In second-order reactions in solution where a species of molecules R is subject to reaction with another species S during mutual diffusion, the inverse of the mean lifetime (given by the mean first passage time) of R is linear in the concentration of S when it is sufficiently small. When the concentration of R is also small, the coefficient in the linearity, giving an average rate constant, can rigorously be expressed by 1/(k(TST)(-1) + k(D)(-1)) where k(TST) represents the rate constant expected from the transition-state theory (TST) and is independent of the diffusion constant D, while the D dependence is carried by k(D) (>0) which decreases as D decreases (Sumi, H. J. Chem. Phys. 1994, 100, 8825). A convenient method for calculating k(D) has been given for general forms of the mutual-distance (r) dependent interaction potential U(r) and intrinsic reactivity k(r) between R and S. The method was utilized to calculate the D dependence of k(D) in the entire D region for a long-ranged k(r) proportional to r(-6) with U(r) = 0, appropriate to excitation-transfer reactions by Forster’s mechanism. In the large-D region where the TST is justified, k(D) becomes proportional to D in agreement with the result of the perturbational treatment of k(r). In the small-D region where the TST is invalidated, k(D) becomes proportional to D-3/4 in agreement with the limit first pointed out by de Gennes.