Coal has a heating value of $30$ MJ$/$kg and the following molecular composition: C$C_{100}{H}_{100}{S}_1{N}_{0\mathrm{.}5}.$It is burnt in the air without excess oxygen.

$($a$)$ Calculate the emission rate of $S{O}_2$and $N{O}_2$in kg$/$MJ of coal. Assume that the total emission rate of $N{O}_2$is twice the emission rate of fuel $N{O}_2$

$($b$)$ Calculate the mole fraction and volume fraction $($ppmv$)$ of $S{O}_2$and $N{O}_2$ in the flue gas.

$($c$)$ The flue gas of the plant is to be treated with flue gas desulfurization $($FGD$)$ using a limestone $(CaC{O}_3)$ wet scrubber to remove the $S{O}_2.$ Assume that $2$ moles of $CaC{O}_3$ are necessary for every mole of $S{O}_2.$ How much limestone is consumed per ton of coal?

$($d$)$ The flue gas of the plant is to be treated with flue gas denitrification $($FGN$)$ using urea $(CO(N{H}_2){)}_2$ injection directly into the boiler. Assume that a molar ratio $N{O}_2$: $CO(N{H}_2{)}_2=1$:$1$ is necessary. How much urea is consumed per ton of coal?