Consider the process shown in the figure below. A slab contains parallel linear channels running through a nonporous slab of thickness $2\mathrm{.}0cm.$ The gas space over the slab contains a mixture of A and B maintained at a constant composition. Gas phase species A diffuses down a straight, $1\mathrm{.}0-$mm$-$diameter channel. At the base of the slab is a catalytic surface that promotes the isomerization reaction $A(g)B(g).$ This reaction occurs very rapidly so that the production of $B$ is diffusion limited$.$ The quiescent gas space in the channel consists of only species A and $B.$ The process is isothermal at $100C$ and isobaric at $2\mathrm{.}0$atm total system pressure. The bulk composition over the slab is maintained at $40$mol$\%$A and $60$mol$\%B.$ The molecular weight of species A and its isomer B is $58\frac{g}{m}ol.$

a$.$ Listing all of your assumptions, simplify the general mass transfer equation for species A$.$

b$.$ Develop a final integrated equation for the flux of product B$.$ Be sure to specify your boundary conditions.

c$.$ The binary gas$-$phase molecular diffusion coefficient of species A in species B is $0\mathrm{.}1c\frac{m_2}{s}$ at $25C$ and $1\mathrm{.}0$ atm. What is a reasonable estimate for the molecular flux of species B in species A under the conditions of the operation?

d$.$ If the total production rate is $0\mathrm{.}01$mol$\frac{B}{m}in,$ what is the required number of $1\mathrm{.}0mm-$diameter channels necessary to accomplish this production rate?