Question

The vapour density of a gas is 16, find its molecular weight.

Answer 1

Hint: Vapour density of a gas is defined as the density of the vapour of a particular gas relative to that of hydrogen at the same pressure and temperature. Vapour density has a relation with molecular weight of gas and based on that relation we will find out the molecular weight of given gas.

Complete answer:
First of all, vapour density is defined as the density of the vapour of a particular gas relative to that of hydrogen at the same pressure and temperature conditions.
So, we can say that vapour pressure of any gas is always found with respect to the hydrogen gas.
Now, the relation between the vapour density of a gas and the molecular weight of that gas is given as:
$V.D. = \dfrac{{M(gas)}}{{M(hydrogen)}}$
Where, V.D. is the vapour density of the gas given.
M (gas) is the molecular weight of the gas given.
M (hydrogen) is the molecular weight of hydrogen gas.
So, if we put the value of molecular weight of hydrogen gas (which is $2gmo{l^{ - 1}}$ )in above equation:
$V.D. = \dfrac{{M(gas)}}{2}$
We can now write the above equation in the form of molecular weight of gas as:
$M(gas) = V.D. \times 2$
Hence, the given value of vapour density of gas is 16, putting this value in above equation,
$M(gas) = 16 \times 2$
$M(gas) = 32gmo{l^{ - 1}}$
Hence, the molecular weight of given gas is $32gmo{l^{ - 1}}$ .

Note:
Vapour density can also be defined as mass of a certain volume of a substance divided by mass of same volume of hydrogen or the mass of n molecules of given gas divided by the mass of n molecules of hydrogen. If a gas has a vapour density less than one, then it will rise in the air and its vapour density is greater than one, then it will sink in air.