Kinetic Theory

JEE Main level, single correct, medium

34 of 168

Question 34 of 168

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 (vrms)\left({v}_{rms}\right) and choose the correct answer from the options given below:

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Answer: (A) vrms(mono)>vrms(dia)>vrms(poly){v}_{rms}(mono)\gt {v}_{rms}(dia)\gt {v}_{rms}(poly)

The RMS speed is given vrms{v}_{rms} =3RTM=\sqrt{\dfrac{3RT}{M}}.
The temperature and pressure is same for all the gases. So the speed is inversely proportional to the square root of the molar mass of the gases.
vrms(mono)=3RT4×10−3vrms(dia)=3RT71×10−3vrms(poly)=3RT352×10−3{v}_{rms}(mono)=\sqrt{\dfrac{3RT}{4\times {10}^{-3}}} {v}_{rms}(dia)=\sqrt{\dfrac{3RT}{71\times {10}^{-3}}} {v}_{rms}(poly)=\sqrt{\dfrac{3RT}{352\times {10}^{-3}}}
vrms∝1M{v}_{\text{rms}}\propto \dfrac{1}{\sqrt{M}}
Hence,
vrms(poly)<vrms(dia)<vrms(mono){v}_{rms}(poly)\lt {v}_{rms}(dia)\lt {v}_{rms}(mono).

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