Thermodynamic Characterization of Iron Oxide−Aqueous Fe2+ RedoxCouplesChristopher A. Gorski,*,† Rebecca Edwards,† Michael Sander,‡ Thomas B. Hofstetter,§,‡

and Sydney M. Stewart†

†Department of Civil & Environmental Engineering, Pennsylvania State University, 212 Sackett Building, University Park,Pennsylvania 16802, United States‡Institute of Biogeochemistry and Pollutant Dynamics (IBP), Swiss Federal Institute of Technology, ETH Zurich, 8092 Zurich,Switzerland§Eawag, Swiss Federal Institute of Aquatic Science and Technology, CH-8600 Dubendorf, Switzerland

*S Supporting Information

ABSTRACT: Iron is present in virtually all terrestrial and aquatic environments, where itparticipates in redox reactions with surrounding metals, organic compounds, contaminants,and microorganisms. The rates and extent of these redox reactions strongly depend on thespeciation of the Fe2+ and Fe3+ phases, although the underlying reasons remain unclear. Inparticular, numerous studies have observed that Fe2+ associated with iron oxide surfaces (i.e.,oxide-associated Fe2+) often reduces oxidized contaminants much faster than aqueous Fe2+

alone. Here, we tested two hypotheses related to this observation by determining if solutionscontaining two commonly studied iron oxideshematite and goethiteand aqueous Fe2+

reached thermodynamic equilibrium over the course of a day. We measured reductionpotential (EH) values in solutions containing these oxides at different pH values and aqueousFe2+ concentrations using mediated potentiometry. This analysis yielded standard reductionpotential (EH

0 ) values of 768 ± 1 mV for the aqueous Fe2+−goethite redox couple and 769 ± 2 mV for the aqueous Fe2+−hematite redox couple. These values were in excellent agreement with those calculated from existing thermodynamic data, andthe data could be explained by the presence of an iron oxide lowering EH values of aqueous Fe3+/Fe2+ redox couples.

■ INTRODUCTION

Iron (Fe) oxides and hydroxides (collectively referred to hereas “iron oxides”) are present in virtually all aquatic environ-ments, where they participate in redox reactions withsurrounding microorganisms, nutrients, metals, and organiccompounds.1−5 These redox reactions profoundly impact theenvironment by influencing organic carbon degradation andsequestration,6−9 global biogeochemical cycles,3,10 rock weath-ering and diagenesis,2 corrosion,11 and microbial activity.5,12

These redox reactions are particularly important for ground-water remediation efforts because they produce Fe2+ that canabiotically reduce several classes of oxidized environmentalcontaminants to less toxic or less mobile forms, includingchlorinated solvents, radionuclides, toxic metals and metalloids,and pesticides.13−19 The rates and extents of these redoxreactions strongly depend on the speciation of Fe2+, which hasimportant ramifications for interpreting the roles iron plays inbiogeochemical cycles as well as pollutant dynamics.20,21 Inparticular, numerous studies have found that Fe2+ associatedwith iron oxide surfaces reduces oxidized contaminants muchfaster than aqueous Fe2+ alone.17−32 Multiple hypotheses havebeen proposed to interpret this phenomenon.The hypothesis most commonly invoked to explain why iron

oxides influence the redox reactivity of Fe2+ is that Fe2+

associated with oxide surfaces has a lower (i.e., more reducing)

reduction potential (EH) value than aqueous Fe2+ in the sameaqueous system.17,20,25,27 This hypothesis is founded on theargument that Fe2+ associated with oxide surfaces has a higherelectron density than aqueous Fe2+ as a result of it becominghydrolyzed at the oxide surface (e.g., to form ≡Fe3+OFe2+OHsurface complexes).4,33−35 While this hypothesis has been usedas a foundation to model contaminant reduction ratesaccurately,27 there are two lines of reasoning that question itsvalidity. First, extensive experimental and theoretical work hasfound that Fe2+ does not form stable, adsorbed complexes oniron oxide surfaces under the experimental conditions used inmany of these studies,36−49 drawing into question if surfacecomplexation modeling is the appropriate conceptual frame-work to interpret results.47,49−55 For this reason, we refer toFe2+ associated with oxide surfaces as “oxide-associated Fe2+” inthis paper, as opposed to the more commonly used term of“adsorbed Fe2+”. Second, and more importantly, an implicit(and often unrecognized) assumption of this model is thataqueous Fe2+ and oxide-associated Fe2+ do not reach redoxequilibrium with each other, despite having reached sorptive

Received: May 27, 2016Revised: July 15, 2016Accepted: July 18, 2016Published: July 18, 2016

Article

pubs.acs.org/est

© 2016 American Chemical Society 8538 DOI: 10.1021/acs.est.6b02661Environ. Sci. Technol. 2016, 50, 8538−8547

equilibrium.56,57 If the two phases were in redox equilibrium,then a single EH value would describe the redox couplesinvolving both aqueous Fe2+ and oxide-associated Fe2+.An alternative hypothesis to explain the enhanced reactivity

of Fe2+ in the presence of an iron oxide has been proposed byFelmy and co-workers.56,57 This model posits that the systemsdo reach redox equilibrium, and that the presence of an ironoxide changes redox reaction rates by altering the oxidationproduct that forms when oxidizing Fe2+. When aqueous Fe2+

oxidizes in solution without any solid phases present, it typicallyforms aqueous Fe3+ complexes or ferrihydrite.58 When aqueousFe2+ or oxide-associated Fe2+ oxidize in the presence of acrystalline iron oxide, however, it can lead to the growth ofexisting iron oxide particles.29,59,60 Since highly crystalline ironoxides have more negative Gibbs free energy (ΔG0) values thanferrihydrite, the standard reduction potential (EH

0 ) values forredox couples between Fe2+ and highly crystalline iron oxidesare more negative than for a redox couple between Fe2+ andferrihydrite.The goal of this study was to test these two hypotheses by

determining if aqueous Fe2+ reaches thermodynamic equili-brium with two commonly studied iron oxides−goethite (α-FeOOH) and hematite (α-Fe2O3)over time scales relevantto those used in previous contaminant fate studies (i.e.,approximately 1 day). If the suspensions reach thermodynamicequilibrium, then coexisting oxide-associated Fe2+ and aqueousFe2+ must be described by the same EH value. To determine ifthermodynamic equilibrium was reached, we measured EHvalues for several solutions containing suspended iron oxideparticles as a function of aqueous Fe2+ concentration and pH.We fit these data to calculate thermodynamic values for therelevant half reactions, then compared them with thermody-namic values obtained from calorimetric measurements. Wealso determined if contaminant reduction by Fe2+ was faster inthe presence of goethite than in its absence for the experimentalconditions used in this study by employing nitrobenzene as amodel oxidized contaminant.To achieve our goal, the main objective of this work was to

develop an experimental methodology to accurately measureEH of aqueous suspensions containing iron oxide particles andaqueous Fe2+ by overcoming well-documented experimentalchallenges. Prior work has shown that that EH measurements ofsolutions containing iron oxide particles made using conven-tional Pt redox electrodes are susceptible to kinetic artifactsbecause the redox equilibration between the electrode andsuspension is sluggish.44,61−64 An alternative approach todetermine EH values for solutions containing iron oxideparticles is to react the solutions with redox-active compoundsthat have well-characterized redox properties and exhibit redox-state-dependent photometric properties.21,63,65 In our previouswork, we tested the latter approach, but found that it did notprovide sufficient accuracies due to the need for highconcentrations of the compounds to achieve adequateabsorbances, which altered EH values of the suspensions.66

Here, we performed EH measurements using mediatedpotentiometry, a technique that combines elements of thetwo aforementioned approaches. In mediated potentiometry,soluble electron transfer mediators are used to facilitate redoxequilibration between an aqueous system and a redox electrodeperforming a potentiometric (i.e., open-circuit potential)measurement.21,67−71 The initial experiments discussed herewere performed to validate this approach and determine theoptimum conditions for performing mediated potentiometric

measurements of solutions containing suspended iron oxideparticles.

