Pitzer ion-interaction parameters

The second data file read by PHRQPITZ (PITZER.DATA) contains values of the Pitzer ion interaction parameters C, 6. A, including a limited amount of... 

Figure 1. Experimental and calculated solubiliti ofSr(OH) 8H20 in NaOK Patterned line represents calculations with Sr OH interactions described solely with the use ofPitzer s form of the extended Debye-HOckel equation. Solid line represents the calculations of our final thermodynamic model, which includes values for the Pitzer ion interaction parameters. Total concentrations in units of molarity. From (3).

This section presents, in Tables A-I and A-II, a conq>lete summary of the thermodynamic data for the Na-Sr-Ca-0H-C03-N03-EDTA-HEDTA-H20 system. The tenq>erature dependent parameters for the Pitzer ion-interaction parameters were fit to an equation of tiie foma,... 

Table A-I. Parameters for the Temperature Dependent Expression (Eq Al) for the Pitzer Ion-Interaction Parameters for the Na-Sr-Ca-OH-COa-NOs- EDTA-HEDTA-H2O System Continued on next page.

According to the equilibria constants and the Pitzer ion-interaction parameters, the solubilities of the quaternary system at 298.15 K have been calculated though the Newton s Iteration Method to solve the non-linearity simultaneous equations system, and shown in Table 9. 

K. S. Pitzer, Volumetric Ion Interaction Parameters for Single-Solute Aqueous Electrolyte Solutions at Various Temperatures, J. Phys. Chem. Ref. Data 2000, 29, 1123. 

K. S. Pitzer, Ion Interaction Approach Theory and Data Correlation , Chapter 3 of Activity Coefficients in Electrolyte Solutions, 2nd Edition, K. S. Pitzer, Editor, CRC Press, Boca Raton, 1991. Parameters for many electrolytes are summarized in this reference. The equations and parameters can also be found in K. S. Pitzer, Thermodynamics, Third Edition, McGraw-Hill, Inc., New York, 1995. 

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. 

Christov calculated the parameters in the Pitzer ion interaction model from isopiestie measurements at 298.15 K by Ojkova and Staneva [890JK/STA]. This reference contains (interpolated) osmotic coefficients of zinc, magnesium, cobalt, and nickel selenate solutions from 0.1 mol-kg to saturated solution. Sodium chloride standards were used and the agreement between duplicate determinations was 0.2% or better. 

The osmotic coefficients were used to find the parameters in the Pitzer ion interaction model. These parameters (see Table A-121) were then employed to find the activity coefficients in saturated solution. 

Terms B a, B ca Z, Cca, F, cc cc corresponding terms for anion pairs) are functions given in full by Pitzer (4) and others (1) and therefore not reproduced here. The B and C functions incorporate ion interaction parameters obtained from pure electrolyte data, (P ca. P ca p ca C ca)- Functions cc those for anions, contain parameters (0cc and 0aaO for interactions between ions of like sign and an unsymmetrical mixing term. The parameters Ycc a d Vcaa account for interactions between one ion of one sign, and two dissimilar ions of opposite sign. 

The same methods used to describe activity coefficients here can also be applied to other thermodynamic properties such as excess volumes, enthalpies, entropies, heat capacities, and so on by manipulating the defining equation (17.38) appropriately (see Pitzer, 1987). Experimental data useful in deriving the ion-interaction parameters of... 

The user can select different models (Pitzer, Davies, and SIT) for calculating the activity coefficients of aqueous solutions. All of the input data are user-defined. The code can be used just as a calculational tool where all of the inputs are defined and solution equilibria calculated, or as a tool to optimise values of chemical potentials for different species and/or ion-interaction parameters, based on best fits to given experimental data. Multiple data sets of a specific chemical system (e.g., solubility of a sohd phase) in different media can be evaluated simultaneously. 

Felmy et al, (18) investigated foe solubility of Pu(OH)3 under reducing conditions in deioni water and brine solution. They deriv a much lower solubility product (log K = -26.2) (see Table I) than foe value (log K = -19.6) reported in foe literature (iP). However, foe solubility in brines [I 6 2Uid I - 10] was found to be larger than foat in deionized (I = 0) waters. The solubility of Pu(OH)3 in brines was accurately predicted with foe Pitzer ion-interaction model using only foe parameters for binary interactions between Pu and Cl". 

As to any electrolyte, its thermodynamic prosperity varied from weak solution to high concentration could be calculated through 3 or 4 Pitzer parameters. Pitzer ion-interaction model and its extended HW model of aqueous electrolyte solution can be briefly introduced in the following (Pitzer, 1975, 1977, 2000 Harvie Wear, 1980 Harvie et al, 1984 Kim Frederich, 1988a-b). 

In equations (15), (16) and (17), y is an adjustable parameter for each pair of anions or cations for each cation-cation and anion-anion pair, called triplet-ion-interaction parameter. The functions, 0 and 0 are fxmctions only of ionic strength and the electrolyte p>air type. Pitzer (1975) derived equations for calculating these effects, and Harvie and Weare (1981) summarized Pitzer s equations in a convenient form as following ... 

As indicated in the previous section, the ion interaction parameters i(K, OH") and 2(K" > OH") have been used, at 25 C, as the starting point for the calculation of other ion interaction parameters. The same strategy will also be used for other temperatures. Activity coefficient data for other temperatures have been provided by Li and Pitzer (1996) and are reproduced here in Table 2.5 but in the moles per kilogram scale rather than mole fraction. 

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) ... 

Recently, the Pitzer equation has been applied to model weak electrolyte systems by Beutier and Renon ( ) and Edwards, et al. (10). Beutier and Renon used a simplified Pitzer equation for the ion-ion interaction contribution, applied Debye-McAulay s electrostatic theory (Harned and Owen, (14)) for the ion-molecule interaction contribution, and adoptee) Margules type terms for molecule-molecule interactions between the same molecular solutes. Edwards, et al. applied the Pitzer equation directly, without defining any new terms, for all interactions (ion-ion, ion-molecule, and molecule-molecule) while neglecting all ternary parameters. Bromley s (1) ideas on additivity of interaction parameters of individual ions and correlation between individual ion and partial molar entropy of ions at infinite dilution were adopted in both studies. In addition, they both neglected contributions from interactions among ions of the same sign. 

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. 

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. 

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.10. Volumetric Pitzer-equation parameters for ion interactions (Marion et al. 2005). (Numbers are in computer scientific notation, where e xx stands for 10 a a ). Reprinted from Marion et al. (2005) with permission...

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