$($a$)$ A gas mixture containing $20g$ each of benzene, phenol and $n-$butane is contained in a vessel.

Determine the mass and mole fractions of the mixture.

$($b$)$ Two engineers $($Steve and Carl$)$ are calculating the average molecular weight of a gas mixture

containing oxygen and a compound A$.$ Steve uses $32$ as the molecular weight of oxygen and reports

the average molecular weight as $39\mathrm{.}2.$ On the other hand, Carl uses $16$ as the molecular weight of

oxygen and determines an average molecular weight as $32\mathrm{.}8.$

Who do you think is right, and why? Next, estimate the mole $\%$ of oxygen. Also, what is the molecular

weight of the compound $A?$

$($c$)$ Air in the vicinity of a power plant is said to contain $17ppmS{O}_2($molar basis$).$ Express this

concentration as a mole fraction. If the air is at a pressure of $\frac{1}{b}ar,$ determine the partial pressure of

$S{O}_2$ in mbar.