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.)

Two containers $A$ and $B$ contain $\mathrm{CO}_2$ gas. Pressure, volume and absolute temperature of the gas in $A$ are 4 times more compared to that in $B$. The mass of the gas in $B$ is $x \mathrm{~g}$, then the mass of the gas in $A$ will be

The rate of diffusion of a gas $A$ is $\sqrt{5}$ times more than that of gas $B$. If the molar mass of $A$ is $x \mathrm{~g} \mathrm{~mol}^{-1}$, the molar mass of $B$ (in $\mathrm{g} \mathrm{mol}^{-1}$ ) is