Pourbaix diagram


In electrochemistry, and more generally in solution chemistry, a Pourbaix diagram, also known as a potential/pH diagram, EH–pH diagram or a pE/pH diagram, is a plot of possible thermodynamically stable phases of an aqueous electrochemical system. Boundaries between the predominant chemical species are represented by lines. As such, a Pourbaix diagram can be read much like a standard phase diagram with a different set of axes. Similarly to phase diagrams, they do not allow for reaction rate or kinetic effects. Beside potential and pH, the equilibrium concentrations are also dependent upon, e.g., temperature, pressure, and concentration. Pourbaix diagrams are commonly given at room temperature, atmospheric pressure, and molar concentrations of 10−6 and changing any of these parameters will yield a different diagram.
The diagrams are named after Marcel Pourbaix, the Belgian engineer who invented them.

Naming

Pourbaix diagrams are also known as EH-pH diagrams due to the labeling of the two axes.

Diagram

The vertical axis is labeled EH for the voltage potential with respect to the standard hydrogen electrode as calculated by the Nernst equation. The "H" stands for hydrogen, although other standards may be used, and they are for room temperature only.
For a reversible redox reaction described by the following chemical equilibrium:
With the corresponding equilibrium constant :
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.
The lines in the Pourbaix diagram show the equilibrium conditions, that is, where the activities are equal, for the species on each side of that line. On either side of the line, one form of the species will instead be said to be predominant.
In order to draw the position of the lines with the Nernst equation, the activity of the chemical species at equilibrium must be defined. Usually, the activity of a species is approximated as equal to the concentration or partial pressure. The same values should be used for all species present in the system.
For soluble species, the lines are often drawn for concentrations of 1 M or 10−6 M. Sometimes additional lines are drawn for other concentrations.
If the diagram involves the equilibrium between a dissolved species and a gas, the pressure is usually set to P0 = 1 atm =, the minimum pressure required for gas evolution from an aqueous solution at standard conditions.
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. They thus give a guide to the stability of a particular metal in a specific environment. Immunity means that the metal is not attacked, while corrosion shows that general attack will occur. 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.

Applicable chemical systems

While such diagrams can be drawn for any chemical system, it is important to note that the addition of a metal binding agent will often modify the diagram. For instance, carbonate has a great effect upon the diagram for uranium.. The presence of trace amounts of certain species such as chloride ions can also greatly affect the stability of certain species by destroying passivating layers.

Limitations

Even though Pourbaix diagrams are useful for a metal corrosion potential estimation they have, however, some important limitations:
  1. Equilibrium is always assumed, though in practice it may differ.
  2. The diagram does not provide information on actual corrosion rates.
  3. Does not apply to alloys.
  4. Does not indicate whether passivation is protective or not. Diffusion of oxygen ions through thin oxide layers are possible.
  5. Excludes corrosion by chloride ions.
  6. Usually applicable only to temperature of, which is assumed by default. The Pourbaix diagrams for higher temperatures exist.

    Expression of the Nernst equation as a function of pH

The and pH of a solution are related by the Nernst equation as commonly represented by a Pourbaix diagram. explicitly denotes expressed versus the standard hydrogen electrode. For a half cell equation, conventionally written as a reduction reaction :
The equilibrium constant of this reduction reaction is:
where curly braces indicate activities, rectangle braces denote molar or molal concentrations, represent the activity coefficients, and the stoichiometric coefficients are shown as exponents.
Activities correspond to thermodynamic concentrations and take into account the electrostatic interactions between ions present in solution. When the concentrations are not too high, the activity can be related to the measurable concentration by a linear relationship with the activity coefficient :
The half-cell standard reduction potential is given by
where is the standard Gibbs free energy change, is the number of electrons involved, and is the Faraday's constant. The Nernst equation relates pH and as follows:
In the following, the Nernst slope is used, which has a value of 0.02569... V at STP. When base-10 logarithms are used, VT λ = 0.05916... V at STP where λ = ln = 2.3026.
This equation is the equation of a straight line for as a function of pH with a slope of volt.
This equation predicts lower at higher pH values. This is observed for the reduction of O2 into H2O, or OH−, and for reduction of H+ into H2. is then often noted as to indicate that it refers to the standard hydrogen electrode whose = 0 by convention under standard conditions.

Calculation of a Pourbaix diagram

When the activities can be considered as equal to the molar, or the molal, concentrations at sufficiently diluted concentrations when the activity coefficients 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.

Vertical boundary line

When no electrons are exchanged, the equilibrium between,,, and only depends on and is not affected by the electrode potential. In this case, the reaction is a classical acid-base reaction involving only protonation/deprotonation of dissolved species. The boundary line will be a vertical line at a particular value of pH. The reaction equation may be written:
and the energy balance is written as, where is the equilibrium constant:
Thus:
or, in base-10 logarithms,
which may be solved for the particular value of pH.
For example consider the iron and water system, and the equilibrium line between the ferric ion Fe3+ ion and hematite Fe2O3. The reaction equation is:
which has. The pH of the vertical line on the Pourbaix diagram can then be calculated:
Because the activities of the solid phases and water are equal to unity:
= = 1, the pH only depends on the concentration in dissolved :
At STP, for = 10−6, this yields pH = 1.76.

Horizontal boundary line

When H+ and OH− ions are not involved in the reaction, the boundary line is horizontal and independent of pH.
The reaction equation is thus written:
As, the standard Gibbs free energy :
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 /, 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.
Eo = 0.771 V with only one electron involved in the redox reaction.
The potential Eh is a function of temperature via the thermal voltage and directly depends on the ratio of the concentrations of the and ions:
For both ionic species at the same concentration at STP, log 1 = 0, so,, and the boundary will be a horizontal line at Eh = 0.771 volts. The potential will vary with temperature.

Sloped boundary line

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 : = = 1.
The Nernst equation thus limited to the dissolved species and is written as:
For, = 10−6 M, this yields:
Note the negative slope of this line in a Eh–pH diagram.