Question

Derive the relationship between Relative molecular mass and Vapour density.

Answer 1

(i) The Relative Molecular Mass of a gas or vapour is the ratio between the mass of one molecule of the gas or vapour to the mass of one atom of Hydrogen.

(ii) Vapour density is the ratio of the mass of a certain volume of a gas or vapour, to the mass of an equal volume of hydrogen, measured under the same conditions of temperature and pressure.

Vapour Density (V.D.) =  `"Mass of a given volume of gas or vapour at S.T.P"/"Mass of the same volume of hydrogen"`.

(iii) According to Avogadro’s law, equal volumes of all gases contain an equal number of molecules. Thus, let the number of molecules in one volume = n, then

(iv) V.D at STP =  `" Mass of molecules of a gas or vapour at S.T.P"/"Mass of 'n' ‘molecules of hydrogen"` 
Cancelling ‘n’ which is common, you get

V.D =  `"Mass of 1 molecule of a gas or vapour at S.T.P."/"Mass of 1 molecule of hydrogen"`.

(v) Since hydrogen is diatomic
V.D. = `"Mass of 1 molecule of a gas or vapour at S.T.P."/"Mass of 2 atoms of hydrogen"`

(vi) By comparing the definition of relative molecular mass and vapour density we can write as follows.

V.D. = `"Mass of 1 molecule of a gas or vapour at S.T.P."/(2 × "Mass of 1 atom of hydrogen")` 

Relative molecular mass (hydrogen scale) = `"Mass of 1 molecule of a gas or vapour at STP."/"Mass of 1 atom of hydrogen"` 

(vii) By substituting the relative molecular mass value in vapour density definition, we get

Vapour density (V.D.) = Relative molecular mass/2

⇒ 2 × vapour density = Relative molecular mass of a gas.