Problom $5.$ Catalyst Speification 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 platanum deposited uniformly throughout a silica$-$alumina support structurre $D_{\text{e}\text{f}\text{f}}={10}^{-8}{m}^3$ Im cat.s$).$ To save on catalyst cost, it has been suggested that ve only impregnate the outer $100Hm$ layer of the pellet with catayst. For the same procersing rate and conversun of gaseous reacant how would this change affed

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

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

he Kinetics and concentrations in our present operations are ives by

$-{}_{A_1,0bs}=1\frac{\text{m}\text{o}\text{l}}{m^3{c}_{\text{c}\text{a}\text{t}}-s^1},at{C}_A=10\frac{\text{m}\text{o}\text{l}}{m^3}$