Question $2($CO$2,$ PO$2,$ C$2,$ C$4)$

Ethane $(C_2{H}_6)$ is formed from dehydrogenation of ethylene $(C_2{H}_2)$ as given below.

$2H_2+C_2{H}_2{C}_2{H}_6$

The fresh feed to the reactor contains $584k\frac{g}{h}$ ethylene $(C_2{H}_2)$ and $200k\frac{g}{h}$ of hydrogen gas $(H_2).$ The outlet stream from the reactor contains $15\%$ hydrogen by mass. Then, the gas mixture enters the membrane separator. $100k\frac{g}{h}$ of product mixture is separated out from the bottom of membrane separator consists of $5\%k\frac{g}{k}g$ hydrogen and $93\%k\frac{g}{k}g$ ethane and $2\%k\frac{g}{k}g$ ethylene. The gas stream leaving the membrane separator is then entered a splitter, where $70\%$ of the mixture is recycle to the reactor and $30\%$ of the mixture is discarded.

a$)$ Redraw and completely label the flow diagram. $(4$ marks$)$

b$)$ Determine the Degree of Freedom for overall system and around membrane separator unit. $(3$ marks$)$

c$)$ Determine the amount of hydrogen reacted $($mol $\frac{?}{h}).(18$ marks$)[$Note: Use the extent of reaction$].$