Pourbaix Diagrams

A knowledge of the equilibrium potential for reactions involving a specified set of elements allows us to determine the species that are thermodynamically stable under a particular set of conditions. A common way to present such data in aqueous media is with a Pourbaix diagram, which has been particularly useful for studying corrosion. For example, the Pourbaix diagram for Zn at 25 °C is shown in Figure 2.2. This diagram presents a regional map of stable species as a function of the potential (versus SHE) and the pH. The construction of this diagram is outlined in the paragraphs that follow.

First, each diagram contains two reference lines (dashed in the figure) that represent the reactions for hydrogen and oxygen. For convenience, we reference reactions and equations to the corresponding lines on the Pourbaix diagram:

and

We can express the potential of these two reactions using the methodology described above. Reaction (a) relative to a standard hydrogen electrode is

since  is zero. If the hydrogen pressure is unchanged (at standard pressure), the cell potential varies only with the proton concentration. Assuming a reference state of ions as 1 M, this variation is most commonly expressed as a function of the pH as follows:

at 25 °C. Note that the switch from concentration to pH required us to change to a base 10 logarithm and then apply the simplified definition of pH (−log₁₀ c, where c is in mole per liter). U_a is represented as a line on the Pourbaix diagram as shown in Figure 2.2. At potentials greater than U_a, the anodic reaction is favored, and H⁺ is the stable species. Conversely, the cathodic reaction is favored below U_a, and the stable species is H₂. The line, of course, represents the equilibrium potential.

Similarly, the potential for reaction (b) is

where the anodic evolution of oxygen takes place at potentials above U_b.

Next, consider equilibrium for the dissolution of zinc:

The equilibrium potential for the dissolution of zinc relative to SHE is

Metallic Zn is stable at potentials below U_c. Since neither H⁺ nor OH⁻ is involved in the reaction, it makes sense that the potential does not depend on pH. Also, whereas the standard equilibrium potential for the dissolution of zinc is  (Appendix A), this is not the value plotted on the graph. As seen by equation (c), if the concentration of the zinc ion changes, the equilibrium potential shifts. A series of lines could be plotted for the dissolution of Zn corresponding to different concentrations of ions in solution. By convention, a concentration of 10⁻⁶ M is usually assumed. At this concentration, the potential shifts negatively to −0.94 V, which is the value plotted in Figure 2.2.

As you may begin to realize, the Pourbaix diagram and associated calculations depend on the selection of species. This choice is not always clear. Up to 16 different species have been used in just the Pourbaix diagram for zinc. We will limit ourselves to just a few of these in order to get an idea of how these diagrams are constructed and how they can be used.

Consider a different type of reaction:

How might this reaction be represented on the diagram? Since this is not an electron-transfer reaction, the reaction is not a function of potential and is therefore represented as a vertical line on the diagram. For our purposes, we use this equation to define the stability boundary between Zn²⁺ and Zn(OH)₂. Specifically, we are looking for the pH where Zn(OH)₂ is in equilibrium with 10⁻⁶ M Zn²⁺. Using the methods described in the previous section, we find

With the concentration of zinc ions specified, the pH can be determined. The calculated pH is 8.74 (see Figure 2.2). Note that the choice of zinc concentration is arbitrary and represents the concentration above which Zn²⁺ is considered to be the stable species. The specified value of 10⁻⁶ M is frequently used for the analysis of corrosion systems.

One more reaction is considered:

This equilibrium is described by

and the line is labeled e on the diagram.

Now is a good time to review the meaning of these lines. These Pourbaix diagrams indicate the regions of stability of different phases and ionic species in equilibrium with the solid phases. Referring to line c, if the potential is below −0.94 V, Zn is stable. When the potential rises above −0.94 V, dissolution of Zn occurs. At higher potentials, when the pH of the solution is increased above 8.74, zinc hydroxide precipitates. Finally, at pH values above 8.74 and potential values higher than those indicated by line e, zinc can react directly with water to form zinc hydroxide.