of (2) are largely untested and include additions to PITZER.DATA for (1) the calculation of the thermodynamic properties of aqueous solutions containing Fe(II), Mn(II), Sr +, Ba2+, Li+, and Br (2) the estimation of the temperature dependence of many of the single-salt parameters from selected literature data and (3) the calculation of the thermodynamic properties of NaCl solutions to approximately 300 °C along the vapor pressure curve of water beyond 100 C (18)-Except for the NaCl-H20 system, the PHRQPITZ aqueous model should not be used outside the temperature range 0 to 60 C. Several recent evaluations of the temperature dependence of Pitzer interaction parameters to relatively high temperatures (19-21) have not yet been incorporated in the PHRQPITZ data base. 

Table 15.3 Calculated Pitzer s Model Parameters for Na iOi and Na iOs-NaOH Systems...

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