Question

one mole of ideal gas at standred 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 size of the hydrogen molecule to be about 1 A)
why is this ratio so large?​

Answer 1

Molar volume =22.4litre=22.4×10-3m3. This ratio is large due to large intermolecular separtions.

hope it helps you

Answer 2

➙ Given:-

• Molar volume = 22.4 L

➙To Find :-

• a] The ratio of molar volume to the atomic volume of a mole of hydrogen = ?
• b] Why is this ratio so large = ?

➙Solution :-

[a] Volume of one mole of ideal gas (Vg)

= 22.4 litre

=22. 4 x 10^-3 m^3

• Radius of hydrogen molecule

▶ 1 A/2

▶ 0.5 A

▶ 0.5 x 10^-10 m

• Volume of hydrogen molecule

▶ 4/3 πr^3

▶ 4/3 x 22/7 [0.5 x 10^(-10)] m^3

▶ 0.5328 x 10^-30 m^3

➨ Now we know, One mole contains

6. 023 x 10^23 molecules

➨Volume of one mole of hydrogen(VH)

=0. 5238 x 10^-30 x 6. 023 x 10^23 m^3

=3. 1548 x 10^-7 m^3

➨ Now ;

▶ Vg/VH

▶ 22.4 x 10^-3 / 3. 1548 x 10^-7

▶ 7. 1 x 10^4

[b]

➨The Ratio is very Large ;

This is because the intratomic separation in the glass is very large compared to the size of a hydrogen molecule!