IB Chemistry HL — Reactivity 1.4: Entropy and Spontaneity (Gibbs Energy)

This whole sub-topic is Higher Level only. Enthalpy alone does not decide whether a reaction happens — some endothermic reactions are spontaneous. The missing ingredient is entropy, and the two combine in the Gibbs energy, ΔG, which is the real test of spontaneity.

👆 Predict ΔS signs · type into the Gibbs calculator · drag temperature on the ΔG–T plot

1. Entropy, S R1.4.1

Entropy (S) measures how dispersed the matter and energy of a system are — the more ways the particles and their energy can be arranged, the higher the entropy. Units are J K⁻¹ mol⁻¹. Entropy rises going solid → liquid → gas, when a solid or liquid produces a gas, when the number of moles of gas increases, and when a solid dissolves. Predict the sign of ΔS:

ΔS sign predictor — pick a change

2. Calculating ΔS° and ΔG° R1.4.2

Every substance has an absolute standard entropy S° (unlike enthalpy, entropy has a true zero — a perfect crystal at 0 K). For a reaction:

ΔS°_reaction = Σ S°(products) − Σ S°(reactants)

The Gibbs energy change combines enthalpy and entropy at a temperature T (in kelvin):

ΔG° = ΔH° − TΔS°

Watch the units. ΔH° is usually in kJ mol⁻¹ but S° (and ΔS°) is in J K⁻¹ mol⁻¹ — you must convert ΔS° to kJ (÷1000) before multiplying by T, or you will be out by a factor of 1000. Try the calculator:

Gibbs energy calculator · ΔG = ΔH − TΔS (ΔS auto-converted from J to kJ)

ΔH° (kJ mol⁻¹)

ΔS° (J K⁻¹ mol⁻¹)

Temperature T (K)

Default values are the thermal decomposition of calcium carbonate, CaCO₃(s) → CaO(s) + CO₂(g).

3. The condition for spontaneity R1.4.3

A reaction is spontaneous (thermodynamically feasible) when ΔG < 0. If ΔG = 0 the system is at equilibrium; if ΔG > 0 the forward reaction is not spontaneous. Because ΔG° = ΔH° − TΔS°, the signs of ΔH and ΔS give four cases — click each:

ΔH < 0, ΔS > 0exothermic + entropy rises

ΔH > 0, ΔS < 0endothermic + entropy falls

ΔH < 0, ΔS < 0exothermic + entropy falls

ΔH > 0, ΔS > 0endothermic + entropy rises

4. How temperature decides it R1.4.3

When ΔH and ΔS have the same sign, spontaneity depends on temperature. Since ΔG° = ΔH° − TΔS° is a straight line in T (slope −ΔS°, intercept ΔH°), it crosses ΔG = 0 at the changeover temperature:

T = ΔH° ÷ ΔS°　(setting ΔG° = 0)

Drag the temperature slider: the plot shows ΔG against T for the CaCO₃ decomposition (ΔH° = +178 kJ, ΔS° = +161 J K⁻¹). It only becomes spontaneous above about 1106 K (≈ 833 °C) — which is why a lime kiln must be so hot.

Common mistakes examiners see

Which quantity decides whether a reaction is spontaneous?✗ ΔH — exothermic means spontaneous. ✓ ΔG. A reaction is spontaneous when ΔG < 0. Some endothermic reactions are spontaneous because a large positive ΔS wins.

In ΔG = ΔH − TΔS, what unit trap catches people out?✗ None — just plug the numbers in. ✓ ΔH is in kJ but ΔS is in J K⁻¹. Convert ΔS to kJ (÷1000) first, or you are wrong by 1000×.

What is the sign of ΔS when gas moles decrease (e.g. N₂ + 3H₂ → 2NH₃)?✗ Positive. ✓ Negative — 4 mol of gas become 2 mol, so matter and energy are less dispersed.

Does a positive ΔG mean the reaction can never happen?✗ Yes, never. ✓ It means not spontaneous at that temperature. If ΔH and ΔS share a sign, changing T can flip ΔG — spontaneity is temperature-dependent.

How do you find the temperature where a reaction becomes feasible?✗ Set ΔH = 0. ✓ Set ΔG = 0, giving T = ΔH ÷ ΔS (with consistent units).

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