Redox disequilibrium

The equilibrium model, despite its limitations, in many ways provides a useful if occasionally abstract description of the chemical states of natural waters. However, if used to predict the state of redox reactions, especially at low temperature, the model is likely to fail. This shortcoming does not result from any error in formulating the thermodynamic model. Instead, it arises from the fact that redox reactions in natural waters proceed at such slow rates that they commonly remain far from equilibrium. 

Complicating matters further is the fact that the platinum electrode, the standard tool for measuring Eh directly, does not respond to some of the most important redox couples in geochemical systems. The electrode, for example, responds incorrectly or not at all to the couples SO -HS-, O2-H2O, CO2-CH4, NOJ-N2, and N2-NH4 (Stumm and Morgan, 1996 Hostettler, 1984). In a laboratory experiment, Runnells and Lindberg (1990) prepared solutions with differing ratios of selenium in the Se4+ and Se6+ oxidation states. They found that even under controlled conditions the platinum electrode was completely insensitive to the selenium composition. The meaning of an Eh measurement from a natural water, therefore, may be difficult or impossible to determine (e.g., Westall, 2002). 

Geochemists (e.g., Thorstenson et al., 1979 Thorstenson, 1984) have long recognized that at low temperature many redox reactions are unlikely to achieve equilibrium, and that the meaning of Eh measurements is problematic. Lindberg and Runnells (1984) demonstrated the generality of the problem. They compiled from the WATSTORE database more than 600 water analyses that provide at least two measures of oxidation state. The measures included Eh, dissolved oxygen content, concentrations of dissolved sulfate and sulfide, ferric and ferrous iron, and so on. 

They calculated species distributions for each sample and then computed the Nernst Eh for the redox couples in the analysis. Their results show that the redox couples generally failed to achieve equilibrium with each other, varying per sample by as much as 1000 mV. In addition, they could demonstrate little relationship between measured and Nernst Eh values. Similarly, Criaud et al. (1989) computed discordant Nernst Eh values for low-temperature geothermal fluids from the Paris basin. 

There are, fortunately, some instances in which measured Eh values can be interpreted in a quantitative sense. Nordstrom et al. (1979), for example, showed that Eh measurements in acid mine drainage accurately reflect the aFe+++/aFe++ ratio. They further noted a number of other studies establishing agreement between measured and Nernst Eh values for various couples. Nonetheless, it is clearly dangerous for a geochemical modeler to assume a priori that a sample is in internal redox equilibrium or that an Eh measurement reflects a sample s redox state. 

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A flexible method for modeling redox disequilibrium is to divide the reaction database into two parts. The first part contains reactions between the basis species (e.g., Table 6.1) and a number of redox species, which represent the basis species in alternative oxidation states. For example, redox species Fe+++ forms a redox pair with basis species Fe++, and HS- forms a redox pair with SO4. These coupling reactions are balanced in terms of an electron donor or acceptor, such as 02(aq). Table 7.1 shows coupling reactions from the llnl database. 

Models of natural waters calculated assuming redox disequilibrium generally require more input data than equilibrium models, in which a single variable constrains the system s oxidation state. The modeler can decouple as many redox pairs as can be independently constrained. A completely decoupled model, therefore, would require analytical data for each element in each of its redox states. Unfortunately, analytical data of this completeness are seldom collected. 

As an example of modeling a fluid in redox disequilibrium, we use an analysis, slightly simplified from Nordstrom et al. (1992), of a groundwater sampled near the Morro do Ferro ore district in Brazil (Table 7.2). There are three measures of oxidation state in the analysis the Eh value determined by platinum electrode, the dissolved oxygen content, and the distribution of iron between ferrous and ferric species. 

To account for the possibility of redox disequilibrium among iron species, we use the analysis for ferrous as well as total iron ... 

By decoupling the ferric-ferrous reaction with the decouple command, we add Fe+++ as a new basis entry in the calculation, setting up a model in which O2 and iron are held in redox disequilibrium. We constrain the new entry using the difference between the total and ferrous iron contents. 

Table 7.3. Concentrations (molal) of predominant iron species in Morro do Ferro groundwater, calculated assuming equilibrium and redox disequilibrium...

To trace a reaction path incorporating redox kinetics, we first set a model in redox disequilibrium by disabling one or more redox couples, then specify the reaction in question and the rate law by which it proceeds. To model the progress of Reaction 17.1, for example, we would disable the redox couple between vanadyl and vanadate species. In a model of the oxidation of Fe++ by manganite (MnOOH), we would likely disable the couples for both iron and manganese. 

Using the modified thermodynamic database, we simulate reaction over 300 minutes in a fluid buffered to a pH of 7. We prescribe a redox disequilibrium model by disabling redox couples for chromium and sulfur. We set 10 mmolal NaCl as the background electrolyte, initial concentrations of 200 (imolal for CrVI and 800 innolal for H2S, and small initial masses of Cr2C>3 and S(aq). Finally, we set Equation 17.29 as the rate law and specify that pH be held constant over the simulation. 

