The following liquid$-$phase series reaction is carried out in a

$500$ dm$3$ batch reactor. Pure A is fed into a reactor with the initial

concentration of $1\mathrm{.}6$ mol dm$-3$

$.$ The desired product is B and the

separation of undesired product C is very difficult and costly$.$ All

the reactions are first order with respect to the indicated reactant

with the rate constants k $1$ and k $2.$

$21$

$->2$

$->$

Question $4$

The following liquid$-$phase series reaction is carried out in a

$500d{m}^3$ batch reactor. Pure $A$ is fed into a reactor with the initial

concentration of $1\mathrm{.}6mold{m}^{-3}.$ The desired product is $B$ and the

separation of undesired product $C$ is very difficult and costly$.$ All

the reactions are first order with respect to the indicated reactant

with the rate constants $k_1$ and $k_2.$

$2A{?}^{k_1}B{?}^{k_2}C$

$($a$)$ Express the concentrations of A and $B$ as a function of

time, $t.$

$[13$ marks$]$

$($b$)$ What is the optimum reaction time to obtain maximum

product $B$ if the reaction rate constants are $k_1=0\mathrm{.}4h^{-1}$

and $k_2=0\mathrm{.}01h^{-1}?$

$[8$ marks$]$

$($c$)$ Determine the conversion of A and concentrations of $A$

and $B$ at the optimum reaction time determined in part

$($b$).$ The same values of $k_1$ and $k_2$ given in part $($b$)$ should

be used.

$[4$ marks$]$

Additional information: $\frac{dy}{dx}+py=$exp$(-px)\frac{d(exp(px)y)}{dx}$