P$8\mathrm{.}9.$ ELEMENTS OF CHEMICAL REACTION NGINEERING FIFTH EDITION $($H$.$ SCOTT FOGLER$)$

The elementary liquid$-$phase series reaction

$A{k}_{1}B{k}_{2}C$

is carried out in a $500-d{m}^3$ batch reactor. The initial concentration of $A$ is $1\mathrm{.}6mo\frac{l}{d}{m}^3.$ The desired

product is $B,$ and separation of the undesired product $C$ is very difficult and costly$.$ Because the

reaction is carried out at a relatively high temperature, the reaction is easily quenched.

$($a$)$ Plot and analyze the concentrations of $A,B,$ and $C$ as a function of time. Assume that each

reaction is irreversible, with $k_1=0\mathrm{.}4h^{-1}$ and $k_2=0\mathrm{.}01h^{-1}.$

$($b$)$ Plot and analyze the concentrations of $A,B,$ and $C$ as a function of time when the first reaction

is reversible, with $k_{-1}=0\mathrm{.}3h^{-1}.$

$($c$)$ Plot and analyze the concentrations of $A,B,$ and $C$ as a function of time for the case where both

reactions are reversible, with $k_{-2}=0\mathrm{.}005h^{-1}.$