■ MATERIALS AND METHODSAll EH values discussed are in reference into the standardhydrogen electrode (SHE). All syntheses and experiments weredone using deionized (DI) water (Millipore Milli-Q system,resistivity >18 M Ω·cm). Details regarding the chemicals usedand the preparations of stock solutions are in Section S1 of theSupporting Information (SI). All experiments were conductedat room temperature inside an anaerobic glovebox (MBraunUnilab Workstation, 100% N2 atmosphere, <0.1 ppm of O2).Aqueous solutions were purged with N2 (99.99%) for at least 3h prior to taking them inside the glovebox. All glassware,plastic, and iron oxides were placed under vacuum in theantechamber overnight prior to taking them inside the gloveboxand were equilibrated in the glovebox atmosphere at least 12 hprior to use.

Iron Oxide Synthesis and Characterization. Goethitewas synthesized using an established method.2 Briefly, 100 mLof 0.1 M ferric nitrate (Fe(NO3)3·9H2O) was added to 180 mLof 5 M KOH, then diluted by adding DI water to reach a finalvolume of 2 L. The solution was heated to 70 °C for 60 h.Hematite was also synthesized using an established method.2 Aflask containing 2 L of 0.002 M HCl was preheated to 98 °C inan oven. Ferric nitrate (Fe(NO3)3·9H2O, 16.6 g) was thenadded to the solution, and the suspension was heated for 7 daysat 98 °C. For both oxides, the solids produced were washed bycentrifuging and replacing the supernatant with DI water 3times, freeze-dried (Labconco benchtop freeze-dry chamber),then ground in a mortar and sieved (100 mesh, Humboldt).BET surface area analysis yielded a specific surface area of 47m2/g for goethite and 49 m2/g for hematite. The samples werenot heated prior to the analysis. The purities of the goethite andthe hematite were confirmed using Mossbauer spectroscopy(Section S2).

Mediated Potentiometric Measurements. All experi-ments were done using batch reactors inside the glovebox. Thevalues presented are the mean and standard deviations fromtriplicate reactors, unless otherwise noted. An initial solution(15 mL) containing pH buffer (50 mM) and an electrolyte(KCl, 25 mM) was prepared, then an aliquot of an Fe2+ stocksolution was added to reach the desired initial aqueous Fe2+

concentration (100 μM to 5 mM). The solution was mixed for1 h, at which point a sample was taken to measure the initialFe2+ concentration, as described below. A preweighed amountof goethite or hematite (15.0 ± 0.1 mg) that was equilibrated inthe glovebox atmosphere was then added to the reactor, whichwas mixed by a magnetic stir bar for 1 h in the dark. Then themediator compound of interest was added from an aqueousstock solution, and the solution was mixed for 24 ± 4 h in thedark. After the equilibration period, a portion of the solutionwas filtered through a 0.45 μm nylon syringe filter to measurethe final aqueous Fe2+ concentration. The initial and finalaqueous Fe2+ concentrations were measured using the 1,10-phenanthroline method,72 with the difference between the twovalues providing the amount of oxide-associated Fe2+. Controlexperiments indicated that the presence of the mediator did notinfluence the amount of Fe2+ taken up by the oxide (data notshown).We measured EH values for the batch reactors using mediated

potentiometry. The measurements were made using a Pt ringcombined redox electrode (Metrohm, part 6.0451.100) inside

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the glovebox. The electrode surface was periodically cleaned byexposing it to 0.1 M HCl for 1 h.73 The electrode was placedinto the batch reactor while the suspension was stirred with amagnetic stir bar. Measurements were made at 2 s intervals fora 1 h period. The EH values reported were the final values after1 h. Between measurements, the electrode was soaked in 3 MKCl for 3 h because we observed measurement drifts due to theinternal KCl solution being diluted during measurements whenwe did not perform this step. The EH values were measured inreference to an internal Ag/AgCl reference electrode, but arereported in reference to SHE. To convert the values, wecalibrated the electrode using quinhydrone (Tokyo ChemicalIndustry Co., LTD) buffers. We measured the EH values of twostandards, one containing 20 mL pH 4.00 reference buffer and0.1 g quinhydrone, and the other containing 20 mL pH 7.00calibration buffer and 0.1 g quinhydrone. The mean differenceat the two pHs between the expected EH values vs SHE and themeasured EH vs Ag/AgCl was used as the conversion value.This conversion value varied by approximately 20 mV over thecourse of the experiments, which was most likely due tovariations in the KCl concentration in the reference electrodecompartment.We selected the mediator compound to use in each

experiment from a pool of compounds tested in our previouswork.67,68,74,75 For a mediator to function properly, it must (1)undergo reversible electron transfer reactions, (2) be solubleand stable over the course of the experiment, and (3) undergosufficiently rapid redox equilibration with the electrode andrelevant redox couples in the system.67 For mediatedpotentiometric measurements, the formal reduction potential(EH

0′) of the mediator at the pH of the solution should be within±120 mV of the EH value of the suspension for a 1 electrontransfer mediator and ±60 mV for a 2 electron transfermediator.67 In this work, we exclusively used 1 electron transfermediators that underwent pH-independent redox reactions(i.e., the EH

0′ was constant over the pH range used).Consequently, the EH

0′ of the mediator was equal to its EH0

value. Since we did not know the EH values of our suspensionsprior to making measurements, we used a trial-and-errorapproach in which we tested multiple mediators on identicallyprepared suspensions and measured the EH values. If thedifference between the measured EH and the EH

0 values of themediators was greater than 120 mV, then we ruled out thatmediator for those experimental conditions. On the basis ofthese preliminary experiments, we found that all our experi-ments could be conducted using three mediators: hexaaminer-uthenium (Ru(NH3)6, EH

0 = +90 mV; used for pH 5.5 and 6.0experiments), cyanomethyl viologen (CMV, EH

0 = −140 mV;used for pH 6.5 and 7.0 experiments), and diquat (DQ, EH

0 =−350 mV; used for pH 7.5 and 7.75). In preliminaryexperiments that led to this study, equilibrating a suite ofmediators having similar EH

0 values with magnetite (Fe3O4)indicated that measured EH did not depend on the mediatorused (data not shown).The data were fit using Igor Pro software (Wavemetrics,

v6.37). The activity coefficient of aqueous Fe2+ (γFe(aq)2+ ) wascalculated to be 0.51 at pH 7.0 for the buffer solutions using theextended Debye−Huckel model (Visual Minteq software, v3.0),and this value was used for modeling all experimental data. Theactivity coefficient could be assumed to be constant for allreactors because the ionic strength was controlled primarily bythe pH buffer (50 mM) and background electrolyte (KCl, 25

mM). Assuming γFe(aq)2+ to be 0.51, as opposed to 1, resulted inthe fitted EH

0 values for the goethite and hematite redox couplesdiscussed in the text to be 17 mV more negative.

