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 hydrogen molecule to be about 1 ). Why is this ratio so large?

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 hydrogen molecule to be about 1 ). Why is this ratio so large?
Answer:
Radius of hydrogen atom, r = 0.5 = 0.5 × 10^–10 m
Volume of hydrogen atom =


Now, 1 mole of hydrogen contains 6.023 × 10^23 hydrogen atoms.
∴ Volume of 1 mole of hydrogen atoms, Va = 6.023 × 10^23 × 0.524 × 10^–30
= 3.16 × 10^–7 m3
Molar volume of 1 mole of hydrogen atoms at STP,
Vm = 22.4 L = 22.4 × 10^–3 m3

Hence, the molar volume is 7.08 × 10^4 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.