Problem $7.$ Formaldehyde $(HCHO)$ is produced when methane $(C{H}_4)$ is reacted with oxygen $(O_2).$ In an unwanted side reaction, methane is combusted to $C{O}_2.$ The reactions are as follows:

$C{H}_4+O_2$HCHO$+H_2{O}_{r}xn1$

$C{H}_4+2O_{2}C{O}_2+2H_{2}Orxn2$

The gas leaving the reactor contains $6\mathrm{.}1mo{l}_{CH}C{H}_4,32\%$HCHO and $3\mathrm{.}2\%C{O}_2$ in addition to the $O_2$ and $H_{2}O.$ A separation process removes all of the HCHO and water as a liquid, the unreacted $O_2$ and $C{O}_2$ leave as the gaseous product and all of the unreacted methane is recycled to the process.

$7$a$.$ Perform a degree of freedom analysis around the reactor. All of the process variables have been provided for clarity. You must choose a basis for this problem.

$7$b$.$ Solve for all of the unknowns on the flowchart.

$7$c$.$ Calculate the fractional conversion of methanol in the reactor