Question

8. One mole of an ideal gas at S.T.P occupres 22.4L, What is the ratio of molar volume to
the atomic volume of a mole of hydrogen? Why is this ratio so large? Take the radius of
hydrogen molecule to be 1 A.​

Answer 1

One mole of an ideal gas at S.T.P occupres 22.4L, What is the ratio of molar volume to

the atomic volume of a mole of hydrogen? Why is this ratio so large? Take the radius of

hydrogen molecule to be 1 A.Molar volume =22.4litre=22.4×10-3m3. ... Molar volumeAtomic volume=22.4×10-33.154×10-7=7.1×104. This ratio is large due tolarge intermolecular separtions.

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, Va = 6.023 × 1023 × 0.524 × 10–30

                                                                        = 3.16 × 10–7 m3

Molar volume of 1 mole of hydrogen atoms at STP, 

Vm = 22.4 L = 22.4 × 10–3 m3

∴VaVm=3.6×10−722.4×10−3=7.08×104

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.