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. Constant volume: (P₁)/(T₁) = (P₂)/(T₂).P₁ = 1 atm, T₁ = 400 K, T₂ = 200 K.P₂ = P₁ × (T₂)/(T₁) = 1 × (200)/(400) = 0.5 atm . Substituting values gives 0.5 atm, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas