# 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?

Given,

Volume of one mole of ideal gas at STP, Vm=22.4L=22.4 × 10-3 m3

Radius of hydrogen atom, r = 1 Å / 2 = 0.5 Å = 0.5 × 10-10 m

Volume of the hydrogen atom, V = (4/3)πr3

V = (4/3)×3.14×(0.5×10-10 m)3

V = = 5.24 × 10-31 m3

One mole of hydrogen atom contains NA = 6.023 × 1023 atoms.

So, Volume of one mole of hydrogen atom,

Vt = 6.023 × 1023 × 5.24 × 10-31 m3

Vt = 3.16 × 10-7 m3

The ratio of molar volume to atomic volume is

Vm �/Vt = 7.089 × 104

This ratio is very high due to the fact that the inter-atomic distance is very high as compared to the size of atoms in hydrogen gas.

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