Consider a closed reactor used to carry out the zero$-$order liquid phase reaction A$+2$B $=4$C$.$ At the initial instant, C$($A$0)=1\mathrm{.}0$ mol$/$L$,$ C$($B$0)=6\mathrm{.}0$ mol$/$L and C $($C$0)=10$ mol$/$L

$($a$)$

Under the conditions presented, what is the limiting reactant? Derive the design equation relating to the conversion of the limiting reactant$-$

$($b$)$

Knowing that the conversion of the reaction $($in relation to the limiting agent$)$ reaches $25\%$ after $50$ minutes of operation, calculate the time necessary to reach a conversion of $50\%.$

$($c$)$

What are the concentrations of A$,$ B and C at the instant of time calculated in the previous paragraph?

$($d$)$

With the same initial concentrations, at $500\backslash$deg C a $100\%$ conversion is achieved in $400$ minutes while at $1000"$C the same conversion is achieved in $100$ minutes. Calculate the activation energy of the reaction.

$($e$)$

Calculate the temperature at which the reactor in line $($b$)$ was operating.