Oxidation– Reduction Reactions
Oxidation– Reduction Reactions
Abstract and Keywords
Soils become flooded occasionally by intense rainfall or by runoff, and a significant portion of soils globally underlies highly productive wetlands ecosystems that are inundated intermittently or permanently. Peat-producing wetlands (bogs and fens) account for about half the inundated soils, with swamps and rice fields each accounting for about one-sixth. Wetlands soils hold about one-third of the total nonfossil fuel organic C stored below the land surface, which is about the same amount of C as found in the atmosphere or in the terrestrial biosphere. This C storage is all the more impressive given that wetlands cover less than 6% of the global land area. On the other hand, wetlands ecosystems are also significant locales for greenhouse gas production. They constitute the largest single source of CH4 entering the atmosphere, emitting about one-third the global total, with half this amount plus more than half the global N2O emissions coming from just three rice-producing countries. A soil inundated by water cannot exchange O2 readily with the atmosphere. Therefore, consumption of O2 and the accumulation of CO2 ensue as a result of soil respiration. If sufficient humus metabolized readily by the soil microbiome (“labile humus”) is available, O2 disappearance after inundation is followed by a characteristic sequence of additional chemical transformations. This sequence is illustrated in Fig. 6.1 for two agricultural soils: a German Inceptisol under cereal cultivation and a Philippines Vertisol under paddy rice cultivation. In the German soil, which was always well aerated prior to its sudden inundation, NO3- is observed to disappear from the soil solution, after which soluble Mn(II) and Fe(II) begin to appear, whereas soluble SO42- is depleted (left side of Fig. 6.1). The appearance of the two soluble metals results from the dissolution of oxyhydroxide minerals (Section 2.4). Despite no previous history of inundation, CH4 accumulation in the soil occurs and increases rapidly after SO42- becomes undetectable and soluble Mn(II) and Fe(II) levels have become stabilized. During the incubation time of about 40 days, the pH value in the soil solution increased from 6.3 to 7.5, whereas acetic acid (Section 3.1) as well as H2 gas were produced.
Keywords: Faraday constant, anoxic soil, carbon corrosion, dissimilatory, electrode potential, flooded soils, iron reduction, microbial catalysis, oxic soil, reductant
(p.107) 6.1 Flooded Soils
Soils become flooded occasionally by intense rainfall or by runoff, and a significant portion of soils globally underlies highly productive wetlands ecosystems that are inundated intermittently or permanently. Peat-producing wetlands (bogs and fens) account for about half the inundated soils, with swamps and rice fields each accounting for about one-sixth. Wetlands soils hold about one-third of the total nonfossil fuel organic C stored below the land surface, which is about the same amount of C as found in the atmosphere or in the terrestrial biosphere. This C storage is all the more impressive given that wetlands cover less than 6% of the global land area. On the other hand, wetlands ecosystems are also significant locales for greenhouse gas production. They constitute the largest single source of CH_{4} entering the atmosphere, emitting about one-third the global total, with half this amount plus more than half the global N_{2}O emissions coming from just three rice-producing countries.
A soil inundated by water cannot exchange O_{2} readily with the atmosphere. Therefore, consumption of O_{2} and the accumulation of CO_{2} ensue as a result of soil respiration. If sufficient humus metabolized readily by the soil microbiome (“labile humus”) is available, O_{2} disappearance after inundation is followed by a characteristic sequence of additional chemical transformations. This sequence is illustrated in Fig. 6.1 for two agricultural soils: a German Inceptisol under cereal cultivation and a Philippines Vertisol under paddy rice cultivation. In the German soil, which was always well aerated prior to its sudden inundation, ${\text{NO}}_{3}^{-}$ is observed to disappear from the soil solution, after which soluble Mn(II) and Fe(II) begin to appear, whereas soluble ${\text{SO}}_{4}^{2-}$ is depleted (left side of Fig. 6.1). The appearance of the two soluble metals results from the dissolution of oxyhydroxide minerals (Section 2.4). Despite no previous history of inundation, CH_{4} accumulation in the soil occurs and increases rapidly after ${\text{SO}}_{4}^{2-}$ becomes undetectable and soluble Mn(II) and Fe(II) levels have become stabilized. During the incubation time of about 40 days, the pH value in the soil solution increased from 6.3 to 7.5, whereas acetic acid (Section 3.1) as well as H_{2} gas were produced. (p.108) These two latter compounds are known products of fermentation, the microbial degradation of humus into simpler organic compounds, especially organic acids, accompanied by the production of H_{2} and CO_{2}. The reported concentrations of acetate (millimolar) and H_{2} gas (micromolar in the soil solution) in the Inceptisol are typical of fermentation. These products accumulate during the early stages of incubation, then typically are consumed as soluble Mn(II) and Fe(II) levels increase or CH_{4} production commences.
Similar trends occur in the Vertisol (right side of Fig. 6.1), which was maintained under paddy conditions before sampling. Nitrate disappears quickly, whereas ${\text{SO}}_{4}^{2-}$ is depleted gradually after soluble Fe(II) rises to a plateau value. (p.109) The increase in pH noted in the Inceptisol is observed in the Vertisol as well. Acetate and H_{2} also follow the same trend as the Inceptisol. The time trend of CO_{2} production is remarkably similar to that of soluble Fe(II) production, suggesting the existence of coupling between the two processes. Detailed C balance measurements indicate the sum total of CO_{2} and CH_{4} produced resulted in the loss of just 8% of the initial total organic C in the soil, with 85% of this loss manifest as CO_{2}. Thus, most of the labile humus C converted into gases is used to produce CO_{2} accompanying the accumulation of soluble Fe(II).
