## Garrison Sposito

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Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780190630881.001.0001

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# Oxidation– Reduction Reactions

Chapter:
6 Oxidation– Reduction Reactions
Source:
The Chemistry of Soils
Publisher:
Oxford University Press
DOI:10.1093/oso/9780190630881.003.0010

# 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.

# (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 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. (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 H2 and CO2. The reported concentrations of acetate (millimolar) and H2 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 CH4 production commences.

Figure 6.1 Temporal sequences of chemical transformations induced by flooding an Inceptisol (left) and a Vertisol (right). Inceptisol data from Peters, V., and R. Conrad. (1996) Sequential reduction processes and initiation of CH4 production upon flooding of oxic upland soils. Soil Biol. Biochem. 28:371–382. Vertisol data from Yao, H., R. Conrad, H. Wassmann, and H. U. Neue. (1999) Effect of soil characteristics on sequential reduction and methane production in sixteen rice paddy soils from China, the Philippines, and Italy. Biogeochemistry 47:269–295.

Similar trends occur in the Vertisol (right side of Fig. 6.1), which was maintained under paddy conditions before sampling. Nitrate disappears quickly, whereas $SO42−$ 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 H2 also follow the same trend as the Inceptisol. The time trend of CO2 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 CO2 and CH4 produced resulted in the loss of just 8% of the initial total organic C in the soil, with 85% of this loss manifest as CO2. Thus, most of the labile humus C converted into gases is used to produce CO2 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 O2, $SO42−$, CH4, 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 $SO42−$, suggests precipitation of secondary Fe(II) sulfides. Layer D, which has no detectable $SO42−$, is associated with the increase of significant CH4 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.

Figure 6.2 Profile of chemical transformations in freshwater sediments. Data from Kappler, A., M. Benz, B. Schink, and A. Brune. (2004) Electron shuttling via humic acids in microbial iron(III) reduction in a freshwater sediment. FEMS Microbiol. Ecol. 47:85–92.

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 $SO42−$ and the production of CH4. Such effects, however, do not occur if typical fermentation products, such as H2 gas or acetic acid, are added. Amending a soil low in labile humus with ferrihydrite particles (Section 2.4) suppresses the depletion of soluble $SO42−$ and slows the production of CH4, whereas addition of soluble $SO42−$ by itself inhibits CH4 production, but these effects again can be reversed by supplying fermentation products, especially H2 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, H2 gas is driven to much lower concentrations in the soil solution by the production of soluble Fe than it is by CH4 production (there is a hint of this in Fig. 6.1), suggesting that the H2-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), $CHO2−$ (formate), N2, $SO42−$, and C6H12O6 (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 N2, 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 O2 and H2.) 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 C6H12O6 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 O2 is the oxidant accepting the electrons. In the reductive dissolution reaction,

(6.1)
$FeOOH(s)+3H++e−=Fe2++2H2O(l)$
goethite is the oxidant in which Fe accepts an electron (e) from an as-yet unidentified reductant, then dissolves under attack by aqueous protons to produce the soluble species Fe2+ plus liquid water. This reduction reaction offers a mechanism for the rise in soluble Fe noted in Fig. 6.1. Equation 6.1 is termed a reduction half-reaction because the source of the aqueous electron has not been identified.

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 CO2 accepts an aqueous electron and binds with protons to be transformed into acetate plus liquid water:

(6.2)
$14CO2(g)+78H++e−=18CH3CO2−+14H2O(l)$

(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 ($CH3CO2−$), the reductant, to create the redox reaction

(6.3)
$FeOOH(s)+18CH3CO2−+178H+=Fe2++14CO2(g)+74H2O(ℓ)$

This redox reaction, which is consistent with observations made about the concurrent rise in soluble Fe and CO2 depicted in Fig. 6.1, is catalyzed by the biogeochemical guild of iron-reducing bacteria that consume acetate and produce CO2. 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 $NO3−$ reduction to $NH4+$ 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 H2 gas to form aqueous protons.

