8.1.4.3: Pourbaix Diagrams are Redox Phase Diagrams that Summarize the most stable form of an element at a given pH and solution potential

Pourbaix diagrams depict the most stable species or phase of an element as a function of potential and pH

Pourbaix or potential-pH/E-pH diagrams were developed and popularized by Marcel Pourbaix, who used them to study corrosion. Pourbaix diagrams depict the most stable species or phase of an element in aqueous solution as a function of potential (on the y-axis) and pH (on the x-axis). Pourbaix's Atlas of Electrochemical Equilibria in Aqueous Solution contains diagrams for many elements along with extensive notes on their construction.¹ An example of a Pourbaix diagram is that for Fe shown in Figure \(\sf{\PageIndex{1}}\).

Figure \(\sf{\PageIndex{1}}\). Pourbaix diagram for Fe at an unknown Fe concentration. (CC BY-SA 2.5, Andel Früh via Wikipedia)

The species shown on Pourbaix diagrams include solution phase species (Fe²⁺, Fe³⁺, HFeO₂^-, and FeO₄^2-) and insoluble or poorly soluble solids (Fe, Fe₂O₃·nH₂O, Fe₃O₄, and Fe(OH)₃). Thus on some diagrams the phase is also indicated using (s), (l), and (aq) designators. This is the case for the Fe Pourbaix diagram in Figure \(\sf{\PageIndex{2}}\).

Figure \(\sf{\PageIndex{2}}\). Partial Pourbaix diagram for Fe, at a different Fe concentration than the diagram in Figure \(\sf{\PageIndex{1}}\). (CC BY-SA 3.0 Unported; Metallos via Wikipedia)

Pourbaix diagrams are similar to phase diagrams in that they show species as a function of potential and pH. Unlike a conventional phase diagram, the regions depict the dominant species instead of the only species present under a given set of conditions (for more detail see Note 1).¹ For solution phase species, the dominant chemical species will not only depend on potential and pH as depicted in the diagram; the formal concentration of the species is important too. For the sort of corrosion applications Pourbaix envisioned, these concentrations are typically quite low, so for this reason the regions depicted in most Pourbaix diagrams correspond to 1 mM total concentration.

The way in which Pourbaix diagrams provide insight into corrosion chemistry may be seen by looking more carefully at the Pourbaix diagram for Fe in Figure \(\sf{\PageIndex{2}}\). Notice that the diagram also shows equilibrium lines for water reduction

\[\ce{2H^{+}~~+~~ 2e^{-} \rightarrow H2} \nonumber \]

and oxidation

\[\ce{O2 + 4H^{+} + 4e^{-} \rightarrow 2H2O}. \nonumber \]

These lines are useful for several reasons.

• First, in cases where water oxidation and reduction are fast relative to the electrochemical phenomenon of interest, the water oxidation and reduction potentials limit the potential that the element can experience - i.e., if a solution is exposed to a more extreme potential in the form of an electrode or a strong chemical or photochemical oxidant or reductant, then that substance will oxidize or reduce water instead of the element depicted in the diagram.
• Second, the oxygen reduction equilibrium is important for corrosion applications taking place in an oxygen-containing environment. In these environments, the pH-dependent standard potential of oxygen reduction depicted by the upper blue line in Figure \(\sf{\PageIndex{2}}\) determines the potential of the system. As can be seen in Figure \(\sf{\PageIndex{2}}\), the potential of this equilibrium is above that of the region of stability of metallic iron. This indicates that metallic iron is not thermodynamically stable at the oxygen partial pressures of the diagram; Fe³⁺ species are instead. Moreover, the precise species that metallic iron will form when it is exposed to a higher potential varies with pH. At higher pH values, an oxide will be produced - either Fe(OH)₂(s), Fe₃O₄(s), or Fe₂O₃(s). If these solid phases coat the surface of the iron so as to insulate it from reaction with oxygen, they will effectively prevent iron's oxidation. Such layers are said to be passivating, and the resulting anodic passivation is a form of kinetic, not thermodynamic, stabilization of the metal.²

Straightforward applications of Pourbaix diagrams involve estimating how the potential of a system at equilibrium changes with conditions, as illustrated in Example \(\sf{\PageIndex{1}}\).

Example \(\sf{\PageIndex{1}}\)

Metal indicator electrodes are used to measure the potential of solutions. The potential is determined by the redox equilibria taking place therein. This potential may be measured by immersing the metal indicator electrode and a reference electrode in the solution to be tested.

