Qu $1$ Show that for the reaction $A+BR+BS$ being carried out in a batch$/$ plug flow reactor:

$\frac{C_{R\text{m}\text{a}\text{s}}}{C_{A_{0}0}}=(\frac{k_1}{k_2}{)}^{\frac{12}{k_2-k1}},k_2{k}_1$

$\frac{C_{R\text{m}\text{a}\text{x}}}{C_{A_0}}=\frac{1}{e}=0\mathrm{.}368,k_2=k_1$

and if carried out in a CSTR

$\frac{C_{R,\text{m}\text{a}\text{x}}}{C_{A0}}=\frac{1}{[1+(\frac{k_2}{k_1}{)}^{\frac{1}{2}}{]}^2}$