The two reactions occur simultaneously in the presence of a silver catalyst in the PBR are as follows and the fractional conversion of methanol is $0\mathrm{.}655.$

$C{H}_{3}OH+\frac{1}{2}{O}_{2}C{H}_{2}O+H_{2}O$

$C{H}_{3}OHC{H}_{2}O+H_2$

$2C{H}_{3}OH+\frac{1}{2}{O}_{2}2C{H}_{2}O+2H_{2}O+H_2$

$(3)$ Overall reaction

The reactor effluents are separated using a distillation column $(T-101)$ set at $(63\mathrm{.}5C$;$1(atm))$ in which the overhead product $(n_4)$ is gases $($Oxygen$,$ Hydrogen, Methanol, Water and Formaldehyde$)$ while the bottoms product $(n_5^{})$ contains $1\%$ formaldehyde, $99\mathrm{.}1\%$ methanol and $99\mathrm{.}1\%$ water from the reactor. After separation, the bottom stream is then heated $(n_6^{})$ to match the temperature and pressure of the feed stream before parts of it is purged and recycled back to react. The recycle stream $(R)$ contains $98\mathrm{.}99\%$ methanol, $28\mathrm{.}99\%$ formaldehyde and $20\mathrm{.}4665\%$ water from stream $(n_6^{}).$ However, stream $(($:$n_6^{}\}$ is removed from the system as a purge stream $(P)$ to lower accumulation of unreacted methanol, water and formaldehyde in the system. The purge stream contains the balances of methanol, formaldehyde and water that were not recycled from stream $(n_6^{}).$ The overhead product gases $($Oxygen$,$ Hydrogen, Methanol, Water and Formaldehyde$)$ of stream $(($:$n_4^{}\}$ are further separated by a distillation column $(T-102)$ set at $(25C$;$1(atm))$ to increase the purity of formaldehyde. The overhead product $(n_7^{})$ is $1\%$ methanol and $1\%$ and, all of the hydrogen and oxygen from stream $(n_4^{}).$ The bottom products $(n_8^{}).$ is mainly the balance of methanol, water and $1\%$ formaldehyde from stream $(n_4^{}).$

Answer the following questions:

Determine the mole flow $(mo\frac{l}{h}r$ and the mole$\%$ of the reactor product.

Determine the moles $(mo\frac{l}{h}r$ and mole $\%$ of methanol and oxygen fed.

Determine the moles $(mo\frac{l}{h}r)$ and mole $\%$ of methanol, oxygen, formaldehyde, water and hydrogen present in each stream. $($Attach an excel sheet showing all the calculations$).$

Determine the degrees of freedom of the overall system. Comment on your findings from the degrees of freedom analysis.

Determine the heat of reaction of methanol oxidation reaction and methanol dehydrogenation. Use the extent of reaction method. What is the overall heat of reaction?

Use excel to draw a fully labelled block flow diagram $($BFD$)$ for this process.

Note: $($Name all your streams and label the streams with the values of the mole$/$hr and mole$\%$ you calculated in $1$ and $2).$

Determine the energy balance on each stream including the purge stream and recycle stream. What is the overall energy balance of the system? $($Attach an excel sheet showing all the calculations$).(20)$

Note: Construct an inlet$-$outlet table to show how you arrived to your answer$/$findings$.$

Calculate the percentage yield of formaldehyde. Is the yield good? Justify your answer.

Determine the heat added$/$removed to keep the reactor temperature constant $400C.$

Determine the heat supplied by the heater to raise the temperature of methanol from $63\mathrm{.}5C$ to $85C.[5]$

Determine the feasibility and energy costs associated with running the system for a month.

$($Hint: Look up the prices of each chemical species and use South Africa's electricity tariffs$).$