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

`1A^(0)=10^(-10)m`
Atomic volume of 1 mole of hydrogen
= Avagadros number `×` volume of hydrogen molecule
`=6.023xx10^(23)xx(4)/(3)xxpixx(10^(-10)m)^(3)`
`=25.2xx10^(-7)m^(3)`
Molar volume = `22.4 L = 22.4 × 10^(–3) m^(3)`
`("Molar volume")/("Atomic volume")=(22.4xx10^(-3))/(25.2xx10^(7))=0.89xx10^(4)~~10^(4)`
This ratio is large because actual size of gas molecule is negligible in comparison to the inter molecular separation.