Table 6.1 Reduction half-reactions and their equilibrium constants at 25 °C

Reduction half-reaction

Log K

$14O2(g)+H++e−=12H2O(ℓ)$

20.75

$12O2(g)+H++e−=12H2O2$

11.50

$H++e−=12H2(g)$

0.00

$13NO3−+43H++e−=13NO(g)+23H2O(ℓ)$

16.15

$12NO3−+H++e−=12NO2−+12H2O(ℓ)$

14.15

$14NO3−+54H++e−=18N2O(g)+58H2O(ℓ)$

18.90

$15NO3−+65H++e−=110N2(g)+35H2O(ℓ)$

21.05

$18NO3−+54H++e−=18NH4++38H2O(ℓ)$

14.90

$Mn3++e−=Mn2+$

25.50

$MnOOH(s)+3H++e−=Mn2++2H2O(ℓ)$

25.36

$12Mn3O4(s)+4H++e−=32Mn2++2H2O(ℓ)$

30.68

$12MnO2(s)+2H++e−=12Mn2++H2O(ℓ)$

21.82

$12MnO2(s)+12CO2(g)+H++e−=12MnCO3(s)+12H2O(ℓ)$

18.00

$Fe3++e−=Fe2+$

13.00

$12Fe2++e−=12Fe(s)$

−7.93

$Fe(OH)3(s)+3H++e−=Fe2++3H2O(ℓ)$

17.14

$FeOOH(s)+3H++e−=Fe2++2H2O(ℓ)$

13.34

$12Fe3O4(s)+4H++e−=32Fe2++2H2O(ℓ)$

18.16

$12Fe2O3(s)+3H++e−=Fe2++32H2O(ℓ)$

12.96

$14SO42−+54H++e−=18S2O32−+58H2O(ℓ)$

4.85

$18SO42−+98H++e−=18HS−+12H2O(ℓ)$

4.25

$18SO42−+54H++e−=18H2S+12H2O(ℓ)$

5.13

$12CO2(g)+12H++e−=12CHO2−$

−5.22

$14CO2(g)+78H++e−=18C2H3O2−+14H2O(ℓ)$

−1.20

$730CO2(g)+2930H++e−=130C6H5COO−+25H2O(ℓ)$

1.76

$14CO2(g)+112NH4++1112H++e−=112C3H4O2NH3+13H2O(ℓ)$

0.84

$14CO2(g)+H++e−=124C6H12O6+14H2O(ℓ)$

−0.20

$18CO2(g)+H++e−=18CH4(g)+14H2O(ℓ)$

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:

(6.4)
$K=(Fe2+)(CO2)1/4(H2O)7/4(FeOOH)(H+)17/8(CH3CO2−)1/8=1014.54$

If the activities of goethite and water are set equal to 1.0, and the usual conventions for the activities of CO2(g) and H+ are used, then Eq. 6.4 reduces to the expression

(6.5)
$(Fe2+)Pco21/41017/spH/(CH3CO2−)1/8=1014.54$

(p.113) (p.114) Choosing pH 6 and = 10–3.52 atm as representative values, one reduces this equation to an even simpler expression:

(6.6)
$(Fe2+)(CH3CO2−)1/8=102.67≈468$

For millimolar soluble Fe(II) [(Fe2+) = 10–3], which is typical of a flooded soil, Eq. 6.6 predicts ≈ 10–45, showing that acetate would be completely oxidized to CO2 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;

(6.7)
$pE≡−log(e−)$

(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

H2O(ℓ) + H+ = H3O+

log K ≡ 0

Acid–base

$H++e−=12H2(g)$

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 O2 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 O2 reduction half-reaction (the first one listed in Table 6.1) and taking pH = 7, one finds

$pE=logK+log[(O2)1/4(H2O)1/2]−pH=20.75+14logPO2−7 =20.75−0.25−7=+13.50$

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 MnO2(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 (MnO2) = 1.0]:

$pE=21.82−12log(Mn2+)−14=7.82−12log(Mn2+)≈+8.8$
if (Mn2+) ≈ 10–2. Anoxic soils can be characterized by the next step in the sequence of transformations in Fig. 6.1: the reductive dissolution of Fe(III) oxyhydroxide. Returning to Eq. 6.1 as an example, one finds, at pH 7,
$pE=13.34−log(Fe2+)−21.0=−7.66−log(Fe2+)≈−4.66$
if (Fe2+) ≈ 10–3. If the reductive dissolution of Fe(OH)3(s), a poorly crystalline solid phase, were instead selected to perform the calculation (its reductive dissolution half-reaction is listed directly above that for goethite in Table 6.1), one finds pE ≈ –0.86 under the same conditions.