The temporal sequence of chemical transformations has a spatial counterpart that can be observed in sediments inundated permanently. Figure 6.2 illustrates this spatial counterpart, showing vertical profiles of soluble O_{2}, ${\text{SO}}_{4}^{2-}$, CH_{4}, and Fe observed in uncontaminated freshwater sediments sampled from the bottom of Lake Constance in Germany. Oxygen is depleted over the first few millimeters of zone A, which has a reported rust-brown color, reflecting the presence of humus (p.110) and Fe(III) oxide minerals. A green-brown zone B immediately below zone A is associated with the increase of Fe(II), whereas the reported black color of zone C, defined chemically by the disappearance of soluble ${\text{SO}}_{4}^{2-}$, suggests precipitation of secondary Fe(II) sulfides. Layer D, which has no detectable ${\text{SO}}_{4}^{2-}$, is associated with the increase of significant CH_{4} concentrations in the pore water. An increase in pH, from 6.8 to 7.3, across the 20-cm depth of the four subsurface zones also was observed.
Implicit in these temporal and spatial sequences of chemical transformations is effective catalysis by biogeochemical guilds in the soil microbiome. Each of these guilds, characterized by the compounds they consume and produce, has adapted uniquely to the highly variable microhabitats determined by soil texture and mineralogy, along with the distribution of plant roots. These unique adaptations influence the sequences illustrated in Figs. 6.1 and 6.2, particularly when the supply of labile soil humus is limited. For example, addition of nitrate to a soil largely depleted of labile humus by prior incubation slightly inhibits the production of soluble Fe, but greatly inhibits both the disappearance of soluble ${\text{SO}}_{4}^{2-}$ and the production of CH_{4}. Such effects, however, do not occur if typical fermentation products, such as H_{2} gas or acetic acid, are added. Amending a soil low in labile humus with ferrihydrite particles (Section 2.4) suppresses the depletion of soluble ${\text{SO}}_{4}^{2-}$ and slows the production of CH_{4}, whereas addition of soluble ${\text{SO}}_{4}^{2-}$ by itself inhibits CH_{4} production, but these effects again can be reversed by supplying fermentation products, especially H_{2} gas. An important general conclusion about the biogeochemical guilds can be drawn from these observations: significant microbial competition for labile humus or fermentation products exists that tends to favor the guilds catalyzing chemical transformations that occur earlier during the sequence. Competitive microbial intervention is also reflected in the extent to which labile humus or the products of fermentation are depleted from soil. For example, H_{2} gas is driven to much lower concentrations in the soil solution by the production of soluble Fe than it is by CH_{4} production (there is a hint of this in Fig. 6.1), suggesting that the H_{2}-consuming guilds associated with the chemical transformations earlier in the sequence function more efficiently than those associated with transformations that occur later.
6.2 Understanding Redox in Flooded Soils
The characteristic sequence of transformations illustrated in Figs. 6.1 and 6.2 can be interpreted as a sequence of oxidation–reduction or redox reactions. A redox reaction is one in which electrons are transferred completely from one chemical species to another. The chemical species donating electrons is called a reductant, (p.111) whereas the one accepting electrons is called an oxidant. The oxidized or reduced status of these species is displayed explicitly through their oxidation number, a hypothetical valence denoted by a positive or a negative roman numeral, which is assigned according to the following rules:
In any compound, the oxygen anion is conventionally designated O(–II) and the proton is conventionally designated H(I).
For a monoatomic species, its oxidation number equals its charge. For a molecule, the sum of the oxidation numbers of its constituent atoms equals its charge.
These two rules can be illustrated by assigning oxidation numbers to the atoms in FeOOH (goethite), ${\text{CHO}}_{2}^{-}$ (formate), N_{2}, ${\text{SO}}_{4}^{2-}$, and C_{6}H_{12}O_{6} (glucose). In FeOOH, Fe is designated Fe(III), because FeOOH has zero charge and, applying the two rules above, 3 + 2(–2) + 1 = 0. A similar computation can be done for , in which C must be designated C(II) because 2 + 2(–2) + 1 = –1. In the case of N_{2}, the second rule leads to the designation N(0) for each N atom because there is no basis for considering them as two different redox species. (This is also true for O_{2} and H_{2}.) For sulfate, S must be S(VI) according to the second rule. In glucose, C must be C(0) because O(–II) and H(I) lead in themselves to a neutral C_{6}H_{12}O_{6} molecule.
In the mineral weathering reaction described by Eq. 1.3 (see also problem 7 in Chapter 1), biotite is the reductant in which Fe donates electrons and O_{2} is the oxidant accepting the electrons. In the reductive dissolution reaction,
Combination of a reduction half-reaction with its reverse, an oxidation half-reaction, creates a redox reaction in which the species e^{–} does not appear explicitly. Equation 6.1 could be combined (“coupled”), for example, with the reverse of the reduction half-reaction in which the oxidant CO_{2} accepts an aqueous electron and binds with protons to be transformed into acetate plus liquid water:
(p.112) This coupling of reduction and oxidation half-reactions will cancel the aqueous electron appearing in both. The reductive dissolution of goethite, the oxidant, is thereby coupled to the oxidation of acetate (${\text{CH}}_{3}{\text{CO}}_{2}^{-}$), the reductant, to create the redox reaction
This redox reaction, which is consistent with observations made about the concurrent rise in soluble Fe and CO_{2} depicted in Fig. 6.1, is catalyzed by the biogeochemical guild of iron-reducing bacteria that consume acetate and produce CO_{2}. If the reductant produced in a redox reaction accumulates outside the microbial cell, the catalysis involved is termed dissimilatory; otherwise, it is assimilatory. For example, the catalysis of ${\text{NO}}_{3}^{-}$ reduction to ${\text{NH}}_{4}^{+}$ which is metabolized to form amino acids, such as glutamic and aspartic acid (Table 3.2), is assimilatory whereas the catalysis of iron reduction in Eq. 6.3 is dissimilatory.
