Reading a Latimer diagram: redox at a glance

A Latimer diagram is a compressed table of standard reduction potentials for one element in aqueous solution. It puts every oxidation state on one horizontal line, connected by arrows labelled with E° values (in volts). One glance tells you which species is the strongest oxidiser, which is the strongest reductant, and which is thermodynamically unstable with respect to disproportionation. This guide walks the notation, the sign convention, the “add potentials by weighted average” trick for computing skipping-step potentials, and the disproportionation test.

Prerequisites: balancing redox equations — Latimer diagrams presume you can write out the half-reaction that each arrow represents. If Ksp comfortable, Ksp from rules to numbers trains the same “small-K decision” habit that Latimer diagrams reward.

What a Latimer diagram looks like

For manganese in acidic solution (Bard, Parsons & Jordan 1985):

$\text{MnO}_4^- \xrightarrow{+0.564} \text{MnO}_4^{2-} \xrightarrow{+2.26} \text{MnO}_2 \xrightarrow{+0.95} \text{Mn}^{3+} \xrightarrow{+1.51} \text{Mn}^{2+} \xrightarrow{-1.18} \text{Mn}$

Reading left to right, oxidation state decreases (+7 → +6 → +4 → +3 → +2 → 0). Each arrow is a reduction, and each label is the standard reduction potential for that specific half-reaction. The number over the arrow is E° in volts, with the sign convention: E° > 0 means the reduction is thermodynamically favourable at standard conditions (1 M, 1 atm, 298 K); E° < 0 means the reverse (the oxidation) is favourable.

Reading the arrows — what each E° means

The arrow MnO₄⁻ → MnO₄²⁻ with E° = +0.564 V represents the half-reaction:

$\text{MnO}_4^- + e^- \to \text{MnO}_4^{2-} \quad E^\circ = +0.564 \text{ V}$

An E° near zero means the two species are close in energy and interconvert easily.

The arrow MnO₂ → Mn³⁺ with E° = +0.95 V represents:

$\text{MnO}_2 + 4H^+ + e^- \to \text{Mn}^{3+} + 2H_2O \quad E^\circ = +0.95 \text{ V}$

The number of electrons transferred per arrow depends on the oxidation-state difference:

• +6 → +4: 2 electrons
• +4 → +3: 1 electron
• +3 → +2: 1 electron
• +2 → 0: 2 electrons

And the H⁺ and H₂O in the balanced half-reaction depend on the acidic-vs-basic form. Latimer diagrams for the same element in acid and in base are usually different (both sets appear in comprehensive tables).

Skipping steps — the weighted-average rule

Latimer diagrams often list only “one-step” reductions between adjacent oxidation states. When you need a multi-step potential (say, MnO₄⁻ all the way down to Mn²⁺), you can’t just add E° values, because E° is not extensive — it’s an intensive quantity (V, not J). The correct additivity is on ΔG° = −nFE°, which is extensive. So:

For two half-reactions A → B (E°₁, n₁ electrons) and B → C (E°₂, n₂ electrons), combined into A → C (n₁+n₂ electrons):

$E^\circ_{A \to C} = \frac{n_1 E^\circ_1 + n_2 E^\circ_2}{n_1 + n_2}$

The combined E° is the electron-weighted average of the individual E°‘s. Same logic extends to three or more steps: multiply each E° by its electron count, sum, then divide by total electron count.

Worked example — MnO₄⁻ to Mn²⁺

Disproportionation — the crossed-diagonal test

A species X disproportionates (splits into a higher and lower oxidation state) when its position on the Latimer diagram has a higher E° to its left than to its right. In other words: the reduction from X→(lower) has a smaller E° than the reduction from (higher)→X, so the couple X/X-lower is a weaker oxidant than the couple X-higher/X. That means X is a stronger oxidant toward another X than X-higher is toward X; some X reduces some other X, giving X-higher + X-lower.

The test is a numerical inequality: for a species X sandwiched between (higher) and (lower) on the diagram:

• Look at E° for higher → X (call it E°_L)
• Look at E° for X → lower (call it E°_R)
• If E°_R > E°_L, X disproportionates.

