Concentration Cell Voltage Calculator

A concentration cell is a special type of galvanic cell where both electrodes are made of the same material, but the electrolyte concentrations are different on each side.

Because both electrodes are identical, E° = 0.

The voltage comes entirely from the concentration difference, via the Nernst equation:

E = (0.05916/n) × log([high] / [low]) at 25°C

Or more generally:

E = (RT/nF) × ln([high] / [low])

How it works:

• Anode (low concentration side): Metal dissolves → metal ions → solution (oxidation) → M → M^n+ + ne⁻
• Cathode (high concentration side): Metal ions deposit → solid metal (reduction) → M^n+ + ne⁻ → M
• Net result: ions move from high to low concentration until equal → voltage drops to 0

Applications:

• Biological membrane potentials (nerve impulses): Na⁺/K⁺ concentration gradients across cell membranes create voltage (−70 mV for neurons)
• pH meters: glass electrode is essentially a H⁺ concentration cell
• Ion-selective electrodes (ISE): measure specific ion concentrations
• Measurement of activity coefficients in chemistry research

Worked example

A copper concentration cell (n = 2) with 1.0 mol/L on one side and 0.001 mol/L on the other:

E = (0.05916 / 2) × log(1.0 / 0.001) = 0.02958 × 3 = 0.0887 V

That is a modest voltage for a thousandfold concentration difference, and it illustrates the central limitation of concentration cells: because the voltage depends on the logarithm of the ratio, you need enormous gradients to get useful potentials. Ten times the ratio buys only another 59 mV divided by n.

As the two sides equalise, E falls to zero. A concentration cell is discharging its own driving force simply by running, which is why nobody builds batteries this way. What the arrangement is superb at is measurement: since E depends on a concentration ratio and nothing else, reading the voltage tells you an unknown concentration directly. That is exactly what a pH meter does.