Given:
Molar volume of an ideal gas at STP = 22.4 L = 2.24 × 10−2 m3
Size (diameter) of a hydrogen molecule ≈ 1 Å = 1 × 10−10 m
So, radius r ≈ 0.5 × 10−10 m
Number of molecules in one mole = Avogadro number,
NA = 6.02 × 1023
Step 1: Atomic (molecular) volume of one hydrogen molecule
Assuming the hydrogen molecule to be spherical:
Volume of one molecule,
V1 = (4/3)πr3
V1 = (4/3)π (0.5 × 10−10)3
V1 ≈ 5.24 × 10−31 m3
Step 2: Atomic volume of one mole of hydrogen
Vatomic = NA × V1
Vatomic = (6.02 × 1023) × (5.24 × 10−31)
Vatomic ≈ 3.15 × 10−7 m3
Step 3: Ratio of molar volume to atomic volume
Required ratio:
= (Molar volume) / (Atomic volume)
= (2.24 × 10−2) / (3.15 × 10−7)
≈ 7.1 × 104
Final Answer:
The ratio of molar volume to atomic volume of one mole of hydrogen is approximately:
≈ 105
Why is this ratio so large?
In a gas, molecules are extremely far apart compared to their own size.
Most of the volume occupied by a gas is empty space, not the actual volume of the molecules.
Weak intermolecular forces and high molecular speeds keep the molecules widely separated.
Hence, the molar volume of a gas is enormously larger than the actual volume occupied by its molecules, making the ratio very large.