Question

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 1Å ). Why is this ratio so large?

Answer 1

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

Now, 1 mole of hydrogen contains 6.023 × 10²³ hydrogen atoms.
Therefore, Volume of 1 mole of hydrogen atoms, Va = 6.023 × 10²³ × 0.524 × 10^–30
= 3.16 × 10^–7 m³
Molar volume of 1 mole of hydrogen atoms at STP,
V_m = 22.4 L = 22.4 × 10^–3 m³

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.