Formaldehyde, is a versatile chemical with numerous industrial applications. It can be efficiently produced from methanol through a catalytic oxidation reaction and methanol dehydrogenation. This method offers a cost$-$effective and widely used route for the production of formaldehyde, which serves as a crucial building block in the synthesis of resins, disinfectants, and various other chemical products. In a chemical process that produces formaldehyde, a vaporized fresh feed stream $(n_1^{})$ of methanol and oxygen $(85C$;$1(atm))$ is met with a vaporized methanol recycle stream $(R)$ from the first distillation column. The mixed streams $)$ are fed to a silver catalytic packed bed reactor $($PBR$)($R$-101)$ isothermally maintained at $5$atm and $400C.$ The reactor product stream $(n_3^{})$ has a flowrate of USE YOUR GROUP FLOWRATE and contains $35\mathrm{.}60wt\%$ Formaldehyde, $38\mathrm{.}10wt\%$ Water, $24\mathrm{.}40wt\%$ Methanol, $1\mathrm{.}10wt\%$ Oxygen and $0,80wt\%$ Hydrogen. 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 $(i_4)$ 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 $(h_6^{}).$ 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 $(i_7^{})$ is $1\%$ methanol and $1\%$ and, all of the hydrogen and oxygen from stream $(i_4^{}).$ 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 $2).$