Nernst Equation Calculator

The Nernst equation corrects a standard electrode potential for concentrations that are not at standard state:

$E = E^{\circ} - \frac{RT}{nF}\ln Q$

• $E$ — the actual cell potential, in volts.
• $E^{\circ}$ — the standard cell potential (all solutes at 1 M, all gases at 1 bar).
• $R = 8.314\ \mathrm{J\,mol^{-1}K^{-1}}$, $T$ — absolute temperature in kelvin.
• $n$ — moles of electrons transferred in the balanced cell reaction.
• $F = 96{,}485\ \mathrm{C\,mol^{-1}}$, the Faraday constant.
• $Q$ — the reaction quotient, products over reactants, each raised to its coefficient. Pure solids and pure liquids are omitted.

At 25 °C the whole prefactor collapses to a single number once the natural log is converted to base 10:

$E = E^{\circ} - \frac{0.0592}{n}\log_{10} Q \quad (\text{volts, at } 298.15\ \mathrm{K})$

What it assumes. Concentrations stand in for activities, which holds in dilute solution; the temperature is uniform and known; and $E^{\circ}$ is the value for the same balanced reaction whose $n$ you used. That 0.0592 belongs to 25 °C only — at 37 °C the base-10 prefactor is 0.0615 V.

Electrochemical cells

1. Balance the half-reactions and read off $n$, the electrons cancelled.
2. Write $Q$ for the overall reaction, omitting solids and pure liquids.
3. Substitute into $E = E^{\circ} - (0.0592/n)\log_{10} Q$ at 25 °C.
4. Interpret: $E > 0$ means the reaction as written is spontaneous. When $Q$ is small — products scarce — the log is negative and $E$ rises above $E^{\circ}$.

At equilibrium the cell is dead: $E = 0$ and $Q = K$, which gives

$\log_{10} K = \frac{n E^{\circ}}{0.0592}$

Concentration cells

With the same electrode material on both sides, $E^{\circ} = 0$ and the potential comes entirely from the concentration difference.

Membrane potentials

For a single ion of charge $z$ distributed across a membrane, the same algebra gives the equilibrium (Nernst) potential:

$E_{\text{ion}} = \frac{RT}{zF}\ln\frac{[\text{ion}]_{\text{out}}}{[\text{ion}]_{\text{in}}} = \frac{61.5\ \mathrm{mV}}{z}\log_{10}\frac{[\text{ion}]_{\text{out}}}{[\text{ion}]_{\text{in}}}$

at 37 °C. This is the voltage at which that ion's electrical and diffusional driving forces cancel. It describes one ion; a real resting potential mixes several.

• Getting $n$ wrong. $n$ is the number of electrons transferred in the balanced overall reaction — 2 for $\mathrm{Zn + Cu^{2+}}$, not 1. It divides the whole correction term.
• Using 0.0592 away from 25 °C. That constant is $RT\ln(10)/F$ at 298.15 K. At body temperature use 0.0615 V (61.5 mV).
• Mixing $\ln$ and $\log_{10}$. The $RT/nF$ form takes $\ln$; the 0.0592 form takes $\log_{10}$. They differ by 2.303.
• Including solids or the solvent in $Q$. Solid zinc and liquid water have unit activity and never appear.
• Inverting the membrane ratio. $E_{\text{ion}}$ uses outside over inside; flipping it flips the sign, turning $-89$ mV into $+89$ mV.
• Forgetting the ion's charge sign. For $\mathrm{Cl^-}$, $z = -1$, which reverses the result relative to a cation with the same gradient.