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

Emisson rate of $S{O}_2=1\mathrm{.}59$ g$/$GJ and $N{O}_2=1\mathrm{.}14$ g$/$GJ

Mole fraction of $S{O}_2=N{O}_2=0\mathrm{.}00159=1590$ ppmv

a$)$ The flue gas of the plant is to be treated with flue gas desulfurization $($FGD$)$ using a limestone $($CaCO$3)$ wet scrubber to remove the SO$2.$ Assume that $2$ moles of CaCO$3$ are necessary for every mole of SO$2.$ How much limestone is consumed per ton of coal?

b$)$ The flue gas of the plant is to be treated with flue gas denitrification $($FGN$)$ using urea $($CO$($NH$2)2)$ injection directly into the boiler. Assume that a molar ratio NO$2$:CO$($NH$2)2=1$:$1$ is necessary. How much urea is consumed per ton of coal?