Nitrobenzene Reduction Experiments. Suspensions ofaqueous Fe2+ in the presence and absence of 1 g/L goethitebuffered at pH 6.0 were equilibrated for 24 h prior to theaddition of nitrobenzene from a methanolic stock to reach anaqueous nitrobenzene concentration of ∼50 μM. Aqueousnitrobenzene and aniline concentrations were measured overthe course of the reaction by sampling an aliquot of thesuspension and filtering it through a 0.22 μm PTFE syringefilter. The samples were analyzed using high-pressure liquidchromatography (HPLC) with a C18 column. For the HPLCmeasurements, we used an oven temperature of 30 °C, aneluent that contained 70% acetonitrile and 30% 0.5 g/Lammonium acetate, and an eluent flow rate of 1 mL/min.Nitrobenzene was measured at a wavelength of 254 nm, andaniline was measured at a wavelength of 235 nm.

■ RESULTS AND DISCUSSIONMediated and Nonmediated Potentiometric Measure-

ments of Goethite Suspensions. To determine if solubleelectron transfer mediators could facilitate redox equilibrationbetween a Pt redox electrode and a solution containing ironoxide particles and aqueous Fe2+, we measured EH values overtime of goethite suspensions containing aqueous Fe2+ in thepresence and in the absence of a mediator at pH 5.5 and 7.75for 1 h (Figure 1). In the absence of a mediator, the measuredEH values at both pH values drifted over time and failed tostabilize over the course of the 1 h measurement, indicating thatthe electrode was still equilibrating with the suspension whenthe measurements were stopped. In contrast, when the same

Figure 1.Mediated and nonmediated potentiometric measurements ofaqueous suspensions containing goethite and aqueous Fe2+ at pH 5.5and 7.75. The red, dashed lines are measurements made in the absenceof mediator; the blue, solid lines are measurements made in thepresence of 10 μMmediator (Ru(NH3)6 at pH 5.5, diquat at pH 7.75).The goethite and aqueous Fe2+ were allowed to equilibrate 24 h priorto performing the potentiometric measurements. The data show thatthe nonmediated measurements continued to drift after 1 h, while themediated measurements stabilized within 5 min. Experimentalconditions: 1 g/L goethite, 1 mM total Fe2+, 25 mM KCl, and pH-buffer (50 mM MES at pH 5.5, 50 mM MOPS at pH 7.75).

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measurements were performed on otherwise identicallyprepared suspensions that contained a small concentration ofmediator (10 μM), the measured EH values at both pH valuesrapidly stabilized over the first 5 min and were constant for theremainder of the measurement time, suggesting that themediator facilitated redox equilibration between the suspensionand redox electrode.The EH values measured in the presence of a mediator were

considerably different than those measured in the absence ofthe mediator (ΔEH = 173 mV at pH 5.5, ΔEH = 147 mV at pH7.75). The more negative values in the presence of themediators were not due the mediators serving as reductants,since the mediators at both pH values were added in theiroxidized forms. Instead, the results suggest that the measure-ments made in the absence of a mediator did not reachequilibrium over the 1 h period. This explanation wassupported by (1) additional experiments that showed EHvalues drifting over longer periods of time (≥4 h) when themediator was absent (data not shown) and (2) previous studiesthat showed that EH values of iron oxide and iron metalsuspensions drifted over several hours in the absence of amediator,44,61 likely due in part to suspensions influencing theinternal reference electrode potential and particle deposition onthe working electrode surface.61 From these experiments, weconcluded that the measured EH values in absence of amediator should not be interpreted as equilibrium EH values.However, it was still unclear if the EH values in the presence ofa mediator represented equilibrium conditions.To further understand the role that the mediator played in

determining the measured EH value and if equilibrium wasreached, we measured EH values as a function of mediatorconcentration (Figure S3). For pH 7.75 suspensions containinggoethite (1 g/L) and 1 mM initial aqueous Fe2+, varying themediator concentration from 5 to 50 μM yielded a remarkablynarrow range of EH values (−414 mV to −418 mV), indicatingthat measured EH values were independent of the mediatorconcentration. Increasing the mediator concentration to 100

μM resulted in a more positive EH value (−396 mV), which wasconsistent with the mediator oxidizing a significant fraction ofthe Fe2+ (1 mM total) to Fe3+ as it reached an equilibriumreduced to oxidized ratio, which increased the systemwide EHto a more positive value. On the basis of these results, weperformed all subsequent EH measurements using a mediatorconnection of 10 μM to minimize the possibility of themediator substantially influencing measured EH values.

Reduction Potential Measurements of GoethiteSuspensions. We used the mediated potentiometric approachdescribed in the previous section to systematically measure EHvalues of goethite suspensions as a function of the aqueous Fe2+

concentration and pH. For the range of pH values examined(5.5−7.75), a portion of the aqueous Fe2+ initially present insolution was taken up the goethite over a 24 h period (Figure2). The amount of oxide-associated Fe2+, which was quantifiedby taking the difference between the initial and final aqueousFe2+ concentrations, increased with larger initial aqueous Fe2+

concentrations and higher pHs (Figure 2). The observed trendsin Fe2+ uptake by goethite were both qualitatively andquantitatively consistent with previous studies.76,77 To accountfor Fe2+ uptake in our mediated potentiometric measurements,all reactors were equilibrated for 24 h prior to measuring thesolution EH value and the final aqueous Fe2+ concentration.The EH values of the solutions containing goethite and

aqueous Fe2+ were increasingly negative (i.e., more reducing) athigher pH values and with higher dissolved Fe2+ activities(Figure 3). To interpret these values quantitatively and test ifthey were consistent with aqueous Fe2+ reaching thermody-namic equilibrium with goethite, we determined if the datacould be modeled according to the corresponding Nernstequation for the following half reaction between Fe3+ ingoethite and aqueous Fe2+ (Fe(aq)

2+ ):

α‐ + + ⇌ +− + +FeOOH e 3H Fe 2H O(s) (aq)2

2 (1)

Figure 2. Fe2+ uptake from solution by suspended goethite as a function of pH and aqueous Fe2+ concentration (presented as sorption isotherms).Error bars represent the standard deviations from triplicate reactors. No error bars are shown for pH 6.0 and 6.5 because measurements were takenfor single reactors. Experimental conditions: 1 g/L goethite, 25 mM KCl, 50 mM pH-buffer, and 24 h equilibration time.