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

(6.8)
$mAax+nH++e−=pAred+qH2O(ℓ)$
where A is a chemical species and “ox” or “red” designates its oxidized or reduced forms, respectively. The two species Aox and Ared related through the half-reaction in Eq. 6.8 are termed a redox couple. In Eqs. 6.1 and 6.2, for example, the redox couples are goethite/Fe2+ and CO2/acetate, respectively. Besides the redox couple, the generic reduction half-reaction features the proton as a reactant and liquid water as a product. Therefore, one may conclude quite generally that reduction results in proton consumption, leading to an increase in pH. Thus, each reduction half-reaction in Table 6.1 represents a mechanism for decreasing soil acidity. Conversely, oxidation reactions increase soil acidity.

Equation 6.8 leads in the usual way to an equation for pE [assuming (H2O) = 1.0]:

(6.9)
$pE=logK+log[ (Aox)m(Ared)p ]−npH$
which is a generic form of the expressions used to calculate pE values for the redox couples that define oxic, suboxic, and anoxic conditions in soils. Equation 6.9 can be applied to any reduction half-reaction listed in Table 6.1 to calculate a pE value corresponding to the transformation the half-reaction represents. This calculation is illustrated in Fig. 6.3, which delineates pE values corresponding to the sequence of chemical transformations discussed in connection to Figs. 6.1 and 6.2. The arrows pointing into the boxes locate these pE values at pH 7 while (p.117) denoting the source of aqueous electrons as humus or H2 gas. Differing biogeochemical guilds oxidize one or the other of these two reductants while transforming the oxidant they respire into a reductant. This reductant, plus H2O and CO2 from the oxidation of humus, are indicated as respiration products labeling the arrows pointing out of the boxes. With pE identified as its quantitative signature, the sequence of transformations in flooded soils corresponds to a sequence of reductions at descending pE values.

Figure 6.3 Typical chemical transformations in flooded soils indexed by their pE values at pH 7, denoted by the location of arrows pointing into the boxes. For each transformation, reductants used by the catalyzing biogeochemical guild are indicated below these arrows, whereas products of the transformation are indicated above the arrows pointing out of the boxes. Concept from Falkowski, P. G., T. Fenchel, and E. F. Delong. (2008) The microbial engines that drive Earth’s biogeochemical cycles. Science 320:1034–1039.

# 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 (H2O(ℓ)) = 1.0.

Rule 2: If the oxidant and reductant are in the same phase, then (Aox) and (Ared) are each set equal to 1.0, yielding a simplified version of Eq. 6.9:

(6.10)
$pE=logK−npH$

Example: The reduction of $SO42−$ to form bisulfide ($HS−$) is described by the reduction half-reaction (Table 6.1)

(6.11)
$18SO42−+98H++e−=18HS−+12H2O(ℓ)$
for which log K = 4.25 at 25 °C. Because both species in the redox couple are aqueous species, Eq. 6.10 can be used and placement of the redox couple $SO42−/HS−$ on the ladder is at pE = –3.63, if pH = 7 (Fig. 6.4). If the activities of the oxidant and reductant are known, they should be used to calculate pE according to the more general Eq. 6.9. For example, ($SO42−$) and (HS) = 10–6 could occur in groundwater, leading to pE = –3.29 at pH 7. Note the small effect on the pE value.

Figure 6.4 A redox ladder constructed for pH 7. Auxiliary conditions imposed on redox species activities are described in the text.

