Nernst equation calculator
Enter the standard potential, the number of electrons and the concentrations of the oxidised and reduced forms to get the potential of a half-cell. For a whole cell, enter E°cell and the reaction quotient Q. The temperature can be changed, and the result also shows the shift from E°, the slope per tenfold change and, for a cell, ΔG and K.
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How to use it
- Pick a half-cell or a whole cell.
- Enter the standard potential E° in volts and the number of electrons n.
- For a half-cell, enter the concentrations of the oxidised and reduced forms (1 for a solid metal). For a cell, enter Q (products over reactants, each to the power of its coefficient).
- Set the temperature. Read E, the shift from E° and, for a cell, ΔG and K.
E = E° − (RT ÷ nF) × ln Q
- R = 8.314462618 J/(mol·K), F = 96,485.33212 C/mol, T in kelvin
- Half-cell (written as a reduction): Q = [Red] ÷ [Ox]
- Slope: 2.303 × RT ÷ nF = 59.16 mV ÷ n at 25 °C
- ΔG = −nFE, K = e^(nFE° ÷ RT)
Worked example
A copper electrode in 0.01 M Cu²⁺ at 25 °C: E° = 0.34 V, n = 2, Q = 1 ÷ 0.01 = 100.
RT ÷ nF = 8.314462618 × 298.15 ÷ (2 × 96,485.33212) = 0.012846 V; × ln 100 = 0.059159 V.
E = 0.34 − 0.059159 = 0.2808 V, 59.16 mV below E° — two decades of concentration at 29.58 mV each.
Daniell cell with [Zn²⁺] ÷ [Cu²⁺] = 10: E = 1.10 − 0.012846 × ln 10 = 1.0704 V, ΔG = −2 × 96,485.33212 × 1.0704 = −206.56 kJ/mol.
Tips
- Sign of E°. Use reduction potentials from the table. For a cell, E°cell = E°(cathode) − E°(anode).
- Q follows the balanced equation. In Zn + Cu²⁺ → Zn²⁺ + Cu, Q = [Zn²⁺] ÷ [Cu²⁺]; solids are left out.
- Tenfold rule. Each tenfold increase of Q lowers E by 59.16 ÷ n mV at 25 °C — a quick check of the result.
Frequently asked questions
What is the Nernst equation?
E = E° − (R × T ÷ (n × F)) × ln Q, where E° is the standard potential, n the number of electrons, F = 96,485.33212 C/mol, R = 8.314462618 J/(mol·K) and Q the reaction quotient. For a reduction Ox + n e⁻ → Red, Q = [Red] ÷ [Ox].
Where does the 0.0592 V come from?
At 25 °C, R × T ÷ F × ln 10 = 0.05916 V, so E = E° − (0.05916 ÷ n) × log Q. The calculator does not use the rounded constant: it recomputes the slope for your temperature (61.54 mV at 37 °C for n = 1).
What concentration do I use for a solid metal?
A pure solid or liquid has an activity of 1, so leave [Red] at 1 for a metal electrode such as Cu²⁺/Cu. Gases are entered as their partial pressure in bar.
How is the cell potential related to ΔG and K?
ΔG = −n × F × E, so a positive cell voltage means a spontaneous reaction. At equilibrium E = 0 and Q = K, which gives K = e^(n × F × E° ÷ (R × T)). For the Daniell cell, E° = 1.10 V and n = 2 give K ≈ 1.54 × 10³⁷.
Does it use concentrations or activities?
Concentrations, as most textbook problems do. In concentrated solutions activities are lower than concentrations, so measured potentials can differ by a few millivolts.