$.$ Sulfur dioxide is oxidized to sulfur trioxide in a reactor : SO$2+(1)/(2)$ O$2->$ SO$3.$ SO$2$ and $100\%$ excess air are fed to the reactor at $400\backslash$deg C$.$ Conversion of sulfur dioxide is $65\%$ and products leave the reactor at $500\backslash$deg C$.$ The production rate of SO$3$ is $1250$ mol$/$h$.$

$($a$)$ Calculate the feed rate of the SO$2$ 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 $25\backslash$deg C and heat is transferred to this water. Exit temperature of the water is $40\backslash$deg C$.$ If the heat transferred from the reactor is $0\mathrm{.}50$ kW$,$ 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.

SO$2$: Cp $($kJ$/$ mol.x $\backslash$deg C$)=38\mathrm{.}91$x $10-3+3\mathrm{.}9$x$10-5$ T $($T is in $\backslash$deg C $)$

SO$3$ Cp $($kJ$/$ mol.x $\backslash$deg C$)=48\mathrm{.}5$x $10-3$