A list of important reduction half-reactions and their thermodynamic equilibrium constants at 25 °C is provided in Table 6.1. The equilibrium constants in the table have the same meaning as in Chapters 4 and 5, even though the reactions to which they refer contain the aqueous electron, a problematic chemical species. This is because the reduction of the proton is defined to have log K = 0 (the third half-reaction listed in Table 6.1). Every reduction half-reaction in Table 6.1 thus may be combined with the reverse of the proton reduction reaction to cancel e^{–} while leaving log K completely unchanged. In this sense, the equilibrium constant for each reduction half-reaction in Table 6.1 is implicitly that for a redox reaction in which the reduction half-reaction has been combined with the half-reaction for the oxidation of H_{2} gas to form aqueous protons.
Table 6.1 Reduction half-reactions and their equilibrium constants at 25 °C
Reduction half-reaction | Log K |
---|---|
$\frac{1}{4}{\text{O}}_{2}(\text{g})+{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}{\text{H}}_{2}\text{O}(\ell )$ | 20.75 |
$\frac{1}{2}{\text{O}}_{2}(\text{g})+{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}{\text{H}}_{2}{\text{O}}_{2}$ | 11.50 |
${\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}{\text{H}}_{2}(\text{g})$ | 0.00 |
$\frac{1}{3}{\text{NO}}_{3}^{-}+\frac{4}{3}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{3}\text{NO}(\text{g})+\frac{2}{3}{\text{H}}_{2}\text{O}(\ell )$ | 16.15 |
$\frac{1}{2}{\text{NO}}_{3}^{-}+{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}{\text{NO}}_{2}^{-}+\frac{1}{2}{\text{H}}_{2}\text{O}(\ell )$ | 14.15 |
$\frac{1}{4}{\text{NO}}_{3}^{-}+\frac{5}{4}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{8}{\text{N}}_{2}\text{O}(\text{g})+\frac{5}{8}{\text{H}}_{2}\text{O}(\ell )$ | 18.90 |
$\frac{1}{5}{\text{NO}}_{3}^{-}+\frac{6}{5}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{10}{\text{N}}_{2}(\text{g})+\frac{3}{5}{\text{H}}_{2}\text{O}(\ell )$ | 21.05 |
$\frac{1}{8}{\text{NO}}_{3}^{-}+\frac{5}{4}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{8}{\text{NH}}_{4}^{+}+\frac{3}{8}{\text{H}}_{2}\text{O}(\ell )$ | 14.90 |
${\text{Mn}}^{3+}+{\text{e}}^{-}={\text{Mn}}^{2+}$ | 25.50 |
$\text{MnOOH}(\text{s})+3{\text{H}}^{+}+{\text{e}}^{-}={\text{Mn}}^{2+}+2{\text{H}}_{2}\text{O}(\ell )$ | 25.36 |
$\frac{1}{2}{\text{Mn}}_{3}{\text{O}}_{4}(\text{s})+4{\text{H}}^{+}+{\text{e}}^{-}=\frac{3}{2}{\text{Mn}}^{2+}+2{\text{H}}_{2}\text{O}(\ell )$ | 30.68 |
$\frac{1}{2}{\text{MnO}}_{2}(\text{s})+2{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}{\text{Mn}}^{2+}+{\text{H}}_{2}\text{O}(\ell )$ | 21.82 |
$\frac{1}{2}{\text{MnO}}_{2}(\text{s})+\frac{1}{2}{\text{CO}}_{2}(\text{g})+{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}{\text{MnCO}}_{3}(\text{s})+\frac{1}{2}{\text{H}}_{2}\text{O}(\ell )$ | 18.00 |
${\text{Fe}}^{3+}+{\text{e}}^{-}={\text{Fe}}^{2+}$ | 13.00 |
$\frac{1}{2}{\text{Fe}}^{2+}+{\text{e}}^{-}=\frac{1}{2}\text{Fe}(\text{s})$ | −7.93 |
$\text{Fe}{\left(\text{OH}\right)}_{3}(\text{s})+3{\text{H}}^{+}+{\text{e}}^{-}={\text{Fe}}^{2+}+3{\text{H}}_{2}\text{O}(\ell )$ | 17.14 |
$\text{FeOOH}(\text{s})+3{\text{H}}^{+}+{\text{e}}^{-}={\text{Fe}}^{2+}+2{\text{H}}_{2}\text{O}(\ell )$ | 13.34 |
$\frac{1}{2}{\text{Fe}}_{3}{\text{O}}_{4}(\text{s})+4{\text{H}}^{+}+{\text{e}}^{-}=\frac{3}{2}{\text{Fe}}^{2+}+2{\text{H}}_{2}\text{O}(\ell )$ | 18.16 |
$\frac{1}{2}{\text{Fe}}_{2}{\text{O}}_{3}(\text{s})+3{\text{H}}^{+}+{\text{e}}^{-}={\text{Fe}}^{2+}+\frac{3}{2}{\text{H}}_{2}\text{O}(\ell )$ | 12.96 |
$\frac{1}{4}{\text{SO}}_{4}^{2-}+\frac{5}{4}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{8}{\text{S}}_{2}{\text{O}}_{3}^{2-}+\frac{5}{8}{\text{H}}_{2}\text{O}(\ell )$ | 4.85 |
$\frac{1}{8}{\text{SO}}_{4}^{2-}+\frac{9}{8}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{8}{\text{HS}}^{-}+\frac{1}{2}{\text{H}}_{2}\text{O}(\ell )$ | 4.25 |
$\frac{1}{8}{\text{SO}}_{4}^{2-}+\frac{5}{4}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{8}{\text{H}}_{2}\text{S}+\frac{1}{2}{\text{H}}_{2}\text{O}(\ell )$ | 5.13 |
$\frac{1}{2}{\text{CO}}_{2}(\text{g})+\frac{1}{2}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}{\text{CHO}}_{2}^{-}$ | −5.22 |
$\frac{1}{4}{\text{CO}}_{2}(\text{g})+\frac{7}{8}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{8}{\text{C}}_{2}{\text{H}}_{3}{\text{O}}_{2}^{-}+\frac{1}{4}{\text{H}}_{2}\text{O}(\ell )$ | −1.20 |
$\frac{7}{30}{\text{CO}}_{2}(\text{g})+\frac{29}{30}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{30}{\text{C}}_{6}{\text{H}}_{5}{\text{COO}}^{-}+\frac{2}{5}{\text{H}}_{2}\text{O}(\ell )$ | 1.76 |
$\frac{1}{4}{\text{CO}}_{2}(\text{g})+\frac{1}{12}{\text{NH}}_{4}^{+}+\frac{11}{12}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{12}{\text{C}}_{3}{\text{H}}_{4}{\text{O}}_{2}{\text{NH}}_{3}+\frac{1}{3}{\text{H}}_{2}\text{O}(\ell )$ | 0.84 |
