Liquid reactant A decomposes as follows:

$A{k}_{1}R,r_R=k_1{C}_A^2,k_1=1\mathrm{.}0\frac{m^3}{\text{m}\text{o}\text{l}-\text{m}\text{i}\text{n}}$

$A{k}_{2}S,r_S=k_2{C}_A,k_2=1\mathrm{.}0mi{n}^{-1}$

$($a$)$ A feed of aqueous $A(C_{A0}=40mo\frac{l}{m^3},v=5\frac{m^3}{m}in)$ enters a PFR$,$ decomposes, and a mixture of $A,R,$ and $S$ leaves. Find $C_R,$ and $C_S$ and reactor volume, $V$ for $x_A=0\mathrm{.}9.$

$($b$)$ Find the $x_A$ and $C_{R,\text{m}\text{a}\text{x}}$ in a mixed flow reactor.