Cell Potential Under Nonstandard Conditions

Learning Objective 9.10.A
Explain the relationship between deviations from standard cell conditions and changes in the cell potential.

Quick Notes

Cell potential depends on the concentrations of the reacting species.
Standard cell potential (E°_cell) applies when all reactants/products are at standard conditions (1.0 M, 1 atm, 25 °C).

When conditions deviate from standard, cell potential (E_cell) changes.

Cell potential (E_cell) decreases as the system approaches equilibrium (Q → K).

When Q < 1, the reaction is far from equilibrium and E_cell > E°_cell.
When Q > 1, the system is closer to equilibrium and E_cell < E°_cell.
At equilibrium, Q = K and E = 0.

Full Notes

Understanding Nonstandard Cell Conditions

In real life, electrochemical cells often don’t operate under standard conditions. Changes in concentration, pressure, or temperature can affect the cell potential (E_cell) – the electrical “push” that drives electrons through the circuit.

Under standard conditions, all solutions are 1.0 M, gases are at 1 atm pressure, and temperature is 25 °C (298 K). But when these conditions differ, the actual Gibbs free energy change (ΔG) and the cell potential (E_cell) can change – sometimes making a reaction that was previously spontaneous become non-spontaneous, or vice versa.

How Nonstandard Conditions Affect Cell Potential

To understand how the actual cell potential (E_cell) changes with conditions, we use the Nernst equation, which helps us think about how far a system is from equilibrium.

AP Chemistry Nernst equation showing E = E° − (RT/nF) ln Q with variable definitions for R, T, n, F, and Q.

Nernst Equation: E = E° − (RT/nF) ln Q

E = actual cell potential under current conditions
E° = standard cell potential (at 1.0 M, 1 atm, 25 °C)
R = ideal gas constant
T = temperature in kelvin
n = number of electrons transferred
F = Faraday’s constant (96,485 C mol⁻¹ e⁻)
Q = reaction quotient, the ratio of product concentrations to reactant concentrations at a given moment

Key idea: As Q increases, the cell potential decreases; as Q decreases, the cell potential increases.

Recap – What Q Tells Us About the Reaction

What is the Reaction Quotient (Q)?

The reaction quotient, Q, (see Topic 7.3) is a snapshot of a reaction’s progress. It is calculated by using concentration values at a specific point in time, which might not be equilibrium values.

AP Chemistry general reaction aA + bB ⇌ cC + dD used to define the reaction quotient Q.

General formula for a reaction:

AP Chemistry expression for the reaction quotient Q equals [C]^c [D]^d divided by [A]^a [B]^b.

If Q < 1 then there are more reactants than products and E_cell > E°_cell.
If Q > 1 then there more products than reactants and E_cell < E°_cell.
If Q = K then the system is at equilibrium and E_cell = 0.

This explains why a cell generates electricity: it's operating to get to equilibrium, and the further it is from equilibrium, the greater the “push” (E_cell) driving electrons through the circuit.

Concentration Cells

A concentration cell is a special type of electrochemical cell where the two half-cells contain the same species, just at different concentrations.

Even though E°_cell = 0 (because both half-reactions are the same), a voltage is produced because of the concentration difference.

The position of equilibrium in each half-cell is different, meaning the electrical potential of each electrode is also different – creating a potential difference between them.

Example: A Zinc Concentration Cell

AP Chemistry diagram of a zinc concentration cell showing different Zn2+ concentrations in each half-cell and electron flow from anode to cathode.

Electrons flow from the lower concentration half-cell (the anode) to the higher concentration half-cell (the cathode).
Anode (0.5 mol dm⁻³): Zn(s) → Zn²⁺(aq) + 2e⁻
Cathode (1.0 mol dm⁻³): Zn²⁺(aq) + 2e⁻ → Zn(s)

This continues until Zn²⁺ concentrations in both half-cells are equal – at which point, the potential difference drops to zero and the cell stops working.

This shows that even when E°_cell = 0, you can still get a measurable voltage if there’s a concentration difference to drive the reaction.

Matt’s exam tip

Important Clarification: Why Le Châtelier's Principle Doesn’t Apply

In most equilibrium problems, we use Le Châtelier’s Principle to predict how systems respond to change. But this does not apply in electrochemical cells.

Why not? Because electrochemical cells are not at equilibrium – they’re designed to work while moving toward equilibrium, using that imbalance to generate electrical work. So instead of thinking in terms of shifting equilibria, it’s better to focus on Q and how far the system is from equilibrium.

Summary

Standard conditions give us E°_cell, the cell potential at Q = 1.
As the system moves toward equilibrium (Q → K), the cell potential decreases.
At equilibrium (Q = K), the cell stops producing current and E_cell = 0.
When Q < 1, the reaction is far from equilibrium and E_cell is greater than E°_cell.
When Q > 1, the reaction is closer to equilibrium and E_cell is less than E°_cell.
Concentration cells use the same redox pair at different concentrations to generate current.
Always think in terms of how far the system is from equilibrium — the greater the distance, the greater the driving force (cell potential).