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one mole of an ideal gas at standard temperature a...

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?

Answer:

Radius of hydrogen atom, r = 0.5 Å = 0.5 × 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 10³⁰ m³

1 mole of hydrogen contains 6.023 × 10²³ hydrogen atoms.

∴ Volume of 1 mole of hydrogen atoms = 6.023 × 10²³ × 0.524 × 10^-30

= 3.16 × 10^-7 m³

Molar volume of 1 mole of hydrogen atoms at STP,

V_m = 22.4 L = 22.4 × 10^-3 m³

∴ V_m / V_a = 22.4 x 10^-3 / 3.16 × 10^-7 = 7.08 × 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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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?

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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?

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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?