Practice question

**Collision frequency** Z = n σ v_rel, σ = π d² cross-section, v_rel = √2 v_avg, so Z ∝ n, for air at STP n≈2.5×10²⁵ m⁻³ d≈3×10⁻¹⁰ m λ≈68 nm, collision frequency ~10⁹ s⁻¹, illustrating frequent collisions at atmospheric pressure. P = (ρ R T)/(M), M = (ρ R T)/(P).P = 2 × 1.01 × 10⁵ = 2.02 × 10⁵ Pa.M = (0.8 × 8.31 × 400)/(2.02 × 10⁵) = 0.01318 kg/mol ≈ 13.2 g/mol. Substituting values gives 13 g/mol, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V = n R T