$($d$)$ A Fischer$-$Tropsch $($FT$)$ plant generates light hydrocarbons gas as by$-$product of the main gasoline fraction. Hydrogen supplementation is required in the FT feed in order to achieve a molar $H_2$:$CO$ ratio of $2.$ The inlet gas composition to the plant is $80$ vol$\%$ methane, $20$ vol$\%$ ethane $(C_2{H}_4).$

$($i$)$ Write the two stoichiometric reactions of steam reforming $($SR$)$ for each compound.

$[2$ marks$]$

$($ii$)$ Assuming $1000$kmo$\frac{l}{h}$ of light hydrocarbons gas are produced at the $FT$ stage, and SR conversions of $70\%$ for $C{H}_4$ and $100\%$ for $C_2{H}_4,$ determine in kmo$\frac{l}{h}$ the maximum yields of $CO,H_2$ and the molar flows of unreacted gas leaving the SR process.

$[2$ marks$]$

$($iii$)$ The steam reformer operates on a molar feed steam to carbon ratio $($S:C$)$ of $2\mathrm{.}5,$ determine the total molar feed rate of water, and the total molar rate of unreacted water leaving the steam reformer.

$[2$ marks$]$