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.


Where, NA is Avogadro’s number.


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.


23