The non$-$catalytic cracking of butene $($A$1)$ into butadiene $($A$2)$ and hydrogen $($A$3)$ can be described by the following relationship: r$=$k$*$p$1($where

p$1$ is the partial pressure$)$

k$=1\mathrm{.}75*10^10*$ exp$(30200/$T$)$ and a reaction enthalpy of $110710$ kJ$/$kmol$.$

The feed mixture supplied to the reactor consists of butene and inert steam. The reaction temperature is $923$ K$,$ and the pressure is $2$ bar.

The feed mixture consists of $1$kmol$/$h of butene and $1$ kmol$/$h of steam $($water Vapor$)$

a$)$ What average hydrodynamic residence time must be maintained in an isothermal plug flow Reactor PFR to convert $90\%$ of the butene? $($It must definitely be integrated$)10$ points

B$).$ What would be the residence time in a reactor that is ideally back$-$mixed and thus behaves like a back$-$mix reactor? $8$ points