Relate cell potential to Gibbs energy
Use ΔG° = −nE°cellF to connect electrochemical feasibility with Gibbs free-energy change.
A Level; Cambridge International Chemistry 9701, 2028–2030 syllabus, Topic 24. Treat all tabulated electrode potentials as reduction potentials; state conditions, phases, signs and units. Written practice is self-checked
Before you begin
- Use AS redox half-equations, oxidation states, mole ratios, current and charge.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is the relationship between standard Gibbs energy and standard cell potential?
What you will learn
- Use ΔG° = −nE°cellF
- Identify n from the balanced cell reaction
- Convert joules to kilojoules and compare signs
Electrical work and Gibbs energy share a sign test
For a balanced cell reaction, ΔG° = −nE°cellF, where n is the number of moles of electrons transferred per mole of reaction as written, E°cell is in volts and F is in C mol⁻¹.
A positive E°cell gives negative ΔG° and indicates a feasible reaction under standard conditions. A negative cell potential gives positive ΔG° for that direction; the reverse direction has the opposite signs.
Use the balanced electron count and compatible units
Calculate with joules per mole because V×C = J. Divide by 1000 to report kJ mol⁻¹ if appropriate. The coefficient n is the electrons cancelled in the balanced net equation, not the number of electrons in one unscaled half-equation.
This relation concerns standard values. It does not give reaction rate, activation energy or a non-standard ΔG without the relevant conditions.
Pause and explain
If E°cell is positive, what sign is ΔG° for the same standard reaction?
Worked example
Calculate ΔG° for a cell reaction transferring 2 mol e⁻ with E°cell=+1.10 V and F=96 500 C mol⁻¹.
Show the worked solution
- Use n=2.
- ΔG°=−nE°cellF=−2×1.10×96 500 J mol⁻¹.
- Convert to kJ mol⁻¹.
Answer ΔG° = −212 300 J mol⁻¹ ≈ −212 kJ mol⁻¹.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
For a balanced reaction transferring 2 mol e⁻, E°cell=+0.80 V and F=96 500 C mol⁻¹. Calculate ΔG° in kJ mol⁻¹.
Give me a hint
Use −nE°F, then convert joules to kilojoules.
Compare my reasoning
- ΔG° = −2×0.80×96 500 J mol⁻¹.
- Calculate −154 400 J mol⁻¹.
- Divide by 1000.
ΔG° = −154.4 kJ mol⁻¹.
Look for these in your work
- Electron number used
- Negative sign correct
- Unit conversion correct
A cell has E°cell=−0.25 V for the reaction as written and transfers one mole of electrons. What is the sign of ΔG° and which direction is feasible?
Give me a hint
Apply the leading minus sign and compare the reverse direction.
Compare my reasoning
- ΔG° = −nE°F, so a negative E° gives positive ΔG°.
- The written direction is not feasible under standard conditions.
- The reverse direction has positive E° and negative ΔG°.
ΔG° is positive for the written direction, so the reverse direction is feasible under standard conditions.
Look for these in your work
- Sign relation applied
- Direction assessed
- Reverse relation stated
A learner uses n=1 because the reduction half-equation contains one electron, although the balanced cell reaction transfers two electrons. Correct the choice.
Give me a hint
Use the number of electrons cancelled in the balanced overall reaction per mole of reaction.
Compare my reasoning
- Balance the two half-equations first.
- Count electrons cancelled in the overall equation.
- Use n=2 in ΔG° = −nE°cellF.
Use n=2 because two moles of electrons are transferred in the balanced cell reaction. The electron count must match the reaction basis used for ΔG°.
Look for these in your work
- Balanced reaction basis identified
- Electron count corrected
- Formula applied consistently
Common mistakes
- Dropping the negative sign
- Using the wrong electron count after balancing
- Reporting V·C as volts instead of joules
- Claiming ΔG° predicts rate
What can you explain now?
What is the relationship between standard Gibbs energy and standard cell potential?
Compare with the explanation
ΔG° = −nE°cellF
The negative sign links a positive cell potential to a negative Gibbs change.
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Make it stick
How do E°cell, the balanced electron count and Faraday's constant determine ΔG° and feasibility?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.