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

p is the partial pressure$)$

k$=1\mathrm{.}75\backslash *10^10*$ 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.

a$)$ What average hydrodynamic residence time must be maintained in an isothermal tubular reactor to convert $90\%$ of the butene?