3.19.
Similarly, the lower limit of the stability of water is the reduction of hydrogen:
Because ΔG°r = 0 and log K = 0 (by convention), we have pε = −pH for this reaction: a slope of 1 and intercept of 0. This is labeled as line ➁ on Figure 3.19. Water is stable between these two lines (region shown in gray on Figure 3.19).
Now let's consider the stabilities of a few simple aqueous iron species. One of the more important reactions is the hydrolysis of Fe3+:
The equilibrium constant for this reaction is 0.00631. The equilibrium constant expression is then:
Region boundaries on pε–pH diagrams represent the conditions under which the activities of two species are equal. When the activities of FeOH2+ and Fe3+ are equal, the equation reduces to:
Thus, this equation defines the boundary between regions of predominance of Fe3+ and Fe(OH)2+. The reaction is independent of pε (no oxidation or reduction is involved), and it plots as a straight vertical line pH = 2.2 (line ➂ on Figure 3.19). Boundaries between the successive hydrolysis products, such as
Now consider equilibrium between Fe2+ and Fe3+ (eqn. 3.102). The pε° for this reaction is 13.0 (Table 3.3), hence from eqn. 3.112 we have:
(3.119)
When the activities are equal, this equation reduces to:
and therefore plots as a horizontal line at pε = 13 that intersects the FeOH2+–Fe3+ line at an invariant point at pH = 2.2 (line ➃ on Figure 3.19).
The equilibrium between Fe2+ 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 (Fe2O3) and magnetite (Fe3O4). 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 (ΔGf = −742.2 kJ/mol for hematite, −1015.4 kJ/mol for magnetite, and −237.2 kJ/mol for water), we can calculate ΔGr using Hess's law and the equilibrium constant using eqn. 3.86. Doing so, we find log K = −5.77. Rearranging eqn. 3.121 we 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 Fe2+ ions. The relevant reaction is:
The equilibrium constant for this reaction is 7 × 1029. 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 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
