Electrochemical Cell Voltage Calculator
Calculate standard cell voltage E°cell from half-reaction reduction potentials.
Find ΔG° and the equilibrium constant K for the cell reaction.
An electrochemical cell converts chemical energy to electrical energy (galvanic/voltaic cell) or uses electrical energy to drive chemical reactions (electrolytic cell).
Standard cell voltage:
E°cell = E°cathode − E°anode
The cathode is where reduction occurs (gains electrons). The anode is where oxidation occurs (loses electrons).
Standard reduction potentials (E°, vs SHE) at 25°C:
| Half-reaction | E° (V) |
|---|---|
| F₂ + 2e⁻ → 2F⁻ | +2.87 |
| MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ | +1.51 |
| Cl₂ + 2e⁻ → 2Cl⁻ | +1.36 |
| O₂ + 4H⁺ + 4e⁻ → 2H₂O | +1.23 |
| Ag⁺ + e⁻ → Ag | +0.80 |
| Fe³⁺ + e⁻ → Fe²⁺ | +0.77 |
| Cu²⁺ + 2e⁻ → Cu | +0.34 |
| 2H⁺ + 2e⁻ → H₂ | 0.00 (SHE) |
| Pb²⁺ + 2e⁻ → Pb | −0.13 |
| Fe²⁺ + 2e⁻ → Fe | −0.44 |
| Zn²⁺ + 2e⁻ → Zn | −0.76 |
| Al³⁺ + 3e⁻ → Al | −1.66 |
| Na⁺ + e⁻ → Na | −2.71 |
| Li⁺ + e⁻ → Li | −3.04 |
Spontaneity: E°cell > 0 → spontaneous (galvanic cell)
Relationship to ΔG° and K:
ΔG° = −nFE°cell
K = e^(nFE°/RT) = 10^(nE°/0.05916) at 25°C
where F = 96,485 C/mol and n = electrons transferred.
Working through a Daniell cell
Take the classic zinc and copper cell. Zinc metal sits in zinc sulfate, copper metal in copper sulfate, and a salt bridge joins the two halves. Zinc is the more reactive metal, so it gives up electrons and dissolves: that half is the anode. Copper ions collect those electrons and plate out as metal: that half is the cathode.
Look up both as reduction potentials, which is how every standard table lists them. Copper is +0.34 V, zinc is −0.76 V. Then subtract:
E°cell = 0.34 − (−0.76) = 1.10 V
The subtraction is the part people get wrong. It is tempting to flip the sign on the anode value first, because the anode is running backwards as an oxidation, and then add. That gets the right answer for the wrong reason and falls apart the moment both electrodes are negative. Keep both numbers as reductions, always subtract, and the sign takes care of itself.
Voltage does not scale with size
Double every coefficient in the reaction and E°cell does not change. A cell is not twice as powerful because you used twice as much zinc. Cell potential is an intensive property, like temperature or density, and it depends only on which reaction is happening, not on how much of it. What does scale is ΔG°, because that carries the n term, and the total charge the cell can deliver before it dies. That is why a AAA and a D cell of the same chemistry both read 1.5 V, while the D cell runs a torch for far longer.
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