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For aquatic systems, the activities of water and goethite areconventionally assumed to be 1,35 yielding the following Nernstequation:

= − ++ +E ERTF

RTF

ln{Fe } 3 ln{H }H H0

(aq)2

(2)

where R is the ideal gas constant, T is absolute temperature, F isthe Faraday constant, and curly brackets denote activity. Atroom temperature (298 K), eq 2 can be rewritten as follows:

= − · − ·+E E 59 log{Fe } 177 pHH H0

(aq)2

(3)

where the potentials are in units of mV. For the pH rangeexamined, the aqueous Fe2+ is predominantly present as freeFe2+, and therefore it can be assumed that {Fe(aq)

2+ } ≈{Fe(aq,Total)

2+ } (Fe2+ + OH− ⇄ FeOH+, log(K) = 4.6).35 Theactivity coefficient for aqueous Fe2+ was calculated to be 0.51, asexplained in the Materials and Methods.We modeled the entire data set in Figure 3 with eqs 2 and 3

using two different approaches. First, we fit the data by floatingthe EH

0 value, the slope for the Fe(aq)2+ term, and the slope for pH

term. The best fit yielded an EH0 value of 753 ± 10 (±95%

confidence intervals) mV, a slope for the Fe(aq)2+ term of −60 ± 2

mV, and a slope for the pH term of −175 ± 2 mV (χ2 = 1357).The agreement between the theoretical and fitted Fe(aq)

2+ and pHslopes were excellent, which confirmed that electron transferwas coupled to the transfer of three protons and suggested thatthe Nernst equation could be used to describe the data. Sincewe simultaneously fit the data as a function of {Fe(aq)

2+ } and pH,it was not possible to calculate an R2 value. To estimate the R2

value, we fit the data for each pH independently using linearregressions, which yielded R2 values ≥0.98 for all pH values.The second approach we used to fit the data was fixing theFe(aq)

2+ and pH slopes at their theoretical values (eq 3) and onlyfloating the EH

0 . This fit yielded an EH0 value of 768 ± 1 mV (R2

= 0.90, fit shown as a gray dashed lines in Figure 3). We believethis latter EH

0 value to be more accurate than the former becausethere was no reason to suspect that the Fe(aq)

2+ and pH slopesshould deviate from their ideal values. The fitted value was ingood agreement with two previous studies that reported values

for goethite samples having a range of crystallinities and surfaceareas (720−790 mV,64 787−844 mV65).To determine if the measured EH

0 value was consistent withthe system reaching thermodynamic equilibrium, we calculatedGibbs free energy (ΔG0) values and compared them withreference thermodynamic values derived from calorimetricmeasurements. The calculated ΔG0 for the half reaction in eq 1(ΔGrxn

0 = −nFEH0 , with n = 1) was −74.1 ± 0.1 kJ/mol (Section

S5.1.1). We calculated the Gibbs free energy of formation(ΔGf

0) of the goethite (ΔGgoethite0 ) using reference ΔGf

0 valuesfor the other species in eq 1 (Section S5.1.2), yielding a value of−490.2 ± 0.1 kJ/mol. The calculated ΔGgoethite

0 was in excellentagreement with the reference value in the Robie andHemingway thermodynamic database (−491.8 kJ/mol)78 andthe value recently reported by Navrotsky et al. (−490.6 ± 1.5kJ/mol).79 Note that the ΔGgoethite

0 value measured here shouldnot be directly compared to all other reported values, becausein many cases the reported values used different thermody-namic databases, which have substantially different ΔGf

0 valuesfor the other species in eq 1.80 The agreement among theΔGgoethite

0 measured here and previously reported values fromcalorimetry experiments indicated that (1) the redox couplebetween Fe3+ in goethite and aqueous Fe2+ reachedthermodynamic equilibrium, (2) the mediator compoundsreached thermodynamic equilibrium with the Fe3+/Fe2+ redoxcouple, and (3) the mediator compounds reached thermody-namic equilibrium with the redox electrode over the course ofthe measurements.To further demonstrate that the goethite suspensions

reached thermodynamic equilibrium, we examined if themeasured EH values were consistent with the expected activityof aqueous Fe3+ ({Fe(aq)

3+ }) based on the solubility of goethite.We hypothesized that the following half reaction was also atequilibrium:

+ ⇌+ − +Fe e Fe(aq)3

(aq)2

(4)

The corresponding Nernst equation has a well-established EH0

value (771 mV vs SHE):81

= −+

+

⎛⎝⎜⎜

⎞⎠⎟⎟E E

RTF

ln{Fe }

{Fe }H H0 (aq)

2

(aq)3

(5)

By assuming that the half reactions in eqs 1 and 4 were both atthermodynamic equilibrium, the solubility product constant(Ksp) could be derived (Section S5.1.3). The calculatedlog(Ksp) value was −42.1, which was within the range ofreported values in the literature (−39.8 to −43.4).2 This simplecalculation and the consistency of its result with previousmeasurements further confirmed that the systems containinggoethite particles and aqueous Fe2+ reached thermodynamicequilibrium.An important implication from this analysis is that for

goethite suspensions containing aqueous Fe2+, the solution EHdid not directly depend on the concentration of goethite oroxide-associated Fe2+. Instead, these concentrations onlyindirectly affect the EH by controlling the aqueous Fe2+

concentration at equilibrium. To test this implication, wemeasured the EH values of pH 7.0 goethite suspensions with 1mM Fe2+ as a function of goethite concentration (0.2 to 4.0 g/L; Figures S6 and S7). As the goethite concentration increased,more Fe2+ was taken by up the oxide, as expected. In agreementwith our predictions, the EH was independent of the

Figure 3. Reduction potential (EH) values of goethite suspensions as afunction of aqueous Fe2+ concentration and pH. Error bars representthe standard deviation from triplicate reactors. No error bars arepresent for the pH 6.0 and 6.5 reactors because only one reactor wasmeasured for each point. The dashed gray lines represent the modelfit. Experimental details: 1 g/L goethite, 25 mM KCl, 50 mM buffer,and 10 μM mediator. These data are replotted against the aqueousFe2+ activity in Figure S4.

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concentration of oxide-associated Fe2+ (Figure S6). The EH ofthe goethite suspensions also became more positive (i.e., lessreducing) with increasing goethite concentrations, due to theremoval of aqueous Fe2+ from solution by the goethite (FigureS7). Fitting the data with eq 3 while holding the Fe2+ slope at59 mV and the pH slope at 177 mV yielded an EH

0 of 786 ± 1mV (R2 = 0.57), in good agreement with the value obtained forfitting the entire data set (768 ± 1 mV). These measurementsconfirmed the implication that EH depends on the aqueous Fe2+

concentration, and not the amount of the oxide-associated Fe2+.Reduction Potential Measurements of Hematite

Suspensions. We also used mediated potentiometry tomeasure the EH of suspensions containing hematite andaqueous Fe2+ as a function of pH and Fe2+concentration todetermine if other systems containing aqueous Fe2+ and ironoxides reach equilibrium. As we observed for goethite, a portionof the aqueous Fe2+ initially present in solution was taken upthe hematite (Figure S8). The collected isotherms wereconsistent with expectations and past work, with more Fe2+

uptake occurring at higher pHs and when there was moreaqueous Fe2+ initially present in solution.38 We tested if thedata could be described by the half-reaction for Fe3+ in hematiteand aqueous Fe2+:

α‐ + + ⇌ +− + +12

Fe O e 3H Fe32

H O2 3(s) (aq)2

2 (6)

which yields a Nernst equation that is identical to the onederived for goethite at room temperature:

