Derive the relationship between relative molecular mass and Vapour density.

Explanation

Relative molecular mass :
( i) (Hydrogen scale ) : The relative molecular mass of a gas or vapour is the ratio between the mass of one atom of hydrogen .
(ii ) 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
`(V.D) =("Mass of given volume of gas or vapour at S.T.P")/("Mass of same volume of hydrogen ")`
According to Avogardro's Law , equal volumes of all gases contain equal - number of molecules .
THus , let the number of molecules in one volume =-n,then
V.D at S.T.P
`=("Mass of 'n' molecules of gas or vapour at S .T.P ")/("Mass of n molecules of hydrogen ")`
Cancelling 'n' which is common , we get
`V.D =("Mass of 1 molecule of gas or vapour at S.T.P ") /(" Mass of 1 molecule of hydrogen ")`
However , since hydrogen is diatomic
`V.D =("Mass of 1 molecules of a gas or vapour at S.T.P ")/(" Mass of 2 atoms of hydrogen")`
` V.D =("Mass of 1 molecule of a gas or vapour at S.T.P")/( 2xx " Mass of 1 atom of hydrogen ")`
Relative molecular mass ( hydrogen scale )
`=("Mass of 1 molecules of a gas or vapour at STP ")/(" Mass of 1 atom of hydrogen ")`
`V.D = ("Relative Molecular Mass ")/(2)`
` therefore 2 xx ` Vapour density = Molecular mass of a gas Relative molecular mass `= 2xx ` Vapour density .