Pourbaix diagram
Boundaries (50 %/50 %) between the predominant chemical species (aqueous ions in solution, or solid phases) are represented by lines.
The vertical axis is labeled EH for the voltage potential with respect to the standard hydrogen electrode (SHE) as calculated by the Nernst equation.
For a reversible redox reaction described by the following chemical equilibrium: With the corresponding equilibrium constant K: The Nernst equation is: sometimes formulated as: or, more simply directly expressed numerically as: where: The horizontal axis is labeled pH for the −log function of the H+ ion activity.
[3] In order to draw the position of the lines with the Nernst equation, the activity of the chemical species at equilibrium must be defined.
If the diagram involves the equilibrium between a dissolved species and a gas, the pressure is usually set to P0 = 1 atm = 101325 Pa, the minimum pressure required for gas evolution from an aqueous solution at standard conditions.
[3] In addition, changes in temperature and concentration of solvated ions in solution will shift the equilibrium lines in accordance with the Nernst equation.
The diagrams also do not take kinetic effects into account, meaning that species shown as unstable might not react to any significant degree in practice.
A simplified Pourbaix diagram indicates regions of "immunity", "corrosion" and "passivity", instead of the stable species.
Passivation occurs when the metal forms a stable coating of an oxide or other salt on its surface, the best example being the relative stability of aluminium because of the alumina layer formed on its surface when exposed to air.
Even though Pourbaix diagrams are useful for a metal corrosion potential estimation they have, however, some important limitations:[4]: 111 The
and pH of a solution are related by the Nernst equation as commonly represented by a Pourbaix diagram (
For a half cell equation, conventionally written as a reduction reaction (i.e., electrons accepted by an oxidant on the left side): The equilibrium constant K of this reduction reaction is: where curly braces { } indicate activities (a), rectangle braces [ ] denote molar or molal concentrations (C),
Activities correspond to thermodynamic concentrations and take into account the electrostatic interactions between ions present in solution.
is the standard Gibbs free energy change, z is the number of electrons involved, and F is the Faraday's constant.
= 0 by convention under standard conditions (T = 298.15 K = 25 °C = 77 F, Pgas = 1 atm (1.013 bar), concentrations = 1 M and thus pH = 0).
) tend to one, the term regrouping all the activity coefficients is equal to one, and the Nernst equation can be written simply with the concentrations (
) denoted here with square braces [ ]: There are three types of line boundaries in a Pourbaix diagram: Vertical, horizontal, and sloped.
When H+ and OH− ions are not involved in the reaction, the boundary line is horizontal and independent of pH.
: Using the definition of the electrode potential ∆G = -zFE, where F is the Faraday constant, this may be rewritten as a Nernst equation: or, using base-10 logarithms: For the equilibrium Fe2+/Fe3+, taken as example here, considering the boundary line between Fe2+ and Fe3+, the half-reaction equation is: Since H+ ions are not involved in this redox reaction, it is independent of pH.
In this case, both electrons and H+ ions are involved and the electrode potential is a function of pH.
The reaction equation may be written: Using the expressions for the free energy in terms of potentials, the energy balance is given by a Nernst equation: For the iron and water example, considering the boundary line between the ferrous ion Fe2+ and hematite Fe2O3, the reaction equation is: The equation of the boundary line, expressed in base-10 logarithms is: As, the activities, or the concentrations, of the solid phases and water are always taken equal to unity by convention in the definition of the equilibrium constant K: [Fe2O3] = [H2O] = 1.
The Nernst equation thus limited to the dissolved species Fe2+ and H+ is written as: For, [Fe2+] = 10−6 M, this yields: Note the negative slope (-0.1775) of this line in a Eh–pH diagram.
It is also depicted here beside by the two dashed red lines in the simplified Pourbaix diagram restricted to the water stability region only.
Under highly reducing conditions (low EH), water is reduced to hydrogen according to:[3] and, Using the Nernst equation, setting E0 = 0 V as defined by convention for the standard hydrogen electrode (SHE, serving as reference in the reduction potentials series) and the hydrogen gas fugacity (corresponding to chemical activity for a gas) at 1, the equation for the lower stability line of water in the Pourbaix diagram at standard temperature and pressure is: Below this line, water is reduced to hydrogen, and it will usually not be possible to pass beyond this line as long as there is still water present in the system to be reduced.
The two upper and lower stability lines having the same negative slope (−59 mV/pH unit), they are parallel in a Pourbaix diagram and the reduction potential decreases with pH.
Pourbaix diagrams have many applications in different fields dealing with e.g., corrosion problems, geochemistry, and environmental sciences.
Using the Pourbaix diagram correctly will help shedding light not only on the nature of the species present in aqueous solution, or in the solid phases, but may also help to understand the reaction mechanism.
[8] Pourbaix diagrams are widely used to describe the behaviour of chemical species in the hydrosphere.
Moreover, pe values in environmental chemistry ranges from −12 to +25, since at low or high potentials water will be respectively reduced or oxidized.
In environmental applications, the concentration of dissolved species is usually set to a value between 10−2 M and 10−5 M for the determination of the equilibrium lines.
