of water is 1 and that magnetite is pure and therefore that its activity is 1. If we again assume unit activity of Fe2+, the predominance area of magnetite would plot as the line:
that is, a slope of −4 and intercept of 0.58. However, such a high activity of Fe2+ would be highly unusual in a natural solution. A more relevant activity for Fe2+ would be perhaps 10–6. Adopting this value for the activity of Fe2+, we can draw a line corresponding to the equation:
This line represents the conditions under which magnetite is in equilibrium with an activity of aqueous Fe2+ of 10−6. For any other activity, the line will be shifted, as illustrated in Figure 3.20. For higher concentrations, the magnetite region will expand, while for lower concentrations it will contract.
Figure 3.20 Stability regions for magnetite and hematite in equilibrium with an iron-bearing aqueous solution. Thick lines are for a Feaq activity of 10−6, finer lines for activities of 10−4 and 10–8. The latter is dashed.
Now consider the equilibrium between hematite and Fe2+. We can describe this with the reaction:
The equilibrium constant (which may again be calculated from ΔGr) for this reaction is 23.79.
Expressed in log form:
Using an activity of 1 for Fe2+, we can solve for pε as:
For an activity of Fe2+ of 10−6, this is a line with a slope of 3 and an intercept of 17.9. This line represents the conditions under which hematite is in equilibrium with
Finally, equilibrium between hematite and Fe3+ may be expressed as:
The equilibrium constant expression is:
For a Fe3+ activity of 10–6, this reduces to:
Since the reaction does not involve transfer of electrons, this boundary depends only on pH.
The boundary between predominance of Fe3+ and Fe2+ is independent of the Fe concentration in solution and is the same as eqn. 3.119 and Figure 3.18, namely pε = 13.
Examining this diagram, we see that for realistic dissolved Fe concentrations, magnetite can be in equilibrium only with a fairly reduced, neutral to alkaline solution. At pH of about 7 or less, it dissolves and would not be stable in equilibrium with acidic waters unless the Fe concentration were very high. Hematite is stable over a larger range of conditions and becomes stable over a wider range of pH as pε increases. Significant concentrations of the Fe3+ ion (>10−6 m) will be found only in very acidic, oxidizing environments.
Figure 3.21 pε and pH of various waters on and near the surface of the Earth. After Garrels and Christ (1965).
Figure 3.21 illustrates the pH and pε values that characterize a variety of environments on and near the surface of the Earth. Comparing this figure with pH–pε diagrams allows us to predict the species we might expect to find in various environments. For example, Fe3+ would be a significant dissolved species only in the acidic, oxidized waters that sometimes occur in mine drainages (the acidity of these waters results from high concentrations of sulfuric acid that is produced by oxidation of sulfides). We would expect to find magnetite precipitating only from reduced seawater or in organic-rich, highly saline waters.
Balancing redox reactions for pε–pH diagrams
While many redox reactions are straightforward, balancing more complex redox reactions for pε–pH diagrams can be a bit more difficult, but a few simple rules make it easier. Let's take as an example the oxidation of ammonium to nitrate. We begin by writing the species of interest on each side of the reaction:
The next step is to balance the oxygen. We don't want to use O2 gas to do this. We used O2 at a partial pressure of 1 to define the top boundary for the water stability region. Within the region of stability of water, the O2 concentration will be lower and we don't necessarily know its value. This is usually best done using water:
Next balance the hydrogen using H+:
Finally, we use electrons to balance charge:
As a check, we can consider the valance change of our principal species and be sure that our reaction makes sense. In ammonium, nitrogen is in the 3− state, while in nitrate it is in the 5+ state, a net change of 8. This is just the number of electrons exchanged in the reaction we have written.
3.11.2 Redox in magmatic systems
High-temperature geochemists use oxygen fugacity to characterize the oxidation state of systems. Consequently, we want to write redox reactions that contain O2. Thus, equilibrium between magnetite and hematite would be written as:
(3.122)
(or alternatively, as we wrote in eqn. 3.101) rather than the way we expressed it in eqn.