Manganese(VI) example. MnO₄²⁻ has E°_L = +0.564 V (from MnO₄⁻) and E°_R = +2.26 V (to MnO₂). E°_R > E°_L, so MnO₄²⁻ disproportionates in acid:

$3\text{MnO}_4^{2-} + 4H^+ \to 2\text{MnO}_4^- + \text{MnO}_2 + 2H_2O$

Which is exactly what happens: green K₂MnO₄ in acid disproportionates to purple KMnO₄ and brown MnO₂ within seconds. In basic solution the same species (MnO₄²⁻) is stable — the E°_R vs E°_L inequality flips because the underlying half-reactions carry different numbers of H⁺.

Frost diagrams — the visual equivalent

A Frost diagram is a Latimer diagram plotted as (oxidation state) × E° on the y-axis vs oxidation state on the x-axis. The slope between two points is the E° between those two oxidation states. The interpretation:

• The lowest point on the curve is the most thermodynamically stable oxidation state under those conditions.
• Any species that lies above the line connecting its neighbours will disproportionate.
• The steepest downward slope from a species names its most favourable reduction.

Frost diagrams turn “which pair oxidises which” from an inequality check into a visual read-off — the graph shows all pairs at once. Housecroft 5e §8.5 has clean examples for the halogens and for nitrogen chemistry (where the Frost diagram for N in acid has NH₄⁺ at the bottom and every intermediate state up on a plateau).

Worked example — chlorine disproportionation

Reading the Latimer diagram for practical questions

The three questions a Latimer diagram answers in seconds:

1. Which species is the strongest oxidiser? The one at the left end of the diagram (highest oxidation state) with the largest downward E° to any product. MnO₄⁻ in acid: E° up to +1.51 V; a monster oxidiser.

2. Which species is the strongest reductant? The one at the right end with the most negative E° for its removal (i.e., the largest E° for the reverse direction). Mn metal: E° = −1.18 V for Mn²⁺/Mn means Mn oxidises easily.

3. Which intermediate is unstable to disproportionation? Any species where E°_R > E°_L. Mn(VI) as MnO₄²⁻ in acid; every halogen(0) in cold base; Cu(I) in aqueous solution (E°_L = +0.15 V for Cu²⁺/Cu⁺, E°_R = +0.52 V for Cu⁺/Cu → disproportionates).

Common pitfalls

Adding E° values directly across steps. Only ΔG° adds; E° is an intensive quantity. Use the electron-weighted-average formula.

Reading acidic and basic diagrams as interchangeable. Half-reactions involving oxygen change dramatically with pH: MnO₄⁻ + 8H⁺ + 5 e⁻ → Mn²⁺ + 4H₂O (acid) vs MnO₄⁻ + 4H⁺ + 3 e⁻ → MnO₂ + 2H₂O (near-neutral) vs different again in base. Look up which conditions match your problem.

Forgetting that disproportionation is thermodynamics, not kinetics. A species that “should” disproportionate can be kinetically stable — hydrogen peroxide is a classic example, thermodynamically doomed at every pH but kinetically slow to decompose. Catalysts (Fe³⁺, MnO₂) unmask the underlying instability.

Confusing oxidation state with formal charge. Latimer diagrams sort by oxidation state, not by charge. MnO₄⁻ has oxidation state +7 on Mn even though the overall charge is −1.

Practice

Where this leads

Latimer diagrams are one visual entry into electrochemistry:

• Nernst equation — E° values on the diagram are 1 M standard-state; the Nernst equation calculator corrects for actual activities.
• Pourbaix diagrams — extend Latimer diagrams to include pH as a second axis, mapping which oxidation state is stable at each (E, pH) point.
• Electrocatalysis — HER, OER, and CO₂RR all live on the corresponding element’s Latimer / Pourbaix landscape.
• Corrosion — Fe metal in aqueous solution: the metal’s negative E° means it should oxidise; whether it does depends on kinetics (passivation) and Pourbaix conditions.

Every one of them starts by locating the species on its Latimer line and comparing E° values.