High proton conductivity in aqueous solutions has been known for a long time and is attributed to the Grotthus mechanism. In this study, we calculated the proton-transfer rate constant associated with prototropic mobility in water as a function of temperature. We found a strong correlation between the proton-transfer rate constant at low temperatures, T < 290 K, and the dielectric relaxation time. The model that we used to calculate the proton-transfer rate constant is based on diffusive propagation of the solvent configuration along a generalized solvent coordinate from the reactant potential surface toward the crossing point with the product potential surface. The proton transfer occurs at the crossing point, and the rate is calculated by a sink term placed at the crossing point. The sink term includes the solvent velocity and the Landau-Zener transmission coefficient. Both the diffusion constant and the Landau-Zener transmission coefficient depend on the dielectric relaxation of the solvent. The calculations are compared with the proton mobility data and an interpolation expression that bridges the nonadiabatic limit and the solvent-controlled limit.