Deduction of relationship between molecular mass and vapour density

Deduction of relationship between molecular mass and vapour density

Relative Molecular Mass

Relative molecular mass is the ratio of the mass of one molecule of a substance to the mass ^th of a carbon atom, or 1 amu.

Vapour Density

Vapour density is the ratio of the mass of a volume of a gas, to the mass of an equal volume of hydrogen, measured under the same conditions of temperature and pressure.

According to Avogadro's law, equal volumes of all gases contain equal number of molecules.

Thus, let the number of molecules in one volume = n,

Cancelling 'n' which is common, we get

However, since hydrogen is diatomic.

When we compare the formulae of vapour density with relative molecular molecular mass, they can be represented as

We can therefore substitute the above equation, and arrive at the below formula

Now on cross multiplication, we have

2 x vapour density = Relative Molecular Mass of a gas

or,

Relative Molecular Mass = 2 x Vapour density