Consider a sample of oxygen behaving like an ideal gas. At 300K ,...

Consider a sample of oxygen behaving like an ideal gas. At $300K$ , the ratio of root-mean-square (RMS) velocity to the average velocity of the gas molecule would be :

(Molecular weight of oxygen is $32g{mol}^{- 1}; R = 8 . 3J{K}^{- 1}{mol}^{- 1}$ )

Options

A $\sqrt{\dfrac{3}{3}}$
B $\sqrt{\dfrac{8}{3}}$
C $\sqrt{\dfrac{3\pi}{8}}$
D $\sqrt{\dfrac{8\pi}{3}}$

Correct answer

C. $\sqrt{\dfrac{3\pi}{8}}$

Step-by-step solution

${v}_{rms} = \sqrt{\dfrac{3RT}{M}}$

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

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

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