Electrodes and Electrode Potentials

Types and Structure of Electrodes

In electrochemistry, an electrode is the interface where electron transfer between an electronic conductor (metal, graphite, semiconductor) and an ionic conductor (electrolyte solution or melt) occurs. The nature of this interface determines the electrode’s behavior and its potential.

Metal Electrodes in Their Own Ion Solutions

A simple and very important class are metal/metal ion electrodes. Their structure is:

• A metal $M$ (solid conductor)
• In contact with an aqueous solution containing ions $M^{z+}$ of the same metal at a certain activity (approximately, concentration)

Example:

• A zinc rod dipped into a solution of zinc sulfate
• Symbolic notation: $ \text{Zn(s)} \,|\, \text{Zn}^{2+}(aq)$

At this interface, the half-reaction
$$
\text{Zn(s)} \rightleftharpoons \text{Zn}^{2+}(aq) + 2\,e^-
$$
can proceed in either direction, depending on the overall cell conditions. The electrode can thus act as:

• Anode if the metal is oxidized (metal atoms → metal ions + electrons)
• Cathode if metal ions are reduced (metal ions + electrons → metal atoms)

The measurable potential of this electrode depends on:

• The nature of the metal
• The activity (effectively, concentration) of $M^{z+}$ in the solution
• Temperature

Gas Electrodes

In gas electrodes, a gas participates in the redox process, but gases are poor electronic conductors. Therefore:

• A chemically inert metal (usually platinum) serves as the electron conductor.
• The metal is in contact with:
• The gas phase at a defined partial pressure
• An aqueous solution containing the ionic form of the gas species

Example: hydrogen electrode

• Composition:
• A platinized platinum electrode (Pt with a rough, porous surface to increase area)
• In contact with a solution containing $ \text{H}^+$ (an acid solution)
• Hydrogen gas bubbled over the electrode at a defined pressure (often $p(\text{H}_2) = 1$ bar)
• Symbolic notation: $ \text{Pt(s)} \,|\, \text{H}_2(g), \text{H}^+(aq)$
• Half-reaction:
  $$
  \text{H}_2(g) \rightleftharpoons 2\,\text{H}^+(aq) + 2\,e^-
  $$

Gas electrodes are used whenever a gaseous substance is involved in the redox equilibrium (e.g., $ \text{Cl}_2/\text{Cl}^-$, $ \text{O}_2/\text{OH}^-$).

Metal–Insoluble Salt–Ion Electrodes

Some electrodes involve a metal covered by a sparingly soluble salt of that metal, in contact with a solution containing the anion of that salt. The classic example is the silver/silver chloride electrode.

Structure:

• Silver metal wire: $\text{Ag(s)}$
• Coated with solid $\text{AgCl(s)}$
• In contact with a solution containing chloride ions $\text{Cl}^-$

Symbolic notation:
$$
\text{Ag(s)} \,|\, \text{AgCl(s)} \,|\, \text{Cl}^-(aq)
$$

Relevant half-reaction:
$$
\text{AgCl(s)} + e^- \rightleftharpoons \text{Ag(s)} + \text{Cl}^-(aq)
$$

The potential depends mainly on the chloride ion activity in the solution. Because the solid phases $\text{Ag}$ and $\text{AgCl}$ are pure (activity ≈ 1), their contribution to potential is constant under fixed temperature. This makes such electrodes very reproducible; they are therefore often used as reference electrodes.

Inert Electrodes for Redox Couples in Solution

Many redox systems involve only ions or molecules in solution, with no solid metal in the redox pair. To measure or use these half-reactions, one employs an inert electrode, typically platinum or carbon, which:

• Does not participate chemically
• Provides a surface for electron transfer between the external circuit and the redox species in solution

Example:

• Redox couple $\text{Fe}^{3+}/\text{Fe}^{2+}$ in solution
• Electrode: $ \text{Pt(s)} \,|\, \text{Fe}^{3+}(aq), \text{Fe}^{2+}(aq)$
• Half-reaction:
  $$
  \text{Fe}^{3+}(aq) + e^- \rightleftharpoons \text{Fe}^{2+}(aq)
  $$

The potential depends on the ratio of $\text{Fe}^{3+}$ to $\text{Fe}^{2+}$ activities, as well as temperature.

