Nernst Equation
Cell potential under non-standard conditions.
Formula
Variables
Example
As reactant concentrations fall, a battery’s voltage drops below its standard value.
How it works
The Nernst equation tells you how far an electrochemical cell is from its standard voltage when the reacting species are not all at standard-state conditions. It works because the driving force for charge transfer depends on Gibbs free energy, and the free-energy change shifts with the reaction quotient Q; that shift translates directly into a change in cell potential. As Q changes during a reaction, the voltage changes in a predictable logarithmic way, and the electron count n determines how strongly each mole of reaction affects the electrical output.
When to use it
Use this when you need the voltage of a battery, galvanic cell, or electrochemical half-cell at nonstandard concentrations, pressures, or pH. It is also essential in redox analysis, electroplating, corrosion, and calculating equilibrium from electrochemical data.
Worked example, step by step
For the zinc-copper cell at 25°C, suppose E° = 1.10 V, n = 2, and the reaction quotient is Q = 0.010. Use E = E° - (RT/nF)ln Q At 25°C, RT/F ≈ 0.0257 V, so RT/nF = 0.0257/2 = 0.01285 V ln(0.010) = -4.605 E = 1.10 - (0.01285)(-4.605) E = 1.10 + 0.0592 E = 1.1592 V Final answer: E ≈ 1.16 V
Common mistakes to avoid
- Using log10 without converting the constant correctly for the natural-log form
- Putting products and reactants into Q in the wrong positions
- Forgetting that n is the number of electrons transferred in the balanced redox equation
Did You Know?
The Nernst equation predicts battery voltage and the electrical signals firing in your neurons.
Share this formula
More in Chemistry
View allIdeal Gas Law
IntermediateRelates pressure, volume, moles and temperature of a gas.
Molarity
BasicConcentration in moles of solute per litre of solution.
Moles from Mass
BasicNumber of moles from mass and molar mass.
pH
BasicAcidity from hydrogen-ion concentration.
pOH
BasicBasicity from hydroxide-ion concentration.
Henderson–Hasselbalch
AdvancedpH of a buffer solution.