$\frac{1}{4}{\text{CO}}_{2}(\text{g})+{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{24}{\text{C}}_{6}{\text{H}}_{12}{\text{O}}_{6}+\frac{1}{4}{\text{H}}_{2}\text{O}(\ell )$ | −0.20 |
$\frac{1}{8}{\text{CO}}_{2}(\text{g})+{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{8}{\text{CH}}_{4}(\text{g})+\frac{1}{4}{\text{H}}_{2}\text{O}(\ell )$ | 2.86 |
The log K data in Table 6.1 also can be combined in the usual way to calculate log K for redox reactions. According to Table 6.1, the reduction of goethite has log K = 13.34, and the oxidation of acetate, the half-reaction that is the reverse of that shown in Eq. 6.2, has log K = 1.20. It follows that the reductive dissolution of goethite by acetate in Eq. 6.3 has log K = 13.34 + 1.20 = 14.54. This equilibrium constant can be expressed in terms of activities in the usual way:
If the activities of goethite and water are set equal to 1.0, and the usual conventions for the activities of CO_{2}(g) and H^{+} are used, then Eq. 6.4 reduces to the expression
(p.113) (p.114) Choosing pH 6 and = 10^{–3.52} atm as representative values, one reduces this equation to an even simpler expression:
For millimolar soluble Fe(II) [(Fe^{2+}) = 10^{–3}], which is typical of a flooded soil, Eq. 6.6 predicts ≈ 10^{–45}, showing that acetate would be completely oxidized to CO_{2} by the reductive dissolution of goethite at pH 6.
Direct application of Eq. 6.1 or 6.2 requires an operational interpretation of (e^{–}), the activity of the aqueous electron. This can be accomplished by following the paradigms already well established for the aqueous proton. Acid–base reactions are proton-transfer reactions, whereas redox reactions are electron-transfer reactions. Soil acidity is assessed quantitatively by the negative common logarithm of the proton activity, the pH value. Similarly, soil redox status can be assessed by the negative common logarithm of the electron activity, the pE value;
(p.115) Large values of pE favor the existence of electron-poor species (oxidants), just as large values of pH favor the existence of proton-poor species (bases). Small values of pE favor electron-rich species (reductants), just as small values of pH favor proton-rich species (acids). It turns out that, unlike pH, pE can take on negative values. This difference results solely from the differing conventions used to define reference values of log K for acid–base and redox reactions, given in Table 6.2.
Table 6.2 Comparing pE with pH
Species | Reaction | Predominance | Condition |
---|---|---|---|
Acid | Donates H^{+} | Low pH | Acidic |
Base | Accepts H^{+} | High pH | Basic |
Reductant | Donates e^{–} | Low pE | Reducing |
Oxidant | Accepts e^{–} | High pE | Oxidizing |
Reference reactions | |||
H_{2}O(ℓ) + H^{+} = H_{3}O^{+} | log K ≡ 0 | Acid–base | |
${\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}{\text{H}}_{2}(\text{g})$ | log K ≡ 0 | Redox |
The value of pE in soils can range from around +13.0 to around –7.0. This very broad range (covering 20 orders of magnitude change in the aqueous electron activity!) can be partitioned into oxic, suboxic, and anoxic subranges based on the sequence of transformations illustrated in Fig. 6.1. Oxic conditions are said to occur if the partial pressure of O_{2} remains well above that leading to hypoxia, which is about 0.1 atm. The corresponding pE value can be calculated by rearranging the expression relating log K for a chemical reaction to log product and reactant activities to solve it for pE as defined in Eq. 6.7. Thus, using the O_{2} reduction half-reaction (the first one listed in Table 6.1) and taking pH = 7, one finds
Thus, at pH 7, pE ≥ 13.5 characterizes oxic soils. Suboxic conditions in a soil can be associated with pE values for the next step in the sequence of transformations exemplified in Fig. 6.1—most commonly, the reductive dissolution of MnO_{2}(s), which offers a mechanism for the production of soluble Mn in flooded soils. The half-reaction for this transformation, listed in the (p.116) middle of Table 6.1, yields the expression [assuming pH = 7 and, as usual, that (MnO_{2}) = 1.0]:
This method of calculating pE is readily generalized, because the reduction half-reactions in Table 6.1 are all special cases of the generic half-reaction
Equation 6.8 leads in the usual way to an equation for pE [assuming (H_{2}O) = 1.0]:
6.3 Generalizing the Sequence: The Redox Ladder
The broad applicability of Eqs. 6.8 and 6.9 can be represented graphically in the redox ladder, which is a vertical line marked off with “rungs” occupied by a chosen set of redox couples, with the oxidant on the left and the reductant on the right. This vertical line is actually a coordinate axis labeled by pE values calculated using Eq. 6.9, assuming a given pH value, usually pH 7.0. Construction of the ladder is based on three rules.
