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Nernst Equation Calculator

Calculate the actual cell potential under non-standard conditions using the Nernst equation: E = E0 - (RT/nF)ln(Q).

Standard Reduction Potentials Reference
Li⁺/Li-3.040 V
K⁺/K-2.924 V
Ca²⁺/Ca-2.868 V
Na⁺/Na-2.714 V
Mg²⁺/Mg-2.372 V
Al³⁺/Al-1.662 V
Zn²⁺/Zn-0.762 V
Cr³⁺/Cr-0.744 V
Fe²⁺/Fe-0.447 V
Ni²⁺/Ni-0.257 V
Sn²⁺/Sn-0.138 V
Pb²⁺/Pb-0.126 V
H⁺/H₂0.000 V
Cu²⁺/Cu0.342 V
I₂/I⁻0.536 V
Ag⁺/Ag0.800 V
Br₂/Br⁻1.066 V
Cl₂/Cl⁻1.358 V
Au³⁺/Au1.498 V
MnO₄⁻/Mn²⁺1.507 V
F₂/F⁻2.866 V
Fe³⁺/Fe²⁺0.771 V
Hg²⁺/Hg0.851 V
Pt²⁺/Pt1.180 V
O₂/H₂O1.229 V
Cr₂O₇²⁻/Cr³⁺1.232 V
Co²⁺/Co-0.280 V
Cd²⁺/Cd-0.403 V
Ti²⁺/Ti-1.628 V
Mn²⁺/Mn-1.185 V

What the Nernst equation computes

Standard cell potentials assume every species is at 1 M (or 1 atm for gases) and 298.15 K. Real cells almost never sit there. The Nernst equation corrects E0 for the actual concentrations:

E = E0 − (RT / nF) ln(Q)

R is 8.314 J/(mol·K), F is 96,485 C/mol, n is the number of electrons transferred in the balanced cell reaction, and Q is the reaction quotient built from current activities. At 298.15 K the prefactor RT/F equals 0.02569 V, and converting to log base 10 gives the textbook shortcut E = E0 − (0.0592/n) log₁₀(Q).

The sign convention follows from Le Chatelier: when Q < 1 (products depleted), the log is negative, the correction adds to E0, and the cell pushes harder forward. When Q > 1 the correction subtracts and E falls.

Inputs

  1. E0 in volts — from a standard reduction potential table, computed as E°cathode − E°anode for the overall cell.
  2. n — electrons transferred in the balanced cell reaction (must match the way Q is written).
  3. Q — reaction quotient at the actual concentrations.
  4. T in kelvin — defaults to 298.15 K. Change it for high-temperature cells, biological systems at 310 K, or industrial conditions.

The calculator returns E plus a sign-of-spontaneity check (E > 0 means the reaction as written is spontaneous).

Worked examples

Zn/Cu cell off standard conditions. E0 = 1.103 V, n = 2, [Zn²⁺] = 0.10 M, [Cu²⁺] = 1.0 M. Q = [Zn²⁺]/[Cu²⁺] = 0.10. E = 1.103 − 0.02569/2 × ln(0.10) = 1.103 − (−0.0296) = 1.133 V. Lower product concentration boosts the driving force.

Concentration cell. Same electrode, different concentrations: [Ag⁺] = 0.001 M on one side, 1.0 M on the other. E0 = 0 V, n = 1, Q = 0.001. E = −0.02569 × ln(0.001) = 0.177 V. The entire potential comes from the concentration gradient.

Temperature effect. Same Zn/Cu cell at 353.15 K (80 °C), Q = 0.10. E = 1.103 − (8.314 × 353.15)/(2 × 96485) × ln(0.10) = 1.138 V. Higher T amplifies the correction.

Frequently Asked Questions

What does the Nernst equation calculate?
The Nernst equation gives the actual cell potential E of an electrochemical cell when the species are not at standard conditions. Standard conditions assume 1 M for every aqueous species, 1 atm for every gas, and 298.15 K. The equation corrects E0 for the actual concentrations through the reaction quotient Q, so E shifts whenever Q deviates from 1.
What is the simplified Nernst equation at 25 °C?
At 298.15 K the prefactor RT/F evaluates to 0.02569 V, and switching from natural log to log base 10 multiplies by 2.303. That collapses the equation to E = E0 - (0.0592/n) log10(Q), which is the form most textbooks use for room-temperature problems. The general form E = E0 - (RT/nF) ln(Q) is what you need any time T is not 298.15 K.
What is the reaction quotient Q in the Nernst equation?
Q has the same algebraic form as the equilibrium constant — products over reactants, each raised to its stoichiometric coefficient — but it uses the current concentrations rather than equilibrium values. Pure solids and pure liquids are omitted; only aqueous species and gases appear. For a cell reaction Q is built from the overall balanced equation, not from either half-reaction in isolation.
When does E equal E0?
E equals E0 exactly when Q equals 1, because ln(1) = 0 and the correction term drops out. That happens when every aqueous species is at 1 M and every gas is at 1 atm — the definition of standard conditions. Any departure from those values, in either direction, makes Q ≠ 1 and pulls E away from E0.
What happens to cell potential at equilibrium?
At equilibrium the forward and reverse rates are equal, no net current flows, and E goes to zero. Setting E = 0 in the Nernst equation and noting that Q has reached K gives E0 = (RT/nF) ln(K). This is the bridge between electrochemistry and thermodynamics — measure E0 and you have ΔG° and K for the reaction.