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Lesson 8 · 35 min

Maps of oxidation states: Latimer, Frost and Pourbaix diagrams

Why is there no Cu⁺ in water? Why does chlorine turn into bleach in base? Why does iron rust while a copper roof lasts centuries? Redraw one table of potentials three ways and the answers appear.

In this lesson

  • Read a Latimer diagram and combine non-adjacent steps by the electron-weighted average
  • Draw and read a Frost diagram: slopes are E°, the lowest point is most stable, a bump disproportionates
  • Compare the stability of oxidation states in acid and base (e.g. chlorine disproportionating in base)
  • Read horizontal, vertical and sloping lines on a Pourbaix diagram and judge immunity, corrosion and passivation

Copper(II) sulfate solutions are everywhere, yet there is no such thing as a copper(I) sulfate solution; chlorine bubbled into water gives chlorine water, into base it gives bleach; iron bridges need paint while copper roofs last for centuries. The answers all hide in one table of standard potentials — redraw it and they become obvious.

Predict first

E∘(CuX+/Cu)=+0.521E^\circ(\ce{Cu+/Cu}) = +0.521 V and E∘(CuX2+/Cu)=+0.3419E^\circ(\ce{Cu^2+/Cu}) = +0.3419 V. What happens to CuX+\ce{Cu+} put into water (acidic, no ligands)?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

Latimer diagrams: a staircase of potentials

Line up the forms of one element from high to low oxidation state and write the standard potential between each neighbouring pair: that is a Latimer diagram. Chlorine in acid, for example:

ClOX4X−→1.19ClOX3X−→1.21HClOX2→1.65HClO→1.61ClX2→1.36ClX−\ce{ClO4-} \xrightarrow{1.19} \ce{ClO3-} \xrightarrow{1.21} \ce{HClO2} \xrightarrow{1.65} \ce{HClO} \xrightarrow{1.61} \ce{Cl2} \xrightarrow{1.36} \ce{Cl-}

Potentials between non-adjacent forms cannot simply be added, because a potential is energy per electron; what adds is the free energy −nFE-nFE. So the steps are averaged, weighted by their electrons.

E1→3∘=n1E1∘+n2E2∘n1+n2E^\circ_{1\to 3} = \frac{n_1 E^\circ_1 + n_2 E^\circ_2}{n_1 + n_2}
Combined potential: multiply each step’s electrons by its potential, add, and divide by the total electrons.
n1, n2n_1,\ n_2
electrons in each step
E1∘, E2∘E^\circ_1,\ E^\circ_2
standard potentials of the steps

Frost diagrams: an energy landscape

Plot NE∘NE^\circ for each form relative to the element — the oxidation state times its potential against the element, i.e. −ΔG∘/F-\Delta G^\circ/F per mole of atoms — against the oxidation state NN: that is a Frost diagram. It turns the Latimer staircase into a landscape:

  • the slope of the line between two points is the E∘E^\circ of that couple; the steeper, the stronger the higher state is as an oxidant;
  • the lowest point is the thermodynamically most stable state in that medium;
  • a point above the line joining its neighbours disproportionates into them; a point below the line joining two others is where they comproportionate.
Oxidation-state maps computed from standard potentials

Latimer and Frost diagrams

Latimer diagram (E° / V between neighbouring states)

MnOX4X−\ce{MnO4-} +0.56→ MnOX4X2−\ce{MnO4^2-} +2.26→ MnOX2\ce{MnO2} +0.91→ MnX3+\ce{Mn^3+} +1.54→ MnX2+\ce{Mn^2+} −1.19→ Mn\ce{Mn}
MnMn²⁺Mn³⁺MnO₂MnO₄²⁻MnO₄⁻01234567Oxidation state N−4−20246NE° / V (relative to the element)
Pick a species

MnO₄²⁻ · manganate · N = +6 · NE° = 4.61 V

MnO₄²⁻ lies 1.14 V above the hull: it ultimately disproportionates into MnO₂ and MnO₄⁻ (ΔG° ≈ −110 kJ per mole of element atoms).

It lies 1.14 V above the line joining its neighbours MnO₂ and MnO₄⁻: E° for disproportionating into them = 1.71 V.

The lowest point, Mn²⁺, is the most stable state in this medium.

Each ordinate NE° = −ΔG°f/F per atom is computed along a chain of CRC standard potentials; basic forms are converted to pH 14 with pKa values (Harris), Kw and hydroxide solubility products (CRC). The slope between two points is that couple’s E°; species above the lower hull are thermodynamically unstable to disproportionation. This is about tendency, not rate: many “unstable” species (MnO₄⁻, H₂O₂) keep for a long time.
Manganese in acid: MnO₄²⁻ and Mn³⁺ both bulge out and disproportionate; Mn²⁺ is the lowest point. Switch to base: Mn(III), as Mn₂O₃, drops back onto the hull. Then look at chlorine: stable Cl₂ in acid, but in base it sits above the Cl⁻–ClO⁻ line — that is where bleach comes from.

