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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?
Solution
Volume of one mole of ideal gas, Vg = 22.4 litre = 22.4 x 10-3 m3
Radius of hydrogen molecule = 1A/2 = 0.5 A = 0.5 x 10-10 m
Volume of hydrogen molecule = 4/3 πr3
= `4/3 xx 22/7 (0.5 xx 10^-10)^3 m^3`
= 0.5236 x 10-30 m3
One mole contains 6.023 x 1023 molecules.
Volume of one mole of hydrogen, VH
= 0.5236 x 10-30 x 6.023 x 1023 m3 = 3.1552 x 10-7 m3
Now `V_g/V_H = (22.4 xx 10^-3)/(3.1548 xx 10^-7)`
=7.1 x 104
The ratio is very large. This is because the interatomic separation in the gas is very large compared to the size of a hydrogen molecule.
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