Three vessel of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). Do the vessels contains equal number of respectice molecules ? Is the root mean square speed of molecules the same in the three cases ? If not, which case is `v_(rms)` the largest?

Explanation

(a) Yes, the vessels contain equal number of respective molecules. It is because equal volumes of all the gases under same temperature and pressure contain equal number of molecules (Avogadro's hypothesis)
(b) The root mean square speed is given by
`v_(rms)=sqrt((3KT)/(m))rArr v_(rms)prop(1)/sqrt(m)`
Since `v_(rms)` depends upon mass of the molecule of the gas, it will not be same in the three cases. Since `v_(rms)` is inversely proportional to the square root of the mass of the molecules of the gas, it will be largest for the gas, whose molecules are lightest. Therefore `v_(rms)`. Will be largest for neon gas.