Reference Electrodes

To measure electrode potentials in a reproducible way, one usually uses a reference electrode with a well-defined, stable potential. The potential of an unknown (indicator) electrode is measured relative to the reference electrode.

Important practical properties of reference electrodes:

• Well-known and stable potential
• Reproducible response
• Chemical compatibility with the system studied

Common types (conceptual overview, not construction details):

Standard Hydrogen Electrode (SHE)

• Conceptual primary reference, defined as:
• Hydrogen gas at $p(\text{H}_2) = 1$ bar
• A solution with $a(\text{H}^+) = 1$ (ideally 1 mol/L under standard conditions)
• Temperature usually $25^\circ\text{C}$
• Electrode notation: $ \text{Pt(s)} \,|\, \text{H}_2(g, 1\,\text{bar}), \text{H}^+(aq, a=1)$
• By definition, its potential is:
  $$
  E^\circ(\text{SHE}) = 0.000 \,\text{V}
  $$

Because of practical difficulties (gas handling, strict conditions), the SHE is mainly a theoretical standard or used in specialized labs.

Silver/Silver Chloride Electrode (Ag/AgCl)

• Structure: $ \text{Ag(s)} \,|\, \text{AgCl(s)} \,|\, \text{Cl}^-(aq)$ at a defined chloride concentration (e.g., saturated KCl).
• Has a nearly constant potential under fixed conditions.
• Widely used as a practical reference electrode in aqueous systems.

Calomel Electrode (Hg/Hg2Cl2)

• Based on mercury and the sparingly soluble salt mercurous chloride ($\text{Hg}_2\text{Cl}_2$), in a chloride solution.
• Historically important and still used, though less favored due to mercury toxicity.

The exact numerical potentials of these reference electrodes relative to the SHE depend on concentration and temperature and are typically looked up in tables.

Electrode Potentials: Concept and Measurement

Half-Cell Potentials Cannot Be Measured Alone

The potential of a single electrode (half-cell) represents the tendency of that redox system to accept or donate electrons. However, in practice:

• Any potential difference measured with a voltmeter is always between two points.
• A single half-cell by itself has no directly measurable absolute potential; its potential becomes meaningful only relative to another half-cell.

Therefore, we define the potential of any electrode relative to a reference electrode (conventionally the SHE).

Standard Electrode Potential $E^\circ$

For a half-reaction of the form:
$$
\text{Ox} + n\,e^- \rightleftharpoons \text{Red}
$$
the standard electrode potential $E^\circ$ is defined as:

• The potential of this half-cell
• When all participating dissolved species have activity 1 (often approximated by concentration 1 mol/L),
• Any gases are at partial pressure 1 bar,
• Pure solids and liquids are in their standard states,
• At a specified temperature (commonly $25^\circ\text{C}$),
• Measured versus the SHE ($E^\circ(\text{SHE}) = 0$).

For example, the standard potential of the $\text{Cu}^{2+}/\text{Cu}$ couple is:
$$
\text{Cu}^{2+}(aq) + 2\,e^- \rightleftharpoons \text{Cu(s)}, \quad E^\circ \approx +0.34 \,\text{V}
$$
This means that, under standard conditions, a $\text{Cu}^{2+}/\text{Cu}$ electrode has a potential of +0.34 V relative to the SHE.

Sign Convention and Direction of the Half-Reaction

By convention, tabulated $E^\circ$ values refer to the half-reaction written in its reduction direction (electrons on the left). This convention implies:

• A more positive $E^\circ$ indicates a stronger tendency to be reduced (to gain electrons).
• A more negative $E^\circ$ indicates a stronger tendency to be oxidized (to lose electrons, if written in the oxidation direction).

Importantly:

• If a half-reaction is written in the reverse direction (oxidation instead of reduction), the sign of $E^\circ$ changes.
• Multiplying a half-reaction by a factor (e.g., doubling the coefficients) does not change $E^\circ$, because potential is an intensive property (independent of the amount of substance).

