9.9 Cell Potential Under Nonstandard Conditions

Nonstandard conditions shift cell potential

Standard cell potential (E°cell) applies only at 1 M concentrations, 1 atm, and 25°C. When concentrations or pressures differ from standard, the actual cell potential (Ecell) changes. As a reaction proceeds, reactant concentrations decrease and product concentrations increase, causing Ecell to drop toward zero as the system approaches equilibrium.

The Nernst equation

The Nernst equation, Ecell = E°cell − (RT/nF)lnQ, relates cell potential to reaction quotient Q. At 25°C this simplifies to Ecell = E°cell − (0.0592/n)logQ. Increasing reactant concentration (Q < 1) raises Ecell above E°cell; increasing product concentration (Q > 1) lowers it below E°cell.

Equilibrium and dead batteries

At equilibrium, Q = K and Ecell = 0 — the cell can do no more work, which is why batteries eventually die. Since ΔG = −nFEcell and ΔG° = −RT lnK, combining these relationships shows E°cell is directly tied to K, linking thermodynamics and electrochemistry.

Key terms

Nernst equation

Ecell = E°cell − (RT/nF)lnQ; relates cell potential to nonstandard concentrations via reaction quotient Q.

Nernst equation at 25°C (simplified)

Ecell = E°cell − (0.0592/n)logQ

Ecell at equilibrium

Ecell = 0, because Q = K; the cell can no longer perform work (a dead battery).

Effect of increasing reactant concentration (Q < 1)

Ecell increases above E°cell.

ΔG and Ecell relationship

ΔG = −nFEcell, linking Gibbs free energy, moles of electrons transferred (n), Faraday's constant (F), and cell potential.

Try an AP-style question

In a galvanic cell, Q < 1. How does Ecell compare with E°cell?

1. Ecell < E°cell
2. Ecell = E°cell
3. Ecell > E°cell
4. Ecell = 0