Cell Potential Under Nonstandard Conditions
Explain composition-dependent potential and concentration cells without calling an operating cell an equilibrium state.
AP Chemistry Topic 9.10 · CED printed p. 176, 177 / PDF p. 183, 184. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Before you start
- Quotients
- Cell direction
- Free energy and equilibrium
A real operating cell is generally not at equilibrium. Its chemical driving force depends on the current reacting-species activities, so changing concentration can change voltage even when the electrodes are unchanged. Use the written net reaction to construct Q; omit pure metal solids. E° is the reference value at Q = 1. It is not “the equilibrium voltage.” Le Châtelier’s principle describes a disturbance of a system already at equilibrium, so do not invoke an equilibrium shift as the whole explanation for an operating galvanic cell. Instead use composition, free-energy driving force, and the approach toward Q = K.
The qualitative Nernst form is . If Q falls below one, the logarithm is negative and E for the written direction exceeds E°. If Q rises above one, E is below E°, but need not yet be negative. At Q = K the actual reaction has zero driving force and E = 0. On the forward-favored branch, increasing Q toward K reduces positive voltage. If Q exceeds K, the written E is negative and the reverse direction is favored. Talk about magnitude and the specified direction carefully when crossing equilibrium. AP requires conceptual reasoning about concentration and potential; algorithmic Nernst substitution alone does not demonstrate that understanding.
A concentration cell uses the same redox couple on both sides but different activities. Metal oxidation on the dilute side makes more dissolved ions; reduction on the concentrated side consumes them. This lowers the concentration imbalance and supplies a driving force even though the standard potentials cancel. The external electrons run from the dilute-side anode to the concentrated-side cathode in this metal-ion model. When the relevant activities become equal, the concentration-cell potential becomes zero. Assume identical specified couples, fixed temperature, suitable ion conduction, and no competing reactions; concentrations approximate activities only within the chosen dilute model.
Let's work through it
- For Zn + Cu2+ → Zn2+ + Cu, take Q = [Zn2+]/[Cu2+]. Doubling Cu2+ while leaving Zn2+ unchanged halves Q.
- The change lowers ln Q. In E = E° − (RT/nF)ln Q, subtracting a smaller logarithmic term raises E for this written direction.
- As the forward reaction consumes Cu2+ and forms Zn2+, Q rises and the forward driving potential decreases toward zero at Q = K.
- Do not call the starting operating cell an equilibrium mixture, and do not say the concentration change alters E° at fixed temperature. It alters the nonstandard E.
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
Is Q = 1 the same as equilibrium?
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
Is Q = 1 the same as equilibrium?
Worked answer and reason
Only if K = 1. Q = 1 gives E = E°; Q = K gives E = 0.
The standard reference and equilibrium composition are distinct.
Retrieval 2
In an M/M2+ concentration cell, where is oxidation favored?
Worked answer and reason
On the dilute side, where metal ion production reduces the imbalance.
The net process moves the cell toward equal ion activities.
Catch the tempting mistake
- Q > 1 always makes E negative.
- It makes E lower than E°; the zero crossing is at Q = K, which may be much greater than one.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 9 problem 14 · ap synthesis · symbolic
- Unit 9 problem 15 · ap application · multiple
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Scientific calculator
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For the teacher
- Require a sign-only Nernst explanation and a separate Q = K statement. Any numerical Nernst model use beyond this qualitative task should be labeled enrichment.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 9.10.A
- Explain the relationship between deviations from standard cell conditions and changes in the cell potential.
- 9.10.A.1
- In a real system under nonstandard conditions, the cell potential will vary depending on the concentrations of the active species. The cell potential is a driving force toward equilibrium; the farther the reaction is from equilibrium, the greater the magnitude of the cell potential.
- 9.10.A.2
- Equilibrium arguments such as Le Châtelier’s principle do not apply to electrochemical systems, because the systems are not in equilibrium.
- 9.10.A.3
- The standard cell potential E° corresponds to the standard conditions of Q = 1. As the system approaches equilibrium, the magnitude (i.e., absolute value) of the cell potential decreases, reaching zero at equilibrium (when Q = K). Deviations from standard conditions that take the cell further from equilibrium than Q = 1 will increase the magnitude of the cell potential relative to E°. Deviations from standard conditions that take the cell closer to equilibrium than Q = 1 will decrease the magnitude of the cell potential relative to E°. In concentration cells, the direction of spontaneous electron flow can be determined by considering the direction needed to reach equilibrium.
- 9.10.A.4
- Algorithmic calculations using the Nernst equation are insufficient to demonstrate an understanding of electrochemical cells under nonstandard conditions. However, students should qualitatively understand the effects of concentration on cell potential and use conceptual reasoning, including the qualitative use of the Nernst equation: EQN: E = E° − (RT/nF) ln Q to solve problems.
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.
Glossary and deeper reading · 5 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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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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Chemical equilibrium
Chemical equilibrium is a dynamic state in which forward and reverse reaction rates are equal. Macroscopic composition remains constant in a closed system under fixed conditions, but reactant and product concentrations need not be equal. For example, a reversible reaction can reach equilibrium with much more reactant than product.
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Le Châtelier’s principle
Le Châtelier’s principle predicts the qualitative response when a system initially at equilibrium is disturbed. A justified explanation distinguishes the immediate disturbance from the subsequent reaction toward a new equilibrium. For example, adding a reactant can favor its net consumption, while temperature changes can also alter the equilibrium constant.
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Concentration cell
A concentration cell uses the same redox couple under differing activities in its two half-cells. The concentration difference can produce a potential even though the standard half-cell potentials cancel. For example, an ideal metal-ion concentration cell can operate in the direction that reduces the ion-concentration imbalance.
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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.