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 $\left.32 \mathrm{~g} / \mathrm{mol} ; \mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$
Correct Option: , 3
Solution:
(3)
$\mathrm{v}_{\mathrm{ms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$
$\mathrm{V}_{\mathrm{avg}}=\sqrt{\frac{8}{\pi} \frac{\mathrm{RT}}{\mathrm{M}}}$
$\frac{\mathrm{v}_{\mathrm{rms}}}{\mathrm{V}_{\mathrm{avg}}}=\sqrt{\frac{3 \pi}{8}}$
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