Reaclant $A$ of $C_{A0}=10$kmo$\frac{l}{m^3}$ decomposes to $B,C,$ or $D,$ with the rates of formation of $r_B=20C_A^{0\mathrm{.}5}$ kmo$\frac{l}{m^3(min)},r_c=15C_A$kmo$\frac{l}{m^3(min)},$ and $r_D=C_A^2$kmo$\frac{l}{m^3(min)},$ respectively. In the feed, the volumetric flow rate $(v_0)$ is $1\frac{m^3}{m}in.$ We wish to design a reactor setup. Answer the following questions with any necessary assumptions, based on your thought of the best sctup.

$($a$)$ Suppose that B is the desired product. Sketch the reactor scheme, calculate the fraction of feed transformed into the desired product, and calculate the volume of reactor needed.

$($b$)$ Suppose that $C$ is the desired product: Find the reactor scheme, the overall yield, and the volume of reactor.

$($c$)$ Suppose that $D$ is the desired product: Find the reactor scheme Jthe overall selectivity, and the volume of reactor.