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(C) The root mean square (rms) velocity of an ideal gas is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.The average velocity of an ideal gas is given by

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

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(C) The root mean square (rms) velocity of an ideal gas is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.The average velocity of an ideal gas is given by $v_{avg} = \sqrt{\frac{8RT}{\pi M}}$.To find the ratio of rms velocity to average velocity,we divide the two expressions:$\frac{v_{rms}}{v_{avg}} = \frac{\sqrt{\frac{3RT}{M}}}{\sqrt{\frac{8RT}{\pi M}}}$.Simplifying the expression,the terms $R$,$T$,and $M$ cancel out:$\frac{v_{rms}}{v_{avg}} = \sqrt{\frac{3RT}{M} 	imes \frac{\pi M}{8RT}} = \sqrt{\frac{3\pi}{8}}$.Thus,the ratio is $\sqrt{\frac{3\pi}{8}}$.

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 gas molecules would be: (Molecular weight of oxygen is $32 \, g/mol$,$R = 8.3 \, J \, K^{-1} \, mol^{-1}$)

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