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 the largest?
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 the largest?

All three vessels are the same size and have the same capacity.

As a result, the pressure, volume, and temperature of each gas are the same.

The three vessels will each contain an equal quantity of the corresponding molecules, according to Avogadro’s law.

This number is equal to Avogadro’s number, that is, .

The relation gives the root mean square speed of a gas with mass and temperature : Where, is Boltzmann constant

For the given gases, and are constants

Therefore, depends only on the mass of the atoms, i.e., As a result, the root mean square speed of the molecules in each of the three scenarios differs.

The mass of neon is the smallest among neon, chlorine, and uranium hexafluoride.

As a result, among the supplied gases, neon has the fastest root mean square speed.