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 solid, C = f × (R)/(2) × N_A = f × (R)/(2) × 1 = f × (R)/(2).Given C = 25 J mol⁻¹ K⁻¹, R = 8.31 J mol⁻¹ K⁻¹.25 = f × (8.31)/(2), f = (25 × 2)/(8.31) ≈ 6. Substituting values gives 6, which matches expected kinetic theory result, confirming mean