Question

Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be 3 Å.

Answer 1

Diameter of an oxygen molecule, d = 3Å

Radius, r = $\frac{d}{2}=\frac{3}{2}$= 1.5 Å× 10–8 cm

Actual volume occupied by 1 mole of oxygen gas at STP = 22400 cm3

Molecular volume of oxygen gas $v=\frac{4}{3}\pi\,r^3.N$

Where, N is Avogadro’s number = 6.023 × 1023 molecules/mole

∴ $V=\frac{4}{3}×3.14(1.5×10-8)^3×6.023×10^{23}=8.51\,\,cm^3$

Ratio of the molecular volume to the actual volume of oxygen = $\frac{8.51}{22400}$

= 3.8 × 10–4