Ethylene $(C_2{H}_4)$ gas enters a well$-$insulated reactor and reacts completely with $400\%$ of theoretical air, each at $25C,2$atm. The products exit the reactor at $2$atm. For operation at steady state and ignoring kinetic and potential energy effects, determine

$($a$)$ the balanced reaction equation

$($b$)$ the temperature, in $K,$ at which the products exit $($Hint: When doing the iterative solving process, get a first trial estimate temperature by assuming all products are nitrogen.$)$

$($c$)$ the rate of entropy production, in $k\frac{J}{K}$ per kmol of ethylene.