One mole of an ideal gas at NTP occupies 22.4 liters (molar volume). What is the ratio of molar volume to atomic volume to atomic volume of a mole of hydrogen ? Take size of hydrogen molecule to be 1 Å. Why is this ratio so large?

Explanation

Volume of one mole of ideal gas, `V_(g)`
`=22.4` litre `=22.4xx10^(-3) m^(3)`
Radius of hydrogen molecule `=1 A//2`
`=0.5 A=0.5xx10^(-10) m`
Volume of hydrogen molecule`=4//3 pi r^(3)`
`=4//3xx22//7(0.5xx10^(-10))^(3) m^(3)`
`=0.5238xx10^(-30) m^(3)`
One mole contains `6.023xx10^(23)` molecules.
Volume of one mole of hydrogen, `VH`
`=0.5238xx10^(-30)xx6.023xx10^(23) m^(3)=3.1548xx10^(-7) m^(3)`
Now `V_(g)//V_(H)=22.4xx10^(-3)//3.1548xx10^(-7)=7.1xx10^(4)`
The ratio is very large. This is because the interatomic separation in the gas is very large compared to the size of a hydrogen molecule.