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What is the ratio of the rms speed of molecules in 8 g of O2 gas at 1200 K (and 10 bar) to the rms speed of molecules in 16 g of O2 gas at 300 K (and 20 bar)?

1. 1
2. sqrt(2)
3. 2
4. 2*sqrt(2)

Correct answer: 2

Solution

The rms speed formula is v_rms = sqrt(3RT/M). Since both samples are O2 (same M), the ratio depends only on temperature: v1/v2 = sqrt(T1/T2) = sqrt(1200/300) = sqrt(4) = 2. Pressure and mass are irrelevant to rms speed.

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