Predict the correct order of rate of diffusion of the following molecules.

What is the relationship between the most probable speed $(\alpha)$,average speed $(v)$,and root mean square speed $(u)$?

The temperature at which $RMS$ velocity of $SO_2$ molecules is half that of $He$ molecules at $300 \ K$ is ............... $K$.

If the $v_{rms}$ is $30 R^{1/2}$ at $27 ^\circ C$,then calculate the molar mass of the gas in kilograms.

The root mean square velocity of one mole of a monoatomic gas having molar mass $M$ is $V_{rms}$. The relation between the average kinetic energy $(E)$ and the $V_{rms}$ is

$RMS$ velocity of one mole of an ideal gas was measured at different temperatures. $A$ graph of $(u_{rms})^2$ (on y-axis) and $T(K)$ (on x-axis) gave a straight line passing through the origin and its slope is $249 \ m^2 \ s^{-2} \ K^{-1}$. What is the molar mass (in $kg \ mol^{-1}$) of the ideal gas? $(R=8.3 \ J \ mol^{-1} \ K^{-1})$