One mole of an ideal gas at standard temperature and pressure occupies

1.	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 11. Why is this ratio so large?
Answer» 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.

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 11. Why is this ratio so large?

Answer»

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.