$1.$ A tubular reactor is to be designed for production of butadiene from butene by the gas phase reaction,

$!"!$# $+$ $

The composition of the feed is $10$ moles of steam per mole of butene and no butadiene and hydrogen. The reactor

operates at $2$ atm with an inlet temperature of $922$ K$.$ The reaction follows the first order, irreversible equation for

which the reaction rate constant as a function of temperature is

T$,$ K $922900877855832$

k$,$ h$-1114\mathrm{.}92\mathrm{.}040\mathrm{.}850\mathrm{.}32$

The heat of reaction may be taken as constant and equal to $\%=263\mathrm{.}6/$ and &$\text{'}$& $=1\mathrm{.}2/.$

a$)$ What would be the volume required to achieve $20\%$ conversion if the reactor operated isothermally at $922$ K

with a butene$+$steam feed rate of $22$ lbmol$/$h$.$

b$)$ Calculate the reactor volume to achieve $20\%$ conversion of butene for adiabatic operation if the feed rate is $2$

lbmol butene$/$h and $20$ lbmol steam$/$h$.$