Diffusion in a bounded potential with coordinate-dependent reactivity serves as a model for the effect of conformational change on ligand-binding to heme-proteins. The effect of increasing solvent viscosity on this biophysical process can be described mathematically as a decrease in the ratio of diffusion to reaction rates. We are investigating this effect in the above mentioned model by obtaining expansions for the survival probability (of the unligated heme) as a function of this ratio, in the limits of large and small diffusion coefficients. The Smoluchowski assumption of independent-pairs for describing the kinetics of (the many-body) diffusion-controlled reactions is used extensively for analyzing fluorescence-quenching experiments in solution, but the range of validity for this approximation is as yet unclear. We have analyzed the kinetics of an excited molecule in a random distribution of quenchers in one-dimension by obtaining the correction-term in the density expansion describing the short- time behavior of the survival probability of the excited-state molecule. This analysis is based on our ability to solve rigorously for the dynamics of three particles on the line. It provides both correction term to the Smoluchowski theory and an assessment of its validity.