Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following is: (a) The root mean square speed of sulfur hexafluoride is the largest (b) All vessels contain unequal number of respective molecules (c) The root mean square speed of molecules is same in all three cases (d) The root mean square speed of helium is the largest

Answer: (d). Same P, V, T means the same number of molecules in each vessel (Avogadro), so (b) is wrong. vrms = √(3RT/M), so at the same T the lightest gas is fastest. Helium ( M = 4) is the lightest, SF₆ the heaviest. So the answer is (d) helium has the largest vrms.

Three vessels of equal capacity have gases at the same temperature… | NEET 2022 (Phase 2)

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Degrees of Freedom & Internal Energy

Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following is:

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Answer: (d)

Same $P$ , $V$ , $T$ means the same number of molecules in each vessel (Avogadro), so (b) is wrong.
$v_{rms} = \sqrt{\frac{3RT}{M}}$ , so at the same $T$ the lightest gas is fastest.
Helium ( $M = 4$ ) is the lightest, $\text{SF}_6$ the heaviest.
So the answer is (d) helium has the largest $v_{rms}$ .

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