The propagation of a reaction front through a packed bed is analyzed theoretically. The chemical reaction rate is represented by Arrhenius temperature kinetics with external transfer limitation and general power law dependency on both gaseous and solid reactant concentrations. Analogous to so-called "Activation Energy Asymptotics" developed for premixed laminar flames, the largeness of the activation energy of the chemical reaction is exploited to derive asymptotic solutions from the three governing differential equations pertaining to transport of heat, of solid reactant, and of gaseous reactant, making use of the method of matched asymptotic expansions. Two regions are distinguished, i.e., an outer region or preheat zone and an inner region or reaction zone. In the preheat zone, the reaction terms can be neglected as compared to the convective and diffusive terms. In the reaction zone, the diffusion of heat is dominating over the convective heat transport mechanism and balances the heat of reaction. In accordance with the magnitudes taken for the Lewis numbers, for solid and gaseous reactants convective transports are dominating and submitting diffusive transports in the reaction zone, respectively. Solutions in closed form are presented for governing variables including reaction front velocity whereby previously published results appear as special cases. The solutions provide direct insight into underlying physical processes and enable the effects of important parameters to be quantified analytically.