The ratio of the vapour densities of two gases is equal to the ratio of their molecular masses. In order to understand why this is the case, let's delve into the concept of vapour density and molecular mass.

Vapour Density
Vapour density is defined as the ratio of the density of a gas to the density of hydrogen gas under the same conditions of temperature and pressure. It is denoted by the symbol "D" and is a dimensionless quantity.

Molecular Mass
Molecular mass refers to the mass of a molecule, which is the sum of the masses of all the atoms present in the molecule. It is usually expressed in atomic mass units (amu) or grams per mole (g/mol).

Relationship between Vapour Density and Molecular Mass
The relationship between vapour density and molecular mass can be understood by considering the ideal gas equation:
PV = nRT

Where:
P = Pressure
V = Volume
n = Number of moles
R = Gas constant
T = Temperature

By rearranging the equation, we get:
n = (PV) / (RT)

We can rewrite the equation as follows:
n = (m/M) / (RT/V)

Where:
m = Mass of the gas
M = Molecular mass
RT/V = Density of the gas

From this equation, it can be observed that the number of moles (n) of a gas is directly proportional to the ratio of mass (m) to the molecular mass (M) of the gas.

Explanation of the Given Ratio
Given that the ratio of the vapour densities of the two gases is 1:3, we can write it as:
D₁ / D₂ = 1 / 3

Using the relationship between vapour density and molecular mass, we can write:
M₁ / M₂ = D₁ / D₂

Substituting the given ratio of vapour densities:
M₁ / M₂ = 1 / 3

Therefore, the molecular masses of the two gases are in the ratio of 1:3.

Conclusion
The ratio of vapour densities of two gases is equal to the ratio of their molecular masses. This relationship can be derived from the ideal gas equation. In the given scenario, the ratio of the vapour densities is 1:3, which implies that the molecular masses of the gases are also in the ratio of 1:3.

It's same 1:3