The reaction,

$C_2{H}_6{C}_2{H}_4+H_2$

is carried out in a plug flow reactor to produce $4\mathrm{.}44kg{s}^{-1}$ of

ethylene $(C_2{H}_4)$ by cracking pure ethane $(C_2{H}_6)$ at $6\mathrm{.}08$ bar

with $80\%$ molar conversion. The reaction is irreversible and

follows an elementary rate law with a rate constant

measured as $0\mathrm{.}072s^{-1}$ at $727C$ and the activation energy is

$343\mathrm{.}3kJmo{l}^{-1}.$

$($a$)$ determine the reactor volume operating at $727C$

$($b$)$ determine the reactor volume operating at $827C$