$(8)$ The gas $-$ phase reaction, A $->$ B$,$ follows an elementary rate law and takes place isothermally in a PBR charged with $1\mathrm{.}0$ kg of catalyst. The feed, consisting of pure A$,$ enters the PBR at a pressure of $20$ atm $.$ The converslon exiting the PBR is $30\%.$ The pressure gradient along the length of the packed $-$bed is approximated as a constant at $d\frac{P}{d}W=-0\mathrm{.}40at\frac{m}{k}g.$

Calculate the quantity FAO$/$KCAO using the design equation for a PBR$.$