At what temperature will the RMS velocity of sulphur dioxide molecules at 400 K be the same as the most probable velocity of oxygen molecules?

The variation of volume of an ideal gas with its number of moles $(n)$ is obtained as a graph at 300 K and 1 atm pressure. What is the slope of the graph ?

At 400 K , an ideal gas is enclosed in a $0.5 \mathrm{~m}^3$ vessel at pressure of 203 kPa . What is the change in temperature required (in K ), if it occupies a volume of $0.2 \mathrm{~m}^3$ under a pressure of 304 kPa ? (Nearest interger)

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.)

At 300 K and 760 torr pressure, the density of a mixture of He and $\mathrm{O}_2$ gases is $0.543 \mathrm{gL}^{-1}$. The mass percent of oxygen approximately is $$ \left(R=0.0821 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right) $$