Derive the relationship between relative molecular mass and Vapour density.

Explanation

The Relative Molecualar 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 certain volume of gas or vapour, to the mass of an equal volume of hydrogen , measured under the same conditions of temperature and perssure .
Vapour Density (V.D) `= ("Mass of 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 gases contain equal number of molecules. Thus , let the number of molecules in one volume = n, then
(d) V.D at S.T.P `= ("Mass of .n. 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 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 2 atoms of hydrogen ")`
(f) By comparing the definintion 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 " )`
Relativen molecular mass (hydrogen scale )
`("Mass of 1 molecuar of a gas or vapour at S.T.P")/("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 molecualr mass / 2 `2 xx` vapour density = Relative molecular mass of a gas .