25.7 Consider one of the cylindrical channels of inner diameter d that run through an isomerization catalyst, as shown in the figure below. A catalyst coats the inner walls of each channel. This catalyst promotes the isomerization of n-butane (n-C4H10, species A) to isobutene (n-C4H10, species B): n-C4H10 (8)→i-C4H10 (8) The gas phase above the channels contains mixture of A and B maintained at a constant composition of 60 mol % A and 40 mol% B. Gas-phase species A diffuses down a straight channel of diameter d = 0.10 cm and length L = 2.0 cm. The base of each channel is sealed. The surface reaction 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. State three relevant assumptions for the mass-transfer pro- cess. Based on your assumptions, simplify the general differential equation for the mass transfer of species A, leaving the differential equation in terms of the ux N₁. b. Simplify Fick's ux equation for each coordinate of interest, and then express the simplified form of general differential equation from part (a) above in terms of the gas-phase concentration CA.

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