Concentration Cell — Nernst Equation EMF

Half-Cell A (left)

[Cu²⁺] concentration 0.500 M

Half-Cell B (right)

[Cu²⁺] concentration 0.020 M

Conditions

Temperature 298 K

Load resistance 100 Ω

Circuit open — no current flows.

Live Readout

Cell EMF (Nernst)

0.0 mV

Current

0.00 mA

[Cu²⁺] A now

0.500 M

[Cu²⁺] B now

0.020 M

How it works

A concentration cell uses the same electrode and electrolyte on both sides — the identical copper half-reaction Cu²⁺(aq) + 2e⁻ ⇌ Cu(s) runs on each electrode, so the standard potentials cancel exactly. The whole EMF comes purely from the concentration difference, via the Nernst equation:

E_cell = (RT / nF) · ln( [Cu²⁺]_high / [Cu²⁺]_low )
R = 8.314 J/(mol·K),  F = 96485 C/mol,  n = 2

The more concentrated half-cell is the cathode (reduction, Cu²⁺ + 2e⁻ → Cu, electrode gains mass and is the + terminal). The dilute half-cell is the anode (oxidation, Cu → Cu²⁺ + 2e⁻, electrode dissolves and is the − terminal). Electrons leave the anode, travel the external wire to the cathode; inside the cell, a salt-bridge carries Cu²⁺ toward the cathode and SO₄²⁻ toward the anode to keep both sides electrically neutral.

Concentration sliders — set each half-cell's [Cu²⁺] while the circuit is open; the EMF readout updates live from the Nernst equation.
Temperature — scales EMF directly through the RT/nF prefactor.
Load resistance — Ohm's law, I = E/R, sets how much current the closed circuit draws and how fast the cell discharges.
Close circuit — lets current actually flow: Cu²⁺ is consumed at the cathode and produced at the anode, so both concentrations drift toward each other and EMF decays toward zero as the driving force disappears. (Simulation time is accelerated roughly 10⁷× — a real concentration cell equalizes over hours, not seconds.)

This is the operating principle behind reference electrodes and behind why an old vs. a fresh battery of the same chemistry never quite match in series — even a tiny concentration mismatch produces a real, measurable voltage.

Cu²⁺ electrolyte (darker = more concentrated) Copper electrode Electrons (external wire)

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Concentration Cell — EMF from the Nernst Equation Alone