When a metal is dipped into a solution of its own ions, an equilibrium is established between the metal atoms on the surface and the metal ions in the solution. This setup forms a half-cell. To measure the relative tendency of different half-cells to gain or lose electrons, we connect them to a universal reference electrode: the Standard Hydrogen Electrode.
Key Principle
It is impossible to measure the absolute potential of a single isolated half-cell. We can only measure the potential difference between two half-cells connected in a complete electrical circuit. By convention, we compare all half-cells to the Standard Hydrogen Electrode, which is assigned a potential of exactly 0.00 V.
Half-Cell Equilibria
In any half-cell, a redox equilibrium is established. Standard IUPAC rules state that half-equations for electrodes must always be written in the reduction direction (gaining electrons):
\( \text{M}^{n+}\text{(aq)} + n\text{e}^- \rightleftharpoons \text{M(s)} \)
Depending on the relative position of this equilibrium, the electrode will accumulate either a positive or negative charge compared to the solution. A position of equilibrium that lies to the left indicates a tendency to lose electrons, while a position to the right indicates a tendency to gain electrons.
The electromotive force (EMF) of a cell composed of a specific half-cell connected to a standard hydrogen electrode under standard conditions of 298 K temperature, 100 kPa gas pressure, and 1.00 mol dm^-3 concentration of all ions.
Standard Conditions
Because the position of a half-cell equilibrium is sensitive to conditions, we must measure electrode potentials under strict standard conditions:
- Temperature: 298 K (25 degrees Celsius).
- Pressure: 100 kPa (1 bar) for any gas involved.
- Concentration: 1.00 mol dm^-3 for all ions in solution.
The reference half-cell used to measure standard electrode potentials. It consists of hydrogen gas at 100 kPa bubbling over a platinum foil electrode coated in platinum black, immersed in a solution of 1.00 mol dm^-3 hydrogen ions at 298 K.
Why is Platinum Used?
The hydrogen half-cell involves a gas (H₂) and ions in solution (H⁺). Neither of these can act as a physical solid electrode to complete an electrical connection. Therefore, we use platinum because it is:
- Inert: It will not react or become oxidized/reduced itself.
- Conductive: It allows the flow of electrons into or out of the half-cell.
- Catalytic: Platinum black has a very high surface area which catalyses the rate of equilibrium establishment between hydrogen gas and hydrogen ions.
When asked to describe the SHE in exams, you must mention all three conditions: 298 K temperature, 100 kPa (or 1 bar) pressure of hydrogen gas, and 1.00 mol dm^-3 concentration of hydrogen ions. A common trap is to write 1.00 mol dm^-3 sulfuric acid. Sulfuric acid is diprotic (H₂SO₄), so a 1.00 mol dm^-3 solution contains 2.00 mol dm^-3 of H⁺. If you use sulfuric acid, the concentration must be exactly 0.50 mol dm^-3 to provide standard conditions!
Measuring Standard Electrode Potentials
To measure the standard electrode potential of any other half-cell, we connect it to the Standard Hydrogen Electrode using a high-resistance voltmeter. For example, connecting a standard zinc half-cell (Zn²⁺/Zn) to the SHE gives a reading of -0.76 V. Connecting a standard copper half-cell (Cu²⁺/Cu) gives a reading of +0.34 V.
Step 1: Write down the equilibrium for the half-cell:
Fe³⁺(aq) + e⁻ ⇌ Fe²⁺(aq)
Since both species in this half-cell are ions in aqueous solution, we need an inert platinum electrode to make electrical contact, just like in the SHE.
Step 2: Define standard conditions:
- Temperature of the system must be 298 K.
- The concentration of Fe³⁺(aq) must be exactly 1.00 mol dm^-3.
- The concentration of Fe²⁺(aq) must be exactly 1.00 mol dm^-3.
- The SHE must have a H⁺ concentration of 1.00 mol dm^-3 and H₂ gas pressure of 100 kPa.
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