Ex$.4\mathrm{.}69$ : In the production of formaldehyde, methanol is fed to a steam$-$heated horizontal vaporiser, which produces vapours at $358K(85C)$ and $0\mathrm{.}123$MPag. Air is introduced using a blower. Compressed air is heated to $343K(70C)$ and then mixed in a controlled ratio with methanol vapours such that the mixture contains approximately one volume of air for each volume of methanol vapours. Mixed gas is passed into the reactor and hot product gases from the reactor are cooled and scrubbed in a scrubber. Gases free from methanol and formaldehyde are found to contain :

$C{O}_2=4\mathrm{.}8\%,CO=0\mathrm{.}3\%,C{H}_4=0\mathrm{.}3\%,O_2=0\mathrm{.}3\%,H_2=20\mathrm{.}2\%$ and $N_2=74\mathrm{.}2\%(mole\frac{?}{?}\%).$

The major reactions taking place in the reactor are :

$C{H}_{3}OH$HCHO$+H_2$

HCHO$CO+H_2$

$C{H}_{3}OH+\frac{1}{2}{O}_2$HCHO$+H_{2}O$

$CO+\frac{1}{2}{O}_{2}C{O}_2$

$C{H}_{3}OHC{H}_4+\frac{1}{2}{O}_2$

Calculate : $($a$)$ the $\%$ conversion of methanol and $($b$)$ yield of formaldehyde.