Theory:

Relative molecular mass (hydrogen scale):
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.
Vapour density:
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.
VapourdensityVD=MassofagivenvolumeofgasorvapouratSTPMassofthesamevolumeofhydrogen
 
According to Avogadro's law, all gases have the same number of molecules in equal volumes.
 
Thus, let the number of molecules in one volume \(= n\), then
 
VDatSTP=Massof"n"moleculesofagasorvapouratSTPMassof"n"moleculesofhydrogengas
 
Cancelling '\(n\)' which is common, you get,
 
VD=Massof1moleofagasorvapouratSTPMassof1moleculesofhydrogen
 
However, since hydrogen is a diatomic,
 
VD=Massof1moleofagasorvapouratSTPMassof2atomsofhydrogen
 
When you compare the formula for vapour density and relative molecular mass, you get,
 
VD=Massof1moleofagasorvapouratSTP2×Massof1atomofhydrogen......1
 
Relative molecular mass (hydrogen scale)
 
VD=Massof1moleofagasorvapouratSTPMassof1atomofhydrogen......2
 
By substituting the equation (\(2\)) into equation (\(1\)), we get,
 
VD=Relativemolecularmass2
 
Now, on cross multiplication, we have,
 
2×Vapourdensity=Relativemolecularmassofagas
or
Relativemolecularmassofagas=2×Vapourdensity