Sulfur dioxide is oxidized to sulfur trioxide in a reactor: $S{O}_2+\frac{1}{2}{O}_{2}S{O}_3.S{O}_2$ and $100\%$ excess air are fed to the reactor at $400C.$ Conversion of sulfur dioxide is $65\%$ and products leave the reactor at $500C.$ The production rate of $S{O}_3$ is $1250mo\frac{l}{h}.$

$($a$)$ Calculate the feed rate of the $S{O}_2$ and air streams and the extent of reaction.

$($b$)$ Calculate the heat in $kW$ that must be transferred from the reactor.

$($c$)$ The reactor is surrounded with a water jacket. Into this jacket water is fed at $25C$ and heat is transferred to this water. Exit temperature of the water is $40C.$ If the heat transferred from the reactor is $0\mathrm{.}50kW,$ What is the flow rate of this cooling water? Use the heat capacity data given below and the additional tabulated enthalpy data for oxygene, nitrogene and water.

$S{O}_2$:$C_p(k\frac{J}{m}ol.xC)=38\mathrm{.}91{10}^{-3}+3\mathrm{.}9{10}^{-5}T((T)isinC)$

$S{O}_3{C}_p(k\frac{J}{m}ol.xC)=48\mathrm{.}5{10}^{-3}$