Cell Potential and Free Energy
Later electrochemical connection: relate energy per charge to free energy for a balanced redox reaction.
Before this connection: Redox and electrochemistry: balanced half-reactions and cell direction.
AP Chemistry Topic 9.9 · CED printed p. 175 / PDF p. 182. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Before you start
- Balanced redox equations
- Anode/cathode
- Standard free energy
A reduction-potential table lists each half-reaction as a reduction. To build a standard-state galvanic direction, keep the half-reaction with the more positive reduction potential as reduction and reverse the other into oxidation. Balance the electron count, cancel electrons, and check atoms and charge. Then E°cell = E°red,cathode − E°red,anode. Both entries in this subtraction are the tabulated reduction values. Alternatively reverse the anode value into an oxidation potential and add; do not change its sign and also subtract it a second time. A negative answer for an already assigned written direction means that direction is unfavorable under the stated standard comparison.
The energy connection is . n is the positive number of moles of electrons transferred per mole of the balanced net reaction; F ≈ 96485 C mol−1 of electrons. Since 1 V = 1 J C−1, the result is joules per mole of reaction. Positive E° gives negative ΔG°; negative E° gives positive ΔG°. The minus sign is part of the chemistry, not an optional sign convention to discard.
Potentials do not scale with equation coefficients. Voltage is energy per charge, so doubling both chemical amount and transferred charge leaves voltage unchanged. ΔG° and n do scale because they refer to the amount of reaction. Specify the ionic oxidation states, phases, and actual reaction: Ti3+/Ti is not the same couple as Ti3+/Ti2+. A model based on tabulated values may omit passivation, complexation, competing water chemistry, and resistance. The ideal sign calculation does not guarantee a practical cell will deliver that voltage or run quickly.
Let's work through it
- For Zn2+ + 2e− → Zn, E°red = −0.76 V, and Cu2+ + 2e− → Cu, E°red = +0.34 V, Cu is the cathode and Zn oxidation is the anode process.
- Net equation: Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s). Electrons cancel in a two-electron reaction, so n = 2.
- E°cell = 0.34 − (−0.76) = 1.10 V. ΔG° = −2(96485)(1.10) = −212267 J ≈ −212 kJ per mole of the written reaction.
- For twice this equation, n becomes 4 and ΔG° doubles, but E° is still 1.10 V. If you reverse it, both E° and ΔG° reverse sign.
Make the picture move
Interactive concept model
A potential is intensive; reaction energy scales with n.
Predict first. Compare the signs of E° and ΔG°. If a balanced equation is doubled, which of E°, n, ΔG°, and K changes?
ΔG° = −nFE°; ln K = nFE°/(RT)
- ΔG° with n = 2
- Labeled selected or reference state
On a small screen, scroll inside the graph or diagram to read its labels. The values and explanation also appear below.
E° = 0.500 V gives ΔG° = -96.48 kJ mol⁻¹ and K = 8.02 × 10^16 at 298.15 K.
Read the data and comparisons
| Reaction scaling | n | E° (V) | ΔG° (kJ mol⁻¹) | log₁₀ K |
|---|---|---|---|---|
| As written | 2 | 0.500 | -96.48 | 16.904 |
| Equation doubled | 4 | 0.500 | -193 | 33.809 |
Macroscopic / data. An ideal reversible cell potential links the chemical driving force to electrical work per charge.
Particle view. The balanced reaction fixes how many moles of electrons transfer per mole of reaction; electrons travel through the external circuit rather than the salt bridge.
Symbolic view. n = 2; T = 298.15 K; log₁₀ K = 16.904.
Why it works. F converts moles of electrons to charge; volts are joules per coulomb. The negative sign connects positive cell potential to negative Gibbs energy for the process as written. Doubling the balanced reaction doubles n and ΔG°, leaves E° unchanged, and squares K. Thermodynamic favorability does not establish a reaction rate.
Conditions and limits. Abstract balanced redox process with supplied E° and electron count, not a specific chemical cell. Changing temperature evaluates thermodynamic relationships using the supplied E° at that temperature; it does not assume a real cell has temperature-independent E°. F = 96485 C mol⁻¹ and R = 8.314 J mol⁻¹ K⁻¹. K and Q use dimensionless activities referenced to standard states; solids and pure liquids have unit activity. Standard states do not by themselves prescribe a temperature. Positive E applies to the reaction orientation as written.
Try it from memory
Pause & retrieve
Try it before you peek.
Write your answer and the reason from memory. Then compare with the worked answer. Your self-assessment is a study decision, not an automatically graded score.
Question 1
Why do you not multiply E° by the balancing coefficient?
See every recall question with its answer
These references preserve each prompt and its answer for direct evidence links. Try the interactive questions above before opening the worked reasoning.
