Q$3$ Methyl bromide is produced from the following elementary, irreversible, liquid$-$phase, isothermal reaction:

$CNBr+C{H}_{3}N{H}_{2}C{H}_{3}Br+NCN{H}_2$

The reaction is carried out in a CSTR $($continuous stirred tank reactor$)$ and a PFR $($plug flow reactor$)$ system. The total volumetric flowrate of the feed entering the CSTR$-$PFR system is $6d{m}^3{s}^{-1}.$ Half of the feed enters the CSTR directly. The CSTR product stream is then mixed with the other half of the feed, and the combined stream then enters the PFR$.$ The concentration of both feed species in the feed is $0\mathrm{.}4mold{m}^{-3}.$ The specific rate constant of the reaction is: $k=0\mathrm{.}15d{m}^{3}mo{l}^{-1}{s}^{-1}.$

$($a$)$ Calculate the volume required to achieve $40\%$ conversion at the exit of the CSTR$.$

$[6$ marks$]$

$($b$)$ Calculate the PFR reactor volume to then raise the overall conversion to $80\%$ at the exit of the CSTR$-$PFR reactors in series system.

$[10$ marks$]$