A modular guide to potential measurement, the hydrogen electrode, and the construction of the electrochemical scale
1. Introduction
In electrochemistry, we often ask: How likely is a given species to gain or lose electrons? This tendency, the driving force behind redox reactions, is quantified by a measurable quantity known as the electrode potential.
However, because all electrical potentials are relative, we must define them against a reference electrode. The most important of these, the Standard Hydrogen Electrode (SHE), provides the universal zero point for all other half-cell potentials. From this foundation arises the electrochemical series, a table ranking elements and ions by their redox power.
In this lecture, you’ll learn:
- How electrode potentials are defined and measured
- Why reference electrodes are essential
- How to use the Standard Hydrogen Electrode (SHE)
- How to interpret and compare standard electrode potentials
- How to construct electrochemical cells using these conventions
By the end, you’ll be able to calculate cell voltages, identify oxidising and reducing agents, and understand the logic that underpins all redox thermodynamics.
Reference: Royal Society of Chemistry – Measuring Electrode Potentials
2. The Concept of Electrode Potential
Every redox couple has an intrinsic tendency to gain or lose electrons. When a metal electrode is dipped into a solution of its ions, an equilibrium develops between the solid and its ionic form:
At equilibrium, an electrical potential difference arises between the metal and the surrounding solution. This potential depends on:
- The nature of the metal
- The ion concentration
- The temperature
- The solvent environment
However, this absolute potential cannot be measured directly; only potential differences between two electrodes can be observed. Thus, a reference point must be chosen to measure all other potentials relative to.
3. Defining Standard Electrode Potentials (E°)
The standard electrode potential, denoted E°, is the potential of a half-cell under standard conditions:
| Condition | Description |
| Temperature | 298 K (25 °C) |
| Ion concentration | 1.00 mol dm⁻³ |
| Gas pressure | 1 atm (100 kPa) |
| Activity of solids and liquids | Taken as 1 |
All potentials are referenced to the Standard Hydrogen Electrode (SHE), which is assigned a value of exactly 0.00 V by definition.
Thus, a standard electrode potential represents the voltage produced when a given half-cell is connected to the SHE.
4. The Standard Hydrogen Electrode (SHE)
The Standard Hydrogen Electrode forms the zero point of the electrochemical scale. Its construction and operation must be precise to ensure reproducibility.
Half-Cell Reaction
This equilibrium defines the standard potential E° = 0.00V.
Construction Details
- Electrode: Platinum foil or wire coated with finely divided platinum (“platinum black”).
- Gas: Pure hydrogen at 1 atm bubbled over the electrode.
- Electrolyte: 1.0 mol dm⁻³ H⁺ (often from HCl).
- Temperature: 298 K.
- Purpose: Acts as a reversible redox interface for the H⁺/H₂ couple.
Diagrammatic representation:
Reference: LibreTexts – The Standard Hydrogen Electrode
5. Measuring Electrode Potentials
To determine the potential of an unknown half-cell, we construct a galvanic cell pairing it with the SHE:
The measured cell EMF (Ecell) under standard conditions equals the standard electrode potential of the unknown half-cell.
Example: Copper(II) / Copper Half-Cell
Cell diagram:
Measured EMF = +0.34 V
Therefore:
A positive voltage means electrons flow from the hydrogen electrode to the copper electrode, hydrogen is oxidised, and copper ions are reduced.
6. Interpreting Sign Conventions
By IUPAC convention:
- E°₍red₎ refers to the reduction potential of a half-cell written as a reduction reaction.
- All tabulated E° values represent reduction potentials.
Thus, for zinc:
and for copper:
This convention simplifies comparison:
- More positive E° → stronger oxidising agent (greater tendency to gain electrons).
- More negative E° → stronger reducing agent (greater tendency to lose electrons).
7. Constructing a Full Cell from Half-Cells
When two half-cells are connected, electrons flow from the one with the lower E° to that with a higher E°.
Example: The Daniell Cell
Half-reactions:
Overall cell potential:
Thus, the spontaneous reaction is:
8. Reference Electrodes Beyond the SHE
While the SHE is the universal reference, it’s impractical for routine uses, as hydrogen gas handling, contamination, and maintenance make it difficult.
Several secondary reference electrodes have been developed for laboratory and industrial use.
(a) Silver/Silver Chloride (Ag/AgCl) Electrode
Advantages:
- Easy to prepare and stable.
- Suitable for aqueous systems.
Diagram:
(b) Calomel Electrode (Hg/Hg₂Cl₂)
Advantages:
- Stable potential over time.
- Common in analytical chemistry.
Disadvantages:
- Mercury toxicity and environmental concerns.
