Problem $5.$ Catalyst Specification and Reactor Size for a Gas$-$Phase Reaction

Our first order reaction $AR$ is run in a packed bed of $6mm$ porous catalyst

particles consisting of platinum deposited uniformly throughout a silica$-$alumina

support structure $D_{\text{e}\text{f}\text{f}}={10}^{-8}\frac{m^3}{m}$ catss$).$ To save on catalyst cost it has been

suggested that we only impregnate the outer $100m$ layer of the pellet with catalyst.

For the same processing rate and conversion of gaseous reactant how would this

change affect

$($a$)$ the amount of platinum needed?

$($b$)$ the size of reactor to be used?

The kinetics and concentrations in our present operations are given by

$-r^{\text{'}}{A}_{,\text{o}\text{b}\text{s}}=1\frac{\text{m}\text{o}\text{l}}{m^3\text{c}\text{a}\text{t}*s},at{C}_A=10\frac{\text{m}\text{o}\text{l}}{m^3}$