Relation between vapour density and relative molecular mass — lesson. Science State Board, Class 10.

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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.

Vapour density (VD) = \frac{Mass of a given volume of gas or vapour at STP}{Mass of the same volume of hydrogen}

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

VD at STP = \frac{Mass of " n " molecules of a gas or vapour at STP}{Mass of " n " molecules of hydrogen gas}

Cancelling '\(n\)' which is common, you get,

VD = \frac{Mass of 1 mole of a gas or vapour at STP}{Mass of 1 molecules of hydrogen}

However, since hydrogen is a diatomic,

VD = \frac{Mass of 1 mole of a gas or vapour at STP}{Mass of 2 atoms of hydrogen}

When you compare the formula for vapour density and relative molecular mass, you get,

VD = \frac{Mass of 1 mole of a gas or vapour at STP}{2 \times Mass of 1 atom of hydrogen} ...... (1)

Relative molecular mass (hydrogen scale)

VD = \frac{Mass of 1 mole of a gas or vapour at STP}{Mass of 1 atom of hydrogen} ...... (2)

By substituting the equation (\(2\)) into equation (\(1\)), we get,

VD = \frac{Relative molecular mass}{2}

Now, on cross multiplication, we have,

2 \times Vapour density = Relative molecular mass of a gas

or

Relative molecular mass of a gas = 2 \times Vapour density

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