Use the information in Figure \(\sf{\PageIndex{2}}\) (Do not use the information in Figure \(\sf{\PageIndex{1}}\) since it corresponds to a different Fe concentration) to:

1. Explain how you might construct a pH-sensitive electrode from a Pt wire metal indicator electrode, FeSO₄ (which is water soluble) and rust, which for the purposes of this problem you may take as equivalent to Fe₂O₃(s) and its hydrates.
2. What would be the pH range limits of the sensor?
3. What voltages would it read (vs. NHE) over this range?
4. Are there any limitations that should be observed when using this electrode to measure pH?

Solution

1. The electrode may be made by dissolving the FeSO₄ in the solution to be tested to give a solution that is ~1mM Fe²⁺. Then enough rust would be added to give a cloudy solution, indicating that solid is present and the equilibrium between Fe²⁺ and FeSO₄ established. Finally, the Pt wire and a suitable reference electrode would be inserted into the solution and the potential measured.
2. The electrode would only work between pH values of ~0.5 and 7. Below pH 0.5 the Fe₂O₃ would dissolve, while above pH 7 the Fe²⁺ will precipitate.
3. The voltages should range from ~0.77 V (vs. SHE) at pH ~0.5 to ~-0.44V (vs. SHE) at pH~7.
4. There are several limitations and much would need to be done to validate this as a suitable method for the determination of pH. First, the potentials listed above assume that the iron concentration in the test solution is the same as that used to construct the diagram in Figure \(\sf{\PageIndex{1}}\). Thus they are at best rough estimates, and the electrode would need to be calibrated using solutions of known pH before use. Second, if the electrode is used in air, over time the Fe²⁺ will oxidize to Fe³⁺ species, shifting the response of the electrode. Because of this the electrode should either be used in an anoxic environment or prepared just before use.

What do the lines in a Pourbaix diagram mean?

The phase lines in Pourbaix diagrams correspond to switchpoints between the dominant species in solution for solution phase species or the points at which precipitation or phase change occurs for equilibria involving solid and/or pure liquid phases. To see how this works it helps to consider the three common cases:

• Equilibria that involve electron transfer only give rise to horizontal lines because the potential does not depend on pH. An example is the line between the Fe³⁺ and Fe²⁺ regions, marked 2 in Figure \(\sf{\PageIndex{2}}\). In this case the reaction potential when \(\sf{\dfrac{Fe^{2+}}{Fe^{3+}}}\)=1 is \(\sf{E^{\circ}_{Fe^{3/2+}}}\):

\[\sf{Fe^{3+}~+~e^-~\rightarrow~Fe^{2+}~~~~~E~=~E^{\circ}_{Fe^{3/2+}}~-~\dfrac{0.05916~V}{1}log{\dfrac{[Fe^{2+}]}{[Fe^{3+}]}}~=~E^{\circ}_{Fe^{3/2+}}~-~(0.05916~V)log{1}~=~E^{\circ}_{Fe^{3/2+}}} \nonumber \]

• Acid-base equilibria that do not involve changes in the redox state of the elements involved give rise to vertical lines, the position of which depend on the stated concentration of the diagram. An example is the line between the Fe³⁺(aq) and Fe₂O₃(s) regions, marked 3 in Figure \(\sf{\PageIndex{2}}\). This corresponds to the equilibrium:

\[\sf{2~Fe^{3+}~~+~~3~H_2O~\rightarrow~Fe_2O_3(s)~~+~~6~H^+} \nonumber \]

The equilibrium line in this case is determined by the reaction's equilibrium constant

\[\sf{K = \dfrac{[H^+]^6}{[Fe^{3+}]^2}} \nonumber \]

From this it can be seen that the pH ([H⁺]) is a function only of the value of [Fe³⁺] used to construct the diagram (since \(\sf{[H^+]~=~(K[Fe^{3+}]^2)^{1/6}}~=~constant\)), so the line is vertical.

• Equilibria that involve a combination of electron transfer and acid-base chemistry give rise to slanted lines. An example is the equilibrium between Fe²⁺ and Fe₂O₃(s), marked 4 in Figure \(\sf{\PageIndex{2}}\). This corresponds to the equilibrium:

\[\sf{Fe_2O_3(s)~~+~~6~H^+~~+~~2~e^-~~\rightarrow~~2~Fe^{2+}~+~~3~H_2O} \nonumber \]

for which

\[\sf{E~=~E^{\circ}_{Fe_2O_3/Fe^{2+}}~-~\dfrac{0.05916~V}{2}log{\dfrac{[Fe^{2+}]^{2}}{[H^+]^{6}}}} \nonumber \]

from which it can be seen that the potential will be pH dependent.

References

1. Pourbaix, M., Atlas of electrochemical equilibria in aqueous solutions. 2nd ed. Houston: National Association of Corrosion Engineers, 1974.
2. The other common corrosion resistance strategy, cathodic protection, couples the metal to be protected to an even more reactive metal that is oxidized in place of the metal to be protected.

Contributors and Attributions

• Stephen Contakes, Westmont College