= − · − ·+E E 59 log{Fe } 177 pHH H0

(aq)2

(7)

As for goethite, the activity coefficient for Fe(aq)2+ was assumed to

be 0.51.The EH measurements conducted for hematite suspensions

as a function of aqueous Fe2+ concentration and pH lookedqualitatively similar to those made for goethite (Figure 4), withEH values becoming increasingly negative for increasing Fe(aq)

2+

concentrations and pH values. We fit the data while floating theEH0 value, the slope for the Fe(aq)

2+ term, and the slope for pHterm. This yielded an EH

0 value of 739 ± 16 mV, a slope for the

Fe(aq)2+ term of 62 ± 3 mV, and a slope for the pH term of 174 ±

3 mV. The excellent agreement between the theoretical andpredicted slope terms for Fe(aq)

2+ and pH terms indicated that themeasured values could be described by the Nernst equation ineq 7. As with goethite, we had no reason to suspect that theseslope parameters would deviate from their ideal values.Consequently, we fit the data assuming the ideal slopes in eq7 and only floating the EH

0 , which yielded a best-fit value of 769± 2 mV (R2 = 0.96, fit shown in Figure 4 as gray dashed lines).The fitted EH

0 value agreed well with the value ranges reportedin two previous studies (764−828 mV,64 774−781 mV65).From this value, we calculated a ΔGrxn

0 value of −74.2 ± 0.2kJ/mol and a ΔGhematite

0 value of −743.0 ± 0.2 kJ/mol (SectionS5.2). The calculated ΔGhematite

0 value was in good agreementwith the reported value in the Robie and Hemingway database(−744.4 ± 1.3 kJ/mol).78 We calculated the log(Ksp) ofhematite to be −42.0, which was approximately in the middle ofthe range of previously reported values (−40.3 to −43.9).2 Theobservations that the hematite EH data could be accuratelymodeled with a single Nernst equation and that themeasurements were in agreement with previously reportedΔGhematite

0 and Ksp values indicated that systems containinghematite particles and aqueous Fe2+ reached thermodynamicequilibrium.

Thermodynamic Insights into the Reactivity of Oxide-Associated Fe2+. We observed that aqueous Fe2+ reachedthermodynamic equilibrium with goethite and hematite inaqueous suspensions. Consequently, our data indicated thateach suspension containing oxide-associated Fe2+ and aqueousFe2+ had a singular EH value, which contradicted the firsthypothesis that oxide-associated Fe2+ has a lower EH value thanaqueous Fe2+ in the same solution. The data were, however,consistent with the second, alternative hypothesis, which positsthat the more negative EH value of aqueous Fe2+ in the presenceof an iron oxide is due to a change in the Fe3+ phase in the halfreaction (and not the speciation of Fe2+ changing due to uptakeby the iron oxide). As discussed earlier, aqueous Fe2+ in theabsence of an iron oxide can form Fe3+ complexes orferrihydrite,58 whereas Fe2+ oxidization in the presence of aniron oxide can result in growth of the iron oxide particles.29,59,60

This change in oxidation product “Fe3+” alters the EH0 of Fe3+/

Fe2+ redox couple, which can be illustrated by comparing theoxidation of aqueous Fe2+ to goethite formation (eq 1) or toferrihydrite formation (Fe(OH)3(s)):

+ + ⇌ +− + +Fe(OH) e 3H Fe 3H O3(s) (aq)2

2 (8)

The measured EH0 value for goethite formation (eq 1, 768 ± 1

mV) is 170 mV more negative than for the EH0 value calculated

from existing thermodynamic data for ferrihydrite formation(eq 8, 937 mV; calculation in Section S5.3), thus makingaqueous Fe2+ a stronger reductant in the presence of goethite.Note that the e−/H+ ratios are the same for eqs 1, 6, and 8, andtherefore the differences among EH

0 values for goethite,hematite, and ferrihydrite formation are constant at all pHs.This thermodynamic framework can also be described by

considering the aqueous half reaction between Fe(aq)2+ and Fe(aq)

3+

(eq 4). In aqueous systems containing iron oxide particles, theaqueous Fe3+ concentration is determined by the solubility ofthe iron oxide. As a rule, more thermodynamically stableminerals are less soluble. For instance, goethite is less solublethan ferrihydrite,58 meaning aqueous systems in equilibriumwith goethite will have lower aqueous Fe3+ concentrations than

Figure 4. Reduction potential (EH) values of hematite suspensions as afunction of aqueous Fe2+ concentration and pH. Error bars representthe standard deviations from triplicate reactors. The dashed gray linesare the model fit. Experimental details: 1 g/L hematite, 25 mM KCl,50 mM buffer, and 10 μM mediator. These data are replotted againstthe aqueous Fe2+ activity in Figure S5.

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those at equilibrium with ferrihydrite (under otherwise identicalsolution conditions). Consequently, the higher aqueous Fe3+

concentration in the presence of ferrihydrite causes the EHvalue for the Fe(aq)

3+ /Fe(aq)2+ redox couple to become more

positive (eq 5) than when goethite is present, if the aqueousFe2+ concentration is the same between the two suspensions.This implies that relative solubilities of iron minerals may beused to estimate their relative EH values.To confirm that our findings were applicable to past studies

observing enhanced contaminant reduction rates by aqueousFe2+ in the presence of iron oxides, we examined the reductionof nitrobenzene, a model oxidized contaminant, by aqueousFe2+ in the presence and absence of goethite. We werespecifically interested in determining if the presence of goethiteincreased nitrobenzene reduction rates by Fe2+ in suspensionsthat had reached thermodynamic equilibrium. In the presenceof goethite, nearly all the nitrobenzene was reduced to astoichiometric amount of aniline over a 24 h period (Figure 5).

When no goethite was present, negligible nitrobenzenereduction occurred. This finding was consistent with previouswork examining the reduction of nitrobenzene compounds byFe2+ in the presence of goethite,20,22,60 and it demonstrated thepresence of goethite substantially enhanced the ability of Fe2+

in suspensions that were initially at equilibrium prior to theaddition of nitrobenzene.Interestingly, thermodynamic calculations revealed that the

reduction of nitrobenzene by aqueous Fe2+ should be favorableboth in the presence and absence of goethite, assuming thatwhen goethite was absent Fe2+ oxidation was coupled toferrihydrite formation (Section S5.4). We could not calculate ifnitrobenzene reduction was favorable for the case in whichaqueous Fe2+ is oxidized to aqueous Fe3+ in a solutionundersaturated with respect to ferrihydrite, because it wouldrequire us to arbitrarily assume an aqueous Fe3+ concentration(since it is too low to measure). These experiments confirmedthat aqueous Fe2+ in the presence goethite is more reactive withoxidized contaminants than aqueous Fe2+ in the absence of aniron oxide under thermodynamic equilibrium conditions. Thethermodynamic calculations for nitrobenzene reductionsuggested, however, that there are likely additional factors

that contribute to contaminant reduction rates besides EHvalues.Indeed, other studies have provided compelling evidence

indicating that thermodynamics cannot be used to solelyexplain why Fe2+ reduces contaminants more quickly in thepresence of an iron oxide than when no iron oxide is present.Several works have found strong correlations between theamount of oxide-associated Fe2+ and reaction rates, indicatingthat oxide-associated Fe2+ (and not aqueous Fe2+) isresponsible for contaminant reduction.17,30,82 This observationmay be due to (1) the contaminant forming an inner-spherecomplex at the oxide surface prior to it being reduced that alterits thermodynamic properties or the collision frequencies forthe reaction or (2) the oxide surface facilitating a two-electrontransfer step that is not possible when reacting with aqueousFe2+ ions.17,83 In either case, it is reasonable to assume thatoxide-associated Fe2+ and aqueous Fe2+ can have differentoxidation reaction rate constants, despite having identical EHvalues. Determining why this difference in reactivity exists willbe critical for advancing the ability to predict contaminantreduction rates by Fe2+.

