The effects of a background polymer on the solution properties of a dilute probe polymer have been studied in detail and reported in a previous paper. In this work, those results are applied toward interpreting the kinetics of bimolecular reactions between macromolecules containing reactive ends. Initial increases in the rates of bimacromolecular reactions with increasing concentration of unreactive polymer have been well established but poorly understood. Specific application is made to the termination reaction in free-radical polymerization at low conversion. We emphasize the ternary character of the solution: reactive chains, unreactive chains, and solvent. Our earlier results showed that the dominant effect of the background polymer in the dilute regime is a decrease in the apparent second virial coefficient of the probe. The background polymer acts to reduce the repulsive potential of interaction between two probe molecules. This effect is evident before there is any significant contraction of the probe coils or decrease in their mobility. In this paper, we argue that this effect leads to an increase in the rate of termination by increasing the probability of reaction between chain ends during a binary encounter, in a manner similar, but not exactly analogous, to that observed experimentally with decreasing quality of a small-molecule solvent.