Practice question

**Molecular mass and density** relation ρ = P M/(R T) allows density calculation, ideal gas law also P = n k_B T where n number density, molecular mass determines mass per molecule, density increases with pressure and decreases with temperature, inverse T dependence. v_rms ∝ (1)/(√(m)), v_CH₄v_O₂ = √(m_O)₂m_CH₄.v_CH₄482 = √((32)/(16)) = √(2) ≈ 1.414.v_CH₄ = 482 × 1.414 ≈ 682 m/s. Substituting values gives 682 m/s, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V = n R T and v_rms = √(3 R T/M) relations.