$[50]$ Methyl chloride $(C{H}_{3}Cl)$ and $HCl$ are the products of a reaction between methane $(C{H}_4)$ and chlorine $(C{l}_2).$ In an undesirable reaetion, the methyl chloride reacts with chlorine to form methylene chloride $(C{H}_{2}C{l}_2)$ and $HCl.$ The reactor feed is a gas mixture containing $80$ moles methane and $20$ moles chlorine. All the chlorine is consumed in the reactor. In the product stream of the reactor, which is a gas mixture, the mole ratio of methyl chloride to methylene chloride is $5$:$1.$

The reactor product flows into a condenser where all the methyl chloride and methylene chloride are condensed into a liquid, which is sent into a distillation column and separated into pure components. The gas mixture from the condenser is sent into a gas separation unit where $C{H}_4$ and $HCL$ are completely separated. The methane is recycled back to the reactor to join the fresh feed and the $HCl$ is let out of the process. The schematics of the individual process units are shown below.

Figure $1$: Individual unit operations

$($a$)[15]$ Write down the two balanced chemical reactions then draw and label the flowsheet of the fully connected process with a basis of $100$mol of reactor feed $(80(mol)C{H}_4+20(mol)C{l}_2).$

$($b$)[10]$ Perform degree of freedom analysis on reactor and overall process to show that the molar flow rates of all components in every stream can be calculated.

$($c$)[15]$ Write down the equations and specifications for $($a$)$ reactor alone and $($b$)$ overall process.

$($d$)[10]$ Calculate the molar flow rates of methane and chlorine in the fresh feed.