Practice question

**Mean free path** λ = 1/(√2 n π d²) is average distance molecule travels between collisions, n number density (m⁻³), d molecular diameter (m), π≈3.14. Inversely proportional to n and d², larger n or d reduces λ. Rearranged d² = 1/(√2 n π λ), so d = √(1/(√2 n π λ)), enabling diameter estimation from measured λ and n. P = (ρ R T)/(M), M = (ρ R T)/(P).P = 1.5 × 1.01 × 10⁵ = 1.515 × 10⁵ Pa.M = (0.72 × 8.31 × 300)/(1.515 × 10⁵) = 0.01185 kg/mol ≈ 11.85 g/mol ≈ 12 g/mol. Substituting values gives 12 g/mol, which matches expected