$4\mathrm{.}57.$ In the Deacon process for the manufacture of chlorine, $HCl$ and $O_2$ react to form $C{l}_2$ and $H_{2}O.$ Sufficient air $)$ is fed to provide $35\%$ excess oxygen, and the fractional conversion of $HCl$ is $85\%.$

$($a$)$ Calculate the mole fractions of the product stream components, using atomic species balances in your calculation.

$($b$)$ Again calculate the mole fractions of the product stream components, only this time use the extent of reaction in the calculation.

$($c$)$ An alternative to using air as the oxygen source would be to feed pure oxygen to the reactor. Running with oxygen imposes a significant extra process cost relative to running with air, but also offers the potential for considerable savings. Speculate on what the cost and savings might be$.$ What would determine which way the process should be run?