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

Molar volume `=22.4` liters `=22.4xx10^(-3)m^(3) (1"litre"= 10^(-3)m^(3))`
Volume of 1 atom of hydrogen `=4"/"pir^(3)`
`=4"/"3xx3.14xx(0.5xx10^(-10))^(3)`
`=4"/"3xx3.14xx0.125xx10^(-30)m^(3)`
Volume of 1 mole of hydrogen atoms
`=6.02xx10^(23)xx(4)/(3)xx3.14xx0.125xx10^(-30)m^(3)`
`=6.02xx0.125xx4"/"3xx3.14xx10^(-7)m^(3)`
`=3.1xx10^(-7)m^(3)`
`("Molar volume")/("Atomic volume of a mole of hydrogen")`
`=(22.4xx10^(-3)m^(3))/(3.1xx10^(-7)m^(3)) approx 7.2xx10^(4)`
This ratio is so large because inter-atomic separation in a gas is much larger than the size of a atom.