Specific ion interaction model

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. 

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).

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 ... 

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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