Ethylene oxide is produced by the catalytic oxidation of ethylene:

$2C_2{H}_4+O_{2}2C_2{H}_{4}O$

An undesired competing reaction is the combustion of ethylene:

$C_2{H}_4+3O_{2}2C{O}_2+2H_{2}O$

The feed to the reactor $($not the fresh feed to the process$)$ contains $3$ moles of ethylene per mole of oxygen. The single$-$pass conversion of ethylene is $20\%,$ and for every $100$ moles of ethylene consumed in the reactor, $90$ moles of ethylene oxide emerges in the reactor products. A multiple$-$unit process is used to separate the reactor products: ethylene and oxygen are recycled to the reactor, ethylene oxide is sold as a product, and carbon dioxide and water are discarded.

a$.$ Assume a quantity of the reactor feed stream as a basis of calculation, draw and label the flowchart, perform degree$-$of$-$freedom analyses around the reactor, separator, and mixing point $[$use ER method$].$

b$.$ Calculate the molar flow rates of ethylene and oxygen in the fresh feed needed to produce $1$ ton per hour of ethylene oxide.