Nernst Equation - A Level Revision Notes

The Nernst Equation

Under non-standard conditions, the cell potential of the half-cells is shown by the symbol E_cell
The effect of changes in temperature and ion concentration on the E_cell can be deduced using the Nernst equation

$E = E^{Θ} + \frac{R T}{z F} l n \frac{[o x i d i s e d s p e c i e s]}{[r e d u c e d s p e c i e s]}$

E = electrode potential under nonstandard conditions

E^θ = standard electrode potential

R = gas constant (8.31 J K^-1 mol^-1)

T = temperature (kelvin, K)

z = number of electrons transferred in the reaction

F = Faraday constant (96 500 C mol^-1)

ln = natural logarithm

This equation can be simplified to

$E = E^{Θ} + \frac{0.059}{z} \log_{10} \frac{[o x i d i s e d s p e c i e s]}{[r e d u c e d s p e c i e s]}$

- At standard temperature, R, T and F are constant
- ln x = 2.303 log₁₀ x
The Nernst equation only depends on aqueous ions and not solids or gases
The concentrations of solids and gases are therefore set to 1.0 mol dm^-3

Applying Nernst Equation

Worked example: Calculating the electrode potential of a Fe³⁺/Fe²⁺ half-cell

Electrochemistry Calculations -Worked example - Calculating the electrode potential of a Fe3+_Fe2+ half-cell, downloadable AS & A Level Chemistry revision notes

Answer

From the question, the concentrations of ions for the Fe³⁺/ Fe²⁺ half-cell are as follows:
- [Fe³⁺] = 0.034 mol dm^-3
- [Fe²⁺] = 0.64 mol dm^-3
- E^Θ = + 0.77 V
The oxidised species is Fe³⁺ as it has a higher oxidation number (+3)
The reduced species is Fe²⁺ as it has a lower oxidation number (+2)
z is 1 as only one electron is transferred in this reaction
The Nernst equation for this half-reaction is, therefore:

$E = E^{Θ} + \frac{0.059}{z} \log_{10} \frac{[o x i d i s e d s p e c i e s]}{[r e d u c e d s p e c i e s]}$

$E = 0.77 + \frac{0.059}{1} \log_{10} \frac{[0.034]}{[0.64]}$

E = (+0.77) + (-0.075)

E = +0.69 V

Worked example: Calculating the electrode potential of a Cu²⁺/Cu half-cell

Electrochemistry Calculations -Worked example - Calculating the electrode potential of a Cu2+_Cu half-cell, downloadable AS & A Level Chemistry revision notes

Answer

From the question, the concentrations of ions for the Fe³⁺/ Fe²⁺ half-cell are as follows:
- [Cu²⁺] = 0.0010 mol dm^-3
- E^Θ = + 0.34 V
The oxidised species is Cu²⁺ as it has a higher oxidation number (+2)
The reduced species is Cu as it has a lower oxidation number (0)
Cu is solid which means that it is not included in the Nernst equation
- Its concentration does not change and is, therefore, fixed as 1.0
z is 2 as 2 electrons are transferred in this reaction
The Nernst equation for this half-reaction is, therefore:

$E = E^{Θ} + \frac{0.059}{z} \log_{10} \frac{[o x i d i s e d s p e c i e s]}{[r e d u c e d s p e c i e s]}$

$E = 0.34 + \frac{0.059}{2} \log_{10} \frac{[0.0010]}{[1.0]}$

E = (+ 0.34) + (– 0.089)

E = + 0.25 V

Examiner Tip

Make sure you always check what the temperature is.

If the temperature is not 298 K (or 25 ^oC) the full Nernst equation should be used.

You don’t need to know how to simplify the Nernst equation to:

$E = E^{Θ} + \frac{0.059}{z} \log_{10} \frac{[o x i d i s e d s p e c i e s]}{[r e d u c e d s p e c i e s]}$

You are only expected to use the equation when the temperature is 298 K (or 25 ^oC).

Nernst Equation (CIE A Level Chemistry)

Revision Note

Applying Nernst Equation

Worked example: Calculating the electrode potential of a Fe3+/Fe2+ half-cell

Worked example: Calculating the electrode potential of a Cu2+/Cu half-cell

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1. Physical Chemistry

1.1 Atomic Structure

1.1.1 Particles in the Atom & Atomic Structure

1.1.2 Mass, Charge & Subatomic Particles

1.1.3 Determining Subatomic Structure

1.1.4 Atomic & Ionic Radius

1.1.5 Isotopes

1.1.6 Electronic Structure

1.1.7 Electron Subshells & Orbitals

1.1.8 Electron Configuration

1.1.9 Determining Electronic Configurations

1.1.10 Ionisation Energy

1.1.11 Ionisation Energy Trends

1.1.12 Ionisation Energies & Electronic Configurations

1.2 Atoms, Molecules & Stoichiometry

1.2.1 Relative Masses

1.2.2 The Mole & Avogadro Constant

1.2.3 Formulae

1.2.4 Balancing Equations

1.2.5 Empirical & Molecular Formulae

1.2.6 Water of Crystallisation

1.2.7 Reacting Masses & Volumes

1.3 Chemical Bonding

1.3.1 Electronegativity

1.3.2 Electronegativity Trends

1.3.3 Electronegativity & Bonding

1.3.4 Ionic Bonding

1.3.5 Ionic Bonding Examples

1.3.6 Metallic Bonding

1.3.7 Covalent Bonding

1.3.8 Coordinate Bonding

1.3.9 Hybridisation

1.3.10 Bond Energy & Length

1.3.11 Shapes of Molecules

1.3.12 Hydrogen Bonding

1.3.13 Polarity & Dipole Moments

1.3.14 Van der Waals' Forces

1.3.15 Inter & Intramolecular Forces

1.3.16 Dot-&-Cross Diagrams

1.4 States of Matter

1.4.1 Gas Pressure

1.4.2 Ideal Gas Law & Equation

1.4.3 Lattice Structures

1.4.4 Bonding & Structure

1.5 Chemical Energetics

1.5.1 Enthalpy Change, ΔH

1.5.2 Energy Level Diagrams

1.5.3 Standard Enthalpy Change

1.5.4 Enthalpy & Bond Energies

1.5.5 Hess’s Law

1.6 Electrochemistry

1.6.1 Oxidation Number Rules

1.6.2 Redox Reactions

1.6.3 Oxidising & Reducing Agents

1.7 Equilibria

1.7.1 Chemical Equilibria

1.7.2 Le Chaterlier's Principle

1.7.3 Equilibrium Constant

1.7.4 Equilibrium Constant Calculations

1.7.5 Changes Affecting the Equilibrium Constant

1.7.6 Industrial Processes

1.7.7 Acids & Bases

1.7.8 Brønsted–Lowry Theory

1.7.9 Acid & Base Dissociation

1.7.10 pH Scale

1.7.11 Strength of Acids & Bases

1.7.12 pH Titration Curves

1.7.13 Indicators used in Titration

1.8 Reaction Kinetics

1.8.1 Collision Theory

1.8.2 Rate of Reaction

1.8.3 Activation Energy & Boltzmann Distribution Curves

Worked example: Calculating the electrode potential of a Fe³⁺/Fe²⁺ half-cell

Worked example: Calculating the electrode potential of a Cu²⁺/Cu half-cell