Considew a sample of oxygen behaving like an ideal gas.
Question:

Considew a sample of oxygen behaving like an ideal gas. At $300 \mathrm{~K}$, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be :

(Molecular weight of oxygen is $32 \mathrm{~g} / \mathrm{mol}$; $R=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ )

1. $\sqrt{\frac{3}{3}}$

2. $\sqrt{\frac{8}{3}}$

3. $\sqrt{\frac{3 \pi}{8}}$

4. $\sqrt{\frac{8 \pi}{3}}$

Correct Option: , 3

Solution:

$\mathrm{v}_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}}$

$\mathrm{v}_{\mathrm{avg}}=\sqrt{\frac{8 \mathrm{RT}}{\pi} \frac{\mathrm{M}}{}}$

$\frac{\mathrm{v}_{\mathrm{rms}}}{\mathrm{v}_{\mathrm{avg}}}=\sqrt{\frac{3 \pi}{8}}$