Electrochemical Cells

How much voltage does a battery made of two metals give, and does the reaction run by itself? Choose the electrode where reduction happens (the cathode) and the one where oxidation happens (the anode) for the cell potential E°, the balanced cell reaction, the Gibbs energy ΔG° and the equilibrium constant K. Add the actual concentrations for the voltage from the Nernst equation.

RedoxBatteriesNernst

Inputs

Input examples

Both electrodes are chosen from a table of standard reduction potentials at 25 °C. The electrode with the higher E° is normally the cathode (+); if you choose them the other way round, E°cell comes out negative and the reaction does not run by itself: that is an electrolytic cell that needs a voltage. Choose Custom half-reaction to type your own, written as a reduction with the electrons on the left (type _ for a subscript and ^ for a charge: Ce^4+ + e^- -> Ce^3+), with its E°. Concentrations in mol/L; gases as partial pressure in bar; solids and liquids do not count in Q.

Cathode (+): reduction

Anode (−): oxidation

Temperature — °C

Concentrations

How Does a Galvanic Cell Work?

Put a zinc strip in zinc sulfate and a copper strip in copper sulfate, connect them with a wire and a salt bridge, and a current flows: zinc atoms give up electrons (oxidation, at the anode), the electrons run through the wire, and copper ions take them up (reduction, at the cathode). This is the Daniell cell, and it gives about 1.10 volts.

Every half-reaction has a standard reduction potential E°, measured against the hydrogen electrode (0 V by definition). The higher it is, the more eagerly the substance takes electrons. The cell voltage is the difference: cathode minus anode. A positive E°cell means a negative ΔG°, so the reaction runs by itself and the cell can do electrical work, −ΔG per mole of reaction.

Away from 1 mol/L the voltage changes, as described by the Nernst equation. At 25 °C every factor 10 in Q changes E by 0.0592/n volt. As a battery runs down, its products build up and its reactants are used up, Q grows, and the voltage falls until it reaches 0 at equilibrium (Q = K): the battery is flat.

E°cell > 0runs by itself (ΔG° < 0)

0.0592/n Vper factor 10 in Q at 25 °C

anodeoxidation, the − pole of a battery

E = 0at equilibrium: the battery is flat

The Electrochemical Series

E°cell

cathode (reduction)

anode (oxidation)

other half-reactions in the table

Result

Choose the electrodes above

Voltage as the Cell Runs Down

Nernst

Standard Reduction Potentials

25 °C; click a row to use it as the cathode

Half-reaction (reduction)	E° (V)

Worked Techniques

Cathode Minus Anode

Look up both reduction potentials and subtract. Never multiply E° by the coefficients: a potential is energy per charge, not per mole.

Example: the Daniell cell Zn | Zn²⁺ ‖ Cu²⁺ | Cu gives 1.10 V.

Energy and Equilibrium

n is the number of electrons that move in the balanced cell reaction. K follows from ΔG° = −RT ln K.

Example: for the Daniell cell K ≈ 1.6 × 10³⁷: copper ions are removed almost completely.

The Nernst Equation

Products on top, reactants below, each to the power of its coefficient; solids and the electrode metals are left out.

Example: diluting the zinc side tenfold raises the voltage by 29.6 mV.

Sources & Verification

References

Standard electrode potential (data page), Wikipedia, read 5 November 2026 — the E° values in the table, compiled there from the CRC Handbook of Chemistry and Physics and other sources.
P. Vanyšek, “Electrochemical series”, in CRC Handbook of Chemistry and Physics, CRC Press — the primary compilation of standard reduction potentials.
P. Atkins and J. de Paula, Atkins’ Physical Chemistry, Oxford University Press — the chapter on electrochemical cells: E°cell, ΔG° = −nFE°, K and the Nernst equation.
CODATA 2018 recommended values, NIST — F = 96 485.33212 C/mol and R = 8.314462618 J/(mol·K).