The smaller-ion shell (SiS) model of strong binary electrolyte solutions extends the Debye-Huckel theory to the case of ions of unequal size; it is effective for many electrolytes of the various families in water at 25 degrees 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 HClO4 at 25 degrees C; theory fits very well with experiment when the mean effective ionic diameter of the proton (H3O+) is chosen as similar to 1.1 angstrom 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 approximate to 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.