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 1

1. Why is this ratio so large?

Answer 1

Atomic volume of a mole of hydrogen 

= (4/3)πr³ x N_A 

= (4/3) × 3.14 × (1 × 10^-10)³ × 6.022 × 10²³

= 2.52 × 10^-6 m³

Required ratio

= (22.4L/(2.52 x 10^-6 m³))

= ((22.4 x 10^-3)/(2.52 x 10^-6))

= 9 × 10³

This ratio is large because the intermolecular separation in a gas is much larger than the size of a molecule.