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Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed (v_rms) and choose the correct answer from the options given below:
(1) v_rms (mono) > v_rms (dia) > v_rms (poly)
(2) v_rms (mono) = v_rms (dia) = v_rms (poly)
(3) v_rms (mono) < v_rms (dia) < v_rms (poly)
(4) v_rms (dia) < v_rms (poly) < v_rms (mono)
- v_rms (mono) > v_rms (dia) > v_rms (poly)
- v_rms (mono) = v_rms (dia) = v_rms (poly)
- v_rms (mono) < v_rms (dia) < v_rms (poly)
- v_rms (dia) < v_rms (poly) < v_rms (mono)
Correct answer: v_rms (mono) > v_rms (dia) > v_rms (poly)
Solution
The root mean square speed of a gas is inversely proportional to the square root of its molar mass. Since neon is monoatomic and has a lower molar mass compared to chlorine (diatomic) and uranium hexafluoride (polyatomic), it will have the highest v_rms, followed by chlorine, and then uranium hexafluoride, which has the highest molar mass.
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