Two reactions of muonium atoms close to the diffusion-controlled limit were analyzed as a function of solute size and solvent viscosity. With Cr(NCS)(6)(3-) as solute in water, the reaction is an electron spin-conversion process, and the observed rate is taken to be half of the actual encounter rate, because of the quantum mechanical statistical factor and the occurrence of multiple collisions due to the solvent cage effect. The encounter rate deduced is 6.2 x 10(10) M-1 s(-1), which implies a large cross section for the Cr complex. In a second series of experiments, the rate of reaction of muonium with I-2 was compared in water, methanol and n-heptane. The bimolecular rate constants determined are (1.7 +/- 0.3), (7.0 +/- 1.2), and (57 +/- 22) x 10(10) M-1 s(-1), respectively, in these three solvents. This similar to 30-fold change in rate is not matched by the change in the inverse of the solvents’ viscosities, which changed overall by a factor of only 2.4. It looks as if quantum tunneling dominates over classical diffusion in less polar media where muonium is unencumbered by solvent clathration.