Equal mass of two gases A and B are kept in two separate containers under the same conditions of temperature and pressure. If the ratio of molar masses of A and B be 2:3, then what will be the ratio of volumes of the two containers?

Explanation

Let the volume of the container holding gas `A=V_(A)` and that of the container holding gas `B=V_(B)` suppose, the molar masses of A and B are `M_(A) and M_(B)`, respectively. Thus, for equal mass (say 'm') of each gas, the number of moles of
`A(n_(A))=(m)/(M_(A))` and that of `B(n_(B))=(m)/(M_(B))`
`therefore` For A `:PV_(A)=(m)/(M_(A))RT and` for `B:PV_(B)=(m)/(M_(B))RT`
`therefore (V_(A))/V_(B) =(M_(B))/(M_(A))=(3)/(2)` [`because` Temperature and pressure of A and B gases are identical]
Hence, the ratio of volumes of the containers=3:2.