$($a$)$ Gaseous $HCl$ undergoes air oxidation to produce chlorine gas according to the equation:

$4HCl+O_2$longrightarrow$2C{l}_2+2H_{2}O$

If $20$moles of $HCl$ are fed to the reactor along with $50\%$ excess air and the reaction achieves $75\%$ conversion, diagram the process and determine:

$($i$)$ the molar composition of the entering air;

$($ii$)$ the composition of the product stream on a mole basis;

$($iii$)$ the process equation for the operation.