Relation to the Overall Cell Potential

When two half-cells are connected to form a galvanic cell:

• One half-cell functions as the anode (oxidation)
• The other functions as the cathode (reduction)
• The measured cell voltage $E_{\text{cell}}$ under standard conditions is related to the standard electrode potentials by:
  $$
  E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}
  $$

This relationship shows how electrode potentials are the building blocks for predicting and understanding cell voltages. (The detailed treatment of cell voltage and its dependence on concentrations is covered elsewhere.)

Factors Influencing Electrode Potentials

Electrode potentials are not constant; they depend on the actual conditions at the electrode.

Effect of Concentration and Activity

For a generic half-reaction:
$$
\text{Ox} + n\,e^- \rightleftharpoons \text{Red}
$$
the equilibrium position is influenced by the activities (effective concentrations) of Ox and Red. As these change, the electrode potential shifts accordingly.

Qualitatively:

• Increasing the activity of the oxidized form (Ox) tends to make the electrode potential more positive (favoring reduction).
• Increasing the activity of the reduced form (Red) tends to make the electrode potential more negative (favoring oxidation).

The precise quantitative relationship is given by the Nernst equation, which connects electrode potential with the reaction quotient; this is treated in detail in the context of cell voltages and reaction equilibria.

Temperature Effects

Temperature changes can influence electrode potentials by:

• Affecting the equilibrium position of the redox pair
• Changing the activities of dissolved species
• Altering gas pressures (for gas electrodes)

Some electrodes exhibit relatively small, predictable temperature coefficients, which is why they can be used as reference electrodes over a range of temperatures with appropriate correction.

Ideal vs. Real Electrode Behavior

Polarization and Overpotential (Qualitative)

Real electrodes often deviate from the ideal equilibrium behavior assumed in thermodynamic electrode potentials. When a current flows:

• The electrode may not remain at its reversible potential
• An additional “extra” potential, called overpotential or overvoltage, may be required to drive the reaction at a given rate

Overpotential can arise from:

• Slow charge-transfer kinetics
• Mass transport limitations (diffusion of reactants/products)
• Formation of surface films or bubbles

Although detailed kinetic treatment belongs to chemical kinetics and applied electrochemistry, it is important to recognize that:

• The tabulated electrode potential describes the equilibrium tendency under negligible current (reversible conditions).
• Under practical operating conditions, the actual electrode potential may differ due to polarization effects.

Reversibility and Quasi-Reversibility

An electrode reaction is called:

• Reversible if it responds rapidly and reproducibly to small changes in conditions, allowing the potential to closely follow the Nernst equation.
• Irreversible or quasi-reversible when large deviations from the equilibrium potential occur under the influence of current because the reaction is kinetically slow or involves complicated intermediate steps.

Many reference electrodes are chosen because their half-reactions are near-reversible and therefore yield stable, well-defined potentials under minimal current draw.

Symbolic Representation of Electrodes in Cell Notation

Half-cells and electrodes are commonly summarized using a line notation. For an individual electrode:

• A single vertical line | denotes a phase boundary (e.g., solid | liquid)
• A comma separates species in the same phase
• Multiple phases in contact define the structure of the electrode

Examples:

• Metal/metal ion:
• $ \text{Zn(s)} \,|\, \text{Zn}^{2+}(aq)$
• Gas electrode:
• $ \text{Pt(s)} \,|\, \text{H}_2(g), \text{H}^+(aq)$
• Metal–insoluble salt electrode:
• $ \text{Ag(s)} \,|\, \text{AgCl(s)} \,|\, \text{Cl}^-(aq)$
• Inert electrode for redox couple in solution:
• $ \text{Pt(s)} \,|\, \text{Fe}^{3+}(aq), \text{Fe}^{2+}(aq)$

When constructing a full cell, the two half-cells are joined and separated by a double vertical line || representing the salt bridge or membrane. The detailed understanding of complete cell notation and how it relates to cell voltage belongs to the subsequent chapter on electrochemical cells and cell voltage; here, the focus is on how individual electrode structures are represented.