According to the literature, when H2SO4 dissolves in water, (1) it retains its molecular formula and tetrahedral structure of two 0 atoms and two OH groups bonded to a central S atom, and (2) it ionizes partially, as a 1-1 electrolyte, to H+ (H3O+) and HSO4-; the latter ion further dissociates at low concentrations (<0.1 M) to H+ and SO42-. Using the Debye-Huckel (DH) limiting law at very low concentration, and the smaller-ion shell (SiS) model of strong electrolyte solutions-an extension of the DH model for ion size dissimilarity-up to moderate concentration, I examine the theory-experiment fit of the mean ionic activity coefficient (gamma(+/-)) of the acid as a function of concentration (at 0 to similar to 6 m) and of temperature (at 0-60 degrees C). The fit is impossible if H2SO4 in water is assumed to be a 1-1 or 1-2 electrolyte, but is excellent when the acid is treated instead as a strong 1-3 electrolyte; that is, aqueous sulfuric acid behaves as a fully dissociated H(3)A acid. At 25 degrees C, the SiS best fit is achieved with the H+ diameter being 1.16 angstrom (as obtained for strong mineral 1-1 protonic acids) and with the A(3-) ionic diameter being 5.77 angstrom. On the basis of the present study, H2SO4 in water may be H4SO5 (dubbed "sulfoxuric", or parasulfuric acid) completely ionized to 3H(+) and the ("bisulfoxate", or parabisulfate) anion HSO53-. The calculated standard potential of a newly proposed half-cell reaction, H-2 + HSO53- <-> H+ + SO42- + H2O + 2e(-), at 25 degrees C, is -1.0933 V.