Question $1(9$ marks$)$ A summer student is transferring a $50LC{O}_2$ gas cylinder at $3000$ psig using a $4$

$m^3$ elevator. The student wants to ride the elevator with the cylinder inside, but as someone who took

CHE$112,$ you know this is very dangerous due to risks such as asphyxiation in the event of gas leakage.

Asphyxiation occurs rapidly when oxygen mole fraction is less than $0\mathrm{.}06.$

Assuming $C{O}_2$ can escape from the cylinder but air in the elevator cannot enter the cylinder, calculate the

mole fraction of oxygen $)$ in the elevator at equilibrium. Consider the elevator to be a closed system

and everything inside is at $25C.$ Assume the composition of air is $21\%$ oxygen and $79\%$ nitrogen.