$(50$ pts$)$ The irreversible first$-$order gas$-$phase reaction, $AB,$ is carried out isothermally in a fluidized catalytic CSTR containing $50$ kg of catalyst. Currently, $50\%$ conversion is obtained for pure A entering at a pressure of $20$ atm $.$ There is virtually no pressure drop in the CSTR$.$ It is proposed to put a PBR containing the same catalyst weight in series and downstream from the CSTR$.$ The pressure drop parameter for the PBR$,=0\mathrm{.}018k{g}^{-1}.$ The particle size is $0\mathrm{.}2$ mm $,$ the bed porosity is $40\%,$ and the viscosity is the same as that of air at $200C.$

a$)$ What is the conversion exiting the last reactor?

b$)$ What is the pressure at the exit of the packed bed?