Acidic protons in zeolites are known to be mobile at elevated temperatures. In this study, density functional theory was used to identify the reaction pathways for proton migration in a model that represents the zeolite ZSM-5. In the absence of water, the acidic proton "hops" or migrates between two of the four O atoms surrounding an aluminum center with an activation barrier of 28 kcal/mol. During proton transfer, the O atoms stretch closer together in order to stabilize the transition state. This is revealed by a 13.4 degrees decrease in the O-Al-O bond angle. Adsorbed water bridges the proton donor and acceptor sites, reducing he barrier height by 24 kcal/mol. Hence proton migration depends heavily on the local geometry and conditions of the zeolite. We show that experimentally undetectable amounts of water can greatly influence the measured rates and apparent activation barriers. We broaden the scope of our study to consider hydrogen exchange with other gas-phase species of the form RO-H (RO = CH3O, CH3CH2O) and R-H (R = H, CH3, C2H5, C3H7, C6H5). It is evident that to a first approximation the activation barrier increases with an increase in the polarizability of the species RO-H. For the chemical series R-H, the activation energy increases with the deprotonation energy of the interacting species R-H. We also calculate the overall reaction rate constants for proton hopping and hydrogen exchange.