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. C_p - C_v = R, C_v = C_p - R.C_v = 35.4 - 8.31 = 27.09 J mol⁻¹ K⁻¹ ≈ 27.1 J mol⁻¹ K⁻¹. Substituting values gives 27.1 J mol⁻¹ K⁻¹, 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.