Problem $2$

The irreversible gas phase reaction inside a batch reactor is given by

$A+B2C$

with

$A+B2C$

$-r_A=k{C}_A{C}_B$;$,k=2{10}^{-4}\frac{m^3}{(mol)*s}$

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.