Rule 1: Each redox couple on the ladder must be related by a reduction half-reaction in which the stoichiometric coefficient of e^{–} is 1.0. If this half-reaction (p.118) has the generic form in Eq. 6.8, then pE values are calculated with Eq. 6.9 after fixing the pH value and setting (H_{2}O(ℓ)) = 1.0.
Rule 2: If the oxidant and reductant are in the same phase, then (A_{ox}) and (A_{red}) are each set equal to 1.0, yielding a simplified version of Eq. 6.9:
Example: The reduction of ${\text{SO}}_{4}^{2-}$ to form bisulfide (${\text{HS}}^{-}$) is described by the reduction half-reaction (Table 6.1)
Rule 3: If either the oxidant or the reductant is a gas or a mineral, the gas-phase species activity is equated to the species partial pressure in atmospheres and the mineral activity is set equal to 1.0. The activity of the remaining aqueous-phase species in the redox couple is then equated numerically to its concentration in moles per liter. Suitable values of the partial pressure and aqueous concentration are then used to calculate pE with Eq. 6.9.
Example: Calculations illustrating Rule 3 were presented in Section 6.2 for the reduction of O_{2}(g) and for the reductive dissolution of MnO_{2}(s) and FeOOH(s). The resulting pE values are also depicted in Fig. 6.4. Another example is provided by the reduction of CO_{2}(g) to form glucose, as occurs in photosynthesis (Table 6.1):
If ${\text{P}}_{{\text{CO}}_{\text{2}}}={10}^{-2}\text{atm}$ and (C_{6}H_{12}O_{6}) ≈ 5 × 10^{–4} (based on a glucose concentration of 0.5 mM), then, at pH 7.0,
Note again the small effect of the redox couple activities on the pE value.
One of the most important applications of a redox ladder is to establish which member of a redox couple is favored (thermodynamically more stable) (p.119) under given conditions in a soil. This application requires knowing how a soil is poised with respect to pE. Poising is to pE what buffering is to pH (Section 3.4). Thus, a well-poised soil resists changes in pE, just as a well-buffered soil resists changes in pH. In soils, the most important redox-active elements are H, C, N, O, S, Mn, and Fe. Poising by a reduction half-reaction involving one of these elements depends on its relative abundance in the form of an oxidant species. For example, abundant O_{2}(g) in the soil atmosphere implies oxic conditions and, therefore, poising by the half-reaction for O_{2} reduction (Table 6.1). As shown in Section 6.2, the pE value is then poised at
(p.120) If ${\text{P}}_{{\text{O}}_{2}}$ drops well below its atmospheric value (0.21 atm), however, O_{2}(g) no longer will be in sufficient supply to poise pE. Poising by the reductive dissolution of MnO_{2}(s) could then occur, especially given that Mn is a relatively abundant metal in soils. As shown in Section 6.2, the pE value is poised at
Note that other oxidant Mn minerals listed in Table 6.1 are unfavored thermodynamically relative to MnO_{2}(s), to which Eq. 6.14 applies. For example, manganite (γ -MnOOH), a precipitation product of air–oxidation of soluble Mn(II), disproportionates into MnO_{2}(s) and Mn^{2+}:
However, manganite or hausmannite (Mn_{3}O_{4}) can occur as metastable minerals.
Under anoxic conditions, reduction half-reactions involving oxidant species of Fe, S, or C can poise pE at values calculated according to Eq. 6.9:
To the extent that pE values are well separated, they are characteristic of the associated reduction half-reactions, as implied in Fig. 6.3. In recognition of this important possibility, as well as the ubiquity of dissimilatory microbial catalysis in soil redox reactions, the oxidants associated with Eqs. 6.13, 6.14, and 6.16 are called terminal electron acceptors, with the half-reactions themselves then called terminal electron-accepting processes (TEAPs). The TEAPs are key chemical reactions associated with microbial respiration. The corresponding biogeochemical guilds are described as O-, Mn-, or Fe-respiring, and so on, as suggested by Fig. 6.3. In light of this terminology, pE in soils is said to be poised by TEAPs involving the redox-active elements O, N, Mn, Fe, S, or C. In heavily polluted soils, TEAPs involving the redox-active elements Cr, Cu, As, Se, Ag, Pb, U, and Pu may instead poise pE if an oxidant species of any of them is abundant.
How is poising quantified in soils? The most common method used to infer pE in soils is quantitation of redox couples. For example, ${\text{P}}_{{\text{O}}_{2}}$ can be measured to determine whether poising is by O_{2} reduction. On the other hand, Mn(II) or Fe(II) concentrations in the soil solution exceeding 100 μM signal pE poising by the reductive dissolution of Mn(IV) or Fe(III) oxy(hydr)oxides, and aqueous CH4 concentrations greater than 50 μM point to methanogenesis as a poiser. Supporting microbiological evidence for the presence of the biogeochemical guild using a proposed pE-poising TEAP is a necessary adjunct.