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 O2(g) and for the reductive dissolution of MnO2(s) and FeOOH(s). The resulting pE values are also depicted in Fig. 6.4. Another example is provided by the reduction of CO2(g) to form glucose, as occurs in photosynthesis (Table 6.1):

(6.12)
$14CO2(g)+H++e−=124C6H12O6+14H2O(ℓ)logK=−0.20$

If and (C6H12O6) ≈ 5 × 10–4 (based on a glucose concentration of 0.5 mM), then, at pH 7.0,

$pE=−0.20+14PCO2−124log(C6H12O6)−pH=−0.20−0.50+0.14−7=−7.56$

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 O2(g) in the soil atmosphere implies oxic conditions and, therefore, poising by the half-reaction for O2 reduction (Table 6.1). As shown in Section 6.2, the pE value is then poised at

(6.13)
$pE=20.75+14logPO2−pH$
which conforms to Eq. 6.9.

(p.120) If $PO2$ drops well below its atmospheric value (0.21 atm), however, O2(g) no longer will be in sufficient supply to poise pE. Poising by the reductive dissolution of MnO2(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

(6.14)
$pE=21.82−12log(Mn2+)−2pH$

Note that other oxidant Mn minerals listed in Table 6.1 are unfavored thermodynamically relative to MnO2(s), to which Eq. 6.14 applies. For example, manganite (γ -MnOOH), a precipitation product of air–oxidation of soluble Mn(II), disproportionates into MnO2(s) and Mn2+:

(6.15)
$MnOOH(s)+H+=12MnO2(s)+12Mn2++H2O(ℓ) logK=3.54$

However, manganite or hausmannite (Mn3O4) 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:

(6.16a)
$pE=17.14−log(Fe2+)−3pH$
if the oxidant is freshly precipitated, poorly crystalline Fe(OH)3(s):
(6.16b)
$pE=4.25+18log[ (SO42−)(HS−) ]−98pH$
if the oxidant is soluble $SO42−$, or
(6.16c)
$PE=2.86+18log[ PCO2PCH4 ]−pH$
if a methanogenic biogeochemical guild is active. As suggested also in Fig. 6.3, pE values for the reductive dissolution of Fe(II) oxyhydroxides, $SO42−$ reduction, and CH4 production form a cluster well down on the redox ladder (Fig. 6.4). This cluster, which includes reduction half-reactions for organic acids and other biomolecules, also locates the likely rungs on which soil humus resides in the redox ladder. Because of its highly heterogeneous composition, humus contains multiple redox-active organic moieties, each with its own reduction half-reaction. Current thinking is that the most important of these moieties are condensed polyaromatic hydrocarbons (Section 3.2 and Fig. 3.7) that include (p.121) both quinone and phenol structures. (A quinone is a benzene ring with a pair of carbonyl (C=O) substituents lying on opposite sides of the ring along an axis of symmetry.) Quinones are oxidants. If its carbonyls are both reduced and thereby transformed into C—OH groups, the phenolic product is called hydroquinone. Hydroquinones are powerful reductants.

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, $PO2$ can be measured to determine whether poising is by O2 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 (EH, in units of volts) can always be defined in terms of pE:

(6.17)
$EH≡RTFln10pE=0.05916pE(25∘C)$
where R = 8.3145 J mol–1 K–1 is the molar gas constant, T is absolute temperature (298.15 K at 25 °C), and F = 96,485 C mol–1 is the Faraday constant. Equation 6.17 is a purely formal relationship amounting to a transformation of units and does not imply that an accurate method of measuring EH exists. In practice, electrode measurements of EH are plagued by serious interferences, notably the inherent ambiguity surrounding the interpretation of a voltage measured at zero net current as a unique signature of any single redox couple (as opposed to being merely the net result from several competing redox couples) and the biased selectivity of (p.122) Pt electrodes for the highly electroactive Fe(III)/Fe(II) couple. Measured values of EH obtained from a Pt electrode thus have only qualitative significance in soils.