Recommended Thermodynamic Values for IronOxide−Aqueous Fe2+ Redox Couples. On the basis ofthe agreement among the measured EH values and thosecalculated from existing thermodynamic data, we recommendthat future works refer the reported EH

0 to approximate EHvalues for systems containing aqueous Fe2+ and goethite (EH

0 =768 mV vs SHE) or aqueous Fe2+ and hematite (EH

0 = 769 mVvs SHE). Using the EH

0 values, the EH of a suspension can beeasily calculated as a function of pH and aqueous Fe2+ activityusing the relevant Nernst eq (eq 3 for goethite, eq 7 forhematite), assuming the suspension is at equilibrium. Note,however, that these calculated EH values should only be used asapproximations. The EH

0 values will vary with respect to particlesize due to surface enthalpy79,84 and possibly surface entropy,85

which will be particularly important when considering nano-particulate oxides. This has been confirmed in other studies,which found that EH values of iron oxides depend on theirsynthesis route and particle size.64,65

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.est.6b02661.

The chemical reagents used, Mossbauer spectra of thesynthesized iron oxides, the influence of mediator andgoethite concentration on measured EH values, EH vsFe2+ activity for goethite and hematite, thermodynamiccalculations, and Fe2+ isotherms for hematite (PDF)

■ AUTHOR INFORMATIONCorresponding Author*Phone: 814-865-5673; fax: 814-863-7304; e-mail: gorski@psu.edu (C.A.G.).NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe thank Tjisse Hiemstra (Wageningen University) forvaluable discussions related to thermodynamic calculations.We thank S. Sarah Cronk (Penn State University) for modelingMossbauer spectra and valuable comments on this paper. We

Figure 5. Nitrobenzene reduction (black markers) and anilineproduction (gray markers) by Fe2+ in the presence (1 g/L) andabsence of goethite. Experimental details: 25 mM KCl, 50 mM buffer,1 mM initial aqueous Fe2+. The reactors were equilibrated 24 h priorto the addition of nitrobenzene.

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thank Prachi Joshi (Penn State University) and MichelleScherer (University of Iowa) for comments that improved thequality of this paper. This work was supported by the U.S.National Science Foundation (grant EAR-1451593 to C.G. andDGE-1255832 to R.E.).

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Supporting Information forEnvironmental Science and Technology

Thermodynamic characterization of ironoxide - aqueous Fe2+ redox couples

Christopher A. Gorski,1* Rebecca Edwards,1 Michael Sander,2Thomas B. Hofstetter,2,3 and Sydney M. Stewart1

1Department of Civil and Environmental Engineering, Pennsylvania State University,University Park, Pennsylvania, USA

2Institute of Biogeochemistry and Pollutant Dynamics (IBP),Swiss Federal Institute of Technology, ETH Zürich, Zürich, Switzerland

3Eawag, Swiss Federal Institute of Aquatic Science and Technology,Dübendorf, Switzerland

∗Corresponding author: E-mail: gorski@psu.edu, Phone: 814-865-5673, Fax: 814-863-7304

The supporting information contains: 17 pages, 8 figures, and 1 table.

Contents

S1 Chemical Reagents 2

S2 Mössbauer Spectroscopy 2

S3 Effect of mediator concentration on EH 5

S4 EH vs. aqueous Fe2+ activity relationships 6

S5 Thermodynamic calculations 8

S6 Effect of goethite concentration on EH 14

S7 Aqueous Fe2+ uptake isotherms for hematite 16

References 17

S1

S1 Chemical Reagents

All the stock solutions used were either (1) purged with N2 for at least 3 hours prior to bringing theminto the glovebox or (2) prepared inside the glovebox by adding a de-gased salt to de-oxygenatedwater. The pH of solutions were adjusted with either 5 M HCl or 5 M NaOH, both prepared fromde-oxygenated stock solutions. The aqueous Fe2+ stock solution (150 mM) was prepared insidethe anaerobic glovebox by dissolving ferrous ammonium sulfate (Fischer Scientific Company) inde-oxygenated DI water containing a few drops of 5 M HCl. Mediator stock solutions (10 mM)were prepared by dissolving the salt in deoxygenated DI water: hexaamineruthenium (E0

H = 0.09V vs. SHE, Acors Organics, 98%), cyanomethyl viologen (E0

H = –0.14 V vs. SHE, synthesized asdescribed in our previous work1), diquat (E0

H = –0.35 V vs. SHE, Chem Services, 99.5%).All pH buffers were prepared outside the glovebox. For pH values 5.5-6.5, the buffer solution

contained 50 mM MES (2-N-morpholinoepropanesulfonic acid monohydrate, pKA = 6.1, Aresco,≥99%) and 25 mM KCl (EM Science). For pHs 7.0-7.75, the buffer solution 50 mM MOPS (3-N-morpholinoepropanesulfonic acid, pKA = 7.2, EMD Chemicals Inc., ≈100%) and 25 mM KCl.

S2 Mössbauer Spectroscopy

Mössbauer spectroscopy was used to confirm the purity of the synthetic goethite and hematite.Spectra were collected using a SVT-400 cryogenic Mössbauer system (SEE Co., USA). The sampleswere prepared by placing the specimen into an aluminum ring sample holder sealed on both sideswith 1 mil Kapton tape. The 57Co radioactive source (∼50 mCi) was in an Rh matrix at roomtemperature during sample collection. Spectra were fit using Recoil software (University of Ottawa,Ottawa, Canada) with the Voigt-based model.2 The instrument was calibrated using α-57Fe foilcollected at room temperature. The Lorentzian linewidth was fixed at 0.14 mm/s during fitting, asthis was the linewidth fitted for an α-57Fe foil with an ideal thickness at room temperature. For allfits, the center shift, quadrupole splitting, hyperfine field distribution, and relative spectral areaswere allowed to float.

S2

Abso

rptio

n [A

rbitr

ary

units

]

86420-2-4-6-8

Velocity [mm/s]

Figure S1: Mössbaur spectrum of the synthesized goethite collected at room temperature (raw data:black open circles, fit: red line). The fit contained a single sextet with two components. The fittedhyperfine parameters were: center shift = 0.29 mm/s, quadrupole split = -0.09 mm/s, and hyperfinefield = 24.6 T. These parameters were consistent with those previously reported for goethite at roomtemperature.3

S3

Abso

rptio

n [A

rbitr

ary

units

]

1050-5-10

Velocity [mm/s]

Figure S2: Mössbaur spectrum of the synthesized hematite collected at 5 K (raw data: black opencircles, fit: blue line). The fit contained a single site. The fitted hyperfine parameters were: centershift = 0.49 mm/s, quadrupole split = 0.21 mm/s, and hyperfine field = 53.8 T. These parameterswere consistent with those previously reported for hematite at 5 K.3

S4

S3 Effect of mediator concentration on EH

-420

-400

-380E H

[mV

vs. S

HE]

100806040200Diquat concentation [µM]

-300-240

Figure S3: Measured EH values of suspensions of goethite and aqueous Fe2+ as a function of themediator (diquat) concentration. The suspensions were buffered at pH 7.75 and contained 1 g/Lgoethite and initially 1 mM aqueous Fe2+ in solution. The reactors equilibrated for 24 hours priorto making the EH measurement.

