Q$.5$ An autocatalytic reaction $A+$dots..$B+$dots. is to be carried out in an isothermal continuous flow reactor. The feed rate is maintained at $0\mathrm{.}5\frac{L}{sec}$ whereas a feed concentration of $1\mathrm{.}5mo\frac{l}{L}$ is used for the reaction. The rate law is given by $-r_A=k{C}_A{C}_B$ with $k=0\mathrm{.}002\frac{L}{m}ol.$sec$.$ There is no $B$ in the feed. For a fractional conversion of $90\%$ calculate

$($a$)$ Volume required for a CSTR

$($b$)$ Volume required for a PFR

$($c$)$ Minimum volume required for PFR with recycle