Ion interaction model

The agreement between the two methods is satisfactory. This is important as it indicates that the deviations from ideality in experimental data can be well described 

VIII Thorium Group 17 (halogens) compounds and complexes 

Ionic strength (M) Source of data Best fit s(Th NONLINT- SIT 7 CL) (kg moL ) SIT (linear regression)  

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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. 

The method preferred in the NBA Thermochemical Data Base review is the specific ion interaction model in the form of the Bronsted-Guggenheim-Scatchard approach. 

The way in which the activity coelficient corrections are performed according to the specific ion interaction model is illustrated below for a general case of a complex formation reaction. Charges are omitted for brevity. 

One method takes into account the individual characteristics of the ionic media by using a medium-dependent expression for the activity coefficients of the species involved in the equilibrium reactions. The medium dependence is described by virial or ion interaction coefficients as used in the Pitzer equations and in the specific ion interaction model. 

Tables 6.3-6.5 contain the selected specific ion interaction coefficients used in this review, according to the specific ion interaction model described in section 6.1. Table 6.3 contains cation interaction coefficients with Cl , CIO4, and NOs Table 6.4 anion interaction coefficients with Li with Na or NH4, and with K. The coefficients have the units of kg mol and are valid for 298.15 K. The species are ordered by charge and appear, within each charge class, in standard order of arrangement [33].

The specific ion interaction approach is simple to use and gives a fairly good estimate of activity factors. By using size/charge correlations, it seems possible to estimate unknown ion interaction coefficients. The specific ion interaction model has therefore been adopted as a standard procedure in the NEA Thermochemical Data Base review for the extrapolation and correction of equilibrium data to the infinite dilution standard state. For more details on methods for calculating activity coefficients and the ionic medium/ ionic strength dependence of equilibrium constants, the reader is referred to Ref. 40, Chapter IX. 

Felmy, A. R., Rai, D. Mason, M. J. 1991. The solubility of hydrous thorium(IV) oxide in chloride media development of an aqueous ion-interaction model. Radiochimica Acta, 55, 177-185. 

Monnin C (1989) An ion interaction model for the volumetric properties of natural waters density of the solution and partial molal volumes of electrolytes to high concentrations at 25 °C. Geochim Cosmochim Acta 53 1177-1188... 

There are three popular hypotheses. Two models propose extreme situations and each encompasses a substantial amount of chromatographic data. These two proposals are the ion-pair model and the dynamic ion-exchange model. The third view, which is broader in scope than the previous two concepts, accommodates both the extreme views without combining the two models. This proposal is the ion-interaction model. 

The first attempts of Bidlingmeyer and co-workers [15,16] to formulate an ion interaction model quantitatively [21-23] did not provide a rigorous description of the system. Stranahan and Deming [22] accounted for electrostatic effects via a simplified activity coefficient in the stationary phase. An interfadal tension decrease with increasing IPR concentration was considered responsible for the appearance of maxima in the plot of retention factor, k versus IPR concentration, but experimental results were at odds with known surfactant chemistry. 

Pitzer (1973) re-examined the statistical mechanics of aqueous electrolytes in water and derived a different but semi-empirical method for activity coefficients, commonly termed the Pitzer specific-ion-interaction model. He fitted a slightly different function for behavior at low concentrations and used a virial coefficient formulation for high concentrations. The results have proved extremely fruitful for modeling activity coefficients over a very large range of molality. The general equation is... 

Figure 12 Pore-water chemistry and saturation indices versus depth at the tailings site of the Heath Steele mine. lA represents saturation indices calculated using an ion-association model, and SII represents saturation indices calculated using a specific ion-interaction model (after Ptacek and Blowes, 2000).

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. 

Finally, in 1979, Bidlingmeyer et al. [13,14] introduced a third model which they termed the ion interaction model. It is based on conductivity measurements, the results of which rule out the formation of ion pairs in the mobile phase. This retention model, also used by Pohl [15] to interpret the retention mechanism on a MPIC phase, neither presupposes the formation of ion pairs nor is it based on classical ion-exchange chromatography. 