Most of the reactions that involve significant fractionation of Se and Cr isotopes appear to be far from chemical or isotopic equihbrium at earth-surface temperatures. Redox disequilibrium is common among dissolved Se species. Dissolved Se(IV) and solid Se(0) are often observed in oxic waters despite their chemical instability (Tokunaga et al. 1991 Zhang and Moore 1996 Zawislanski and McGrath 1998). In one study of shallow groundwater, Se species were found to be out of equilibrium with other redox couples such as Fe(III)/Fe(II) (White and Dubrovsky 1994). The kinetics of abiotic Se(VI) reduction, like those of sulfate, are quite slow. In the laboratory, conversion of Se(VI) to Se(IV) requires one hour of heating to ca. 100°C in a 4 M HCl medium. 

Biologically mediated redox reactions tend to occur as a series of sequential subreactions, each of which is catalyzed by a specific enzyme and is potentially reversible. But despite favorable thermodynamics, kinetic constraints can slow down or prevent attainment of equilibrium. Since the subreactions generally proceed at unequal rates, the net effect is to make the overall redox reaction function as a imidirectional process that does not reach equilibrium. Since no net energy is produced imder conditions of equilibrium, organisms at equilibrium are by definition dead. Thus, redox disequilibrium is an opportunity to obtain energy as a reaction proceeds toward, but ideally for the sake of the organism does not reach, equilibrium. 

Of the various factors that cause redox disequilibria, the most effective are biologic activity (photosynthesis) and the metastable persistence of covalent complexes of light elements (C, H, O, N, S), whose bonds are particularly stable and difficult to break (Wolery, 1983). For the sake of completeness, we can also note that the apparent redox disequilibrium is sometimes actually attributable to analytical error or uncertainty (i.e., difficult determination of partial molalities of species, often extremely diluted) or even to error in speciation calculations (when using, for instance, the redox couple Fe /Fe, one must account for the fact that both Fe and Fe are partly bonded to anionic ligands so that their free ion partial molalities do not coincide with the bulk molality of the species). 

Information on the speciation states of solutes and their equilibria with condensed phases furnished by Eh-pH diagrams is often simply qualitative and should be used only in the initial stages of investigations. The chemical complexity of natural aqueous solutions and the persistent metastability and redox disequilibrium induced by organic activity are often obstacles to rigorous interpretation of aqueous equilibria. 

O Shea (2006) has summarized the redox steps involved in the mobilization of arsenic in natural hydro-logic systems (Table 6.2). It should be noted that in natural environments, discrete redox zones are not always observable and redox disequilibrium can occur, thus complicating arsenic mobilization and resorption (Mukherjee, 2006). 

Thallium (Tl), which appears to exhibit conservative behaviour in seawater, has two potential oxidation states. As Tl1, thallium is very weakly complexed in solution. In contrast, Tl111 should be strongly hydrolysed in solution ([T13+]/[T13+]t — 10 20 5) with Tl(OH)3 as the dominant species over a very wide range of pH. The calculation of Turner et at. (1981) indicated thatTl111 is the thermodynamically favoured oxidation state at pH 8.2. Lower pH and p()2 would be favourable to Tl1 formation. Within the water column, pH can be considerably less than 8.2 and /)( )2 lower than 0.20 atm. In view of these factors, and the observation that redox disequilibrium in seawater is not uncommon, the oxidation state of Tl in seawater is somewhat uncertain. The existence of Tl in solution as Tl+, a very weakly interactive ion, would reasonably explain the conservative behaviour of Tl in seawater. However, the extremely strong solution complexation of Tl3+ suggests that Tl3+ may be substantially less particle reactive than other Group 13 elements (with the exception of boron). 

The failure of antioxidant mechanisms to correct redox disequilibrium could lead to the escalation of oxidative to tier 2. Tier 2 cellular responses are characterized by the activation of cellular signaling pathway such as stress-activated kinases (p38 MAP kinase and JNK) along with activation and nuclear translocation of transcription factors NF-kB and STAT-1. NF-KB-induced transcriptional activation leads to the production of a number of pro-inflammatory cytokines, including the neutrophil chemoattractant IL-8. STAT-1 activation stimulates the increased production of CXC-motif chemokines that function in lymphocyte recruitment and activation. Therefore, tier 2 oxidative responses result in an inflammatory response in the lung. 

The results also show redox disequilibrium in the waste pond, which is not unusual. The analytical data show the co-existence of organic carbon, carbonate, nitrate, and ammonia in the pond. This has not been modeled in our example, because we did not feel it was an important part of the problem.4... 

Note that to model redox disequilibrium in phreeqc, a new species must be defined for each disequilibrium redox species (Parkhurst and Appelo, 1999, Example 15). Program react (The Geochemist s Workbench ) has a simpler decouple command. 

Redox Disequilibrium in the Aqueous Phase. Aqueous redox disequilibrium modeling is permitted in the 3245 version of EQ3NR, but not the corresponding version of EQ6. It will be permitted in the 3270 version of EQ6. This will allow, for example, calculation of seawater/basalt reaction models in which total sulfate is conserved instead of partially reduced to sulfide. 

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