Pourbaix Diagram

A weather map for metals in water

Drop a piece of iron into a beaker and the fate of that iron depends on exactly two numbers: how oxidising the solution is (its electrode potential, E) and how acidic it is (its pH). A Pourbaix diagram puts those two numbers on the two axes of a single chart — E running up the vertical axis, pH running across the horizontal — and then colours in which form of the metal wins at every point.

The result reads like a weather map. Some regions are safe: the metal stays metallic and refuses to react. Some are stormy: the metal dissolves into solution as ions. And some are sheltered: the metal reacts, but the product is a clinging solid oxide that can seal the surface off. These three territories have names — immunity, corrosion, and passivation — and learning to read which one you are standing in is the whole point of the diagram.

  E /V
   ↑
1.2│············ (b) O₂/H₂O ············           ← water oxidises above
   │      Fe³⁺          ┌──────────────┐
0.8│   (corrosion)      │   Fe₂O₃      │
   │                    │ (passivation)│
0.4│      Fe²⁺          │              │
   │   (corrosion)      │   Fe₃O₄      │
0.0│··············(a) H⁺/H₂··············           ← water reduces below
   │                    └───┬──────────┘
-0.4│                        HFeO₂⁻
   │  ┌──────────────────────────────────┐
-0.8│  │            Fe (immunity)         │
   │  └──────────────────────────────────┘
   └────┬────┬────┬────┬────┬────┬────┬──→ pH
        0    2    4    6    8   10   12  14

The schematic above is the iron diagram in cartoon form. The two dashed lines (a) and (b) are the stability window of water itself; everything between them is the chemistry that can actually happen in aqueous solution. Notice the geography: acid plus oxidiser (top left) dissolves iron, low potential (bottom) keeps it immune, and the neutral-to-alkaline middle-right grows protective oxide.

Every boundary is a Nernst equation

A Pourbaix diagram is not drawn by hand from intuition — every single line on it is the graph of one equilibrium, plotted as E against pH. The engine behind each line is the Nernst equation, which gives the potential of a half-reaction in terms of the concentrations of the species involved:

E = E° − (RT / nF) · ln(Q)

at 25 °C, converting ln → log₁₀:

E = E° − (0.0592 / n) · log₁₀(Q)

Here E° is the standard potential, n is the number of electrons transferred, F is the Faraday constant (96 485 C/mol), and Q is the reaction quotient. The factor 0.0592 V = (RT/F)·ln(10) at 298 K is the number that gives every Pourbaix line its characteristic 59 mV scale. Three kinds of half-reaction give three kinds of line:

1. Pure redox, no protons → horizontal line. The metal/ion boundary involves electrons but no H⁺, so pH drops out entirely:

Fe²⁺ + 2e⁻  ⇌  Fe(s)
E = −0.44 − (0.0592/2)·log₁₀(1/[Fe²⁺])
   → flat horizontal line, independent of pH

2. Pure acid–base, no electrons → vertical line. A precipitation that consumes protons but moves no charge depends only on pH:

Fe³⁺ + 3H₂O  ⇌  Fe(OH)₃(s) + 3H⁺
no electrons → potential irrelevant
→ vertical line, fixed at the pH set by Ksp

3. Coupled proton-electron transfer → sloped line. When the boundary reaction moves both m protons and n electrons, the Nernst equation produces a line whose slope is exactly −0.0592·(m/n) volts per pH unit:

e.g.  Fe₂O₃ + 6H⁺ + 2e⁻ ⇌ 2Fe²⁺ + 3H₂O
m = 6 protons, n = 2 electrons
slope = −0.0592 × (6/2) = −0.178 V per pH unit

The most common case m = n gives the canonical −59 mV/pH slope.

So the geometry of the diagram is not arbitrary: a horizontal line is a tip-off that the reaction is pure electron transfer, a vertical line means pure proton transfer, and a downward slope means the two are coupled. You can reconstruct the chemistry just by reading the angles.

The two dashed lines: where water itself breaks down

Before a metal's lines are even drawn, every Pourbaix diagram carries two dashed reference lines. They mark the stability window of liquid water, and they are the most important pair of lines on the chart because they decide whether a reaction is even possible in water.