Ranville, R. j. 1988. The application of an ion-interaction model to solubilities of some alkaline-earth carbonates, Th02 and UO2 in brines. MS thesis, T-3232, Colorado School of Mines, Golden, CO. 

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. 

The extrapolation procedure used in this review is the specific ion interaction model outlined in Appendix B. The objective of this review is to provide selected data sets at standard conditions, i.e., among others, at infinite dilution for aqueous species. Equilibrium constants determined at different ionic strengths can, according to the specific ion interaction equations, be extrapolated to / = 0 with a linear regression model, yielding as the intercept the desired equilibrium constant at / = 0, and as the slope the stoichiometric sum of the ion interaction coefficients, As. The ion interaction coefficient of the target species can usually be extracted from As and is listed in the corresponding table of Appendix B. 

According to the specific ion interaction model the following equation is used to correct for ionic strength for the reaction considered here ... 

The ion-interaction model is a theoretically based approach that uses empirical data to account for complexing and ion pair formation by describing this change in free ion activity with a series of experimentally defined virial coefficients. Several philosophical difficulties have resulted from the introduction of this approach the lack of extensive experimental database for trace constituents or redox couples, incompatibility with the classical ion pairing model, the constant effort required to retrofit solubility data as the number of components in the model expand using the same historical fitting procedures, and the incompatibility of comparing thermodynamic solubility products obtained from model fits as opposed to solubility products obtained by other methods. 

The purpose of this paper is to review two thermodynamic models for calculating aqueous electrolyte properties and give examples of parameter evaluations to high temperatures and pressures as well as applications to solubility calculations. The first model [the ion-interaction model of Pitzer (1) and coworkers] has been discussed extensively elsewhere (1-4) and will be reviewed only briefly here, while more detail will be given for an alternate model using a Margules expansion as proposed by Pitzer and Simonson (5). 

The principal interests in this study are osmotic and activity coefficients of NaCl(ac ) and KCl(aq) solutions at temperatures to 350°C and up to saturation concentration. In the range 25-300 C and at 1 bar or saturation pressure, NaCl(aq) osmotic coefficients up to 4 m were taken from a comprehensive thermodynamic treatment of Pitzer et al. (9). Above 4 m, the values were taken from Liu and Lindsay (39). At temperatures above 300°C, osmotic coefficients were calculated from vapor pressure data of Wood et al. (4. Additional vapor pressure data are given in Refs. 41-47, but a critical evaluation of these data indicated that these are less precise measurements and were therefore given smaller weights in the regression. For KCl(aq), osmotic coefficients to 6 m at temperatures from 25-325 C at 1 bar or saturation pressure were taken from the ion interaction model of Pabalan and Pitzer (9). Additional values up to 350 C and saturation concentration were derived from Refs. 40,41, and 48. 

To calculate the partial pressures of volatile electrolytes above solutions of known composition, values of the activity coefficients of the dissolved components are needed in addition to the appropriate Henry s law constants. In this work activity coefficients are calculated using the ion-interaction model of Pitzer (4). While originally formulated to describe the behavior of strong electrolytes, it is readily combined with explicit recognition of association equilibria (1,1), and may be extended to include neutral solutes (4, . The model has previously been used to describe vapor-liquid equilibria in systems of chiefly industrial interest (2). 

Thermodynamic activities of ionic species in aqueous solutions with ionic strength (I) < 0.01 molal (m) commonly are calculated using the ion-pair model (3), which is valid also for solutions with I < 0.1 m. In dominantly NaCl solutions, the ion-pair model can be used for I < 3 m with appropriate adjustments to the activity coefficients (4). The specific ion interaction model ( may be more appropriate for solutions of high ionic strengths. The effect of pressure on the thermodynamic activities of single ions in this model can be estimated from the stoichiometric partial molal volume and compressibility data (]) However, a complete data set for all the ion-interaction parameters is not yet available for this model to be used in complex geochemical solutions. 

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