NCERT Solutions Class 11 Physics - Solved Exercise Question 2.17

Question 2.17:

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 ?

Solution:

Radius of hydrogen atom, r = 0.5 Å = 0.5 X 10-10 m
Volume of hydrogen atom = (4/3) π r3
= (4/3) X (22/7) X (0.5 X 10-10)3
= 0.524 X 10-30 m3
Now, 1 mole of hydrogen contains 6.023 × 1023 hydrogen atoms.
∴ 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,
Vm = 22.4 L = 22.4 × 10–3 m3
∴ Vm / Va = 22.4 X 10-3 / 3.16 X 10-7 = 7.08 X 104
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.


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