$(35$ p$)$ Vanadium oxide was used as a catalyst in the oxidation reaction of methane to produce formaldehyde in a reactor operating at $973K.$ Carbon dioxide was also produced in an undesired side reaction. The feed to the reactor contains $60$ mole$\%$ methane and $40$mole$\%$ oxygen. The reactor is designed on the methane fractional conversion of $0\mathrm{.}622$ and a selectivity of $4\mathrm{.}1$molHCH$\frac{O}{m}$olCO$2.$

$C{H}_4+O_2$HCHO$+H_{2}O$

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

By using these information,

$($a$)$ Draw and label the flow chart.

$($b$)$ Calculate the molar amounts of reactor output stream.

$($c$)$ Calculate the fractional yield of formaldehyde production.