Retrieval 1
Why do you not multiply E° by the balancing coefficient?
Worked answer and reason
Voltage is energy per charge; both energy and charge scale together.
It is an intensive property of the cell process.
Retrieval 2
Why must n come from the balanced net equation?
Worked answer and reason
It counts the electrons transferred for that stated amount of reaction.
A half-reaction coefficient can change during electron cancellation.
Catch the tempting mistake
- More negative reduction potential makes that species the preferred galvanic cathode.
- Under the standard-state comparison, the more positive reduction potential stays as reduction at the cathode.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 9 problem 12 · ap synthesis · multiple
- Unit 9 problem 13 · ap application · symbolic
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For the teacher
- Audit the sign of the oxidation half-reaction and the overall atom/charge balance. A correct voltage with an unbalanced reaction does not establish a correct ΔG°.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 9.9.A
- Explain whether an electrochemical cell is thermodynamically favored, based on its standard cell potential and the constituent half-reactions within the cell.
- 9.9.A.1
- Electrochemistry encompasses the study of redox reactions that occur within electrochemical cells. The reactions are either thermodynamically favored (resulting in a positive voltage) or thermodynamically unfavored (resulting in a negative voltage and requiring an externally applied potential for the reaction to proceed).
- 9.9.A.2
- The standard cell potential of electrochemical cells can be calculated by identifying the oxidation and reduction half-reactions and their respective standard reduction potentials.
- 9.9.A.3
- ΔG° (standard Gibbs free energy change) is proportional to the negative of the cell potential for the redox reaction from which it is constructed. Thus, a cell with a positive E° involves a thermodynamically favored reaction, and a cell with a negative E° involves a thermodynamically unfavored reaction. EQN: ΔG° = −nFE°
Science references for this teaching
- AP Chemistry Course and Exam Description, effective Fall 2024 — Required topic-numbered learning objectives and essential knowledge, all continuations and AP exclusions; supplied PDF SHA256 b5dfe8677ef3d88c613865d2e2a3e8d6125d652e2b24c71ef1e8ce4e011094f0.
- OpenStax Chemistry 2e §17.4, Potential, Free Energy, and Equilibrium — Relations among E°, ΔG°, K and nonstandard Q.
- OpenStax Chemistry 2e Appendix L, Standard Electrode Potentials — Source of the conventional Zn/Cu and Ti2+/Ti reduction-potential examples; tasks specify rounded values.
Glossary and deeper reading · 9 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Redox reaction
A redox reaction combines oxidation of one species with reduction of another. Electron loss and gain must balance in the net equation along with atoms and total charge. For example, zinc reducing copper ions involves zinc oxidation and copper-ion reduction.
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Anode
The anode is the electrode where oxidation occurs. This definition applies to both galvanic and electrolytic cells. For example, a zinc electrode releasing zinc ions and electrons is an anode in the zinc–copper galvanic model.
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Cathode
The cathode is the electrode where reduction occurs. It may deposit metal or host another reduction without necessarily gaining mass. For example, a copper electrode receiving electrons that reduce dissolved copper ions is a cathode.
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Gibbs free energy
Gibbs free energy combines enthalpy and entropy contributions to a system at specified temperature and pressure. For a reaction at constant temperature and pressure, a negative actual reaction free-energy change favors its forward direction, while standard and actual values must be distinguished. For example, a favorable reaction can still be slow if its pathway has a large activation barrier.
Read more: Gibbs Free Energy and Thermodynamic Favorability →
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Reduction
Reduction is electron gain, represented by a decrease in oxidation number. It is paired with oxidation in an electron-transfer reaction. For example, a copper ion with charge +2 gaining two electrons to form copper metal undergoes reduction.
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Half-reaction
A half-reaction describes either the oxidation or reduction part of a redox process. It includes electrons explicitly so that charge and electron transfer can be balanced. For example, zinc forming a zinc ion and two electrons is an oxidation half-reaction.
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Mole
A mole is an amount of substance containing exactly 6.02214076 × 10²³ specified entities. The entities can be atoms, molecules, ions, or formula units, so the counted entity must be named. For example, one mole of oxygen molecules contains two moles of oxygen atoms.
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Oxidation number
An oxidation number is a formal electron-accounting value assigned using specified rules. Changes in oxidation number help identify oxidation and reduction but are not always actual atomic charges. For example, oxygen usually has oxidation number −2 in water while hydrogen has +1.
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Passivation
Passivation occurs when a surface layer reduces further reaction of the underlying material. It can make an idealized redox prediction differ from the observed reaction rate or cell behavior. For example, a protective oxide layer can slow a metal's further oxidation.