One method of industrially manufacturing $C{O}_2$ involves the Haber$-$Bosch process.

$C{H}_4+H_{2}OCO+3H_2$ Step $1$

$N_2+3H_{2}2N{H}_3$ Step $2$

$CO+H_{2}OC{O}_2+H_2$ Step $3$

Ammonia $($the product of Step $2)$ is widely used to produce fertiliser. Fertiliser production is

often stopped over the summer. Combined with the increase in demand for soft$-$drinks during

the hot summer last year, the halt in fertiliser production contributed to the $C{O}_2$ shortage.

In Step $3$ an initial mixture of $40$mol of $CO,20$mol of $H_2,$ and $20$mol of $C{O}_2$ in contact with

$40$mol of steam was allowed to come to equilibrium in a reactor at $1100K.$ At $1100K$ this

reaction has a $K_p$ of $0\mathrm{.}64.$

$($d$)$ Calculate the number of moles of each gas leaving the reactor after equilibration.

The standard enthalpies of formation of $C{O}_{(g)},C{O}_{2(g)}$ and $H_2{O}_{(g)}$ are $-110\mathrm{.}5,-393\mathrm{.}5$ and

$-241\mathrm{.}1kJmo{l}^{-1}$ respectively.

$($e$)$ Calculate the enthalpy of reaction for the reaction between $CO$ and steam to form $C{O}_2$

and $H_2.$