$2.$ Ethanol can be produced commercially by the hydration of ethylene:

C$2$H$4+$ H$20->$ C$2$H$5$OH $($Reaction $1)$

Some of the product is converted to diethyl ether, an unwanted byproduct, in the side reaction:

$225->(2$H$5)2$O$+2$O $($Reaction $2)$

The feed to the reactor contains ethylene, steam, and an inert gas. The reactor exit stream contains $41\mathrm{.}3$ mole$\%$ ethylene, $3\mathrm{.}5\%$ ethanol, $0\mathrm{.}18\%$ ether, $11\mathrm{.}32\%$ inerts, and the balance water. The exit stream flow rate is $500$ mol$/$min$.$

a$.$ Sketch and label the flow diagram.

b$.$ Write out the atomic balance equations for the process. Do not solve.

c$.$ Calculate the molar flow rate of each component in the inlet feed stream.

d$.$ Which component is the limiting reactant.

e$.$ Calculate the extent of reaction for reaction $1.$