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LearnYCH11WCH14 · Unit 4: Rates, Equilibria and Further Organic ChemistryEntropy and energeticsEntropy and Gibbs free energy
Entropy and energetics · Subtopic 2 of 2

Entropy and Gibbs Free Energy

Entropy (SS) measures the number of ways particles and their energy can be arranged; units J K⁻¹ mol⁻¹. SS increases from solid → liquid → gas, with more moles of gas, with dissolving and with temperature. ΔS=∑S(products)−∑S(reactants)\Delta S=\sum S(\text{products})-\sum S(\text{reactants}). Gibbs free energy: ΔG=ΔH−TΔS\Delta G=\Delta H-T\Delta S (convert ΔS\Delta S to kJ). A reaction is feasible when ΔG≤0\Delta G\le0. If ΔH\Delta H and ΔS\Delta S have the same sign, feasibility depends on temperature; the switch occurs at T=ΔH/ΔST=\Delta H/\Delta S. A feasible reaction may still be slow (high activation energy): kinetic vs thermodynamic stability.

Cambridge 9701 Paper 4Edexcel YCH11 WCH14AQA 7405 Paper 1≈ 50 minRevision 1 · updated 2026-10-30
Section 1 of 14

Learning objectives

  • Predict the sign of ΔS\Delta S.
  • Calculate ΔS\Delta S from standard entropies.
  • Use ΔG=ΔH−TΔS\Delta G=\Delta H-T\Delta S to decide feasibility.
  • Find the temperature at which a reaction becomes feasible.
Pause and think

Ice melting is endothermic, yet it happens on its own above 0 °C. How?

Section 2 of 14

Core idea

Start hereWhy do endothermic reactions happen at all?

Ice melts, salt dissolves and baking soda decomposes, all taking in heat. Energy alone can't be what drives change. Entropy is the missing piece.

The big idea

Reactions are feasible when ΔG = ΔH − TΔS is zero or negative. Entropy increase can outweigh an unfavourable enthalpy change at high enough temperature.

1. Four sign combinations

When is a reaction feasible?

The sign of ΔG depends on ΔH, ΔS and T.

Switch temperature
  1. ΔG=ΔH−TΔS\Delta G=\Delta H-T\Delta S
    Gibbs equation.
  2. 0=ΔH−TΔS0=\Delta H-T\Delta S
    At the boundary, ΔG = 0.
  3. T=ΔHΔST=\frac{\Delta H}{\Delta S}
    Rearrange; ΔS in kJ K⁻¹ mol⁻¹.
Worked exampleDecomposing limestone

CaCO3→CaO+CO2\mathrm{CaCO_3\rightarrow CaO+CO_2}: ΔH = +178 kJ mol⁻¹, ΔS = +161 J K⁻¹ mol⁻¹. Minimum temperature?

Goal
TT in K.
Strategy
Set ΔG = 0.
  1. ΔS=0.161 kJ K−1mol−1\Delta S=0.161\ \text{kJ K}^{-1}\text{mol}^{-1}
    Match units with ΔH.
  2. T=1780.161=1106 KT=\frac{178}{0.161}=1106\ \text{K}
    Switch temperature.
AnswerAbout 1106 K (833 °C).
✓ CheckLime kilns run at about 900 °C ✓.
Common misconceptionUnits ΔS is usually given in J; ΔH in kJ. Convert before calculating.

Summary

  • Gas > liquid > solid entropy.
  • ΔG = ΔH − TΔS ≤ 0 → feasible.
  • T = ΔH/ΔS.
  • Feasible is not the same as fast.
Key words
Entropy
Measure of the number of ways particles and energy can be arranged.
Gibbs free energy
ΔG = ΔH − TΔS; negative for feasible reactions.
Kinetic stability
Feasible reaction prevented by a high activation energy.
HistoryGibbs. Josiah Willard Gibbs, working alone at Yale in the 1870s, published the theory of free energy in an obscure journal. Its importance was recognised only years later in Europe.
Fun factDiamonds are not forever. Diamond turning into graphite has negative ΔG at room temperature, but the activation energy is so high it would take longer than the age of the universe.
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