No 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.

The almost century-old dispute over the validity of the experimentally derived activity of a single ion, a(i), is still unsettled; current interest in this issue is nourished by recent progress in electrochemical cell measurements using ion-specific electrodes (ISEs) and advanced liquid junctions. Ionic solution theories usually give expressions for a(i) values of the positive and negative ions, that is, the respective a(+) and a(-), and combine these expressions to compute the mean ionic activity, a(±), that is indisputably a thermodynamically valid property readily derivable from experiment. Adjusting ion-size parameters optimizes theory's fit with experiment for a(±) through "optimizing" a(+) and a(-). Here I show that theoretical a(i) values thus obtained from the smaller-ion shell treatment of strong electrolyte solutions [Fraenkel, Mol. Phys. 2010, 108, 1435] agree with a(i) values estimated from experiment; however, theoretical a(i) values derived from the primitive model, the basis of most modern ionic theories, do not agree with experiment.