Latimer and Frost Diagrams: Reading Redox Chemistry From a Picture
Two ways of displaying the same data, each answering a different question — one about individual couples, one about which species survive.
Latimer diagrams
A Latimer diagram writes the oxidation states of an element in a row, from highest to lowest, with the standard reduction potential written above each arrow connecting adjacent states.
Reading it is straightforward for adjacent couples — the number above the arrow is the potential. The complication arises when you need a potential between non-adjacent states.
This is a weighted average by number of electrons, which is what the free-energy argument reduces to. Deriving it rather than memorising it makes the reasoning clear and prevents misuse.
Predicting disproportionation from a Latimer diagram
A species disproportionates when the potential for its reduction is greater than the potential for its oxidation — that is, when the potential on its right is larger than the potential on its left.
Physically, this means the species is a better oxidising agent than it is a reducing agent, so it reacts with itself: some is reduced, some oxidised. Scanning a Latimer diagram for a state where the right-hand potential exceeds the left-hand one is a routine exam task.
Frost diagrams
A Frost diagram plots nE° — which is proportional to the free energy relative to the element — against oxidation state. This turns thermodynamic questions into geometry.
| Feature of the plot | What it means |
|---|---|
| Lowest point | The most thermodynamically stable oxidation state |
| A point above the line joining its neighbours | That species disproportionates |
| A point below the line joining its neighbours | Its neighbours comproportionate to give it |
| Steep downward slope to the right | Strong oxidising agent |
| Steep upward slope to the right | Strong reducing agent |
The convexity test is the most useful feature. A species sitting above the straight line connecting the states either side is unstable with respect to those two, so it converts into them. Reading that off a diagram takes seconds, where the same conclusion from a Latimer diagram requires comparing numbers.
Why the slope gives the potential
Since the vertical axis is nE° and the horizontal is oxidation state, the slope between two points is the potential for the couple joining them. So any potential can be read as a gradient, and the steepest downward slopes identify the strongest oxidising agents immediately.
The effect of pH
Many of these potentials involve hydrogen ions, so they shift with pH. Diagrams are therefore quoted for specified conditions, conventionally acidic and basic solution separately.
Species that are stable in one medium may disproportionate in the other, and questions frequently exploit this by giving both diagrams and asking which conditions stabilise a particular state. Always check which medium a diagram refers to before drawing conclusions.
Frequently asked questions
Why can potentials not simply be added?
Because potential is free energy per electron, not free energy. Adding intensive quantities is meaningless; the extensive free energies must be added and then divided by the total electron count.
What is comproportionation?
The reverse of disproportionation — two species in different oxidation states react to give one intermediate state. It occurs when that intermediate lies below the line joining the two on a Frost diagram.
Does a Frost diagram tell me about rate?
No. It is purely thermodynamic. A species predicted to disproportionate may do so extremely slowly, and such kinetically persistent species are common.
Which diagram should I use?
Latimer for looking up or computing a specific potential; Frost for judging at a glance which species are stable and which disproportionate. They contain the same information presented for different purposes.
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