Line (a) — hydrogen evolution. Below this line, water (or H⁺) is reduced to hydrogen gas:

2H⁺ + 2e⁻  ⇌  H₂(g)        E°= 0.000 V
E = 0 − 0.0592·pH    (at 1 atm H₂)
   → slope −59 mV/pH, passing through (pH 0, E 0)

Line (b) — oxygen evolution. Above this line, water is oxidised to oxygen:

O₂ + 4H⁺ + 4e⁻  ⇌  2H₂O    E°= +1.23 V
E = 1.23 − 0.0592·pH
   → parallel to line (a), offset by 1.23 V

The two lines are parallel (both −59 mV/pH) and 1.23 V apart — that 1.23 V gap is precisely the thermodynamic decomposition voltage of water, the reason water electrolysis needs at least 1.23 V. A metal whose immunity region sits entirely above line (a), like gold or platinum, cannot reduce water and is called noble. A metal whose immunity region lies below line (a) — iron, zinc, aluminium — is thermodynamically capable of evolving hydrogen as it corrodes.

Reading the iron diagram, region by region

Iron is the canonical example, both because it is the most economically destructive corroding metal and because its diagram shows all three regions cleanly. Walk across it:

• Bottom band — immunity. At sufficiently negative potential (below about −0.62 V vs SHE at pH 7), metallic Fe(0) is the stable species. The metal simply cannot oxidise. This is the regime you create deliberately with cathodic protection: wire the steel to a more active metal or a power supply and push its potential down into the immunity band.
• Upper-left field — corrosion. In acid (low pH) at moderate-to-high potential, the stable species are soluble Fe²⁺ and, higher up, Fe³⁺. Iron dissolves: Fe → Fe²⁺ + 2e⁻. This is why acid rain (pH 4–5) and de-icing salt brine eat through car bodies.
• Right-of-centre field — passivation. From roughly pH 8 upward, the stable solids are the oxides Fe₂O₃ (hematite) and Fe₃O₄ (magnetite). Iron still reacts, but the product is an adherent oxide film. In the high-pH, oxidising corner the surface is genuinely protected — the principle behind passivating steel in alkaline concrete pore water (pH ≈ 13).
• Far-right sliver — re-corrosion. Push pH above ~14 and a soluble hydroxo-anion, HFeO₂⁻ (dihypoferrite, iron still +2), reappears: the oxide dissolves again. Passivation is a window, not a one-way door — over-alkalinity can be as destructive as acid.

The standard convention is to draw the boundaries for a dissolved-ion activity of 10⁻⁶ M (the threshold below which corrosion is considered negligible). Raising the assumed concentration to 1 M shifts the corrosion fields outward; this is why a Pourbaix diagram is always labelled with the ion activity it assumes.

Pourbaix versus Latimer versus Frost

Pourbaix diagrams are one of three classic ways to compress redox thermodynamics into a picture. They differ in what they hold fixed.

	Pourbaix (E–pH)	Latimer	Frost
Axes / form	E vs pH plane	Linear chain of E° values	n·E° vs oxidation state
pH treatment	Swept continuously	Fixed (pH 0 or 14)	Fixed (pH 0 or 14)
Shows stable species?	Yes, at every E and pH	Implied by signs	Yes — lowest point
Shows passivation?	Yes, directly	No	No
Best for	Corrosion, geochemistry	Quick potential lookup	Disproportionation
Dimensionality	2-D map	1-D line	2-D plot, 1 pH

A Latimer diagram is the fastest way to look up the potential between two adjacent oxidation states at one pH; a Frost diagram makes disproportionation obvious (a species above the line connecting its neighbours is unstable to disproportionation). But only the Pourbaix diagram sweeps pH continuously and only it maps the corrosion/immunity/passivation distinction — which is why it is the corrosion engineer's tool of choice.

Real numbers and real reactions

The lines on a Pourbaix diagram are anchored to measured standard potentials. A few of the key ones for iron and water, at 25 °C versus the standard hydrogen electrode (SHE):

• Fe²⁺ + 2e⁻ ⇌ Fe, E° = −0.44 V — the floor of the corrosion field.
• Fe³⁺ + e⁻ ⇌ Fe²⁺, E° = +0.77 V — the horizontal divide between the two soluble ions.
• O₂ + 4H⁺ + 4e⁻ ⇌ 2H₂O, E° = +1.23 V — the upper water line (b).
• 2H⁺ + 2e⁻ ⇌ H₂, E° = 0.000 V — the lower water line (a), the definition of the SHE.

