How much free energy corresponds to a cell voltage?
You will be able to: Use ΔG°=−nFE° with the correct electron count and units.
How much free energy corresponds to a cell voltage?
Two reactions can have the same voltage yet transfer different total energy if they move different amounts of charge. Voltage and total reaction free energy are related but are not the same quantity.
A useful starting point: How do reduction potentials combine into a cell voltage? →
Words and symbols before equations
- n
- Moles of electrons transferred per mole of the balanced reaction as written.
- Faraday constant, F
- Charge per mole of electrons, about 96485 C/mol e⁻.
- Coulomb, C
- Unit of electric charge.
- ΔG°=−nFE°
- Relation between standard cell potential and standard reaction free energy.
What this picture assumes
Original teaching model with supplied rounded data. Numerical states, units and assumptions are specified below; no measured reaction rate is implied. A supplied balanced redox reaction with chosen n and E°. F=96485 C/mol e⁻; ΔG° is reported per mole of that reaction. These controls compare hypothetical reactions rather than changing an ion’s actual charge.
Read the picture in three steps
- Read the species and labels first. Identify what each symbol and line represents. Read the units and fixed conditions before comparing quantities.
- n=2 and E°=1.10 V give ΔG°=-212.3 kJ/mol reaction. The standard forward reaction is favored. A voltage is not a total energy amount.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the chemistry
Find n by canceling electrons in the balanced overall reaction. Do not add electron counts from both half-reactions; they describe the same transferred electrons.
Multiply nFE° to obtain joules per mole of reaction because C×V=J. The minus sign makes a positive E° correspond to negative ΔG°.
Scaling the equation multiplies n and ΔG° by the same factor while E° stays fixed. Reversing it keeps the positive electron count n but changes E° and ΔG° signs.
Combining this relation with ΔG°=−RT ln K gives ln K=nFE°/(RT). This connects voltage to equilibrium preference, without implying that standard potential describes every nonstandard operating mixture.
A worked example, step by step
For Zn+Cu²⁺→Zn²⁺+Cu, n=2 and E°=1.10 V. Calculate ΔG°.
- Identify n=2 mol e⁻ per mol reaction.
- ΔG°=−2×96485×1.10 J/mol.
- ΔG°=−212267 J/mol≈−212 kJ/mol.
- The negative sign matches favored standard discharge; doubling the equation would double this value, not the voltage.
Use n from the balanced net reaction and convert joules to kilojoules when reporting kJ/mol.
Do the two half-reactions’ two-electron counts add to n=4?
Compare with an explanation
No. The same two electrons are lost and gained; n=2 for the balanced transfer.
Predict. Change one thing. Explain.
Vary n for a supplied fixed E° and then reverse the reaction. Explain why the energy amount scales while the voltage is held fixed.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
n=2 and E°=1.10 V give ΔG°=-212.3 kJ/mol reaction. The standard forward reaction is favored. A voltage is not a total energy amount.
Original teaching model with supplied rounded data. Numerical states, units and assumptions are specified below; no measured reaction rate is implied. A supplied balanced redox reaction with chosen n and E°. F=96485 C/mol e⁻; ΔG° is reported per mole of that reaction. These controls compare hypothetical reactions rather than changing an ion’s actual charge.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using energy and entropy contributions, electron and ion bookkeeping, or the stated cell reaction. Identify what the representation cannot tell you.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA balanced reaction transfers 3 electrons and has E°=+0.20 V. Find ΔG°, state standard favorability and explain the effect of doubling the equation.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: n=3 mol e⁻ per mol reaction.
- 1 point: ΔG°=−3×96485×0.20≈−57.9 kJ/mol.
- 1 point: The forward reaction is favored under standard conditions.
- 1 point: Doubling the equation doubles n and ΔG° to about −115.8 kJ/mol, while E° remains +0.20 V.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What is one volt?
One joule per coulomb.
RECALL 2What does F convert?
Moles of electrons to charge.
RECALL 3Which n is used?
The balanced reaction’s transferred electron count.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
How much free energy corresponds to a cell voltage?
- ΔG°=−nFE°; F=96485 C/mol e⁻.
- Positive E° ↔ negative ΔG° ↔ K>1 at specified T.
Remember: Use n from the balanced net reaction and convert joules to kilojoules when reporting kJ/mol.
Conditions: Original teaching model with supplied rounded data. Numerical states, units and assumptions are specified below; no measured reaction rate is implied. A supplied balanced redox reaction with chosen n and E°. F=96485 C/mol e⁻; ΔG° is reported per mole of that reaction. These controls compare hypothetical reactions rather than changing an ion’s actual charge.
Refresh Kid · AP Chemistry Unit 9 · Objectives 9.9.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 9.9, objective 9.9.A. CED effective Fall 2024 and June 2026 clarifications checked September 17, 2026. Unit 9: Thermodynamics and Electrochemistry, Topics 9.1–9.11. Focused lesson names, examples, models and assessments are original Refresh Kid teaching materials, not additional official topics or official AP questions. Official corrections.
The model states its assumptions beside the diagram. Numerical thermodynamic examples state standard conditions, temperature, reaction scaling and unit conventions. Supplied data and schematic geometry are teaching models. Standard ΔG° describes standard-state favorability and relates to K; actual direction depends on composition. Thermodynamic favorability does not predict rate. Nonstandard cell potential is taught through Q, distance from equilibrium and qualitative Nernst reasoning; algorithmic substitution alone does not demonstrate the assessed understanding. Electrode positive/negative labeling is excluded from assessed scope. Oxidation at the anode and reduction at the cathode remain essential. Faraday calculations assume the stated current efficiency and electron stoichiometry. Rotatable particle models are schematic inventories, not measured molecular trajectories. Virtual models do not replace required supervised laboratory work.
Teaching resources: The Organic Chemistry Tutor video titles/descriptions and topic coverage were checked for optional links; no claim is made to have watched every video. No creator scripts, examples, worksheets or artwork were copied. GitHub’s 3D website collection and its Three.js camera-control example informed the idea of controllable spatial inspection. Scientific diagrams, geometry and interactions here are original. The self-hosted Three.js runtime retains its MIT license. Camera rotation changes the view, not the chemistry.
Independent teacher review and observation of students remain pending. Implementation checks do not certify scientific accuracy, accessibility or learning effectiveness. This is a review edition.
Optional official resource: Released AP Chemistry questions and scoring guides. This archive contains questions across units; it is not an assignment of every question to this lesson.
The teaching sequence is informed by the IES learning guide; this exact implementation has not been evaluated with learners.
Want to work through this with a tutor?
Bring your question about How much free energy corresponds to a cell voltage? Your explanation and answers remain free to access.