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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 A ). Why is this ratio so large?

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Radius of hydrogen atom, r = 0.5 = 0.5 × 10–10 m

Volume of hydrogen atom = (4/3)πr3 

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, 

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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