Why 2xVAPOUR DENSITY =RELATIVE MOLECULAR MASS ?

Dear Student
Solution to your asked query is provided below:

Vapour density (VD) 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 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 vapor density = Relative Molecular Mass (RMM) of a gas

or,

Relative Molecular Mass (RMM) = 2 x Vapour density

Hope this information clears your doubt about the topic.
Regards