SIT model

Yang, C., Nicholas, M. A. and Ogden, J. (2006). Comparison of idealized and real-world city station sitting models for hydrogen distribution. UCD-ITS-RP-06-09, Institute of Transportation Studies, University of California, Davis. In... 

Originally the extended DH term was similar to that in Equation (3.5), i.e. with an average ion size parameter, a = 3. Scatchard showed that a better fit with experimental data was obtained using an average value of fli = 4.6, i.e. 0.33ai = 1.5, and so the extended DH expression used in the SIT model is often... 

The water is dominantly a NaCl brine with important amounts of Ca and Mg. The analysis indicates a stoichiometric ionic strength of 2,88 mol/kg, too high to justify use of the Davies equation. Because solubility of the akaline earth sulfates is directly proportional to the activity coefficients of Ca ", Sr +, Ba +, and SO ", we are interested in their values in the brine. We will compute the activity coefficients using the Truesdell-Jones (TJ) and SIT models. 

For cations and anions in a predominantly sodium chloride solution, the activity coefficient equations in the SIT model are... 

Truesdell-Jones model SIT model Pitzer model... 

The denominator of the DH term in the SIT model (Eqs. 4.32 and 4.33) equals 1 + 1.5V/, which is equivalent to assuming a, 4.6 and constant in the extended DH equation. The SIT model accounts for binary interactions of anions and cations with interaction parameters that are specific for individual ions in chloride or other media. Lacking an adjustable ion size parameter, the SIT model is less accurate than the extended DH model at low ionic strengths. It does, however, give accurate results in some solutions up to / = 3.5 mol/kg. 

To provide as complete a model of the thermochemistry of zirconium as possible, the reviewers adopted the following approach each experiment is evaluated, reviewed, and, if necessary and possible, the results are recalculated to be consistent with other experimental conclusions and the SIT model (Appendix A). Uncertainties are assigned at this point, subjectively, if necessary. These results, with their associated uncertainties, are accepted if there is no clear reason to reject them and such data are reported in Chapter V. Accepted results are used in the determination of the relevant thermodynamic parameter or to confirm a parameter derived by other methods. Uncertainties assigned at the review stage and associated with the extrapolation to the 7=0 standard state are propagated (Appendix C), to the extent possible, throughout the procedure and the final recommended results with the associated uncertainties are given in Chapter III. In some cases, uncertainties are derived from a sensitivity analysis of the... 

At best, the tyndallometric method could only be used to estimate an upper limit of the solubility. Kovalenko and Bagdasarov [61KOV/BAG], for example, found a solubility more than 100 times less than reported here (see Section V.3.2.2.2). Some of this effect might be the result of complexing due to seawater anions. Due to the complexity of the experimental seawater solution, this solubility cannot be interpreted using simple SIT models and therefore is not accepted by this review. 

The results of this consistency test are shown in Figure A-33, where the selected log p° (42.9) and hydrolysis data (including log K° = - 7.0) have been applied with the SIT model to reproduee the experimental data of [2001 POU/CUR]. It is evident that the caleulated model curve (continuous line) misses the data obtained in... 

The authors mentioned, that the dissolution of nickel hydroxide in alkaline solutions up to 15 M NaOH was so slight that only estimates of its solubility could be made. When the reported experimental data were re-evaluated it became evident that, at best, only one constant,, 3, can be determined. The solubility of Ni(OH)2(cr) increases with increasing NaOH molality, but the solubility curve flattens out at [OH ] > 1 m. This may be due to ion-ion interactions at the high ionic strengths, but there is no evidence whatever for formation of Ni(OH)4". Equation (A.7) can be fit reasonably to the data at lower NaOH molalities. When the SIT model is applied ... 

Their data have been recalculated with the standard potential of the Hg2Cl21 Hg electrode ((0.2681 0.0026) V, [89COX/WAG]) and the chloride activity of a saturated KCl solution a(KCl) = 2.829 [89LOB]. The activity of Ni in the solution was calculated using the SIT model supported by ChemSage. The results are listed in Table A-4. 

The thermodynamic parameters for the formation of several metal-cyanide complexes, among others those of Ni(CN)4 , have been determined using pH-metric and calorimetric methods at 10, 25 and 40°C. In case of nickel(II), the thermodynamic data were determined by titration of Ni(C104)2 solutions with NaCN solutions. The ionic strength of the solutions were 1 < 0.02 M in all cases. The Debye-Huckel equation, related to the SIT model, was used to correct the formation constants to thermodynamic constants valid at 7 = 0. Since previous experiments indicated that the dependence of A,77° in the ionic strength in dilute aqueous solutions is small compared to the experimental error, the measured heats of reaction (A,77 = - 189.1 kJ mol at 10°C A,77 ,= -183.7 kJ mol at 40 C) were taken to be valid at 7 = 0, but the uncertainties were estimated in this review as 2.0 kJ moT. From the values of A,77 , as a function of temperature, average A,C° values were calculated. 

The paper provides the results of a conductance study. The results were analysed using the equation of d Aprano [71 APR]. No values are reported for the nickel sulphate system other than the limiting equivalent conductance at infinite dilution and the association constant. These values are not inconsistent with values from other conductance studies, but reanalysis of the data to ensure consistency with the SIT model is not possible. 

Figure A-39 Logarithm of stability constants of nickel bisulphide complexes in seawater (NaCl solutions) plus the Debye-Hiickel term for ionic strength correction plotted as a function of ionic strength, T= 298.15 K. The solid lines correspond to least squares fits of the SIT model to the experimental data, [96LUT/RIC], A [94ZHA/MIL].

Figure A-41 Ionic strength dependence of theophrastite solubility. Inert electrolyte NaC104. / (mol kg ) 0.5 , 1.0 , 2.0 , 3.0 A, + mean value and error bar (A logm K = + 0.2). Solid curve calculated according to the SIT model [97GRE/PLY2] with the interaction parameter s(Ni, CIO ) = 0.37 kg mol selected in this review.

One aspect of the present review that is different from earher voltrmes is that a fitting code incorporating the SIT model, NONLINT-SIT, has been used in some systems to optimise the values of /RT of the relevant sohd and aqueotts species and the SIT ion-interaction parameters, using all the experimental solubility, ion-exchange, and solvent extraction data. From these, the optimised values of the different quantities can be compared with the other reported values. Appendix D describes the modus operand of the NONLINT-SIT program, with an illustrative example. 

These data, when combined with other auxiliary data, provide a log, K° value of -(36.829 + 0.790) based on the SIT model the value of logj K° = -33.898 found in [1993FEL/RA1] was based on the Pitzer model for Reaction (V111.6). 

Since both values are based on the same experimental data and the solubiUty study was conducted at relatively low ionic strengths where both the Pitzer and the SIT models should be in good agreement, the major difference in these values is as a result of the differences in values for equilibrium constants of aqueous complexes, particularly for ThFg, used in interpretation of data. 

Table VIII-20 Experimental equilibrium data for the reaction Th + CP ThCT. These data, with the exception of [1964NAB/KUD2] and [1976SOU/SHA], have been described using the SIT model that results in log,o °= (1.70 + 0.10) and Ae = -(0.11+ 0.05) kg mol (see text for details).

However, an equally good description may be obtained by using the SIT model (strict ion interaction approach excluding the formation of chloride complexes) in particular in perchlorate-chloride mixtures of high ionic strength and chloride concentration. Fitting the data at / = 2.0 through 6.0 M yields s(Th", CF) values very close to the value of e(Th", Cl ) = (0.25 + 0.03) kg-mol selected by this review, cf. Table VIII-19. 

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