Question

If the vapour density for a gas is 20, then what is the volume of 20 g of this gas at NTP?

Answer 1

Hint: The information given to us is of the vapour density. Do not confuse between density and vapour density. Vapour density is the density of a vapour with respect to that of Hydrogen gas. It may be defined as the ratio of the Molar Mass of the gas to that of the hydrogen. It is also said to be the ratio of molar masses.

Complete answer:
The vapor density of a gas is equal to the ratio of Molar Mass of n moles of the gas to the molar mass of the equal moles of hydrogen gas. The molar mass of hydrogen gas was found to be $ = 2 \times 1\mu = 2\mu $
The vapour density $ = \dfrac{{Molar{\text{ }}Mass{\text{ }}of{\text{ }}gas}}{{Molar{\text{ }}Mass{\text{ }}of{\text{ }}{H_2}}} $
The given Vapour density is 20. Substituting in the formula we get,
 $ 20 = \dfrac{{M.M{\text{ }}of{\text{ }}Gas}}{2} $
So, the molar mass of gas $ = 20 \times 2 = 40 $
Given that the mass of the gas is 20g. The no. of moles of the gas given to us is: $ Moles = \dfrac{{Mass}}{{M.M}} $
 $ Moles = \dfrac{{20}}{{40}} = 0.5mol $
The conditions for NTP conditions are: Temperature = 273.15K , Pressure = 1 atm and R = 0.0821 L.atm/mol
According to ideal gas equation: $ P{V_{gas}} = nRT $
 $ {V_{gas}} = \dfrac{{nRT}}{P} $
Given that n =0.5 moles, the volume of the gas will be $ = {V_{Gas}} = \dfrac{{0.5 \times 0.0821 \times 273.15}}{1} = 11.212L $
This is the required answer.

Note:
The vapour density of air is found to be 1. Therefore, if any gas is denser than air it has a vapour density greater than 1, if a gas is less dense than air then it’ll have a vapour density less than 1. The vapour density is a unitless quantity since it is the ratio of Molar Masses.