Solve

$4\mathrm{.}78.$ Ethylene oxide is produced by the catalytic oxidation of ethylene:

$2C_2{H}_4+O_2$longrightarrow$2C_2{H}_{4}O$

An undesired competing reaction is the combustion of ethylene:

$C_2{H}_4+3O_2$longrightarrow$2C{O}_2+2H_{2}O$

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 emerge in the reactor products. A multiple$-$unit process is used to separate the 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 a degree$-$of$-$freedom analysis, and write the equations you would use to calculate $($i$)$ the molar flow rates of ethylene and oxygen in the fresh feed, $($ii$)$ the production rate of ethylene oxide, and $($iii$)$ the overall conversion of ethylene. Do no calculations.

$($b$)$ Calculate the quantities specified in Part $($a$),$ either manually or with an equation$-$solving program.

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