A statistical phase space theory of chemical kinetics, developed by Light, Pechukas, and Nikitin, is used to predict the reaction cross sections and rates of the processes H + AB → HA + B and HB + A, where AB = DCl, DBr, DI, and HI. The theory contains no adjustable parameters and agreement with experiment for the abstraction fraction [HA]/([HA] + [HB]) is fair. The predicted rates are too large, indicating that the statistical assumption is not completely valid. The predicted dependence of the reaction probabilities on initial orbital angular momentum and the predicted internal energy distributions of the products are also presented and discussed. For AB = DI, the prediction for the fraction of I atoms produced in the 2P1/2 electronically excited state is in disagreement with recent experiments.