The irreversible gas phase reaction inside a batch reactor is given by $A+B2C$ with

$-r_A=k{C}_A{C}_B$;$,k=210-4m3$mol$*s$

Initially, the reactor contains: $20$mol$\%$ of $A,30$mol$\%$ of $B,$ and $50$mol$\%$ of $C.$

The initial pressure and temperature in the vessel are $P_0=100$kPa and $T=298K.$

For this problem, assume isothermal condition and that all gases are ideal.

$($a$)$ Given that the reactor is a CVBR $($constant volume batch reactor$),$ determine the time it takes for

component A to reach $90\%$ conversion. Give your answer in min.

For Parts $($b$)$ and $($c$),$ suppose the volume of the reactor is made to decrease linearly with time, at a rate of

$0\mathrm{.}1V_0$ every is the volume of batch reactor at time $t=0).$

$($b$)$ Compared to the case of a CVBR$,$ does this "shrinking batch reactor" take longer or less time for

component A to reach $90\%$ conversion? Explain your answer in less than $30$ words and without the use of

equations. $($No explanation, no marks.$)$

$($c$)$ For the shrinking batch reactor, determine the time it takes for component A to reach $90\%$

conversion. Give your answer in min.