Calculating standard cell potential
Cell potential is E°cell = E°cathode − E°anode, both as reductions. Work the Daniell cell (+1.10 V) and connect the sign to spontaneity through ΔG° = −nFE°.
Quick answer
The standard cell potential is the difference between the cathode's and anode's standard reduction potentials: E°cell = E°cathode − E°anode. A positive value means the cell reaction is spontaneous under standard conditions.
Example: For the Daniell cell, E°cell = (+0.34 V) − (−0.76 V) = +1.10 V, so the zinc–copper reaction is spontaneous and the cell delivers about 1.10 volts.
What you will learn
- State the formula E°cell = E°cathode − E°anode and apply it correctly
- Identify cathode and anode from tabulated reduction potentials
- Compute the Daniell cell potential step by step (+1.10 V)
- Interpret the sign of E°cell as a spontaneity prediction
- Relate cell potential to Gibbs free energy through ΔG° = −nFE°
The cell potential formula
A galvanic cell's voltage comes from the gap between its two half-reactions' eagerness to gain electrons. The standard cell potential captures that gap in one formula:
E°cell = E°cathode − E°anode
Both potentials are taken as reductions, exactly as they appear in the standard table. The cathode is the half-reaction that actually runs as a reduction; the anode is the one that runs backward as an oxidation. Because the table lists everything as a reduction, subtracting the anode's value automatically accounts for running it in reverse.
The formula only applies under standard conditions: all solutes at 1 M, gases at 1 atm, 25 °C. For other concentrations you need the Nernst equation.
Worked example: the Daniell cell
Work the Daniell cell completely. The two half-reactions and their tabulated potentials:
- Cathode (reduction): Cu2+ + 2e− → Cu, E° = +0.34 V
- Anode (reduction as tabulated): Zn2+ + 2e− → Zn, E° = −0.76 V
How do you know which is the cathode? The more positive potential wins the reduction: +0.34 V beats −0.76 V, so copper is reduced and zinc is oxidized.
E°cell = E°cathode − E°anode = (+0.34 V) − (−0.76 V) = +1.10 V
The two electrons in each half-reaction already match, so no multiplication is needed — and even if it were, E° values never scale. The positive sign predicts a spontaneous reaction, which is exactly what the Daniell cell does.
Sign, spontaneity, and Gibbs free energy
The sign of E°cell is a direct spontaneity readout:
- E°cell > 0: the reaction as written is spontaneous under standard conditions — a working galvanic cell.
- E°cell < 0: the reaction as written is nonspontaneous — the reverse reaction is the spontaneous one. Apply an external voltage larger than |E°cell| and it runs as electrolysis.
- E°cell = 0: the system is at equilibrium; a real cell reads 0 V when dead.
The quantitative link is the Gibbs free energy: ΔG° = −nFE°cell, where n is moles of electrons transferred and F is Faraday's constant (96485 C/mol). The negative sign guarantees that positive E° means negative ΔG° (spontaneous) and vice versa.
For the Daniell cell: ΔG° = −(2)(96485 C/mol)(1.10 V) = −212,267 J/mol ≈ −212 kJ/mol. The large negative value confirms a strongly spontaneous reaction.
Common calculation mistakes
Most mistakes with cell potentials are procedural, not conceptual:
- Picking the wrong cathode. Always assign the cathode to the half-reaction with the more positive reduction potential. If you swap them, the sign flips and a spontaneous cell looks nonspontaneous.
- Adding instead of subtracting. The formula is cathode minus anode. Writing E°anode − E°cathode (or adding both) is the classic error.
- Scaling E° with coefficients. If you multiply a half-reaction by 2 to balance electrons, the E° stays the same. Potentials are intensive.
- Mixing standard and nonstandard values. The formula gives E°cell at 1 M concentrations. A real battery at other concentrations needs the Nernst equation — its voltage will differ from E°cell.
Check every calculation with the spontaneity sense-test: if you know the reaction happens on its own, E°cell must come out positive.
Variables and units
| Symbol | Name | Unit | Meaning |
|---|---|---|---|
| moles of electrons | mol e− | Moles of electrons transferred in the balanced redox equation | |
| Faraday constant | C/mol | Faraday's constant, the charge of one mole of electrons |
Common mistakes
You subtract: E°cell = E°cathode − E°anode, with both values taken as reductions from the table. Adding is the most common sign error in electrochemistry.
It means the reaction as written is nonspontaneous — the reverse reaction would have a positive potential. Connect a power supply and you have an electrolytic cell.
E° is intensive and never scales with coefficients. Balance the electrons for the equation, but leave the tabulated potentials untouched.
Real-world applications
Predicting whether a proposed battery chemistry will work
Comparing candidate redox pairs for energy storage
Computing the standard Gibbs free energy of a redox reaction
Deciding which metal protects another in corrosion design
Checking homework cell diagrams for sign errors
Frequently asked questions
If I double the balanced equation, does E°cell double?
No. Potential is intensive: it measures energy per unit charge, not total energy. Doubling the reaction doubles the charge transferred, so the volts stay the same — just as doubling a waterfall's water does not double its height.
What does a positive cell potential tell me?
A positive E°cell means ΔG° is negative (since ΔG° = −nFE°), so the reaction is spontaneous under standard conditions. A negative E°cell means the reverse reaction is the spontaneous one.
Why subtract instead of adding the oxidation potential?
Because the tabulated values are reduction potentials. Subtracting the anode's reduction potential is mathematically identical to adding its oxidation potential — the formula just keeps you in one consistent table.
What does a cell potential of zero mean?
An E°cell of exactly zero means the system is at equilibrium under standard conditions — no net driving force in either direction. Real cells at equilibrium read 0 V.