Concentration Cells

Introduction

Two identical metal electrodes can form a galvanic cell if their ion activities differ. The standard potentials of the identical couples cancel, so E°cell = 0, yet nonstandard composition creates a positive voltage for the direction that tends to equalize the solutions. A concentration cell is a direct demonstration of the Nernst equation.

Core explanation

Consider M(s) M²⁺(dilute) M²⁺(concentrated) M(s), with suitable ionic connection. Each electrode has the same M²⁺/M reduction couple, so the standard potential difference is zero. At the dilute side, oxidation M → M²⁺ + 2e⁻ increases ion activity. At the concentrated side, reduction M²⁺ + 2e⁻ → M decreases ion activity. Electrons flow from the dilute-side anode to the concentrated-side cathode in the ordinary idealized galvanic direction.

The overall chemical effect is transfer of M²⁺ equivalents from the concentrated solution toward the dilute solution through paired electrode reactions, without transporting an individual metal ion directly through the wire. The concentration difference supplies free energy. As the activities approach equality, the voltage approaches zero. Exact final concentrations depend on volumes and transported charge. The salt bridge provides ionic compensation so charge does not accumulate and stop the process.

For a two-electron metal couple at 25 °C, the idealized cell voltage magnitude is E = (0.05916 V/2)log₁₀(a concentrated/a dilute) when the stated direction is from dilute anode to concentrated cathode. If the activity ratio is 100, E ≈ 0.05916 V. Reversing the notation and reaction direction changes the sign. The formula should be derived from the half-cell potentials or overall Q rather than applied without labels.

Concentration cells emphasize that a potential difference is not simply a property of different metals. The same chemical couple at different activities has different electrode potentials. This principle supports electrochemical sensors and measurements of ion activity, though real sensors use membranes or other selective components. A measured potential can also include junction effects, nonideal activity coefficients, or surface kinetics. At high ionic strength, raw molarity ratios are not reliable substitutes for activity ratios.

A useful chemical check is direction of spontaneous equalization. Oxidation on the dilute side makes more ions there; reduction on the concentrated side removes ions there. A proposed opposite flow that increases the concentration difference would require an external source, not spontaneous galvanic operation. This check can catch a sign error before numerical calculation.

Step-by-step reasoning

1. Confirm the two half-cells use the same redox couple. 2. Place oxidation at the dilute side and reduction at the concentrated side. 3. Set E°cell = 0 and form the activity ratio. 4. Use Nernst with the electron count and check equalization direction.

Visual explanation

Draw two identical M electrodes in dilute and concentrated ion solutions. Show electrons from dilute to concentrated and a shrinking concentration gap over time.

Real-world analogy

Two water reservoirs at different heights can run a turbine even if both contain the same water. The difference, not the material identity, supplies the driving force.

Real-world example

A concentration cell can be built using two copper electrodes immersed in copper-ion solutions of different effective concentrations, joined by a salt bridge and voltmeter.

Why?

Why does standard voltage cancel? Both electrodes use the same standard reduction potential; only their different nonstandard activities create the measured potential difference between the half-cells.

Common misconception

“Identical metal electrodes must give zero voltage.” They give zero only when the relevant activities and other conditions are equal, not merely when materials match.

Worked example

At 25 °C, two M²⁺/M half-cells have activities 0.001 and 0.100, a ratio of 100. With the dilute side as anode and the concentrated side as cathode, n=2 and E°cell=0. Then E = (0.05916/2)log₁₀(100) = 0.05916 V. The direction increases ions on the dilute side and consumes them on the concentrated side. When both activities become equal, the ideal concentration-cell voltage becomes zero.

Quick check

1. Which side is the anode in the simple M²⁺ concentration cell? Answer: The lower-activity, dilute side, where metal oxidizes and supplies more M²⁺.

Exam focus

Label high and low activity before using a log ratio. The standard potentials cancel, but the actual cell potential need not be zero.

Advanced insight

Liquid junction potentials and activity coefficients can affect measured concentration-cell voltage. Precision measurements use controlled reference junctions and activity models rather than assuming molarity alone.

Summary

A concentration cell converts an activity difference of one redox couple into voltage. Dilute-side oxidation and concentrated-side reduction tend to equalize the solutions, driving E toward zero.

Practice questions

1. Why is E°cell zero for two identical standard couples? Answer: Their standard reduction potentials subtract to zero. 2. What happens to E as two ion activities become equal? Answer: It approaches zero in the idealized cell. 3. Which quantity belongs in the rigorous Nernst ratio, molarity or activity? Answer: Activity; molarity is an approximation for suitable dilute solutions.