9. Building the Electrochemical Series
By systematically pairing each half-cell with the SHE, we can tabulate their standard electrode potentials. Ordering these E° gives the electrochemical series.
| Half-Cell Reaction (Reduction Form) | E°/V |
| Li⁺ + e⁻ → Li(s) | −3.04 |
| K⁺ + e⁻ → K(s) | −2.93 |
| Zn²⁺ + 2e⁻ → Zn(s) | −0.76 |
| H⁺ + e⁻ → ½H₂(g) | 0.00 |
| Cu²⁺ + 2e⁻ → Cu(s) | +0.34 |
| Ag⁺ + e⁻ → Ag(s) | +0.80 |
| Cl₂(g) + 2e⁻ → 2Cl⁻(aq) | +1.36 |
| F₂(g) + 2e⁻ → 2F⁻(aq) | +2.87 |
Interpretation:
- Metals like lithium and potassium (negative E°) are strong reducing agents.
- Halogens like fluorine and chlorine (positive E°) are strong oxidising agents.
Reference: Chemguide – The Electrochemical Series
10. Predicting Reaction Direction Using E° Values
To predict whether a redox reaction is spontaneous:
- Write both half-reactions as reductions.
- Identify the more positive E°. This is the reduction (cathode).
- The less positive E° is oxidised (anode).
- Compute E°₍cell₎ = E°₍cathode₎ − E°₍anode₎.
- If E°₍cell₎ > 0, the reaction is spontaneous.
Example:
Will Fe²⁺ reduce Cu²⁺?
Reaction:
11. Relationship to Gibbs Free Energy
The thermodynamic relationship between cell potential and free energy is:
Where:
- n = number of electrons transferred
- F = Faraday constant (96,485 C/mol)
- ΔG° = Gibbs free energy change under standard conditions
A positive E°₍cell₎ implies negative ΔG°, indicating a spontaneous process.
Reference: LibreTexts – Electrochemical Thermodynamics
12. Practical Considerations in Measurement
To ensure accuracy when measuring electrode potentials:
- Use high-impedance voltmeters to minimise current draw.
- Minimise liquid junction potential by matching ionic strength.
- Keep the temperature constant at 25 °C.
- Use a freshly prepared salt bridge (often KCl).
- Rinse electrodes with distilled water between uses.
For precise work, all potentials should be corrected to the Standard Hydrogen Scale or another accepted reference.
13. Applications of Standard Potentials
- Predicting Reaction Feasibility:
Determines whether a redox reaction will occur spontaneously. - Designing Batteries and Cells:
The cell voltage is directly calculated from the tabulated E° values. - Corrosion Studies:
Metals with more negative E° are prone to oxidation and corrosion. - Analytical Chemistry:
Used in potentiometric titrations, electrode calibration, and sensor design. - Biochemistry:
Redox couples such as NAD⁺/NADH and cytochromes are characterised by their standard reduction potentials.
14. Standard Potentials and Biological Systems
In biological contexts, potentials are often reported relative to the Standard Hydrogen Electrode but at pH 7.0 rather than 1.0 M H⁺ ; this is called the Standard Biochemical Potential (E°).
Example:
These adjusted potentials account for physiological conditions and are crucial in understanding metabolic energy transfer.
15. Alternative Reference Systems and Miniaturisation
Modern electrochemistry increasingly uses micro-reference electrodes in sensors, fuel cells, and lab-on-chip devices.
Examples include:
- Miniature Ag/AgCl references integrated into pH electrodes.
- Non-aqueous reference electrodes for lithium-ion batteries (Li/Li⁺).
- Quasi-reference systems in solid-state electrochemistry.
Such designs extend the principles of standard potentials into new technological contexts.
16. Worked Example
Determine the EMF of the cell:
Given:
E°₍Cu²⁺/Cu₎ = +0.34 V
E°₍Ag⁺/Ag₎ = +0.80 V
Solution:
Cathode = Ag⁺/Ag (higher potential)
Anode = Cu²⁺/Cu (lower potential)
Spontaneous reaction:
17. The Universal Nature of Reference Cells
Reference cells underpin all electrochemical measurements, whether in industrial sensors, fuel cells, analytical instruments, or academic laboratories.
Without them, we could not compare potentials meaningfully or construct universal data tables. The concept of relative potential ensures that chemistry remains a quantitative science of energy and electrons.
18. Summary and Learning Outcomes
By completing this lecture, you should be able to:
Define standard electrode potential and explain its meaning.
Describe and draw the Standard Hydrogen Electrode (SHE).
Understand why all potentials are measured relative to a reference.
Interpret sign conventions and relate E° to oxidising/reducing strength.
Use E° values to calculate cell EMFs and predict spontaneity.
Recognise and select appropriate reference electrodes for practical use.
Explain how the electrochemical series is constructed and applied.
Further Reading and References
- Royal Society of Chemistry: Measuring Electrode Potentials
- Chemguide: The Electrochemical Series
- LibreTexts: Standard Hydrogen Electrode
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