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

Radius of hydrogen atom, r = 0.5 Å = 0.5 × 10-10 m

Volume of hydrogen atom = 43πr3

=43×227×0.5×10-103
=0.524×10-30m3

Now, 1 mole of hydrogen contains 6.023 × 1023 hydrogen atoms.

 The volume of 1 mole of hydrogen atoms,

Va=6.023×1023×0.524×10-30=3.16×10-7m3

Molar volume of 1 mole of hydrogen atoms at STP,

Vm=22.4L=22.4×10-3m3
VmVa=22.4×10-33.16×10-7=7.08×104

Hence, the molar volume is 7.08×104 times higher than the atomic volume. For this reason, the inter-atomic separation in hydrogen gas is much larger than the size of a hydrogen atom.