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. Boyle’s law: P₁ V₁ = P₂ V₂.P₁ = 1.5 atm, V₁ = 18 litres, P₂ = 0.75 atm.V₂ = (P₁ V₁)/(P₂) = (1.5 × 18)/(0.75) = 36 litres. Substituting values gives 36 litres, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas