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 conversion exiting the PBR is $30\%.$ The pressure gradient along the length of the packed$-$bed is approximated as a constant at dP$/$dW $=-0\mathrm{.}40$ atm$/$kg$.$

Calculate the quantity FA$0/$kCA$0$ using the design equation for a PBR$.$