Q$2$: Ammonia synthesis more sustainable using the reaction : $N_2+H_{2}N{H}_3.$ This elementary gas$-$phase reversible reaction is carried out in an isothermal plug flow reactor. The molar feed is stoichiometric in $N_2$ and $H_2,$ at a constant pressure of $15$ atm and a temperature of $227C.$

$($A$)$: Calculate the equilibrium conversion.

$($B$)$: How would your answer to part $($A$)$ change if the reaction were instead carried out in a constant volume isothermal batch reactor?

Given that: $k_1=1\mathrm{.}34d\frac{m^3}{m}ol.sec$ and $K_{\text{e}\text{q}\text{b}\text{m}}=10.$

$(20$ Marks$)$