Practice question

**Ideal gas equation** P V = n R T = (m/M) R T, density ρ = m/V = P M/(R T), molecular mass M (kg/mol), P pressure (Pa), T temperature (K). At given P,T density proportional to M, heavier gases denser, e.g., at 1.5 atm 300 K V=24 L n= P V/(R T)=1.5×1.013×10⁵×0.024/(8.314×300)≈1.46 mol. l = (1)/(√(2) n π d²), n = (1)/(√(2) π d² l).n = (1)/(1.414 × 3.14 × (2 × 10⁻¹⁰))² × 1 × 10⁻⁷ = (1)/(1.77 × 10⁻²⁶) ≈ 5.65 × 10²⁵ m⁻³. Substituting values gives 5.65 × 10²⁵ m⁻³, which matches expected kinetic theory result, confirming mean free path λ