Problem $3(10$ pts$)$ Toluene $(C_7{H}_8)$ reacts with $H_2$ to form benzene $(C_6{H}_6),$ but a side reaction occurs in which a byproduct, diphenyl $(C_{12}{H}_{10}),$ is formed:

$Rxn1$: $C_7{H}_8+H_2{C}_6{H}_6+C{H}_4$

$Rxn2$: $2C_7{H}_8+H_2{C}_{12}{H}_{10}+2C{H}_4$

Hydrogen is added to the gas recycle stream to make the mole ratio of $H_2$ to $C{H}_{4}1$ to $1$ before the gas enters the mixer. The mole ratio of $H_2$ to toluene entering the reactor is $4$ to $1.$ The conversion of toluene to benzene on one pass through the reactor is $80\%,$ and the conversion of toluene to the by$-$product diphenyl is $8\%$ on the same pass. For a fresh feed rate of $100mo\frac{l}{h},$ calculate the molar flowrate of methane in the Purge stream.