Derive the relationship between relative molecular mass and Vapour density.

Explanation

(a) The Relative Molecular Mass of a gas or vapour is the ratio between the mass of one molecule of the gas or vapour to mass of one atom of Hydrogen .
(b) 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 same volume of hydrogen")`
(c ) According to Avogadro.s law, equal volumes of all gaese contain equal number of molecules.
(d) V.D. at S.T.P = `("Mass of .n. molecules of a gas a 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 molecules of hydrogen")`
(e ) Since hydrogen is diatomic
V.D = `("Mass of 1 molecule of a gas or vapour at S.T.P")/("Mass of 1 molecules of hydrogen")`
(f) 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 xx "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")`
(g) By substituting the relative molecular mass value in vapour density definition, we get Vapour density (V.D.) = Relative molecular mass/2.
`2 xx "vapour density = Relative molecular mass of a gas"`.