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Q.Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains Neon (monatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic).
(a) Do the vessels contain equal number of molecules?
(b) Is the root mean square speed of the molecules same in three cases? Justify.
Meghalaya MboseMBOSE Meghalaya 11th Board 2020Subjective· 3mImportance★★★★★
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Start your 14-day free trial to unlock the full solution →Avogadro's law guarantees equal molecule counts in equal volumes at the same T and P, independent of the gas; but rms speed depends on molar mass (v_rms = sqrt(3RT/M)), so the three gases — despite having equal molecule counts — move at very different average speeds.
- Number of molecules: By Avogadro's law/hypothesis, equal volumes of any (ideal) gas at the same temperature and pressure contain equal numbers of molecules, regardless of the nature, mass, or molecular complexity of the gas. This follows directly from the ideal gas equation, PV = NkT (N = number of molecules): for fixed P, V, and T, N is the same for every gas. So YES, all three vessels (Neon, chlorine, uranium hexafluoride) contain an equal number of molecules, since they are at the same T, P, and V.
- Root mean square speed: v_rms = sqrt(3RT/M), where M is the MOLAR MASS of the gas. At the same temperature T, v_rms depends only on M — heavier molecules (larger M) move slower on average, lighter molecules (smaller M) move faster. Approximate molar masses: Neon (monatomic) M ≈ 20 g/mol; Chlorine (Cl2, diatomic) M ≈ 71 g/mol; Uranium hexafluoride (UF6, polyatomic) M ≈ 352 g/mol. …
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