A semianalytical technique is presented for solving the equations describing an isothermal, irreversible reaction of a trace component in a packed bed of a solid reactant or adsorbent The reaction-rare expression is assumed to have an arbitrary dependence on the solid reactant concentration, but a first-order dependence on the trace gas component. The technique relies on an integral transformation that reduces the set of partial differential equations to a set of two coupled ordinary differential equations in the spatial variables. Solving these two equations is simpler than solving the original equations by finite differences or finite elements, especially in the presence of steep concentration gradients. Two examples presented illustrate the technique : a progressive conversion model with reaction occurring at dispersed sites within the adsorbent pellet and a reaction proceeding in the shrinking core mode.