If the density of a mixture of nitrogen and oxygen gases at 400 K and l atm pressure is $0.920 \mathrm{gL}^{-1}$, what is the mole fraction of nitrogen in the mixture? ( $R=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$; assume ideal gas behaviour for oxygen and nitrogen)

An open vessel containing air was heated from $27^{\circ} \mathrm{C}$ to $727^{\circ} \mathrm{C}$. Some air was expelled. What is the fraction of air remaining in the vessel ? (Assume air as an ideal gas.)