A feed stream containing $70$ mole$\%$ acetaldehyde $(C_2{H}_{4}O)$ and the balance oxygen

enters a reactor. The following reactions occur inside the reactor:

Reaction $1$: $C_2{H}_{4}O+(\frac{1}{2})O_2=>C_2{H}_4{O}_2$

Reaction $2$: $C_2{H}_{4}O+(\frac{5}{2})O_2=>2C{O}_2+2H_{2}O$

Produces desired product $($acetic acid$)$

Side reaction for combustion of acetaldehyde

Acetic acid $(C_2{H}_4{O}_2)$ is the desired product. A separation process following the reactor generates

three product streams: one stream containing $84\%$ of the unreacted acetaldehyde is recycled

back to the reactor; the second contains the remaining acetaldehyde and $C{O}_2$; and the third

contains acetic acid and water. Assume a basis of $100mo\frac{l}{h}$ fed to the reactor.

a$.(4$ pts$)$ Identify the overall system and all of the subsystems on the given flowchart above by

drawing a dashed outline around each. You can redraw the diagram exactly as shown above

on your own paper or copy and paste the above diagram.

b$.(15$ pts$)$ Perform the DOF analysis for the overall system and each of the identified

subsystems. Rules:

$($i$)$ Use the extent of reaction DOF approach for reactive systems.

$($ii$)$ Specify the unknown variables and type of equations used when doing DOF analysis.

$($iii$)$ Treat every DOF analysis separate from the other systems.

$($iv$)$ Do not assume or carry over "known" variables from previous systems with $0$DOF.

$($v$)$ DO NOT write the complete equations in the DOF.

C$.(16$ pts$)$ Write the equations you would use to calculate $n_3,i_4,i_5,$ the fractional yield of

acetic acid in the reactor $($hint: think of which species this expression needs to be written in

terms of$),$ and the selectivity of acetic acid to carbon dioxide production in the reactor.

Use extent of reaction balances for any reactive species. Label each equation using words

$($e$.$g$.,$ extent of reaction for $O_2).$ De not perform anycalculations.