# Consider a sample of oxygen behaving like an ideal gas.

Question:

Consider 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 $\left.32 \mathrm{~g} / \mathrm{mol} ; \mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$

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

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

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

4. (4) $\sqrt{\frac{8 \pi}{3}}$c

Correct Option: , 3

Solution:

(3)

$\mathrm{v}_{\mathrm{ms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$

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

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