Last updated: 2026-06-15

Understanding the Nernst equation

The Nernst equation gives the electromotive force (EMF) of an electrochemical cell when reactant and product concentrations differ from standard conditions. Standard electrochemistry tables report potentials measured at 1 M, 1 atm, and 25 °C; real cells almost never sit exactly at those conditions, and the Nernst equation corrects for the difference.

The formula

The natural logarithm of $Q$ captures how far the system is from standard conditions. When $Q \lt 1$ (products depleted relative to standard), $\ln Q$ is negative and $E > E^\circ$. When $Q \gt 1$ (products accumulated), $\ln Q$ is positive and $E < E^\circ$.

Reaction spontaneity

The sign of $E$ tells you the direction of spontaneous change:

This connects directly to Gibbs free energy: $\Delta G = -nFE$. A positive $E$ corresponds to a negative $\Delta G$, meaning the cell can do useful electrical work.

Worked example

Given: a zinc–copper cell with standard cell potential 1.10 V, two electrons transferred, reaction quotient 0.001, and temperature 298.15 K.

The cell potential rises above the standard value because the low $Q$ (product-depleted conditions) drives the reaction forward more strongly.

Simplified form at 25 °C

At $T = 298.15\ \text{K}$, substituting $R$, $T$, and $F$ gives:

Converting the natural log to base-10 log ($\ln x = 2.3026 \log_{10} x$) yields the textbook approximation:

This form is convenient for quick calculations without a calculator and is accurate to within about 0.01% at room temperature.

The reaction quotient Q

$Q$ has the same algebraic form as the equilibrium constant $K$ — products over reactants raised to stoichiometric powers — but uses actual concentrations or partial pressures instead of equilibrium values. Pure solids and liquids (activity = 1) are excluded. Three regimes:

• $Q < K$: reaction proceeds forward, with positive $E$
• $Q = K$: equilibrium, with zero $E$
• $Q > K$: reaction proceeds in reverse, with negative $E$

Concentration cells

A concentration cell uses identical electrodes but different ion concentrations in the two half-cells. The standard potential is zero, so:

Because $[\text{dilute}] < [\text{concentrated}]$, the fraction is less than one, its natural log is negative, and $E$ is positive. The cell drives current spontaneously until the concentrations equalize. This principle underlies pH electrodes, lithium-ion batteries, and biological ion channels.