$(35$p$)$ Q$1.$ An adiabatic CSTR of $10000L$ carry out a reaction in gas phase $AR,$ with a feed rate of $50000\frac{L}{h}(1$atm and $300C).$ The feed composition is $40\%$A and $60\%$ inert $($ I $).$

a$)$ What will be the conversion of A and the reactor outlet temperature?

b$)$ For the reactor operates at $300C,$ what should be the temperature of feed?

Please state all assumptions and show step$-$by$-$step your solution.

Data: $K_c=4\mathrm{.}19($at $300C),I_{rxn}=3500ca\frac{l}{m}ol($temperature independent$),$ Cpp $=7ca\frac{l}{m}$olK, at $($:$300C\}$