# 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 O2(g), whereas low pE favors reductants, such as humus and biomolecules. Suppose that pE is poised by the reductive dissolution of MnO2(s). If (Mn2+) = 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, $PO2≈10−5$ atm and O2(g) has effectively disappeared, replaced by H2O(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 Fe2+ 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 H2(g). As these electrons accumulate, dropping the pE value below around 12.0, enough of them become available to reduce O2(g) to H2O(ℓ). Under these circumstances, O2(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 $NO3−$. This reduction is catalyzed by anaerobic guilds in the soil microbiome that respire $NO3−$ and excrete $NO2−$, N2, N2O, NO, or $NH4+$. 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 $SO42−$ reduction, with typical soluble products H2S, HS, or thiosulfate ($S2O3−$) 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 O2 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 Fe2+/Fe0 couple perched at the very bottom of the redox ladder in Fig. 6.4 involves Fe(s): “zero-valent iron” (Fe0). Perched just above it on the ladder is the CO2/C6H12O6 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/Fe2+ couple is added to that for Fe2+/Fe0 to cancel Fe2+ while maintaining the stoichiometric coefficient of e at 1.0:

(6.18)
$13FeOOH(s)+H++e−=13Fe(s)+23H2O(ℓ) logK=−0.84$
a half-reaction that can be compared directly to Eq. 6.12. Both half-reactions now connect the highest to the lowest positive oxidation numbers for C and Fe, and both have remarkably similar log K values. The reverse of the reaction in Eq. 6.12 is carbon respiration, but it might be termed “carbon corrosion” instead to show its similarity to the reverse of the reaction in Eq. 6.18, which is iron corrosion. Carbon corrosion and iron corrosion are both spontaneous processes, thermodynamically speaking, and the couples CO2/C6H12O6 and FeOOH/Fe0 occupy nearly the same place on the redox ladder at any pH value. Moreover, the very low pE values at which they are perched ensures that poising a system with their half-reactions will favor the reduction of almost all oxidant species. That this possibility in the case of C has been exploited to great advantage evolutionarily in the life cycles of the biogeochemical guilds of the soil microbiome is well known. In the case of Fe, it has recently provided the principle behind engineered processes to attenuate hazardous oxidants by reducing them with iron metal.

# (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$(Si(OH)40)$ 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); FeCO3(s), siderite, an Fe(II) carbonate mineral observed in anoxic soils (Section 2.5); and the aqueous species, Fe2+. 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,

(6.19)
$FeCO3(s)=Fe2++CO32− logKs0=−10.8$
is expressed more conveniently for the current application after combining it with Eq. 5.25, and the bicarbonate dissociation reaction,
(6.20)
$HCO3−=H++CO32− logK2=−10.329$
(p.125) similar to what was done to transform the calcite dissolution reaction in Section 5.5. The resulting dissolution reaction is
(6.21)
$FeCO3(s)+2H+=Fe2++H2O(ℓ)+CO2(g)$
for which log K = –10.8 + 1.462 + 6.352 + 10.329 = 7.34 at 25 °C. Note the similarity to Eq. 5.12c, although the difference in log K values indicates that siderite is less soluble than calcite. The final reaction needed to construct a pE–pH diagram is found by combining the two mineral dissolution reactions:
(6.22)
$Fe(OH)3(s)+CO2(g)+H++e−=FeCO3(s)+2H2O(ℓ)$
for which log K = 17.14 – 7.34 = 9.80 at 25 °C. Note the similarity to the reaction in Table 6.1 relating MnO2(s) to MnCO3(s).

The pE–pH relationships that define the boundary lines in a pE–pH diagram describing the three Fe redox species are then

(6.23a)
$pE=17.14−log(Fe2+)−3pH$
(6.23b)
$0=7.34−log(Fe2+)−logPCO2−2pH$
(6.23c)
$pE=9.80+logPcO2−pH$

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 (Fe2+) and $PCO2$ are selected. Reference to Fig. 6.1 indicates that $PCO2$ ≈ 0.12 atm after about 100 days of incubation of the Philippines soil. A measured value of (Fe2+) is not available, but (Fe2+) ≈ 2 × 10–4 is reasonable for a flooded acidic soil. With these data incorporated, Eq. 6.23 become the set of boundary-line equations

(6.24a)
$pE=20.84−3pH$
(6.24b)
$pH=5.98$
(6.24c)
$pE=8.88−pH$

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 Fe2+ 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 Fe2+ as the predominant species under the given conditions of Fe2+ activity and CO2 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 (Fe2+) or $PCO2$ For example, if (Fe2+) decreases to 10–6, or if $PCO2$ decreases to 10–3.52 atm (the atmospheric value), the pH value for siderite precipitation is increased to about 7.0. Increasing (Fe2+) 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 CO2 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 FeCO3(s) field.

