Thermodynamics
Unit 6 tests the first and second laws, enthalpy, Hess's law, entropy and Gibbs free energy as the criterion of spontaneity.
Core rules
- A system exchanges energy and matter with its surroundings; state functions depend only on the initial and final states.
- First law: ΔU = q + w, where w is work done on the system; for reversible expansion, w = −PΔV.
- Enthalpy H = U + PV; at constant pressure, qp = ΔH.
- Standard enthalpy of formation of an element in its standard state is zero.
- Hess's law: the enthalpy change is independent of the route.
- Entropy is a measure of disorder; the second law requires ΔS(total) > 0 for a spontaneous process.
- Gibbs energy: ΔG = ΔH − TΔS; ΔG < 0 spontaneous, ΔG = 0 at equilibrium, ΔG > 0 non-spontaneous.
Worked example
A reaction has ΔH = +50 kJ mol⁻¹ and ΔS = +100 J K⁻¹ mol⁻¹. Find the temperature above which it becomes spontaneous. Convert ΔS to kJ: 0.100 kJ K⁻¹ mol⁻¹. Set ΔG = ΔH − TΔS < 0, so T > ΔH/ΔS = 50/0.100 = 500 K. Above 500 K the entropy term dominates and the reaction is spontaneous.
Traps
- Watch the sign convention: work done by the system is negative in ΔU = q + w.
- ΔH equals ΔU only when Δn(gas) = 0.
- Entropy changes in J K⁻¹ mol⁻¹ must be converted to kJ before combining with ΔH.
- A reaction with ΔH < 0 is not automatically spontaneous; ΔS and T matter.
- Standard conditions mean 298 K, 1 bar and specified states, not arbitrary conditions.