$($d$)$ The sulphur content from the light naphtha $($LN$)$ product stream of an atmospheric distillation unit that processes Assam crude oil is entirely in the form of thiols $($R$SH.$

$($i$)$ Write the general chemical equation that performs hydrodesulphurisation of thiols, and determine the stoichiometric number of moles of hydrogen gas demand per mole of thiol compound.

$[1$ mark$]$

$($ii$)$ The thiol compounds that are present in the LN are methane$-$thiol, ethanethiol, and propane$-2-$thiol, re$-$write the HDS equation for these three compounds.

$[1$ mark$]$

$($iii$)$ Using the data below, determine the mass of sulphur in $kg($use $4$ significant figures $(\text{'}4$ s$.$f$.\text{'}))$ contained in $100$ barrels of the LN$.$

$[1$ mark$]$

$($iv$)$ Determine the number of moles of hydrogen gas $(4$ s$.$f$.)$ required to hydrodesulphurise individually the methane$-$thiol, the ethane$-$thiol and the propane$-2-$thiol, for $100$ barrels of LN using the elemental sulphur mass distribution in the LN given below:

Methane$-$thiol $55\mathrm{.}00wt\%$

Ethane$-$thiol $32\mathrm{.}70wt\%$

Propane $2-$thiol $12\mathrm{.}30$ wt$\%$

$[1$ mark$]$

$($v$)$ Calculate the total net volume $(4$ s$.$f$.)$ of hydrogen in $m^3($at $0C$ and $1$atm, i$.$e$.$ STP$)$ required to hydrodesulphurise all the thiol content in $100$ barrels of Assam LN$.$

$[2$ marks$]$

Data:

$1$ barrel $=159\mathrm{.}0L$

Assam's $LN$ has $7mg$ of $S$ per litre

Specific Gravity of Assam $LN=0\mathrm{.}6650$

Density of water at $15C,1$atm$=999\mathrm{.}0kg{m}^{-3}$

Molar mass of $S$ is $32\mathrm{.}07gmo{l}^{-1}$

According to the ideal gas law, $1$mol of $H_2$ at $0C$ and $1$atm $($STP$)$ is equivalent to $22\mathrm{.}41L.$