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9476 / 2027
Electrochemistry

Lesson 4 of 7

Gibbs energy and combined potentials

Use electron amounts to combine energy changes correctly.

A-Level 9476 (2026-2027)

  • I can apply the Gibbs energy and potential relationship.Syllabus

    Syllabus 9476, 12(i). Apply the Gibbs energy and potential relationship.

Add Gibbs energies when combining half-reactions

The electron count connects an intensive potential to an extensive energy change.

ΔG° = -nFE°cell. Here n is the number of moles of electrons transferred per mole of the cell reaction as written, and F is the charge per mole of electrons. With F in C mol-1 and E in V, ΔG° is in J mol-1 of reaction because 1 V = 1 J C-1.

Worked exampleConvert a cell voltage into free energy

Find ΔG° for Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s), with E°cell = 1.10 V and F = 9.65 × 104 C mol-1.

Try it first. Then show the worked stepsHide the worked steps
  1. The balanced reaction transfers two electrons, so n = 2.
  2. ΔG° = -2(9.65 × 104)(1.10) = -212300 J mol-1.
  3. Divide by 1000 to express the result in kJ mol-1.
Answer

ΔG° = -212 kJ mol-1. Doubling the reaction would double n and ΔG°, but E°cell would remain 1.10 V.

When two reduction steps combine to make a new reduction half-equation, their E° values cannot simply be added. Convert each to its corresponding -nFE° energy contribution relative to the same reference, add those contributions with the required signs, then divide by -nF for the combined half-equation.

Worked exampleFind the potential for a combined iron reduction

Given Fe3+ + e- → Fe2+, E°1 = +0.77 V, and Fe2+ + 2e- → Fe, E°2 = -0.44 V, find E° for Fe3+ + 3e- → Fe.

Try it first. Then show the worked stepsHide the worked steps
  1. The first step contributes -F(0.77); the second contributes -2F(-0.44).
  2. Add: ΔG°combined = -F[0.77 + 2(-0.44)] = +0.11F.
  3. The combined step transfers three electrons, so -3FE°combined = +0.11F.
  4. E°combined = [0.77 + 2(-0.44)]/3 = -0.0367 V from the rounded supplied data.
Answer

Approximately -0.04 V, consistent with the Data Booklet. The result is electron-weighted, not the sum +0.33 V or an unweighted average.

Check your understanding

A cell reaction has E = +0.50 V and transfers two electrons. What changes if the equation is written in reverse?

  1. E becomes -1.00 V, since reversing the cell doubles the voltage
  2. E becomes -0.50 V and delta G changes sign; n is still 2
  3. E stays +0.50 V, since an electrode potential keeps its sign
Show the answer

E becomes -0.50 V and delta G changes sign; n is still 2

Reversing the reaction reverses its direction, so E and delta G change sign. The same two electrons are transferred, so n stays 2.