Monoprotic Mineral Acids Analyzed by the Smaller-Ion Shell Model of Strong Electrolyte Solutions

Abstract

The smaller-ion shell (SiS) model of strong binary electrolyte solutions extends the Debye-Hückel theory to the case of ions of unequal size; it is effective for many electrolytes of the various families in water at 25 °C up to moderate concentrations, with ion-size parameters (ISPs) of co-ions being equal to the ionic diameters, and with a varying degree of ISP additivity. A SiS analysis is now provided for aqueous solutions of the acids HCl, HBr, HI, and HClO(4) at 25 °C; theory fits very well with experiment when the mean effective ionic diameter of the proton (H(3)O(+)) is chosen as ~1.1 Å and the mean anion size is the corresponding crystallographic diameter, as with other electrolytes having the same anion. The ISP nonadditivity is positive and large, apparently reflecting a strong polarizing effect of the small proton on the large anion. The SiS-derived single-ion activity coefficients of the proton allow calculation of the pH of the acids, and reliable values are obtained below the known limit of pH ≈ 2, i.e., smaller and even negative values. The computed pH compares well with the experimentally derived Hammett acidity function, H(0), up to moderate concentration; differences between the two functions at higher concentration shed light on the activity coefficients of Hammett indicators and their response to increasing acid strength.

Response to “Comment on ‘The nonmonotonic concentration dependence of the mean activity coefficient of electrolytes is a result of a balance between solvation and ion–ion correlations’” [J. Chem. Phys. 134, 157101 (2011)]

“…Fraenkel summarized the main points of our theory nicely. Also, he offered his smaller-ion-shell (SiS) model 3,4 as an alternative to our approach. In this response, we categorize our thoughts along a few main issues.…”

“…Until this is possible, our model offers a realistic physical picture that includes all the important physical effects (ion-ion and ion-water correlations) that can be handled in the implicit solvent framework. PB treatments, such as the SiS theory of Fraenkel, 3,4 offer an easy-to-use alternative.…”

Comment on “The nonmonotonic concentration dependence of the mean activity coefficient of electrolytes is a result of a balance between solvation and ion–ion correlations” [J. Chem. Phys. 133, 154507 (2010)]

“…4 For example, such polarization may explain the essence of Brønsted acidity and the variation of pH at high acid concentration. 5 Boda's approach [like most others in the unrestricted PM (UPM) realm 2 ] is based on ISP additivity, which is usually assumed in applying the PM that is, by definition, a model of hard spheres.…”

“…The calculated SiS curve is below the experimental data because the electrostatic repulsion effect is smaller than that with the larger counterion's ISP and since in the case of complete ISP additivity, there is a quite strong extra-attraction effect of the chloride ion. 2,5 In contrast, Boda's IW term seems to strongly exaggerate the repulsion effect; the combined II + IW effect gives a better fit for CaCl 2 , but with an almost constant negative deviation from experiment that does not diminish with a decrease in c; for NaCl, however, the combined II + IW effect is considerably above the experimental curve, and in the KCl case, the only calculated lnγ ± value given at 1 M (∼1 m) deviates from experiment even more strongly [ Fig. 1(b)].…”

“…I have devoted much effort 2,5 to distinguish the SiS model from blunt and "unashamedly" empirical modifications, such as those of Guggenheim, Davies, and Pitzer, showing that ISPs of the SiS model are strictly emanating from model development, whereas in empirical DH theories, parameters are arbitrarily introduced into mathematical expressions (e.g., of γ ± vs I) without any clear and coherent physical justification. The very fact that a fit of a model (such as SiS) with experiment is done by adjusting ISPs does not necessarily mean that the model is empirical.…”