$[24]$ A coal$-$fired power plant burns bituminous coal at a rate of $20\mathrm{.}0$ kg$/$s$.$ Composition analysis shows that the coal contains $2\mathrm{.}0$ wt$\%$ of sulfur. Assume that the combustion efficiency of sulfur in the coal is $98\%($i$.$e$.,98\%$ of the sulfur will convert to SO$2($g$),$ and $2\%$ of the sulfur will be present in the ash$).$a$)$ What is the daily rate of emission of SO$2($g$)$ without the installation of any flue gas desulfurization $($FGD$)$ system? Give your answer in kg$/$d$.$b$)$ A FGD system is installed to remove SO$2($g$)$ by the reaction: SO$2($g$)+$ CaCO$3($s$)+2$H$2$O $+0\mathrm{.}5$O$2($g$)=$ CO$2($g$)+$ CaSO$42$H$2$O$($s$)$What mass of the product CaSO$42$H$2$O$($s$)$ will be produced in one day? Assume a $100\%$ yield of the above reaction $($i$.$e$.,$ all SO$2($g$)$ can be converted to CaSO$42$H$2$O$).$ Give your answers in kg$/$d$.$