Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root-mean-square (RMS) velocity to the average velocity of the gas molecule would be :
(Molecular weight of oxygen is 32 g mol$$^{-1}$$; $$R = 8.3$$ J K$$^{-1}$$ mol$$^{-1}$$)

The root-mean-square (RMS) velocity of a gas molecule is $$v_{\text{rms}} = \sqrt{\frac{3RT}{M_0}}$$, where $$M_0$$ is the molar mass.

The average velocity of a gas molecule is $$v_{\text{avg}} = \sqrt{\frac{8RT}{\pi M_0}}$$.

The ratio of RMS velocity to average velocity is: $$\frac{v_{\text{rms}}}{v_{\text{avg}}} = \frac{\sqrt{\frac{3RT}{M_0}}}{\sqrt{\frac{8RT}{\pi M_0}}} = \sqrt{\frac{3RT}{M_0} \cdot \frac{\pi M_0}{8RT}} = \sqrt{\frac{3\pi}{8}}$$.

This ratio is independent of temperature, molar mass, and the type of gas.