Entropy and spontaneityEdexcel A-Level Chemistry: Revision notes
Section 1
Why enthalpy change alone is not enough
Most spontaneous reactions are exothermic, but some endothermic reactions occur at room temperature: dissolving ammonium nitrate, ethanoic acid with ammonium carbonate, and barium hydroxide octahydrate with ammonium chloride. So ΔH alone does not control whether a reaction occurs.
The missing factor is entropy.
Section 2
Entropy and the direction of change
Entropy, S, is a measure of the disorder of a system: the number of ways the particles and their energy can be arranged. The natural direction of change is towards increasing total entropy.
Standard entropy units: J K⁻¹ mol⁻¹. Gases ≫ liquids > solids.
Entropy is in joules, enthalpy is usually in kilojoules. Convert ΔH to J before dividing by T.
Section 3
Why entropy changes occur
Changes of state: solid → liquid → gas gives increasing entropy as particles become freer to move.
Dissolving an ionic lattice: an ordered lattice becomes freely moving aqueous ions, so entropy generally increases (ammonium nitrate).
Reactions where the number of moles changes: more moles of gas in the products means a large increase (CaCO₃ → CaO + CO₂); fewer moles of gas means a decrease (burning magnesium: 2Mg(s) + O₂(g) → 2MgO(s), ΔS system negative).
Section 4
ΔS total and ΔS system
ΔS total = ΔS system + ΔS surroundings. A reaction is feasible if ΔS total is positive.
ΔS system = ΣS(products) − ΣS(reactants)
Worked example: CaCO₃ → CaO + CO₂ with S = 92.9, 39.7, 213.6: ΔS system = (39.7 + 213.6) − 92.9 = +160.4 J K⁻¹ mol⁻¹.
Section 5
ΔS surroundings
ΔS surroundings = −ΔH / T (ΔH in J mol⁻¹, T in kelvin).
An exothermic reaction gives energy to the surroundings, so ΔS surroundings is positive; an endothermic reaction takes energy in, so it is negative. The effect is smaller at higher temperatures.
Worked example: CaCO₃ decomposition at 298 K: −178 000 ÷ 298 = −597 J K⁻¹ mol⁻¹, so ΔS total = 160.4 − 597.3 = −437 J K⁻¹ mol⁻¹: not feasible at 298 K.
Always show: formula, substitution with J (not kJ), answer with sign and unit, and the conclusion about feasibility.
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Entropy and spontaneity
- In a demonstration, solid barium hydroxide octahydrate is mixed with solid ammonium chloride in a flask. The mixture becomes a liquid, ammonia gas is given off and the flask becomes so cold that it freezes a wet wooden block to the bench. The reaction is Ba(OH)₂·8H₂O(s) + 2NH₄Cl(s) → BaCl₂(s) + 2NH₃(g) + 10H₂O(l). It happens spontaneously at room temperature even though it is endothermic.Explain, in terms of disorder, why the entropy of the system increases in this reaction.2 marks
- The Haber process for making ammonia, N₂(g) + 3H₂(g) → 2NH₃(g), is exothermic with ΔH = −92 kJ mol⁻¹. A student uses it to practise calculating the entropy change of the surroundings, and assumes that ΔH does not change with temperature.Explain why the entropy change of the surroundings is positive for an exothermic reaction.2 marks
- Calcium carbonate decomposes on heating: CaCO₃(s) → CaO(s) + CO₂(g). The enthalpy change is ΔH = +178 kJ mol⁻¹. Standard entropies in J K⁻¹ mol⁻¹: CaCO₃(s) 92.9; CaO(s) 39.7; CO₂(g) 213.6.Calculate the entropy change of the system, ΔS system, for the decomposition.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).