The equations describing this system for the reaction are:

,

,

with the following initial and boundary conditions:

,

,

,

where and are the concentrations of the adsorbed and product components, respectively, is time, represents the coordinate along the thickness of the slab, is the thickness of the slab, is the diffusion coefficient, is the reaction constant, stands for the order of reaction with respect to component , and is the concentration of component at both sides of the slab.