Consider one of the cylindrical channels that run through an isomerization catalyst as shown below. A catalyst coats the inner walls of each channel. This catalyst promotes the isomerization of...

Consider one of the cylindrical channels that run through an isomerization catalyst as shown below. A catalyst coats the inner walls of each channel. This catalyst promotes the isomerization of n-butane (n
C₄H₁₀) species A to isobutene (i
C₄H₁₀) species B.

The gas phase above the channels contains mixture of A and B maintained at a constant composition of 60 mol % n
C₄H₁₀
(A) and 40 mol % i
C₄H₁₀
0 (B). Gas phase species A diffuses down a straight channel of diameter d
 0:1 cm and length L
 2:0 cm. The base of each channel is sealed. This is rapid reaction so that the production rate of B is diffusion limited. The quiescent gas space in the channel consists of only species A and B.

a. State three relevant assumptions for the mass transfer process.

b. Based on your assumptions, simplify the general differential equation for the mass transfer of species A, leaving the equation in terms of the flux N_A.

c. Using equations for the flux of A in your determined equation, express the general differential equation in terms of the concentration c_A.

d. Specify relevant boundary conditions for the gas phase concentration c_A.