Concentration cell

In an ordinary galvanic cell, two different redox couples drive electron flow, producing a nonzero standard cell potential. A concentration cell is the special case where the electrodes and the ionic species are identical on both sides, differing only in concentration. Because the two half-reactions are the same, the standard cell potential E°cell equals zero, and the entire voltage comes from the concentration gradient.

The Nernst equation quantifies it: Ecell = E°cell − (RT/nF)lnQ, which for a concentration cell reduces to Ecell = −(RT/nF)ln([dilute]/[concentrated]), or at 25 °C approximately Ecell = (0.0592/n)log([concentrated]/[dilute]). For a copper cell with 1.0 M Cu²⁺ on one side and 0.10 M on the other, n = 2, so Ecell = (0.0592/2)log(10) ≈ 0.0296 V. The voltages are small — typically tens of millivolts — because they depend on the logarithm of a concentration ratio.

The direction of the reaction follows from Le Châtelier's principle. The dilute half-cell acts as the anode, where the metal oxidizes and adds ions to solution, raising its concentration. The concentrated half-cell acts as the cathode, where ions plate out and the concentration falls. The cell runs until both concentrations are equal, at which point Q = 1, the voltage drops to zero, and the system reaches equilibrium. This is a useful reasoning shortcut: the cell always operates in whatever direction moves the two solutions toward the same concentration.

Concentration cells are more than a textbook curiosity. The resting membrane potential of a neuron is essentially a biological concentration cell, arising from unequal ion concentrations across a selectively permeable membrane, and the Nernst equation is used directly to calculate equilibrium potentials for potassium and sodium. Concentration differences also drive localized corrosion in metals. The MCAT tests concentration cells in general chemistry and physics, and returns to the same equation in biology when explaining nerve cell electrochemistry and signaling.