Soil pH is typically quantified by a direct pH measurement in a soil solution sample (Section 4.1) using a glass electrode. Unfortunately, equivalent success has not occurred in the development of Pt electrodes to measure pE in soils. An electrode potential (E_{H}, in units of volts) can always be defined in terms of pE:
6.4 Exploring the Redox Ladder
A redox reaction consists of two reduction half-reactions combined after one of them has been reversed, such that the redox reaction does not exhibit e^{–}(aq). How does one determine which of the two contributing half-reactions to reverse? The rule is as follows: electron transfer is from low pE (electron-rich species) on the redox ladder to high pE (electron-poor species) on the ladder. As an illustration of this rule, consider Eqs. 6.1 and 6.2. At pH 6, the reduction half-reaction for acetate is perched on a lower rung than that for the reductive dissolution of goethite. Therefore, to combine the two reduction half-reactions into a redox reaction, the half-reaction involving acetate must be reversed, making acetate a reactant and yielding the redox reaction in Eq. 6.3. In terms of the redox ladder in Fig. 6.4, electron transfer is from a reductant perched on the right side of a rung to an oxidant perched on the left side of some rung above it, with subsequent transformation of the reductant into the oxidant perched directly to its left, and of the oxidant into the reductant perched directly to its right.
As noted in Section 6.2, high pE favors oxidants, such as O_{2}(g), whereas low pE favors reductants, such as humus and biomolecules. Suppose that pE is poised by the reductive dissolution of MnO_{2}(s). If (Mn^{2+}) = 10^{–2} and pH = 7, pE is poised at 8.8, as shown in Section 6.2 and Fig. 6.4. Above this rung on the redox ladder there are oxidants that can survive only if pE > 8.8. If pE is poised below their rungs, these oxidants are destabilized and the reductants perched to their right become the favored species. For example, if pE = 8.8 is introduced into Eq. 6.13 at pH 7, ${\text{P}}_{{\text{O}}_{2}}\approx {10}^{-5}$ atm and O_{2}(g) has effectively disappeared, replaced by H_{2}O(ℓ). On the other hand, just the opposite trend applies to oxidants perched on rungs below pE = 8.8. For these oxidants, it is their reductant partners that are destabilized. If pE = 8.8 is introduced into Eq. 6.16a, for example, the resulting Fe^{2+} activity is only about 2 × 10^{–13}. The general rule operating here is as follows:
If pE is poised at a certain value, the favored species on the redox ladder in all redox couples perched at higher (lower) pE values than the poised pE is the reductant (oxidant) species in the couples.
It is in the context of this rule that the sequence of chemical transformations in flooded soils, shown in Figs. 6.1 to 6.3, can be understood as reductions occurring as pE descends down the redox ladder. Reactive electrons are produced (p.123) by the microbial oxidation of humus or H_{2}(g). As these electrons accumulate, dropping the pE value below around 12.0, enough of them become available to reduce O_{2}(g) to H_{2}O(ℓ). Under these circumstances, O_{2}(g) can be consumed in respiration processes by the aerobic guilds in the soil microbiome. As the pE value decreases further, electrons are available to reduce ${\text{NO}}_{3}^{-}$. This reduction is catalyzed by anaerobic guilds in the soil microbiome that respire ${\text{NO}}_{3}^{-}$ and excrete ${\text{NO}}_{2}^{-}$, N_{2}, N_{2}O, NO, or ${\text{NH}}_{4}^{+}$. As pE drops below 9, electrons become plentiful enough to support the dissimilatory reduction of Mn(IV) minerals. As pE decreases below 2, the dissimilatory reduction of Fe(III) minerals becomes possible. When pE < 0, enough electrons become available for dissimilatory ${\text{SO}}_{4}^{2-}$ reduction, with typical soluble products H_{2}S, HS^{–}, or thiosulfate (${\text{S}}_{2}{\text{O}}_{3}^{-}$) ions. Methane production ensues for pE ≤ –4. This is the chemical interpretation of Figs. 6.1 to 6.3. The sequence of transformations induced by decreasing pE is a sequence of ecological succession among biogeochemical guilds mediating these transformations. Aerobic guilds that use O_{2} to oxidize humus do not function below pE 5; nitrate-reducing bacteria thrive in the pE range between 10 and 0, for the most part; and sulfate-reducing bacteria do not do well at pE > 2.
The Fe^{2+}/Fe^{0} couple perched at the very bottom of the redox ladder in Fig. 6.4 involves Fe(s): “zero-valent iron” (Fe^{0}). Perched just above it on the ladder is the CO_{2}/C_{6}H_{12}O_{6} couple. In glucose, C has oxidation number 0 and is designated C(0); thus, glucose represents “zero-valent carbon.” This analogy becomes even more evident if the reduction half-reaction for the goethite/Fe^{2+} couple is added to that for Fe^{2+}/Fe^{0} to cancel Fe^{2+} while maintaining the stoichiometric coefficient of e^{–} at 1.0:
(p.124) 6.5 pE–pH Diagrams
A pE–pH diagram is a predominance diagram (Section 5.3) in which electron activity is the dependent variable chosen to plot against pH. Thus, the pE value plays the same role as log$\left(\text{Si}{\left(\text{OH}\right)}_{4}^{0}\right)$ in Figure 5.5. The construction of a pE–pH diagram is, accordingly, a particular example of the construction of a predominance diagram. The only new wrinkle appears whenever an aqueous species predominates instead of a mineral. The steps in constructing a pE–pH diagram are summarized as follows:
Establish a set of redox species and obtain values of log K for all possible reactions between the species.
Unless other information is available, set the activities of liquid water and all minerals equal to 1.0. Set all gas-phase species’ activities equal to partial pressures.
Develop each expression for log K into a pE–pH relationship. In one relationship involving an aqueous species and a mineral wherein a change in oxidation number is involved, choose a value for the activity of the aqueous species.
In each reaction involving two aqueous species, set the activities of the two species equal.
The resulting pE–pH diagram is partitioned into regions that represent domains of stability of either an aqueous species or a mineral, with boundary lines generated by pE–pH relationships based on Eq. 6.9. A pE–pH diagram for a redox-active element can predict the redox species expected at equilibrium under oxic, suboxic, or anoxic conditions in a soil at any pH value.
