Latimer diagram

An element like manganese can exist in many oxidation states, and the chemistry between them is a thicket of potentials. A Latimer diagram is the simplest way to pin it all on one line. You write the species in a horizontal row, from the highest oxidation state on the left to the lowest on the right, and over each arrow joining two neighbours you write the standard reduction potential connecting them. It is a compact ledger of all the adjacent-state potentials for one element at one pH.

Reading manganese in acid, for instance: MnO4- (+0.56) MnO4^2- (+2.27) MnO2 (+0.95) Mn3+ (+1.51) Mn2+ (-1.18) Mn. Each number is the potential for reducing the species on the left of that arrow to the one on the right. Two practical tricks fall out. To get the potential for a non-adjacent jump (say MnO4- straight to Mn2+), you cannot just average the numbers — you must weight each by the electrons it transfers, summing n times E° and dividing by the total n. And a species is unstable to disproportionation precisely when the potential on its right is larger than the potential on its left, because then it would rather reduce part of itself and oxidize the rest.

Latimer diagrams pack an element's entire redox behaviour into one readable line, which is why they are the standard descriptive tool for the transition metals and the p-block. Their limits are honest ones: the potentials are pH-specific (acid and base diagrams differ), and a flat row of numbers makes trends harder to see at a glance than a graph does — which is exactly why the same data is often replotted as a Frost diagram.