Q$3.(4$ marks$)$

Based on the statement given below, answer the following questions:

Liquid reactant A decomposes as follows:

$AR$;$r_R=k_1(C_A{)}^2$;$k_1=0\mathrm{.}4\frac{m^3}{m}ol.$min

$AS$;$r_S=k_2{C}_A$;$k_2=2mi{n}^{-1}$

A feed of aqueous $)=(40\frac{\text{m}\text{o}\text{l}}{m}3$ enters in an ideal mixed flow reactor $($MFR$),$ decomposes into $R$&$S.$ A mixture of $A,R$ and $S$ exit the reactor. Find out the following for $x_A=0\mathrm{.}9.$

$($a$)$ Determine the exit concentration of $R.$

$($b$)$ Determine the time constant.