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)/(n), n ∝ P. If P increases by 4 times (0.25 to 1), n increases 4 times, l reduces to (1)/(4).New l = 3.0 × 10⁻⁶/4 = 7.5 × 10⁻⁷ m. Substituting values gives 7.5 × 10⁻⁷ m, which matches expected kinetic theory result, confirming mean free path λ