Some quantitative consequences read straight off the geography:

• Cathodic protection. The Fe/Fe²⁺ immunity boundary sits near −0.62 V vs SHE (drawn for 10⁻⁶ M Fe²⁺), so forcing steel below it pushes it into immunity. In the field this is enforced with the empirical "−850 mV criterion" — holding the structure at or below −0.85 V versus a Cu/CuSO₄ (CSE) reference, which is ≈ −0.53 V vs SHE once the +0.32 V CSE-to-SHE offset is applied. That conservative rule governs how every buried pipeline and ship hull is protected.
• Galvanising with zinc. Zinc's immunity region sits below iron's corrosion field across most of the pH range, so a zinc coating preferentially corrodes and holds the steel at a protective potential. The zinc Pourbaix diagram, overlaid, explains why the sacrifice works.
• Aluminium's passive window. Al₂O₃ is stable from about pH 4 to pH 9; outside that window aluminium dissolves as Al³⁺ (acid) or AlO₂⁻ (alkaline). This is exactly why aluminium cookware survives lemon juice briefly but is destroyed by oven cleaner (NaOH).
• Geochemistry. The same diagram, with uranium or iron species, predicts where ore bodies precipitate. Iron's Fe²⁺/Fe₂O₃ boundary explains the banded iron formations laid down 2.5 billion years ago as the early ocean's potential crossed the line.

Building one from scratch

To draw a Pourbaix diagram for a metal you carry out a fixed recipe:

1. List every relevant species: the metal, each soluble ion (Fe²⁺, Fe³⁺, HFeO₂⁻…), and each solid (Fe(OH)₂, Fe₂O₃, Fe₃O₄…).
2. Write the half-reaction connecting each pair of species and look up its ΔG° or E°.
3. For each reaction, convert to a line using the Nernst equation: horizontal if no H⁺, vertical if no e⁻, sloped at −0.0592·(m/n) otherwise.
4. Fix a reference activity for dissolved ions (conventionally 10⁻⁶ M) so the soluble/solid boundaries are pinned.
5. Keep only the lowest-free-energy species at each point — the surviving boundaries enclose the stability fields.

Modern practice automates step 5 with software (HSC Chemistry, the Materials Project's online Pourbaix module) that minimises free energy across a fine E–pH grid, but the logic is identical to what Pourbaix did by hand in 1945.

Common misconceptions and pitfalls

• Treating it as kinetics. The single biggest error. A Pourbaix diagram is purely thermodynamic; "corrosion" means dissolution is downhill, not that it is fast. Aluminium sits in its corrosion field in mild acid (stable species Al³⁺) yet barely dissolves because its Al₂O₃ film is kinetically inert. The diagram tells you the destination, never the speed.
• Assuming passivation always protects. The diagram only says an oxide is the stable solid — it cannot tell you whether that oxide is dense and adherent (protective, like Cr₂O₃ on stainless steel) or porous and flaky (non-protective, like ordinary iron rust). Two metals can share an identical-looking passivation field and behave completely differently.
• Forgetting the assumed ion activity. Every soluble/solid boundary moves with the assumed dissolved-ion concentration. A diagram drawn for 1 M looks meaningfully different from one drawn for 10⁻⁶ M; comparing two diagrams with different activities is meaningless.
• Ignoring complexing agents. Standard diagrams assume only H₂O, H⁺, OH⁻, and the metal. Chloride, ammonia, EDTA or cyanide create entirely new soluble complexes that punch corrosion fields into regions the bare diagram calls safe — which is why chloride pitting attacks "passive" stainless steel.
• Reading at the wrong temperature. The 0.0592 V factor and every E° are tabulated at 25 °C. In a boiler at 300 °C the lines shift substantially; high-temperature Pourbaix diagrams are a separate, recomputed family.
• Confusing the reference electrode. Diagrams are drawn versus SHE, but field measurements use Cu/CuSO₄ or saturated calomel. Forgetting the ~0.32 V (Cu/CuSO₄) or ~0.24 V (SCE) offset between scales puts you in the wrong region entirely.