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. Average translational KE = (3)/(2) k_B T.1.035 × 10⁻²⁰ = (3)/(2) × 1.38 × 10⁻²/³ × T.T = 1.035 × 10⁻²⁰ × 23 × 1.38 × 10⁻²/³ = 500 K . Substituting values gives 500 K, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π