Nernst Equation

What is this formula?

The Nernst equation calculates the actual electrochemical cell potential under non-standard conditions.

It relates cell voltage to temperature, reaction composition, and the reaction quotient.

When to use it

Use this equation when calculating cell voltages at concentrations, pressures, or activities different from standard conditions.

Example

Given:

E° = 1.10 V

T = 298 K

n = 2

Q = 10

R = 8.314 J·mol^-1·K^-1

F = 96485 C/mol

Formula:

E = E° − (RT/nF)ln(Q)

Substitution:

E = 1.10 − ((8.314×298)/(2×96485))ln(10)

Result:

E ≈ 1.07 V

The cell potential decreases because the reaction quotient is greater than one.

Applications

Electrochemistry

Battery analysis

Corrosion studies

Fuel cells

Electrochemical sensors

Industrial electrolysis

Note

The Nernst equation shows how cell potential changes as the reaction approaches equilibrium.

Important cases:

Q < 1 → E > E°

Q = 1 → E = E°

Q = K → E = 0

At equilibrium the cell can no longer perform electrical work because the driving force of the reaction has vanished.

At 25°C, the Nernst equation is often written in base-10 logarithm form:

E = E° − (0.05916/n)log(Q)

This is mathematically equivalent to the natural logarithm form used here.