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