SIT Interaction coefficients

It is clear that, if Pr represents, for example, an SIT interaction coefficient for a given species and that species is not constrained by the data in set /, large increments Ap, will be needed to produce a nominal increment in the transformed calculated experimental quantities A (z ) and that data set will contribute largely to the overall uncertainty of the parameter. Conversely, parameters that are well constrained by several data sets, will receive small contributions from each of those datasets resulting in a small 

The set of species with the lowest overall objective function was considered as the best fit and the results are used in the present hydrolysis model. Sections V.2.1.2, V.3.1 and V.3.2.1.3 detail, respectively, the results obtained from the best fit for the following model paremeters Af/f°(Zr , 298.15K), complex formation equilibria and solubility of Zr02 (mono). 

In the overall fit, the constants log, , and log, 3 and associated Ae values in perchlorate media were fixed whereas in reality uncertainties are assigned to these values. To take these uncertainties into account, sensitivity analyses were performed within the 95% confidence limit uncertainty of these constants (given in Sections V.3.1.1.3 and V.3.1.2.2). The effect of the variation of these constants on the value of the overall uncertainty of the fit was always less than 0.5%. This indicates that the datasets used to obtain these constants are largely independent from those used to determine the other constants in the overall fit. Also fixed in the overall fit were the As values involving the neutral species Zr(OH)4(aq) and Zr4(OH)i6(aq) given that for neutral species SIT theory assumes 8=0, hence, As and the corresponding uncertainty are directly obtained from the 8 values of the Zr ion. 

Given the presenee in the model of neutral species, that should bear no interactions according to the SIT formulation, two approaches were followed for assigning values to the Ae for the formation of Zr(OH)4 and Zr OHis. 

In the second approach, individual 8 values of in the three different ionic media were fitted directly within the overall fit of hydrolysis relevant data. In this approach, the slope Ae of neutral species is considered as being constrained by the experimental data and from the Ae values and values for e(Zr , anion) are calculated. The results of this approach are given in Table D-5. The value of s(Zr CIO ,) = (0.88 0.30) kg-moP is similar to that derived from the correlation method (Table D-4) and the value determined experimentally from complexation (Section V.4.1.1). All of the results derived by the second methodology have much higher uncertainties than the values determined by the correlation method. 

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Table B-7 SIT interaction coefficient z(j,k) kg mol for neutral species,/ with k, electroneutral combination of ions.

Table B-7 SIT interaction coefficients (j,k) (kg-mol ) for nentral species, 7, with k, electronentral combination of ions.

In case of low charged species, and approximately below 3 mol kg 1 the Specific Ion interaction Theory (SIT) [29] can be applied for the calculations of activity coefficients. Data available on interaction coefficients are scarce. But, paradoxically for actinide ions such data are relatively well known. However, in certain cases, they can be estimated from the model developed by L. Ciaviatta [33,34],... 

SIT ion interaction coefficient between substance B and substance 62 stoichiometric coefficient of substance B (negative for reactants, positive for products) stoichiometric coefficient general equation for a chemical reaction equilibrium constant... 

Ion interaction coefficients, for the selenocyanate ion and its metal ion complexes are not available. Data for the thiocyanate ion have therefore been used as an approximation for extrapolation by SIT of selenocyanate equilibrium constants to standard conditions. 

Similar uncertainties are true for the effect of ionic strength on the stability constants, as described using SIT, and the corresponding interaction coefficients that are determined. A re-interpretation is necessary that considers polynuclear complex formation. 

Earlier reviews [82WAG/EVA], [99ARC] gave substantial weight to the emf study of Nair and Nancollas [59NAI/NAN]. As shown in Appendix A, recalculation of values from that study to be consistent with the SIT procedure described in Appendix B, requires values for the dissociation constant of HSO, and several interaction coefficients, e(Ni, Cl), (H, C1), e(H, HSO ) and e(Ni, FISO ). The values calculated for the formation constant of NiS04(aq) are extremely sensitive to the activity coefficient model, to the values used for the interaction coefficients and to the values assumed... 

K, the formation constant was recalculated to be (173 64). However, if the value for log,/f°(A.16) was changed from 1.98 to 1.96, well within the assessed uncertainty bound, the value became (140 72). The uncertainties here are merely the 2ct uncertainties in the set of seven values recalculated from [59NA1/NAN], and do not include uncertainties in the auxiliary data. Even though the solute concentrations are low (/ < 0.05), and the overall changes to the activity coefficients from the SIT interaction terms are small, the calculated value of log, AT (A.15) increases from (173 64) to (201 35) if all the e values are set to zero (but the maximum change in from the interaction terms is 0.004). 

Plyasunova et al. critically evaluated the standard thermodynamic quantities of Ni, its hydrolysis reactions and hydroxo-complex formation on the basis of published experimental studies and the specific interaction theory (SIT) for activity coefficient modelling [97GRE/PLY2]. Recommended thermodynamic functions and interaction coefficients relevant for the present review and its compounds were presented, see Table A-... 

As illustrated in Figure Vt-5, the different approaches and ion interaction coefficients can lead to appreciably discrepant activity coefficients for the Th" ioa For instance the values of in 0.1 or 0.5 m NaCl and hence the solubility constants calculated in [2000RAI/MOO] and [2003NEC/ALT] with the Pitzer model and SIT respectively for microcrystalline Th02(cr) at low pH, where hydrolysis is actually negligible, differ by about two orders of magnitude. 

The conditional equilibrium constants reported for the complex Th(OH) are listed in Table VII-10. For better comparison they are extrapolated to zero ionic strength with the SIT using the following interaction coefficients for Th(OH), estimated from Figure VII-13 in Section VII.3.6.1 ... 

For polynuclear Th(IV) hydroxide complexes which are found to be major species or at least species with significant contributions in potentiometric studies, Ae(n,m) values are derived in Section VII.3.4.1 by hnear SIT regression from the conditional equilibrium constants logm ,(Th (OH) , 298.15 K) in perchlorate, nitrate and chloride media. The ion interaction coefficients for the Th(IV) hydroxide complexes 8(Th (0H) ,X ), withX = CIO, NOj and CT are calculated according to ... 

The equilibrium constants and SIT coefficients selected in this table refer to a strict ion interaction approach where the effect of chloride or nitrate complexation is included in the interaction coefficients. Therefore these values must not be combined with the formation constants of chloride and nitrate complexes discussed in Sections VIII.2.2.1 and X. 1.3.3. 

However, the uncertainty in the NONLINT-SIT calculation does not account for the uncertainty in the estimated interaction coefficients. This review has therefore increased the uncertainty by a factor of two and selects... 

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