P$8-9$ B 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 reac$-$

tion 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 $k_{-2}=0\mathrm{.}005h^{-1}.$

$($d$)$ Compare $($a$),($b$),$ and $($c$)$ and describe what you find.

$($e$)$ Vary $k_1,k_2,k_{-1},$ and $k_{-2}.$ Explain the consequence of $k_1>100$ and $k_2<mn\; id="EditorElement\_5590476">0</mn><mn\; id="EditorElement\_5590477">.</mn><mn\; id="EditorElement\_5590478">1</mn>$ with $k_{-1}=k_{-2}=0$

and with $k_{-2}=1,k_{-1}=0,$ and $k_{-2}=0\mathrm{.}25.$