William M. White - Geochemistry

The equilibrium between Fe 2+and Fe(OH) 2+is defined by the reaction:

Two things are occurring in this reaction: reduction of ferric to ferrous iron, and reaction of H+ ions with the OH– radical to form water. Thus, we can treat it as the algebraic sum of the two reactions we just considered:

or:

This boundary has a slope of −1 and an intercept of 15.2 (line ➄ on Figure 3.19). Slopes and intercepts of other reactions may be derived in a similar manner.

Now let's consider some solid phases of iron as well, specifically hematite (Fe 2O 3) and magnetite (Fe 3O 4). First, let's consider the oxidation of magnetite to hematite. We could write this reaction as we did in eqn. 3.101, however, that reaction does not explicitly involve electrons, so that we would not be able to derive an expression containing pε or pH from it. Instead, we'll use water as the source of oxygen and write the reaction as:

(3.120)

Assuming unit activity of all phases, the equilibrium constant expression for this reaction is:

(3.121)

From the free energy of formation of the phases (Δ G f= −742.2 kJ/mol for hematite, −1015.4 kJ/mol for magnetite, and −237.2 kJ/mol for water), we can calculate Δ G rusing Hess's law and the equilibrium constant using eqn. 3.86. Doing so, we find log K = −5.77. Rearranging eqn. 3.121we have:

The boundary between hematite and magnetite will plot as a line with a slope of −1 and an intercept of 2.88. Above this line (i.e., at higher pε ) hematite will be stable; below that magnetite will be stable ( Figure 3.20). Thus, this line is equivalent to a phase boundary.

Next let's consider the dissolution of magnetite to form Fe 2+ions. The relevant reaction is:

The equilibrium constant for this reaction is 7 × 10 29. Written in log form:

or:

We have assumed that the activity of water is 1 and that magnetite is pure and therefore that its activity is 1. If we again assume unit activity of Fe 2+, 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 Fe 2+would be highly unusual in a natural solution. A more relevant activity for Fe 2+would be perhaps 10 –6. Adopting this value for the activity of Fe 2+, 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 Fe 2+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 Fe aqactivity of 10 −6, finer lines for activities of 10 −4and 10 –8. The latter is dashed.

Now consider the equilibrium between hematite and Fe 2+. We can describe this with the reaction:

The equilibrium constant (which may again be calculated from Δ G r) for this reaction is 23.79.

Expressed in log form:

Using an activity of 1 for Fe 2+, we can solve for pε as:

For an activity of Fe 2+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 = 10 −6. Again, for any other activity, the line will be shifted as shown in Figure 3.20.

Finally, equilibrium between hematite and Fe 3+may be expressed as:

The equilibrium constant expression is:

For a Fe 3+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 Fe 3+and Fe 2+is independent of the Fe concentration in solution and is the same as eqn. 3.119and 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 Fe 3+ion (>10 −6m) will be found only in very acidic, oxidizing environments.