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 Å). why is this ratio so large?

Answer 1

V_molar = 22.4 litre = 22.4 x 10^-3 m³

and r = 1/2 Å = 0.5 x 10^-10 m

For sphere, V = 4/3 πr³

We get volume of hydrogen molecule

= 4/3 πr³ = 4/3 x 3.14 x (0.5 x 10^-10)³

= 0.5236 x 10^-30 m³

Volume of molecule in 1 mole of hydrogen,

V_molecular = 0.523 x 10^-30 x 6.0225 x 10²³

=3.153 x 10^-7 m³

V_molar/V_molecular = (22.4 x 10^-3)/(3.153 x 10^-7)

= 7.1 x 10³ =10⁴

This high ratio is because of intermolecular spaces in gas being much larger than size of the molecule.