To illustrate these concepts, consider a pE–pH diagram for Fe based on conditions in the Philippines Vertisol with the sequence of transformations depicted on the right in Fig. 6.1. First, a set of three redox species is chosen: Fe(OH)_{3}(s), a poorly crystalline mineral akin to ferrihydrite that could form preferentially according to the GLO Step Rule (Section 5.4); FeCO_{3}(s), siderite, an Fe(II) carbonate mineral observed in anoxic soils (Section 2.5); and the aqueous species, Fe^{2+}. The reductive dissolution of Fe(OH)_{3}(s) is listed in Table 6.1, and its associated pE–pH relationship following the steps listed previously appears in Eq. 6.16a. The dissolution reaction for siderite,
The pE–pH relationships that define the boundary lines in a pE–pH diagram describing the three Fe redox species are then
Because Eq. 6.21 is not a reduction half-reaction, it cannot involve pE when log K is expressed in terms of log activity variables. Thus, it is represented as a vertical line in a pE–pH diagram. Equation 6.23 cannot be implemented in a pE–pH diagram until fixed values for (Fe^{2+}) and ${\text{P}}_{{\text{CO}}_{2}}$ are selected. Reference to Fig. 6.1 indicates that ${\text{P}}_{{\text{CO}}_{2}}$ ≈ 0.12 atm after about 100 days of incubation of the Philippines soil. A measured value of (Fe^{2+}) is not available, but (Fe^{2+}) ≈ 2 × 10^{–4} is reasonable for a flooded acidic soil. With these data incorporated, Eq. 6.23 become the set of boundary-line equations
The boundary lines based on Eq. 6.24 are drawn in Fig. 6.5. Equation 6.24a is the boundary between Fe(OH)_{3}(s) and Fe^{2+} in respect to predominance of one redox species or the other. Above the line, pE increases, so Fe(OH)_{3}(s) must predominate; below the line, this mineral dissolves to form Fe^{2+} as the predominant species under the given conditions of Fe^{2+} activity and CO_{2} partial pressure. At pH 6, however, siderite becomes the predominant Fe(II) species at low pE under the fixed conditions assumed. The vertical boundary line signaling this (p.126) transition in Fig. 6.5 is remarkably robust under shifts in the values of (Fe^{2+}) or ${\text{P}}_{{\text{CO}}_{2}}$ For example, if (Fe^{2+}) decreases to 10^{–6}, or if ${\text{P}}_{{\text{CO}}_{2}}$ decreases to 10^{–3.52} atm (the atmospheric value), the pH value for siderite precipitation is increased to about 7.0. Increasing (Fe^{2+}) to 10^{–3} (the value assumed in Fig. 6.4) decreases the pH value to 5.6. Thus, siderite precipitation can be expected in a flooded soil as pH increases from above 5 to above 7 during the sequence of reduction, according to Eq. 6.24. The initial pH value in the Philippines Vertisol was 5.8, which climbed to 7.0 when the CO_{2} partial pressure achieved its plateau value. Thus, siderite precipitation in this soil may well have occurred. The initial pE value in the soil was estimated by Pt electrode to be roughly +8, dropping rapidly to and remaining around –0.6 after only a few days. The initial state of the soil plots well within the Fe(OH)_{3}(s) field in Fig. 6.5, whereas the final state fits nicely into the FeCO_{3}(s) field.
For Further Reading
Bibliography references:
Burgin A. J., W. H. Yang, S. K. Hamilton, and W. L. Silver. (2011) Beyond carbon and nitrogen: How the microbial energy economy couples elemental cycles in diverse ecosystems. Front. Ecol. Environ. 9:44–52.
Falkowski P. G., T. Fenchel, and E. F. Delong. (2008) The microbial engines that drive Earth’s biogeochemical cycles. Science 320:1034–1039.
Inglett P. W., K. R. Reddy, W. C. Harris, and E. M. D,’Angelo. (2012) Biogeochemistry of wetlands. In: P. M. Huang, Y. Li, and M. E. Sumner, (eds.). Handbook of Soil Sciences: Resource Management and Environmental Impacts, 2nd ed. CRC Press, Boca Raton, FL, Chap. 20.
(p.127) James B. R., and D. A. Brose. (2012) Oxidation–reduction phenomena. In: P. M. Huang, Y. Li, and M. E. Sumner, (eds.). Handbook of Soil Sciences: Properties and Processes, 2nd ed. CRC Press, Boca Raton, FL, Chap. 14.
Kirk, G. (2004) The Biogeochemistry of Submerged Soils. Wiley, Chichester, UK, Chaps. 4 and 5.
Martínez, C., L. H. Alvarez, L. B. Celis, and F. J. Cervantes. (2013) Humus-reducing microorganisms and their valuable contribution in environmental processes. Appl. Microbiol,. Biotechnol. 7:10293–10308.
Tratnyek P. G., T. J. Grundl, and S. B. Haderlein, (eds.). (2011) Aquatic Redox Chemistry. Oxford University Press, New York.
Problems
Soil bacteria in the genus Nitrobacter catalyze the oxidation of ${\text{NO}}_{2}^{-}$ resulting from the microbial oxidation of ${\text{NH}}_{4}^{+}$ to produce ${\text{NO}}_{3}^{-}$ while respiring O_{2}(g). Develop a balanced redox reaction for this process (nitrification) and calculate log K. What is the ratio of ${\text{NO}}_{3}^{-}$ to ${\text{NO}}_{2}^{-}$ concentration when pE = 7 at pH 6?
Methane oxidation coupled to denitrification with N_{2}(g) as the product has been observed below the oxic zone in freshwater sediments such as that described in Fig. 6.2. Develop a balanced redox reaction for this process and calculate log K.
