At constant temperature and pressure,which gas will diffuse first,$H_2$ or $O_2$?

According to the kinetic molecular theory of gases,the root mean square velocity is proportional to .......

The average speed $(U_{avg})$ of $O_2$ at $\pi \times 10 \ bar$ pressure in an $8 \ L$ container containing $2 \ moles$ is:

Among the following gases,which one has the lowest root mean square velocity at $25 \ ^oC$?

The ratio of root mean square velocity of hydrogen at $50 \, K$ to that of nitrogen at $500 \, K$ is closest to

Case $-1:$ An ideal gas of molecular weight $M$ at temperature $T$.
Case $-2:$ Another ideal gas of molecular weight $2M$ at temperature $T/2$.
Identify the correct statement in the context of the above two cases.