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

$C_4{H}_8{C}_4{H}_6+H_2$

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 $922K.$ The reaction follows the first order, irreversible equation for which the reaction rate constant as a function of temperature is

$\backslash$table$[[T,K,922,900,877,855,832],[k,h^{-1},11,4\mathrm{.}9,2\mathrm{.}04,0\mathrm{.}85,0\mathrm{.}32]]$

The heat of reaction may be taken as constant and equal to $H_R=263\mathrm{.}6ca\frac{l}{m}ol$ and ${}_i{C}_{}=1\mathrm{.}2ca\frac{l}{m}ol*K.$

a$)$ What would be the volume required to achieve $20\%$ conversion if the reactor operated isothermally at $922K$ with a butene$+$steam feed rate of $22$lbmo$\frac{l}{h}.$

b$)$ Calculate the reactor volume to achieve $20\%$ conversion of butene for adiabatic operation if the feed rate is $2$ lbmol butene$/$h and $20$lbmolstea$\frac{m}{h}.$