S5

S4 EH vs. aqueous Fe2+ activity relationships

-400

-300

-200

-100

0E H

[mV

vs. S

HE]

102 4 6 8

1002 4 6 8

10002 4 6

Dissolved Fe2+ {µM}

pH 5.5 pH 6.0 pH 6.5 pH 7.0 pH 7.5 pH 7.75

pH 5.5

6.0

6.5

7.0

7.5

7.75

Figure S4: Reduction potential (EH) values of goethite suspensions as a function of aqueous Fe2+

activity and pH. Error bars represent the standard deviation from triplicate reactors. No error barsare present for the pH 6.0 and 6.5 reactors because only one reactor was measured for each point.Experimental details: 1 g/L goethite, 25 mM KCl, 50 mM buffer, 10 µM mediator.

S6

-400

-300

-200

-100

0Re

duct

ion

pote

ntia

l, E H

[mV

vs. S

HE]

810

2 4 6 8100

2 4 6 81000

2 4

Dissolved Fe2+ {µM}

Ev#4 Ev#3 Ev#6

pH 5.5

6.5

7.0

7.5

Figure S5: Reduction potential (EH) values of hematite suspensions as a function of aqueous Fe2+

activity and pH. Error bars represent the standard deviations from triplicate reactors. Experimentaldetails: 1 g/L hematite, 25 mM KCl, 50 mM buffer, 10 µM mediator.

S7

S5 Thermodynamic calculations

Table S1: Gibbs free energies of formation (∆G0f , kJ/mol) for the species used in thermodynamic

calculations at room temperature and 1 atm of pressure. All values were taken from the Robie andHemingway database,4 except the valus denoted with a star (*), which were taken from Narvotskyet. al 2008.5

Chemical species ∆G0f (kJ/mol)

H2O(l) –237.14Fe2+(aq) –90.0H+ 0e– 0α–FeOOH –491.8α–FeOOH –490.6±1.5*α–Fe2O3 –744.4Fe(OH)3 –711.0±2.0*

S5.1 Goethite calculations

S5.1.1 Calculation of ∆G0rxn from E0

H

∆G0rxn = −nFE0

H (S5.1.1)

∆G0rxn = −(1)(96.485)(0.768± 0.001) (S5.1.2)

∆G0rxn = −74.1± 0.1 kJ/mol (S5.1.3)

S5.1.2 Calculation of ∆G0goethite

α−FeOOH(s) + e− + 3 H+ ⇀↽ Fe2+(aq) + 2 H2O (S5.1.4)

∆G0rxn = ∆G0

Fe2+(aq)+ 2×∆G0

H2O −∆G0goethite −∆3×G0

H+ (S5.1.5)

∆G0goethite = −∆G0

rxn + ∆G0Fe2+(aq)

+ 2×∆G0H2O − 3×∆G0

H+ (S5.1.6)

∆G0goethite = 74.1± 0.1− 90.0− 474.28− 0 (S5.1.7)

∆G0goethite = −490.2± 0.1 kJ/mol (S5.1.8)

S8

S5.1.3 Calculation of the solubility product of goethite (Ksp)

EFe2+(aq)/α−FeOOH = E0Fe2+(aq)/α−FeOOH

− RT

Fln{Fe2+(aq)}+ 3

RT

Fln{H+} (S5.1.9)

EFe2+(aq)/Fe3+(aq)

= E0Fe2+(aq)/Fe

3+(aq)− RT

Fln({Fe2+(aq)}

{Fe3+(aq)})

(S5.1.10)

At equilibrium : EFe2+(aq)/α−FeOOH = EFe2+(aq)/Fe3+(aq)

(S5.1.11)

E0Fe2+(aq)/α−FeOOH

− RT

Fln{Fe2+(aq)}+ 3

RT

Fln{H+} = E0

Fe2+(aq)/Fe3+(aq)− RT

Fln({Fe2+(aq)}

{Fe3+(aq)})

(S5.1.12)

At std. conditions : 0.768− 0.771 = 0.059log({H+}−3{Fe3+(aq)}

)(S5.1.13)

− 0.0508 = log({OH−}3{Fe3+(aq)}

{Kw}3)

(S5.1.14)

{Fe3+(aq)}{OH−}3 = Ksp = 10−42.05 (S5.1.15)

S9

S5.2 Hematite calculations

S5.2.1 Calculation of ∆G0rxn from E0

H

∆G0rxn = −nFE0

H (S5.2.1)

∆G0rxn = −(1)(96.485)(0.769± 0.002) (S5.2.2)

∆G0rxn = −74.2± 0.2 kJ/mol (S5.2.3)

S5.2.2 Calculation of ∆G0hematite

1

2α−Fe2O3(s) + e− + 3H+ ⇀↽ Fe2+(aq) +

3

2H2O (S5.2.4)

∆G0rxn = ∆G0

Fe2+(aq)+

3

2×∆G0

H2O −1

2∆G0

hematite − 3×∆G0H+ (S5.2.5)

∆G0hematite = 2× (−∆G0

rxn + ∆G0Fe2+(aq)

+3

2×∆G0

H2O − 3×∆G0H+) (S5.2.6)

∆G0hematite = 2× (74.2± 0.2− 90.0− 3

2× 237.14− 0) (S5.2.7)

∆G0hematite = −743.0± 0.2 kJ/mol (S5.2.8)

S10

S5.2.3 Calculation of the solubility product of hematite (Ksp)

EFe2+(aq)/α−Fe2O3= E0

Fe2+(aq)/α−Fe2O3− RT

Fln{Fe2+(aq)}+ 3

RT

Fln{H+} (S5.2.9)

EFe2+(aq)/Fe3+(aq)

= E0Fe2+(aq)/Fe

3+(aq)− RT

Fln({Fe2+(aq)}

{Fe3+(aq)})

(S5.2.10)

At equilibrium : EFe2+(aq)/α−Fe2O3= EFe2+(aq)/Fe

3+(aq)

(S5.2.11)

E0Fe2+(aq)/α−Fe2O3

− RT

Fln{Fe2+(aq)}+ 3

RT

Fln{H+} = E0

Fe2+(aq)/Fe3+(aq)− RT

Fln({Fe2+(aq)}

{Fe3+(aq)})

(S5.2.12)

At std. conditions : 0.769− 0.771 = 0.059log({H+}−3{Fe3+(aq)}

)(S5.2.13)

− 0.0339 = log({OH−}3{Fe3+(aq)}

{Kw}3)

(S5.2.14)

{Fe3+(aq)}{OH−}3 = Ksp = 10−42.03 (S5.2.15)

