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The root-mean-square (rms) speed of a hydrogen molecule (H2) at a given temperature and pressure is 4 km/s. What is the rms speed of an oxygen molecule (O2) under the same conditions?

1. 1 km/s
2. 1.5 km/s
3. 2 km/s
4. 2.5 km/s

Correct answer: 1 km/s

Solution

The rms speed formula: v_rms = sqrt(3RT/M). At constant temperature T, v_rms is proportional to 1/sqrt(M). Molar mass of H2 = 2 g/mol, molar mass of O2 = 32 g/mol. Ratio: v(H2)/v(O2) = sqrt(M_O2/M_H2) = sqrt(32/2) = sqrt(16) = 4. Given v(H2) = 4 km/s: v(O2) = v(H2)/4 = 4/4 = 1 km/s.

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