Standard Cell Notation and Electrode Potentials

Cell notation is a shorthand for describing a galvanic cell, with the anode on the left, a single vertical line for each phase boundary and a double line for the salt bridge, and standard electrode potentials, measured against the standard hydrogen electrode, tell how strongly each half-reaction tends to occur. In brief: the Daniell cell is written Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s), and its E° = 0.34 − (−0.76) = +1.10 V.

The potential of a single half-cell cannot be measured alone, because every measurement needs two electrodes. Chemists therefore define a reference electrode and give all other half-cells potentials relative to it. This article explains the notation, the standard hydrogen electrode, a table of standard reduction potentials and the ways in which they are used to rank oxidizing and reducing agents.

How is a cell written in shorthand?

The rules of cell notation (line notation) are:

The anode (oxidation) is written on the left and the cathode (reduction) on the right.
A single vertical line (|) separates different phases in contact, such as a solid electrode and a solution.
A double vertical line (||) shows the salt bridge or porous barrier between the half-cells.
Species in the same phase are separated by commas.
Concentrations (or pressures) are given in brackets. If an inert electrode is used, it is written at the end of its half-cell.

Examples:

Zn(s) | Zn²⁺(1.0 M) || Cu²⁺(1.0 M) | Cu(s)
Zn(s) | Zn²⁺(aq) || Ag⁺(aq) | Ag(s)
Pt(s) | Fe²⁺(aq), Fe³⁺(aq) || MnO₄⁻(aq), Mn²⁺(aq), H⁺(aq) | Pt(s)
Pt(s) | H₂(1 bar) | H⁺(1 M) || Cu²⁺(1 M) | Cu(s)

What is the standard hydrogen electrode?

The standard hydrogen electrode (SHE) is the reference to which all electrode potentials are compared. It consists of a platinum electrode covered with finely divided platinum (platinum black), immersed in an acid solution with a hydrogen ion activity of 1 (about 1 M) and bathed with hydrogen gas at a pressure of 1 bar:

2H⁺(aq, 1 M) + 2e⁻ ⇌ H₂(g, 1 bar) E° = 0.00 V (by definition)

The standard electrode potential (E°) of another half-cell is the voltage of a cell that consists of this half-cell, with all species at standard conditions (1 M for solutions, 1 bar for gases, usually 25 °C), and the SHE. By convention, the tabulated values are reduction potentials: they refer to the half-reaction written as a reduction.

Table of standard reduction potentials

Standard reduction potentials at 25 °C (V versus SHE)
Half-reaction	E° (V)	Half-reaction	E° (V)
Li⁺ + e⁻ → Li	−3.04	2H⁺ + 2e⁻ → H₂	0.00
K⁺ + e⁻ → K	−2.93	Cu²⁺ + 2e⁻ → Cu	+0.34
Ca²⁺ + 2e⁻ → Ca	−2.87	Fe³⁺ + e⁻ → Fe²⁺	+0.77
Na⁺ + e⁻ → Na	−2.71	Ag⁺ + e⁻ → Ag	+0.80
Mg²⁺ + 2e⁻ → Mg	−2.37	Br₂ + 2e⁻ → 2Br⁻	+1.07
Al³⁺ + 3e⁻ → Al	−1.66	O₂ + 4H⁺ + 4e⁻ → 2H₂O	+1.23
Zn²⁺ + 2e⁻ → Zn	−0.76	Cl₂ + 2e⁻ → 2Cl⁻	+1.36
Fe²⁺ + 2e⁻ → Fe	−0.44	MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O	+1.51
Pb²⁺ + 2e⁻ → Pb	−0.13	F₂ + 2e⁻ → 2F⁻	+2.87

What are the rules for using the table?

The more positive E°, the stronger the tendency to be reduced, so the species on the left is a stronger oxidizing agent. F₂ is the strongest oxidizing agent in the table.
The more negative E°, the stronger the reducing agent on the right of the half-reaction. Li metal is the strongest reducing agent.
Reversing a half-reaction changes the sign of E°. For example, Zn → Zn²⁺ + 2e⁻ has E° = +0.76 V.
E° does not depend on the amounts: it is an intensive quantity, so multiplying a half-reaction by a factor does not change its potential.

What does the table tell you?

The metals with negative potentials are more reactive than hydrogen, and can be oxidized by acids (releasing H₂): Zn + 2H⁺ → Zn²⁺ + H₂. The metals with positive potentials, such as Cu, Ag and Au, do not react with non-oxidizing acids. A metal can reduce the ion of any metal below it in the list, so Zn reduces Cu²⁺, and Cu reduces Ag⁺. This ordering is the electrochemical (activity) series.

Worked examples

Example 1: writing the notation for a cell

A cell uses the reaction Zn + 2Ag⁺ → Zn²⁺ + 2Ag. Zn is oxidized, so it is the anode on the left. The notation is Zn(s) | Zn²⁺(aq) || Ag⁺(aq) | Ag(s). The standard cell potential is E° = E°(cathode) − E°(anode) = 0.80 − (−0.76) = +1.56 V.

Example 2: reading a notation

For the cell Pt(s) | H₂(1 bar) | H⁺(1 M) || Cu²⁺(1 M) | Cu(s), the anode is the hydrogen electrode (oxidation: H₂ → 2H⁺ + 2e⁻) and the cathode is copper (Cu²⁺ + 2e⁻ → Cu). The measured voltage is the standard potential of copper, +0.34 V.

Example 3: ranking oxidizing agents

Rank Ag⁺, Cu²⁺, Zn²⁺ and Fe³⁺ as oxidizing agents. By E° (0.80, 0.34, −0.76 and 0.77 V for Fe³⁺ → Fe²⁺), the order from strongest to weakest is Ag⁺ > Fe³⁺ > Cu²⁺ > Zn²⁺.

Example 4: will a reaction occur?

Will copper metal dissolve in 1 M HCl? The possible reaction is Cu + 2H⁺ → Cu²⁺ + H₂, with E° = 0.00 − 0.34 = −0.34 V. This is negative, so no. Copper dissolves in nitric acid, where the oxidizing agent is nitrate and not H⁺.

How were the values established?

The standard hydrogen electrode was proposed as a reference in the early 20th century, in work by Walther Nernst and others. The tables of standard potentials were compiled by Wendell Latimer, whose book The Oxidation States of the Elements and Their Potentials in Aqueous Solutions (1938) became the standard reference. The practical measurement uses reference electrodes that are easier to handle, such as Ag/AgCl or the saturated calomel electrode, whose potentials relative to the SHE are known.

Which mistakes are common?

Multiplying E° by the coefficient: potentials are not additive in this way.
Forgetting to reverse the sign for oxidation: tables list reductions.
Placing the cathode on the left: the anode is written first.
Calling E° the actual cell voltage: E° applies to 1 M and 1 bar; other conditions need the Nernst equation.
Mixing up the strength of the oxidizing agent with that of the reducing agent: they sit on opposite sides of the half-reaction.