Practice question

**RMS speed** v_rms = √(3 R T/M) = √(3 k_B T/m) where M molar mass (kg/mol), m molecular mass (kg), k_B=1.38×10⁻²/³ J/K, R=8.314 J/mol·K, T absolute temperature (K). Proportional to √T and 1/√M, lighter gases faster at same T, e.g., H₂ faster than O₂, temperature increase raises v_rms as √T. For a diatomic gas (rigid rotator), 5 degrees of freedom (3 translational + 2 rotational).C_v = (5)/(2) R = (5)/(2) × 8.31 = 20.775 J mol⁻¹ K⁻¹ ≈ 20.8 J mol⁻¹ K⁻¹ . Substituting values gives 20.8 J mol⁻¹ K⁻¹, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π