Two gases, A and B having equal mass are kept in two separate vessels under identical conditions of temperature and pressure. If the ratio of their molecular masses be 2:3, find the ratio of the volumes of the vessels.

Explanation

Let, `M_(A)&M_(B)` be the molar rmasses off A & B respectively.
As per given data, `M_(A):M_(B)=2:3`
`therefore M_(A)=(2)/(3)xxM_(B)`
here, mass of A=mass of B=Wg(say)
`therefore` In W g of each A and B, the ratio of number of moles,
`n_(A):n_(B)=(W)/(M_(A)),(W)/(M_(B))=(M_(B))/(M_(A))=(M_(B))/((2)/(3)xxM_(B))=3/2 =3:2`
Since under the identical conditions of temperature and pressure, the volumes of gases are directly proportional to their number of moles, [because according to Avogadro's law, `V prop n` at the same temperature and pressure.] the ratio of volumes of two gases, i.e., the ratio of volumes of two vessels.
`V_(A): V_(B)=n_(A): n_(B)=3:2`.