Calculate voltage for galvanic cells and apply the Nernst equation
Note: Enter as reduction potential, will be reversed for oxidation
Standard Cell Potential (E°_cell): Voltage produced by a galvanic cell under standard conditions (1 M concentrations, 1 atm pressure, 25°C).
Nernst Equation: E = E° - (RT/nF)ln(Q) adjusts potential for non-standard conditions. At 298 K: E = E° - (0.0592/n)log(Q)
Cell potential (also called electromotive force or EMF) is the voltage difference between two half-cells in an electrochemical cell. It measures the driving force for the electron transfer reaction.
E°_cell = E°_cathode - E°_anode
E_cell = E°_cell - (RT/nF)ln(Q)
At 298 K: E = E° - (0.0592/n)log(Q)
Memory Aid: "Red Cat" and "An Ox" - Reduction atCathode, Anode for Oxidation
These values are measured relative to the Standard Hydrogen Electrode (SHE), which is defined as 0.00 V.
| Half-Reaction (Reduction) | E° (V) | Category |
|---|---|---|
| F₂ + 2e⻠→ 2F⻠| +2.87 | Strong oxidizer |
| Au³⺠+ 3e⻠→ Au | +1.50 | Noble metal |
| Cl₂ + 2e⻠→ 2Cl⻠| +1.36 | Halogen |
| Br₂ + 2e⻠→ 2Br⻠| +1.07 | Halogen |
| Ag⺠+ e⻠→ Ag | +0.80 | Noble metal |
| Cu²⺠+ 2e⻠→ Cu | +0.34 | Transition metal |
| 2H⺠+ 2e⻠→ H₂ | 0.00 | Reference (SHE) |
| Pb²⺠+ 2e⻠→ Pb | -0.13 | Active metal |
| Ni²⺠+ 2e⻠→ Ni | -0.26 | Transition metal |
| Fe²⺠+ 2e⻠→ Fe | -0.45 | Transition metal |
| Zn²⺠+ 2e⻠→ Zn | -0.76 | Active metal |
| Al³⺠+ 3e⻠→ Al | -1.66 | Reactive metal |
| Na⺠+ e⻠→ Na | -2.71 | Alkali metal |
| Li⺠+ e⻠→ Li | -3.04 | Strong reducer |
Positive E°: Strong oxidizing agents (good at gaining electrons). Prefer to be reduced.
Negative E°: Strong reducing agents (good at losing electrons). Prefer to be oxidized.
Calculate the standard cell potential for a galvanic cell with zinc and copper electrodes.
Step 1: Identify the half-reactions and their E° values
Cu²⺠+ 2e⻠→ Cu, E° = +0.34 V
Zn²⺠+ 2e⻠→ Zn, E° = -0.76 V
Step 2: Determine which is cathode (higher E°) and anode (lower E°)
Cathode (reduction): Cu²⺠+ 2e⻠→ Cu (E° = +0.34 V)
Anode (oxidation): Zn → Zn²⺠+ 2e⻠(E° = -0.76 V)
Step 3: Calculate E°_cell
E°_cell = E°_cathode - E°_anode
E°_cell = (+0.34 V) - (-0.76 V)
E°_cell = +1.10 V
Interpretation: Positive E°_cell (+1.10 V) means the reaction is spontaneous. This cell will produce electricity! The Daniell cell is one of the first practical batteries.
Overall Cell Reaction:
Zn(s) + Cu²âº(aq) → Zn²âº(aq) + Cu(s)
Cell potential is directly related to the thermodynamic spontaneity of a reaction through Gibbs free energy.
ΔG° = -nFE°_cell
E°_cell > 0
ΔG° < 0: Spontaneous (galvanic cell produces voltage)
E°_cell = 0
ΔG° = 0: At equilibrium (no net reaction)
E°_cell < 0
ΔG° > 0: Non-spontaneous (needs external voltage - electrolytic cell)
Example: For the Daniell cell (E° = 1.10 V, n = 2):
ΔG° = -2 × 96,485 × 1.10 = -212,267 J = -212.3 kJ/mol
Large negative ΔG° confirms highly spontaneous reaction!
The Nernst equation adjusts the cell potential for concentrations different from 1 M, temperatures other than 25°C, and pressures other than 1 atm.
E_cell = E°_cell - (RT/nF)ln(Q)
Where Q is the reaction quotient: Q = [products]^coeff / [reactants]^coeff
E = E° - (0.0592/n)log(Q)
Most commonly used in chemistry courses. Uses log base 10.
All standard potentials in tables are reduction potentials. Even for the anode (where oxidation occurs), use the tabulated reduction potential in the formula E°_cell = E°_cathode - E°_anode. Don't flip the sign of the anode potential!
Unlike ΔG or ΔH, cell potential is an intensive property. Even if you multiply the half-reaction by 2, the E° value stays the same. It's a potential difference, not a total amount.
As a battery discharges, reactant concentrations decrease and product concentrations increase. By the Nernst equation, this lowers the cell potential until E = 0 at equilibrium (dead battery).