In a reactor surrounded by a cooling jacket, to which water at $23\backslash$deg C is fed, sulfur dioxide is oxidized to sulfur trioxide. SO$2$ and $110\%$ excess air are fed to the reactor at $420\backslash$deg C$.$ The reaction proceeds up to $68\%$ conversion of SO$2$ and the products emerge from the reactor at $525\backslash$deg C$.$ The SO$3$ production rate is $2\mathrm{.}0$ X $102$ kg $/$ min.

a$)$ Calculate the feed rates $($standard cubic meters per second$)$ of the

SO$2$ and air feed streams and the degree of progress of the reaction, $($kmol $/$ s$).$

b$)$ Calculate the standard heat of the oxidation reaction of SO$2,$ AH $\backslash$deg r $($kJ $/$ mol$).$ After, taking the molecular species at $25\backslash$deg C as references, prepare and fill in the table of input$-$output enthalpies and write an energy balance to calculate the heat $($kW$)$ that is must transfer from the reactor to the cooling water.

c$)$ Calculate the minimum flow rate of the cooling water if its increase in

temperature should be kept below $14\backslash$deg C$.$