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  • 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).

Q13.8  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). Do the vessels contain equal number of respective molecules? Is the root mean square speed of molecules the same in the three cases? If not, in which case is vrms the largest ?

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As per Avogadro's Hypothesis under similar conditions of temperature and pressure equal volumes of gases contain equal number of molecules. Since the volume of the vessels are the same and all vessels are kept at the same conditions of pressure and temperature they would contain equal number of molecules.

Root mean square velocity is given as

v_{rms}=\sqrt{\frac{3kT}{m}}

As we can see vrms is inversely proportional to the square root of the molar mass the root mean square velocity will be maximum in case of Neon as it's molar mass is the least.

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