S5.3 Ferrihydrite calculations

Fe(OH)3(s) + e− + 3 H+ ⇀↽ Fe2+(aq) + 3 H2O (S5.3.1)

∆G0rxn = ∆G0

Fe2+(aq)+ 3×∆G0

H2O −∆G0Fe(OH)3

− 3×∆G0H+ (S5.3.2)

∆G0rxn = −90.0− 711.42 + 711.0− 0 (S5.3.3)

∆G0rxn = −90.42 kJ/mol (S5.3.4)

∆G0rxn = −nFE0

H (S5.3.5)

E0H = 0.937 V (S5.3.6)

S11

S5.4 Nitrobenzene calculations

S5.4.1 The reduction of nitrobenzene to aniline coupled to the oxidation of Fe2+ togoethite

NB = nitrobenzene,AN = aniline

NB + 6 e− + 6H+ −−→←−− AN + 2 H2O (S5.4.1)

E0AN/NB = +830mV∗ (S5.4.2)

EAN/NB = E0AN/NB −

RT

6Fln

{AN}{NB}{H+}6

(S5.4.3)

EFe2+(aq)/α−FeOOH = E0Fe2+(aq)/α−FeOOH

− RT

Fln{Fe2+(aq)}+ 3

RT

Fln{H+} (S5.4.4)

At equilibrium : EFe2+(aq)/α−FeOOH = EAN/NB (S5.4.5)

E0AN/NB −

RT

6Fln

{AN}{NB}{H+}6

= E0Fe2+(aq)/α−FeOOH

− RT

Fln{Fe2+(aq)}+ 3

RT

Fln{H+} (S5.4.6)

E0AN/NB − E

0Fe2+(aq)/α−FeOOH

= −0.059log{Fe2+(aq)} − (2)0.059pH +0.059

6log{AN}{NB}

(S5.4.7)

At pH = 6, {Fe2+(aq)} = 10−3 :

0.062 = −0.059log{10−3} − 0.118(6) + 0.0098log{AN}{NB}

(S5.4.8)

{AN}{NB}

= 1060 (S5.4.9)

* ref. 6

S12

S5.4.2 The reduction of nitrobenzene to aniline coupled to the oxidation of Fe2+ toferrihydrite

NB = nitrobenzene,AN = aniline

NB + 6 e− + 6H+ −−→←−− AN + 2 H2O (S5.4.10)

E0AN/NB = +830mV∗ (S5.4.11)

EAN/NB = E0AN/NB −

RT

6Fln

{AN}{NB}{H+}6

(S5.4.12)

EFe2+(aq)/Fe(OH)3= E0

Fe2+(aq)/Fe(OH)3− RT

Fln{Fe2+(aq)}+ 3

RT

Fln{H+} (S5.4.13)

At equilibrium : EFe2+(aq)/Fe(OH)3= EAN/NB (S5.4.14)

E0AN/NB −

RT

6Fln

{AN}{NB}{H+}6

= E0Fe2+(aq)/Fe(OH)3

− RT

Fln{Fe2+(aq)}+ 3

RT

Fln{H+} (S5.4.15)

E0AN/NB − E

0Fe2+(aq)/Fe(OH)3

= −0.059log{Fe2+(aq)} − (2)0.059pH +0.059

6log{AN}{NB}

(S5.4.16)

At pH = 6, {Fe2+(aq)} = 10−3 :

− 0.107 = −0.059log{10−3} − 0.118(6) + 0.0098log{AN}{NB}

(S5.4.17)

{AN}{NB}

= 1043 (S5.4.18)

* ref. 6

S13

S6 Effect of goethite concentration on EH

-300

-290

-280

-270

-260

-250

-240E H

[mV

vs. S

HE]

4003002001000Oxide-associated Fe2+ [µM]

0.2

0.5

1.01.5 2.0

3.0

4.0

Figure S6: Measured EH values versus the concentration of oxide-associated Fe2+ for suspensionsof goethite and aqueous Fe2+ as a function of goethite concentration. The values shown within themarkers represents the goethite concentration in units of g/L. Experiments were conducted at pH7.0. The reactors were allowed to equilibrated for 24 hours prior to measuring the EH and finalaqueous Fe2+ concentrations. All reactors initially contained 1 mM Fe2+(aq).

S14

-300

-290

-280

-270

-260

-250

-240E H

[mV

vs. S

HE]

4 5 6 7 8 91000

Dissolved Fe2+ [µM]

0.2

0.5

1.01.52.0

3.0

4.0

Figure S7: Measured EH values versus the log of aqueous Fe2+ concentrations for suspensions ofgoethite and aqueous Fe2+ as a function of goethite concentration. The yellow pentagon markers areidentical to the data points shown in Figure 3 in the main text. The values shown within the yellowcircles represents the goethite concentration in units of g/L. The gray dashed line is the model fitfor the overall dataset, as shown in Figure 3 in the main text. Experiments were conducted at pH7.0. The reactors were allowed to equilibrated for 24 hours prior to measuring the EH and finalaqueous Fe2+ concentrations. All reactors initially contained 1 mM Fe2+(aq).

S15

S7 Aqueous Fe2+ uptake isotherms for hematite

100

80

60

40

20

0

Oxi

de-a

ssoc

iate

d Fe

2+ [µ

mol

/g]

40003000200010000

200

150

100

50

03000200010000

Dissolved Fe2+ [µM]

400

300

200

100

010008006004002000

400

300

200

100

08006004002000

pH 5.5 pH 6.5

pH 7.0 pH 7.5

Figure S8: Fe2+ uptake from solution by hematite as a function of pH and aqueous Fe2+ concen-tration (presented as sorption isotherms). Experimental conditions: 1 g/L hematite, 25 mM KCl,50 mM pH-buffer, equilibration time = 24 hours.

S16

References

[1] C. A. Gorski, L. Klupfel, A. Voegelin, M. Sander, and T. B. Hofstetter. Redox properties ofstructural fe in clay minerals. 2. electrochemical and spectroscopic characterization of electrontransfer irreversibility in ferruginous smectite, swa-1. Environ. Sci. Technol., 46(17):9369–9377,2012.

[2] D. G. Rancourt and J. Y. Ping. Voigt-based methods for arbitrary-shape static hyperfine pa-rameter distributions in mössbauer spectroscopy. Nucl. Instrum. Meth. B, 58(1):85–97, 1991.

[3] R.M.; Cornell and U. Schwertmann. The Iron Oxides: Structure, Properties, Reactions, Occur-rences and Uses. Wiley-VCH, Weinheim, Germany, 2nd properties, reactions, occurrences anduses edition, 2003.

[4] R.A. Robie and B.S. Hemingway. Thermodynamic properties of minerals and related substancesat 298.15 k and 1 bar (105 pascals) pressure and at higher temperatures. Technical Report 2131,U.S. Geological Survey Bulletin, 1995.

[5] A. Navrotsky, L. Mazeina, and J. Majzlan. Size-driven structural and thermodynamic complexityin iron oxides. Science, 319(5870):1635–1638, 2008.

[6] R.P. Schwarzenbach, P.M. Gschwend, and D.M. Imboden. Environmental Organic Chemistry.Wiley, 2005.

S17