Reversible bimolecular chemical reactions of the AB reversible arrow A + B type were predicted theoretically to deviate from exponential kinetics, obeying convolution kinetics at intermediate times and ultimately approaching equilibrium:as a power law, t-(3/2), with a concentration-dependent amplitude. By careful application of time-resolved fluorescence methods, we verify these-predictions for excited-state proton transfer from 2-naphthol-6,8-disulfonate to acidified water. The variation of the asymptotic amplitude with concentration is due predominantly to screening of the proton-anion Coulomb potential, and this masks the many-body effects on reversible binding itself. Better signal-to-noise in the long-time tails is required for clearly establishing the asymptotic behavior.