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 1).

Why is this ratio so large ?

Answer 1

Radius of hydrogen atom, r = 0.5 Å = 0.5 × 10^-10 m
Volume of hydrogen atom = (4/3) π r³
= (4/3) × (22/7) × (0.5 × 10^-10)³
= 0.524 × 10^-30 m³

Now, 1 mole of hydrogen contains 6.023 × 10²³ hydrogen atoms.
∴ Volume of 1 mole of hydrogen atoms, V_a = 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

$\therefore \frac{V_m}{V_a}=\frac{22.4\times {10}^{-3}}{3.6\times {10}^{-7}}=7.08\times {10}^4$

Hence, the molar volume is 7.08 × 10⁴ times higher than the atomic volume.

The ratio is so large because inter-atomic separation in hydrogen gas is large.