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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 molecule would be: (Molecular weight of oxygen is 32 g/mol; R = 8.3 J K⁻¹ mol⁻¹)

1. √(3/3)
2. √(8/3)
3. √(3π/8)
4. √(8π/3)

Correct answer: √(3π/8)

Solution

vrms = sqrt(3RT/M) and vavg = sqrt(8RT/(pi*M)). Their ratio is sqrt(3/(8/pi)) = sqrt(3*pi/8), independent of T and M.

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