Develop reduction half-reactions relating ${\text{NO}}_{2}^{-}$ and ${\text{NH}}_{4}^{+}$ to N_{2}(g). Compare the rungs occupied by these two half-reactions on the redox ladder at pH 7 to that occupied by the denitrification half-reaction relating ${\text{NO}}_{3}^{-}$ to N_{2}(g). Assume ${\text{P}}_{{\text{N}}_{2}}$ = 0.78 atm along with 1 mM concentration for all aqueous species. Combine the ${\text{NO}}_{2}^{-}$ and ${\text{NH}}_{4}^{+}$ half-reactions into a single redox reaction describing anaerobic ammonium oxidation (“anammox”):
${\text{NO}}_{2}^{-}+{\text{NH}}_{4}^{+}={\text{N}}_{2}(\text{g})+2{\text{H}}_{2}\text{O}(\ell )\text{\hspace{1em}}\mathrm{log}\text{K}=62.5$Perchloroethene (PCE; Cl_{2}C = CCl_{2}, top line in Fig. 3.7) is a relatively water-soluble dry-cleaning solvent that has become ubiquitous in groundwater because of improper waste disposal. This chlorinated ethene undergoes reductive dechlorination, catalyzed by bacteria, to form trichloroethene (TCE; CICH = CCl_{2}), which is a hazardous organic chemical used as a degreasing solvent:
$\frac{1}{2}\text{PCE}+\frac{1}{2}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}\text{TCE}+\frac{1}{2}{\text{Cl}}^{-}\text{\hspace{1em}}\mathrm{log}\text{K}=12.18$$\frac{1}{2}\text{TCE}+\frac{1}{2}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}\text{cDCE}+\frac{1}{2}{\text{Cl}}^{-}\text{\hspace{1em}}\mathrm{log}\text{K}=11.35$$\frac{1}{2}c\text{CDE}+\frac{1}{2}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}\text{VC}+\frac{1}{2}{\text{Cl}}^{-}\text{\hspace{1em}}\mathrm{log}\text{K}=9.05$$\frac{1}{2}\text{VC}+\frac{1}{2}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}\text{ETH}+\frac{1}{2}{\text{Cl}}^{-}\text{\hspace{1em}}\mathrm{log}\text{K}=8.82$Prepare a redox ladder for the hazardous elements Cr, As, and Se based on the following reduction half-reactions:
$\frac{1}{3}{\text{CrO}}_{4}^{2-}+\frac{5}{3}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{3}\text{Cr}{\left(\text{OH}\right)}_{3}(\text{s})+\frac{1}{3}{\text{H}}_{2}\text{O}(\ell )\text{\hspace{1em}}\mathrm{log}\text{K}=21.06$$\frac{1}{2}{\text{H}}_{2}{\text{AsO}}_{4}^{-}+\frac{3}{2}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}\text{As}{\left(\text{OH}\right)}_{3}^{0}+\frac{1}{2}{\text{H}}_{2}\text{O}(\ell )\text{\hspace{1em}}\mathrm{log}\text{K}=10.84$$\frac{1}{2}{\text{H}}_{2}{\text{AsO}}_{4}^{2-}+2{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}\text{As}{\left(\text{OH}\right)}_{3}^{0}+{\text{H}}_{2}\text{O}(\ell )\text{\hspace{1em}}\mathrm{log}\text{K}=14.32$$\frac{1}{2}{\text{SeO}}_{4}^{2-}+\frac{3}{2}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{2}{\text{HSeO}}_{3}^{-}+\frac{1}{2}{\text{H}}_{2}\text{O}(\ell )\text{\hspace{1em}}\mathrm{log}\text{K}=13.14$$\frac{1}{4}{\text{HSeO}}_{3}^{-}+\frac{5}{4}{\text{H}}^{+}+{\text{e}}^{-}=\frac{1}{4}\text{Se}(\text{s})+\frac{3}{4}{\text{H}}_{2}\text{O}(\ell )\text{\hspace{1em}}\mathrm{log}\text{K}=13.14$(p.129) Over what pH range will poising by fermentation, represented by the acetate/CO_{2} couple, be favorable to the reductive dissolution of goethite? Take ${\text{P}}_{{\text{CO}}_{2}}$ = 10^{–2.5} atm, (acetate) = 10^{–6}, and (Fe^{2+}) = 10^{–5}.
Over what range of pH will poising by the reductive dissolution of MnO_{2}(s) be favorable to the complete reductive dechlorination of PCE to ETH (see problem 5)? Take (Cl^{–}) = 2 × 10^{–3} and (Mn^{2+}) = 10^{–2}.
Discuss the changes in Fig. 6.5 that would occur if (1) goethite were the Fe(III) mineral instead of Fe(OH)_{3}(s) or (2) the activity of Fe^{2+} were increased to 10^{–3}.
Measurements of E_{H} along a climosequence in Hawaii (annual rainfall range, 2200–5000 mm) showed that ferrihydrite began disappearing from soil profiles when the average electrode potential dropped below 330 mV (annual rainfall, 4000 mm), and disappeared entirely when E_{H} reached –100 mV (annual rainfall, 5000 mm). Construct a pE–pH diagram like that in Fig. 6.5 for ${\text{P}}_{{\text{CO}}_{2}}$ = 10^{–2} atm to interpret these observations, given that the soil pH = 5.0.
Prepare a pE–pH diagram for the three redox species MnO_{2}(s), MnCO_{3}(s), and Mn^{2+} given (Mn^{2+}) = 10^{–3} and ${\text{P}}_{{\text{CO}}_{2}}$ = 0.12 atm. Figure 6.5 can serve as a guide, but shift the pE range to acknowledge the difference between anoxic and suboxic conditions.