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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 ?

Q 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?

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Radius of hydrogen atom = 0.5 \AA = 0.5 x 10-10 m  (Size here refers to Diameter!)

Volume occupied by the hydrogen atom= \frac{4}{3} \pi r^3

4/3 \times 22/7 \times ( 0.5 \times 10^{-10})^3

= 0.524 \times 10^{-30} m^3

1 mole of hydrogen contains 6.023 x 1023 hydrogen atoms.

Volume of 1 mole of hydrogen atom = 6.023 x 1023 x 0.524 x 10-30

= 3.16 x 10-7 m3

V_{m} = 22.4 L = 22.4 \times 10^{-3} m^3

\frac{V_{m}}{V_{a}} = \frac{22.4\times10^{-3}}{3.16\times10^{-7}} = 7.09 \times 10^4

The molar volume is 7.09 \times 10^4 times greater than the atomic volume.

Hence, intermolecular separation in gas is much larger than the size of a molecule.

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