A quantum mechanical theory for the model adiabatic reaction A + BC $\rightarrow$ AB + C, with the atoms constrained to move in a plane and B having infinite mass, is developed in terms of a mathematically meaningful reaction coordinate. Estimates are derived for the limiting initial impact parameters between which reaction takes place. It is also shown how the relation between the internal states of the reactants, the products, and the transition complex A..B..C may be used to estimate the final internal energy of AB. The theory is applied to the reaction K+HI \rightarrow KI+H, two hypothetical potential surfaces being used. For a typical set of starting conditions the removal of a 1 kcal activation barrier is found to increase the possible product internal energy from 3.3 to 8.3 kcal.