The ability to predict the pressure dependence of chemical reaction rates would be a great boon to kinetic modeling of processes such as combustion and atmospheric chemistry. This pressure dependence is intimately related to the rate of collision-induced transitions in energy E and angular momentum J . We present a scheme for predicting this pressure dependence based on coupling trajectory-based determinations of moments of the E,J -resolved collisional transfer rates with the two-dimensional master equation. This completely a priori procedure provides a means for proceeding beyond the empiricism of prior work. The requisite microcanonical dissociation rates are obtained from ab initio transition state theory. Predictions for the CH ₄ = CH ₃ + H and C ₂ H ₃ = C ₂ H ₂ + H reaction systems are in excellent agreement with experiment.