Styrene is produced from ethylbenzene in a gas$-$phase reaction.

The true equilibrium constant at $900K$ is $0\mathrm{.}36$ :

Ethylbenzene $C_8{H}_{10}(g)>$ Styrene $C_8{H}_8(g)+H_2(g)$

$($a$)$ The reaction is carried out in an isobaric isothermal continuous flow reactor $($open system, steady$-$state$)$ at $1$ bar and $900K.$ Pure ethylbenzene is fed into the reactor. What maximum conversion can be achieved? $20$ points

$($b$)$ Steam is co$-$fed into the reactor from problem $($a$)$ along with ethylbenzene at a $9$:$1$ molar ratio $(9$ moles of steam are added per $1$ mole of ethylbenzene$).$ Find the maximum conversion and molar composition of the gas mixture at equilibrium. $30$ points

$($c$)$ Now the reaction is carried out in an isothermal constant$-$volume batch reactor $($closed system$)$ at $900K.$ Note that the reactor is not isobaric anymore. The initial pressure is $\frac{1}{b}ar.$ Pure ethylbenzene is loaded into the reactor. Find maximum conversion and pressure in the reactor at equilibrium. $50$ points