Estimation of the Pitzer Parameters for 1–1, 2–1, 3–1, 4–1, and 2–2 Single Electrolytes at 25 °C

Abstract

The Pitzer model is one of the most important thermodynamic models to predict the behavior of aqueous electrolyte solutions, especially at high ionic strengths. However, most of the parameters in the Pitzer equations have to be obtained experimentally and this represents an important drawback to this model. Therefore, in order to make the Pitzer equations less dependent on experimental data and more dependent on the properties of the solution, new equations that correlate the Pitzer equations with the properties of the solution have been successfully developed for 1-1, 2-1, 3-1, 4-1 and 2-2 electrolytes. In particular, these equations were developed for two cases: (i) considers the original Pitzer equations and (ii) considers some simplifications to the Pitzer equation (assuming C  B and  ). In particular, for case (ii), the second virial coefficients B and Bof the Pitzer equations were re-estimated using published experimental data of the osmotic coefficient obtained from the literature. As a conclusion, both the simplified and the original Pitzer equations presented a very good match with this published experimental data for the osmotic coefficients.Additionally, the second virial coefficients B and B for both cases were successfully correlated with the ionic radius and the ionic charge, and this is confirmed by the very high coefficients of determination achieved (R 2 >0.96). However, these new equations are valid only to cases in which no significant ion association occurs, which is also the basic premise of the original Pitzer model.

Estimation of the Thermochemical Radii and Ionic Volumes of Complex Ions

“…The thermochemical radius plays a very important role in electrolyte solutions since most of the interactions between the ions in the solution are, to some extent, distance-dependent. For instance, the thermodynamic, transport, kinetics and solvation are highly dependent on the size of the ions 1,2 . In addition to this, the thermochemical radii can be used to calculate the lattice energy of the crystals, for example, either via the Kapustinskii equation 3 , which has been more recently generalized by Glasser 4 , or through the volume based equations developed by Jenkins et al 5 , and these lattice energies can be important parameter to be evaluated when assessing the feasibility of synthesizing new inorganic materials 5 .…”

Temperature Dependence of the Parameters in the Pitzer Equations

“…They do not include the following electrolytes that are likely to form ion pairs: (i) 1–1 electrolytes, nitric and perchloric acids, as well as alkali metal hydroxides and fluorides. [in particular, the alkali metal hydroxides and fluorides were excluded because the results obtained in a previous study, using the equations that correlate the virial coefficients with the properties of the ions, presented a poor agreement with the experimental data. Furthermore, it is possible to find in the literature experimental evidence that shows that these alkali metal hydroxides and fluorides tend to the ion pair formation; for instance, Manohar and Atkinson investigated the association constants of the alkali metal fluorides using spectrophotometry and Moskovits and Michaelian used Raman spectroscopy to investigate ion pair formation of aqueous alkali hydroxides]; (ii) all 1–2 and 2–2 electrolytes; , (iii) all 2–1 and 3–1 electrolytes nitrates. , …”

“…Comparison plots of 1–1 electrolytes: (a) HBr and (b) HCl [symbols, experimental activity coefficients obtained from the literature − for case ii (□, 0 °C; •, 25 °C; *, 50 °C; ○, 60 °C); lines, calculated activity coefficients using eqs – (dashed–dotted line, 0 °C; solid line, 25 °C; dashed line, 50 °C; dotted line, 60 °C)].…”

“…Comparison plots of 2–1 electrolytes for case ii: (a) BaCl 2 , (b) MgCl 2 , and (c) SrCl 2 [symbols, experimental osmotic coefficients obtained from the literature ,, (□, 25 °C; •, 109.8 °C; ○, 140.2 °C); lines, calculated osmotic coefficients using eqs – (dashed–dotted line, 25 °C; solid line, 109.8 °C; dashed line, 140.2 °C)].…”

Thermodynamic Modeling of Aqueous Electrolyte Systems: Current Status

“…This is because the numerous parameters it requires cannot feasibly be determined experimentally . Attempts to solve the problem by various methods of parameter estimation have been described − but such initiatives generally consider only the simple reactant species (e.g., metal and ligand ions) and they fail to address the product species (e.g., complexes), which actually represent the main challenge.…”