An expression for the nucleation rate of a binary vapor mixture of H2O and H2SO4 at 25°C is derived which explicitly considers the contribution of H2SO4 hydrates to the droplet growth process. The continuum approximation used in earlier binary rate treatments has been abandoned in favor of treating the droplet composition in a discrete fashion. Rates of nucleation are calculated for a H2O–H2SO4 vapor mixture at 50%, 200%, and 300% relative humidities for various H2SO4 vapor activities. A finite nucleation rate is predicted with a relative humidity of 50% and a monomer H2SO4 vapor activity of 10−3. This translates to a vapor pressure of monomer H2SO4 of 3.6×10−7 mm Hg or 0.5 ppb of pure H2SO4 at 1 atm. At higher relative humidities (i.e., 300%), a finite nucleation rate is predicted for monomer H2SO4 concentrations of ∼0.04 ppt. This represents a vapor pressure of 3.2×10−11 mm Hg for monomer H2SO4.