Worked example

How completely does Cu⁺ disproportionate?

From E∘(CuX2+/Cu)=+0.3419E^\circ(\ce{Cu^2+/Cu}) = +0.3419 V and E∘(CuX+/Cu)=+0.521E^\circ(\ce{Cu+/Cu}) = +0.521 V, find the equilibrium constant of 2 CuX+⇌Cu+CuX2+\ce{2Cu+} \mathrel{\ce{<=>}} \ce{Cu} + \ce{Cu^2+} at 25 °C.

Pourbaix diagrams: a map of potential and pH

The Frost diagram fixes the pH; a Pourbaix diagram frees it: pH across, potential EE up, and each region labelled with the form of lowest Gibbs energy — the predominant species. Boundaries come in only three kinds:

  • horizontal: pure electron transfer with no HX+\ce{H+}, such as FeX3+/FeX2+\ce{Fe^3+/Fe^2+} at 0.771 V;
  • vertical: pure acid–base or precipitation with no electrons, such as FeX3+\ce{Fe^3+} precipitating as Fe(OH)X3\ce{Fe(OH)3} near pH 3.1 (dissolved species at 10−610^{-6} M);
  • sloping: both electrons and HX+\ce{H+}, such as Fe(OH)X3+3 HX++eX−→FeX2++3 HX2O\ce{Fe(OH)3} + \ce{3H+} + \ce{e-} \mathrel{\ce{->}} \ce{Fe^2+} + \ce{3H2O}, with slope −0.177 V per pH unit.

Two dashed lines bound water itself: above the upper one water is oxidised to OX2\ce{O2}, below the lower one it is reduced to HX2\ce{H2}.

Predominance regions computed from E° and Ksp

Pourbaix (E–pH) diagram

FeFe²⁺Fe³⁺Fe(OH)₂Fe(OH)₃FeO₄²⁻ 02468101214pH−1−0.500.511.52E / V (vs SHE)
  • metal
  • dissolved ion
  • solid
pH · E
7.0 · 0.20 V
Predominant species
Fe(OH)₃ (iron(III) hydroxide)
Water
stable

Passivation: a solid may form a protective layer

Each region is a convex polygon where that species has the lowest Gibbs energy (from CRC standard potentials, pKa values, Kw and CRC solubility products at 25 °C). Dissolved species share one activity (10⁻⁶ by default, the corrosion convention); solids have unit activity. Dashed lines bound water’s stability (1 bar of H₂ and O₂). Only the listed species compete: real iron diagrams also contain Fe₃O₄, Fe₂O₃ and HFeO₂⁻, manganese has Mn₃O₄; whether a passive film actually protects depends on how dense it is — a question of kinetics.
Drag the probe: the region of iron metal lies entirely below the H₂ line, so iron dissolves in acid with hydrogen evolution (corrosion); in neutral aerated water the probe lands in Fe(OH)₃ (rust). Switch to copper: its metal region reaches above the H₂ line, so dilute hydrochloric acid cannot dissolve copper. Change the activity and watch the vertical lines move.

Concept check

Which manganese species disproportionates spontaneously in acidic solution?

Try the calculation

From the acidic chlorine Latimer diagram (ClO₃⁻ →1.214→ HClO₂ →1.645→ HClO →1.611→ Cl₂ →1.358→ Cl⁻, the first two steps 2 electrons each, the last two 1 each), find E∘(ClOX3X−/ClX−)E^\circ(\ce{ClO3-/Cl-}).

V

Key takeaways

  • A Latimer diagram lists E° between neighbouring states; non-adjacent combinations are electron-weighted averages.
  • A Frost diagram plots NE°: slopes are couple potentials, the lowest point is most stable, and a point above its neighbours’ line disproportionates.
  • The medium reshapes the landscape: Cl₂ is stable in acid but disproportionates in base; Cu⁺ disproportionates in water (K ≈ 10⁶).
  • Pourbaix boundaries are horizontal (electrons only), vertical (acid–base or precipitation only) or sloping (both); whether a metal sits in immunity, corrosion or passivation decides its fate.
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Data and references

  1. M. Pourbaix, Atlas of Electrochemical Equilibria in Aqueous Solutions, 2nd English ed., NACE (1974).
  2. D. F. Shriver, P. W. Atkins et al., Inorganic Chemistry, 5th ed., Oxford University Press (2010), ch. 5 (redox reactions: Latimer, Frost and Pourbaix diagrams).
  3. A. J. Bard, R. Parsons, J. Jordan (eds.), Standard Potentials in Aqueous Solution, Marcel Dekker (1985).
  4. P. Vanýsek, “Electrochemical Series”, CRC Handbook of Chemistry and Physics, 91st ed. (2010); D. C. Harris, Quantitative Chemical Analysis, 8th ed., Appendix G (pKa values).