Problem $2.$ Effectiveness Factor for a First$-$Order Reversible Reaction.

Develop an expression for Thiele modulus, the concentration profile and the catalyst

effectiveness factor when the reversible reaction A $=$ B occurs in a porous catalyst

whose half$-$length is L with a height H and width W$.$ The equilibrium constant is K

$=$ kf$/$kr$.$ Assume that diffusion mainly occurs in the x$-$coordinate, which is also

associated with the catalyst half$-$length L$.$ The effective diffusivity for specie A is

DAe and the local concentrations of species A and B are CA$($x$)$ and CB$($x$),$

respectively. The concentrations of A and B at the catalyst surface are CAS and CBS$,$

respectively. Use CGS units for all the variables