Figure 6.5 A pE–pH diagram for the system Fe(OH)3(s), FeCO3(s), and Fe2+.

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 $NO2−$ resulting from the microbial oxidation of $NH4+$ to produce $NO3−$ while respiring O2(g). Develop a balanced redox reaction for this process (nitrification) and calculate log K. What is the ratio of $NO3−$ to $NO2−$ concentration when pE = 7 at pH 6?

• Methane oxidation coupled to denitrification with N2(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 $NO2−$ and $NH4+$ to N2(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 $NO3−$ to N2(g). Assume $PN2$ = 0.78 atm along with 1 mM concentration for all aqueous species. Combine the $NO2−$ and $NH4+$ half-reactions into a single redox reaction describing anaerobic ammonium oxidation (“anammox”):

$NO2−+NH4+=N2(g)+2H2O(ℓ) logK=62.5$
Anammox can account for up to 40% of the N2(g) produced by denitrification in rice paddies receiving ammonium fertilizer.

• Perchloroethene (PCE; Cl2C = CCl2, 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 = CCl2), which is a hazardous organic chemical used as a degreasing solvent:

$12PCE+12H++e−=12TCE+12Cl− logK=12.18$
(p.128) The product species TCE then undergoes reductive dechlorination to form cis1,2-dichloroethene (cDCE),
$12TCE+12H++e−=12cDCE+12Cl− logK=11.35$
which can be dechlorinated reductively to form monochloroethene (or VC, vinyl chloride):
$12cCDE+12H++e−=12VC+12Cl− logK=9.05$
Finally, VC can be transformed into the relatively harmless ethene (ETH, H2C = CH2):
$12VC+12H++e−=12ETH+12Cl− logK=8.82$
Prepare a redox ladder for this set of reduction half-reactions under the assumption that (Cl) = 2 × 10–3. Compare your results with the principal redox couples in Fig. 6.4. At what value should pE be poised at pH 7 so a plume of PCE can be biodegraded completely to ETH by reductive dechlorination?

• Prepare a redox ladder for the hazardous elements Cr, As, and Se based on the following reduction half-reactions:

$13CrO42−+53H++e−=13Cr(OH)3(s)+13H2O(ℓ) logK=21.06$
$12H2AsO4−+32H++e−=12As(OH)30+12H2O(ℓ) logK=10.84$
$12H2AsO42−+2H++e−=12As(OH)30+H2O(ℓ) logK=14.32$
$12SeO42−+32H++e−=12HSeO3−+12H2O(ℓ) logK=13.14$
$14HSeO3−+54H++e−=14Se(s)+34H2O(ℓ) logK=13.14$
Assume pH 7.0 and aqueous species concentrations of 1.0 μM. Given that reduced forms of the three elements are the less toxic forms, which of them can be detoxified by poising pE at pH 7 with the reductive dissolution of MnO2(s)? Take (Mn2+) = 10–3.

• (p.129) Over what pH range will poising by fermentation, represented by the acetate/CO2 couple, be favorable to the reductive dissolution of goethite? Take $PCO2$ = 10–2.5 atm, (acetate) = 10–6, and (Fe2+) = 10–5.

• Over what range of pH will poising by the reductive dissolution of MnO2(s) be favorable to the complete reductive dechlorination of PCE to ETH (see problem 5)? Take (Cl) = 2 × 10–3 and (Mn2+) = 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 Fe2+ were increased to 10–3.

• Measurements of EH 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 EH reached –100 mV (annual rainfall, 5000 mm). Construct a pE–pH diagram like that in Fig. 6.5 for $PCO2$ = 10–2 atm to interpret these observations, given that the soil pH = 5.0.

• Prepare a pE–pH diagram for the three redox species MnO2(s), MnCO3(s), and Mn2+ given (Mn2+) = 10–3 and $PCO2$ = 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.