Conversion and optimization of the parameters from an extended form of the ion-interaction model for Ca(NO 3) 2(aq) and NaNO 3(aq) to those of the standard Pitzer model, and an assessment of the accuracy of the parameter temperature representations

Abstract

The electrolytes Ca(NO 3) 2(aq) and NaNO 3(aq) are both extremely soluble but differ in several important respects. Ca(NO 3) 2(aq) has complex behavior at low ionic strengths and forms several thermodynamically stable and metastable solid phases, whereas NaNO 3(aq) forms only an anhydrous solid phase. The thermodynamic properties of both have previously been modeled using extended Pitzer ion-interaction models that include higher-order virial terms, in addition to those of the standard Pitzer model. The parameters of the original Pitzer model, however, are often needed for thermodynamic modeling calculations. In this paper, we convert the parameters of the extended ion-interaction models for Ca(NO 3) 2(aq) and NaNO 3(aq) to the standard Pitzer model using an extension of the methodology previously described by Rard and Wijesinghe [J. Chem. Thermodyn. 35 (2003) 439–473]. In this variant, the exponential coefficient α 1 P of Pitzer’s model is also optimized to yield the most accurate overall representation of the osmotic coefficients ϕ over the ionic strength and temperature ranges of interest. The optimal values of α 1 P = 0.87 kg 1 / 2 · mol - 1 / 2 for Ca(NO 3) 2(aq) and α 1 P = 1.43 kg 1 / 2 · mol - 1 / 2 for NaNO 3(aq) are smaller than the value α 1 P = 2.00 kg 1 / 2 · mol - 1 / 2 normally used for electrolytes of these valence types. In both cases, the accuracy of the osmotic coefficients predicted by the standard Pitzer model was nearly equal to that of the extended Pitzer model up to the solubility limit for T = (298.15 to 423.15) K. This result is consistent with the findings of Rard, Wijesinghe, and Wolery [J. Chem. Eng. Data 49 (2004) 1127–1140] who obtained a substantial improvement in model accuracy for Mg(NO 3) 2(aq) at T = 298.15 K by optimizing α 1 P . The use of a temperature-dependent α 1 P that is optimal at each temperature did not yield a significant improvement in accuracy over using a constant optimal value. We also investigated the impact of choosing different temperature functions to develop temperature correlations for the Pitzer parameters. Higher-order temperature functions were needed for evaluations with solubility limited maximum ionic strength compared to evaluations performed at constant maximum ionic strength over the temperature range, especially for Ca(NO 3) 2(aq) because of its more complex thermodynamic behavior. Accurate temperature correlations are presented for both Ca(NO 3) 2(aq) and NaNO 3(aq).