A chemical reactor catalyzes the gas$-$phase isomerization of n$-$butane $($A$)$ to isobutene $($B$).$ Above the catalyst, the bulk mixture of $60$ mol$\%$ A and $40$ mol$\%$ B is well$-$mixed. The catalyst has a porous structure with straight, sealed pores of radius R and length L with active sites lining the walls and bottom of each pore. At the active site, the reaction is rapid such that production of B is diffusion limited$.$ Assume that the temperature is uniform throughout the system. a$.$ Draw a picture of the problem. List the control volume $($domain$),$ the species to be modeled, and the sources and sinks of each species. b$.$ List the variables and assumptions about mass transfer that will affect your model. c$.$ Write the continuity equation in terms of the molar flux. Cross out any terms that are zero. d$.$ Write the flux equation for this system. e$.$ Write the initial and boundary conditions. f$.$ Should the fluxes and concentration gradients be positive or negative?