$2.$ The elementary irreversible gas phase catalytic reaction

A $+$ B $$ C $+$ D

Is to be carried out in a PBR at constant temperature. The reactor contain $2\mathrm{.}5$ kg catalyst. The feed is stoichiometric A and B$.$ The entering concentration of A is $0\mathrm{.}2$ mol$/$dm$3.$ The catalyst decay law is zero order with kD $0\mathrm{.}2$ s$-1$ and k $=1\mathrm{.}0$ dm$3/($mol$.$kg cat.s$)$ and the volumetric flowrate is v$0=1$ dm$3/$s$.$

Given that the decay rate law;

a$=($k$\_$D W$)/$U$\_$S ; where Us is catalyst feed rate

Calculate the conversion will be achieved for a catalyst feed rate of $0\mathrm{.}5$ kg$/$s$.$