Ethane is chlorinated in a continuous reactor:

$C_2{H}_6+C{l}_2{C}_2{H}_{5}Cl+HCl$

Some of the product monochloroethane is further chlorinated in an undesired side reaction:

$C_2{H}_{5}Cl+C{l}_2{C}_2{H}_{4}C{l}_2+HCl$

Take a basis of $100mol{C}_2{H}_{5}Cl$ produced. Assume that the feed contains only ethane and

chlorine and that all of the chlorine is consumed, and

$($a$)$ carry out a degree$-$of$-$freedom analysis based on atomic species balances.

$($b$)$ carry out a degree$-$of$-$freedom analysis based on extent of reaction.

$($c$)$ The reactor is designed to yield a $15\%$ conversion of ethane and a selectivity of $14$mol

$C_2{H}_{5}C\frac{l}{m}ol{C}_2{H}_{4}C{l}_2,$ with a negligible amount of chlorine in the product gas. Calculate the feed ratio $\frac{\text{m}\text{o}\text{l}{C}_2}{\text{m}\text{o}\text{l}{C}_2{H}_6}$