The following elementary liquid$-$phase reaction system takes place in an isothermal

constant$-$volume batch reactor, with CA$0=2$ mol dm$3$

:

A

k$1$

$->$ B

k$2$

$->$ C

k$1=1\mathrm{.}3\backslash$times $109$

exp $[$

$(83,000+$ n$)$ J mol$1$

RT $]$ min$1$

k$2=2\mathrm{.}4\backslash$times $107$

exp $[$

$(72,000+$ n$)$ J mol$1$

RT $]$ min$1$

n $=$ last three digits of your Student ID

$($a$)$ Derive the time$-$dependent expressions that describe the concentration profiles

for each species.

$($b$)$ On a single graph, plot the concentration profiles for a constant reactor

temperature of $443$ K$.$

$($c$)$ The overall selectivity of B with respect to C should be $2\mathrm{.}5$ mol B$/$mol C when the

concentration of B is at a maximum. Determine the reactor temperature required

to enable this.

$($d$)$ Discuss alternative ways of achieving the selectivity requirement in part $($c$).$