Concentration Cells

Oxidation raises the ion concentration where it occurs, so it must occur in the dilute half-cell. The dilute side is therefore the anode and loses electrode mass, while the concentrated side is the cathode and gains mass. This is worth memorizing because it feels backwards to many students.

For matching Cu²⁺/Cu half-cells, oxidation on the dilute side produces Cu²⁺ and electrons; reduction on the concentrated side consumes Cu²⁺. Write the net transfer as Cu²⁺(high activity) → Cu²⁺(low activity). Its reaction quotient is alow/ahigh, and the two identical standard potentials cancel. The driving force is the ion chemical-potential difference; no difference in the identity of the metals is required.

Since E° = 0, the Nernst equation reduces to E = -(0.0592/n) log Q, with Q equal to the dilute concentration over the concentrated one. That ratio is less than 1, its log is negative, and the leading minus sign makes E positive, as it must be for a spontaneous cell.

At 25 °C, E = (0.0592/2)log₁₀(ahigh/alow) for Cu²⁺/Cu. Approximating activities by concentrations, 1.00 M versus 0.00100 M gives log ratio = 3 and E = 0.0888 V. For Ag⁺/Ag the electron number is one, so the same ratio gives twice that voltage. This is a ratio comparison, not a difference-of-concentrations formula. Reversing the cell's written orientation changes the sign of the measured voltage.

Electrodes can respond approximately logarithmically to ion activity and therefore serve as concentration sensors. A glass pH electrode develops an ion-selective membrane potential; it should not be described as a hydrogen-ion reduction involving one electron. Its ideal potential response has magnitude about 59.2 mV per pH unit at 25 °C because the sensed ion has unit charge, with sign depending on measurement convention.

Differential oxygen availability can also create electrochemical differences on a metal surface, contributing to localized corrosion. Such gas- and oxygen-reduction systems need their own half-reactions; the simple “dilute metal-ion side is the anode” rule is specific to the matching metal/metal-ion cells derived here, not every device called a concentration cell.

A concentration cell uses identical electrode materials and half-reactions, so E°_cell=0. Its voltage comes from different ion activities; for the same metal ion on both sides, E=(0.0592/n)log(C_high/C_low) at 25 °C under ideal conditions. The dilute side is the anode, supplying ions until the difference shrinks.

The concentration substitution assumes sufficiently ideal behavior. At high ionic strength, unequal activity coefficients and liquid-junction potentials can affect a real reading. The simplest textbook formula neglects the junction contribution. With closed reservoirs and adequate electrode material, operation reduces the activity difference until E tends to zero. Finite electrode exhaustion, a broken ionic path or other practical limits can stop current first; equal concentrations are the ideal matching-cell endpoint, not the only possible cause of a stopped real circuit.