States of Matter and Thermodynamics
This section covers States of Matter and Thermodynamics: gas laws and kinetic molecular theory, real-gas deviations, and the first law, enthalpy, Hess's law, entropy and Gibbs energy. Expect numerical work on ΔH, ΔU and ΔG, plus reasoning about spontaneity.
Core rules
- Ideal gas: PV = nRT. Van der Waals equation corrects pressure and volume: (P + an²/V²)(V − nb) = nRT.
- First law: ΔU = q + w, where w is work done on the system. At constant pressure, ΔH = ΔU + PΔV; for ideal gases, ΔH = ΔU + Δn_gRT.
- Hess's law: enthalpy change is path-independent. Standard enthalpies of formation can be combined.
- Gibbs energy: ΔG = ΔH − TΔS. ΔG < 0 means spontaneous under the stated conditions; at equilibrium ΔG = 0.
Worked example
For N₂(g) + 3H₂(g) ⇌ 2NH₃(g), ΔH° = −92.4 kJ mol⁻¹ and ΔS° = −198 J K⁻¹ mol⁻¹. At 298 K: ΔG° = −92.4 − 298(−0.198) = −92.4 + 59.0 = −33.4 kJ mol⁻¹, so the forward reaction is spontaneous under standard conditions. The entropy term becomes more positive as T rises; ΔG° = 0 at T = ΔH/ΔS = 467 K, above which the forward reaction is no longer spontaneous under standard conditions.
Traps
Use consistent units for ΔH and ΔS; do not omit Δn_g when converting ΔH to ΔU; do not treat ΔG° as a criterion at non-standard concentrations; remember that a spontaneous reaction can be endothermic if TΔS is large and positive.