Nernst Equation Calculator

Results

Each tenfold change in Q shifts E by (RT ln 10) ÷ nF, which is 59.16 mV ÷ n at 25 °C. Q uses mol/L for solutes and bar for gases; pure solids and liquids are left out.

How to Use the Nernst Equation Calculator

1. 1. Choose the mode. Use the first to apply the Nernst equation, the second to get E°cell by picking a cathode and an anode, and the third for ΔG = −nFE.
2. 2. Pick the unknown and fill in the rest. The cell potential E is the usual answer, but E°, Q and T can be solved for too. Voltage can be in V or mV and temperature in K, °C or °F; the temperature is converted to kelvin and must be above absolute zero.
3. 3. Give Q as a number. Write it as 10, 0.025 or 1e14. It is a ratio with no unit, so enter concentrations in mol/L and gas pressures in bar before dividing.
4. 4. Read the result and the working. You also get ΔG, log₁₀ K, whether the cell is spontaneous as written, and how many millivolts E changes for every tenfold change in Q.

The Nernst Equation

E = E° − (RT / nF) ln Q

E = E° − (0.05916 V / n) log₁₀ Q

ΔG = −nFE        ΔG° = −nFE°

E° = (RT / nF) ln K

E° is the standard cell potential (all solutes at 1 mol/L, gases at 1 bar), n is the number of electrons in the balanced equation, and Q is the reaction quotient — products over reactants, with pure solids and liquids left out. The constants are exact: the gas constant R = 8.314 462 618 J/(mol·K) and the Faraday constant F = 96 485.332 12 C/mol follow from the 2019 SI definitions (NIST). As the reaction proceeds Q rises toward K, E falls, and at equilibrium E reaches zero, which is why a battery goes flat.

Standard Reduction Potentials

Mode two draws on a hand-picked set of common couples from OpenStax Chemistry 2e, Appendix L (Table L1), measured at 25 °C against the standard hydrogen electrode, with values as printed. A sample:

To combine two couples the calculator takes E°cell = E°cathode − E°anode, where the cathode is the half-reaction run as a reduction and the anode is the one reversed into an oxidation. It then scales both so the electrons cancel (using the least common multiple), cancels species such as H⁺ and H₂O that appear on both sides, and writes the overall equation. E° is an intensive property: doubling an equation to balance electrons does not double its potential. Other tables differ slightly in the third decimal for some couples, for example Cu²⁺/Cu, so quote the table your course uses.

Worked Examples

Nernst equation (the default inputs). A Daniell cell has E° = 1.10 V, n = 2 and Q = [Zn²⁺] ÷ [Cu²⁺] = 10.0 at 25.0 °C. RT ÷ nF = (8.314 462 618 × 298.15) ÷ (2 × 96 485.332 12) = 0.012 846 V, so E = 1.10 − 0.012 846 × ln 10.0 = 1.07 V. The free energy is ΔG = −2 × 96 485.332 12 × 1.0704 = −207 kJ/mol, and each tenfold change in Q moves E by 29.6 mV.

E°cell from the table. Choose Cu²⁺ | Cu as the cathode and Zn²⁺ | Zn as the anode: E°cell = 0.337 − (−0.7618) = 1.099 V, n = 2, and the reaction is Cu²⁺ + Zn → Cu + Zn²⁺. That gives ΔG° = −212.0 kJ/mol and K = 1.403 × 10³⁷ at 25 °C.

Hydrogen electrode at pH 7. For 2H⁺ + 2e⁻ → H₂ with H₂ at 1 bar, Q = 1 ÷ [H⁺]² = 1.0 × 10¹⁴ and E° = 0, so E = −0.012 846 × ln(1.0 × 10¹⁴) = −0.41 V. This is the −0.059 V per pH unit that a pH electrode relies on.

ΔG from E. A cell with E = 1.10 V and n = 2 has ΔG = −nFE = −2 × 96 485.332 12 × 1.10 = −212 kJ/mol. A negative ΔG always goes with a positive E for a spontaneous cell.

Common Mistakes

• Doubling E° when you double the equation. Potentials are per electron transferred, not per mole of reaction, so E° stays the same. ΔG° does scale with n.
• Subtracting the wrong way round. E°cell = E°cathode − E°anode. A negative result means the reaction as written is not spontaneous; swap the electrodes and the sign flips.
• Using Celsius for T. T in RT ÷ nF is in kelvin. The calculator converts for you and refuses a value at or below 0 K.
• Putting solids in Q. Pure solids and liquids (the metal electrodes, water) have activity 1 and are omitted. Only dissolved species and gases appear.
• Using ln where the formula says log. E = E° − (RT/nF) ln Q is the same as E° − (0.05916/n) log Q at 25 °C. Mixing the two gives a factor-of-2.303 error.

Frequently Asked Questions

What is the Nernst equation used for?

It gives the potential of an electrochemical cell when the conditions are not standard, E = E° − (RT/nF) ln Q. It explains why a battery's voltage drifts as it discharges, how concentration cells work, and how pH and ion-selective electrodes turn a concentration into a voltage.

How do you calculate E°cell?

Subtract the anode's standard reduction potential from the cathode's: E°cell = E°cathode − E°anode. Do not change either value when you balance the electrons. For Cu²⁺/Cu (+0.337 V) and Zn²⁺/Zn (−0.7618 V) the answer is +1.099 V.

What is the Nernst equation at 25 °C?

E = E° − (0.05916 V ÷ n) log₁₀ Q. The constant is RT ln 10 ÷ F evaluated at 298.15 K, which is 59.16 mV. Many textbooks round it to 0.0592 V, and the calculator uses the unrounded value.

What is the relationship between E°, ΔG° and K?

ΔG° = −nFE° = −RT ln K, so E° = (RT/nF) ln K. A positive E° means a negative ΔG° and K greater than 1. Every 59.2 mV ÷ n of E° at 25 °C is a factor of 10 in K.

What does a negative cell potential mean?

The reaction as written is not spontaneous; its reverse is. The cell would have to be driven by an external voltage, as in electrolysis or charging a battery. Swapping the cathode and anode changes the sign of E°cell.

How do I write Q for a cell reaction?

Put the product concentrations (mol/L) and gas pressures (bar) over the reactant ones, each raised to its coefficient, and leave out pure solids and liquids. For Zn + Cu²⁺ → Zn²⁺ + Cu, Q = [Zn²⁺] ÷ [Cu²⁺].