Standard electrode potentials E°, standard cell potentials E°cell and the Nernst equation

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Introduction to Half-Cells and Electrochemical Cells

A half-cell is part of an electrochemical system where either oxidation or reduction happens.

It usually consists of:

• A metal dipped into a solution of its own ions, OR
• A solution containing ions of the same element in different oxidation states (with a platinum electrode).

Two half-cells can be connected together to form a full electrochemical cell, allowing electrons to flow from one half-cell (where oxidation happens) to the other (where reduction happens), generating electricity.

Different half-cells are more or less likely to undergo oxidation or reduction, and this tendency can be measured by their electrode potentials.

Oxidation and Reduction in a Half-Cell

Each half-cell contains two forms of a species, one in a higher oxidation state and one in a lower oxidation state.

• Reduction happens when the oxidised form gains electrons.
• Oxidation happens when the reduced form loses electrons.

Example (Copper Half-Cell):

Cu²⁺(aq) + 2e⁻ ⇌ Cu(s)
Cu²⁺ can gain electrons to form Cu (reduction).
Cu can lose electrons to form Cu²⁺ (oxidation).

What is a Standard Electrode Potential (E°)?

The standard electrode potential (E°) of a half-cell measures how easily it undergoes reduction compared to the standard hydrogen electrode.

It’s measured under standard conditions:

• 1 mol dm⁻³ ion concentration
• 298 K temperature
• 100 kPa pressure (for gases)

A more positive E° value means a greater tendency for reduction to occur.
A more negative E° value means a greater tendency for oxidation to occur.

Key Point:
When we describe an electrode potential (E°), we are talking about the ease with which the oxidised form of an element or ion in a half cell gains electrons (undergoes reduction).

What is Standard Cell Potential (E°_cell)?

The standard cell potential (E_cell) is the overall voltage produced when two half-cells are connected under standard conditions.

We can calculate E_cell values using the standard electrode potentials of each half-cell:

Note:

• The cathode is the half-cell where reduction happens.
• The anode is the half-cell where oxidation happens.

Meaning you can also write the above equation as:

The Standard Hydrogen Electrode (SHE)

The standard hydrogen electrode (SHE) is used as a reference point and is assigned an E° of exactly 0.00 V.

Setup:

• H₂ gas at 100 kPa
• 1 mol dm⁻³ H⁺ ions (typically from HCl)
• Platinum electrode (inert and conducts electrons)
• 298 K temperature

This means that when two standard hydrogen electrodes are connected together, the potential difference is 0.00 V.

All other standard electrode potentials are measured relative to the SHE. If the right-hand half-cell is now changed, a potential difference (voltage) is measured.

Measuring Standard Electrode Potentials

A half-cell is connected to the SHE and the voltage measured is called the half-cell’s standard electrode potential, E°.

These standard electrode potentials are often put into a table called the electrochemical series.

Key Points:

• The more positive the E°, the more likely a species is to be reduced (forward direction).
• The more negative the E°, the more likely a species is to be oxidised (reverse direction).

Half-cells can be made in different ways depending on the species involved:

Metal or Non-Metal Half-Cells:

Example: A zinc rod in Zn²⁺ solution.

Different Oxidation States of the Same Element:

Example: A solution containing both Fe³⁺ and Fe²⁺ ions (with a platinum electrode).

Calculating a Standard Cell Potential

We can calculate the standard cell potential (E_cell) of two connected half-cells using their individual standard electrode potentials (see above).

• The cathode will be the one with the more positive E°.
• The anode will be the one with the more negative E°.

Formula:

Using E°_cell to Predict Electron Flow and Feasibility

Electron Flow:
Electrons flow from the more negative half-cell (anode) to the more positive half-cell (cathode).

Feasibility:

• If E°_cell is positive then the overall reaction is feasible.
• If E°_cell is negative then the reverse reaction is favoured.

Reactivity Trends from E° Values

We can rank how reactive elements and ions are in redox reactions based on their standard electrode potentials.

• A more positive E° = stronger oxidising agent (gains electrons easily).
• A more negative E° = stronger reducing agent (loses electrons easily).

Redox Equations from Half-Equations

Steps to construct redox equations:

• Write both half-equations as reductions.
• Reverse the more negative one to show oxidation.
• Balance the electrons and combine.

Example Zn / Cu²⁺

Zn²⁺ + 2e⁻ → Zn
Cu²⁺ + 2e⁻ → Cu
Overall: Zn + Cu²⁺ → Zn²⁺ + Cu

How Electrode Potentials Vary with Concentration

Standard E° values assume 1 mol dm⁻³ concentration.
If concentrations change, then the actual potentials of each half-cell will change.

• Increasing the concentration of oxidised species in the half-cell makes E more positive.
• Increasing the concentration of reduced species in the half-cell makes E more negative.

This affects how easily redox reactions occur under non-standard conditions.

The Nernst Equation

When conditions are not standard, the Nernst equation can be used to calculate the actual electrode potential:

Where:

• E = electrode potential under non-standard conditions
• E° = standard electrode potential
• z = number of electrons transferred
• [oxidised] and [reduced] = concentrations of ions

Example Fe³⁺/Fe²⁺

For Fe³⁺ + e⁻ ⇌ Fe²⁺, if [Fe³⁺] > [Fe²⁺], the electrode potential becomes more positive.

Link Between Gibbs Free Energy and Electrode Potentials

Gibbs free energy change can be related to the cell potential by the following equation:

Where:

• ΔG° = Gibbs free energy change (J mol⁻¹)
• n = number of electrons transferred
• F = Faraday constant (96500 C mol⁻¹)
• E°_cell = standard cell potential (V)

If ΔG° is negative, the reaction is spontaneous.

Summary

• Half-cells combine to make electrochemical cells; electrons flow from anode to cathode.
• E° measures a half-cell’s tendency to be reduced relative to the SHE (0.00 V).
• E°_cell = E°(cathode) − E°(anode); positive values indicate feasibility.
• Changing concentrations shifts E; use the Nernst equation for non-standard conditions.
• ΔG° = −nFE°_cell links thermodynamic spontaneity with cell potential.