$(4$e $25\mathrm{.}5,6$e $25\mathrm{.}7)$: 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?