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Geochimica et Cosmochimica Acta 292 (2021) 235–253

Chromium isotope fractionation during reduction ofChromium(VI) by Iron(II/III)-bearing clay minerals

Claresta Joe-Wong a,⇑, Karrie L. Weaver b, Shaun T. Brown c, Kate Maher b

aDepartment of Geological Sciences, Stanford University, 450 Serra Mall, Building 320, Stanford, CA 94305, USAbDepartment of Earth System Science, Stanford University, 473 Via Ortega, Stanford, CA 94305, USA

cEnergy Geosciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA

Received 10 April 2020; accepted in revised form 25 September 2020; available online 6 October 2020

Abstract

Chromium stable isotope ratios are used to trace the reduction of Cr(VI) to Cr(III) in both ancient and modern systems.However, quantitative interpretation of Cr isotopic signatures has been stymied by the large variability in isotopic fraction-ation factors for Cr(VI) reduction by different reductants. Here we determine Cr isotope fractionation factors during Cr(VI)reduction by Fe(II/III)-bearing clay minerals, which are abundant in subsurface environments. Several variables were tested:pH, total Fe content of the clay, and the fraction of reduced Fe within the clay (Fe(II)/Fe(total)). The latter controls the stan-dard reduction potential of the clay. Our results demonstrate that neither pH nor total Fe content of the clay have majoreffects on isotopic fractionation. In contrast, as the effective standard reduction potential of the clay and thus the standardfree energy of Cr(VI) reduction become more negative, Cr isotope fractionation factors decrease in magnitude from �4.9to �1.3‰ according to a linear free energy relationship. This linear free energy relationship can be predicted from Marcuselectron transfer theory and allows first-order predictions of Cr isotope fractionation factors to be made from the standardreduction potential or Fe(II)/Fe(total) of a clay, potentially improving our ability to model Cr isotope signatures in geochem-ical systems. Chromium is the first isotope system to show such a linear free energy relationship over a diverse range of reduc-tants, including both aqueous and solid-phase reductants, and may provide a model for determining other redox-drivenkinetic isotope effects in environmentally important isotope systems.� 2020 Elsevier Ltd. All rights reserved.

Keywords: Stable isotope fractionation; Redox; Marcus theory; Chromium; Clay minerals

1. INTRODUCTION

Stable isotope fractionation during Cr(VI) reduction hasbeen proposed as a means to track the oxygenation of earlyEarth (Frei et al., 2009; D’Arcy et al., 2017) as well asreductive remediation of Cr(VI) (Ellis et al., 2002; Basuand Johnson, 2012; Wu et al., 2017). Chromium has fourstable isotopes (50Cr, 52Cr, 53Cr, and 54Cr) (Meija et al.,2016) and naturally occurs as Cr(VI), which is toxic and

https://doi.org/10.1016/j.gca.2020.09.034

0016-7037/� 2020 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: cjoewong@lbl.gov (C. Joe-Wong).

water-soluble (Cieslak-Golonka, 1996; Oze et al., 2007;McClain et al., 2017), or as Cr(III), which is nontoxic(Anderson, 1997) and less soluble (Rai et al., 2007). Reduc-tion of Cr(VI) is consistently accompanied by significantkinetic isotope fractionation because the lighter isotopesof Cr are reduced more quickly, enriching the Cr(III) prod-ucts in the lighter isotopes and enriching the remaining Cr(VI) reactants in the heavier isotopes (Ellis et al., 2002). Incontrast, dilution and adsorption of Cr(VI) cause little tono isotopic fractionation (Ellis et al., 2004). Changes inCr stable isotope ratios in the rock record thus may signalchanges in past redox conditions, and changes in Cr stableisotope ratios in soil and groundwater may distinguish

236 C. Joe-Wong et al. /Geochimica et Cosmochimica Acta 292 (2021) 235–253

between the long-term removal of Cr(VI) from solution viareduction and the temporary apparent attenuation of Cr(VI) via dilution or adsorption.

Although reduction is the major driver of Cr isotopefractionation, quantifying Cr(VI) reduction from theobserved isotopic fractionation is difficult. The isotopicfractionation factor for Cr(VI) reduction (e = a � l � ln(a), where a = (53Cr/52Cr)product/(

53Cr/52Cr)reactant) variesfrom around �1 to �5‰ for naturally occurring reductants(Basu and Johnson, 2012; Qin and Wang, 2017; Zhanget al., 2018). Because the multitude of possible reductantsand wide range of environmental conditions (e.g., pH)make it impractical to measure e for every reductant andunder every condition, the ability to predict e for relatedreductants from limited experimental data is valuable inorder to interpret isotopic fractionation observed in naturalsystems.

In this study, we determine whether kinetic isotope frac-tionation during Cr(VI) reduction by Fe(II/III)-bearingclay minerals can be predicted from variables such as pH,Fe content, and the Fe(II)/Fe(total) (XFe(II)) ratio. Clayminerals were chosen because they are ubiquitous in sub-surface environments and are important natural reductantsfor Cr(VI) (Bishop et al., 2014; Joe-Wong et al., 2017;Bishop et al., 2019), radionuclides (Jaisi et al., 2008a;Qafoku et al., 2017), and other pollutants (Haghsereshtet al., 2009; Pham et al., 2012). Not only does the high sur-face area of clays make them good adsorbents, but Fe(II/III)-bearing clays can also act as redox buffers that can reg-ulate environmental redox conditions (Eh) or directlyreduce contaminants (Gorski et al., 2012a; Gorski et al.,2012b; Gorski et al., 2013). Two 2:1 clay minerals are con-sidered here, an Fe-poor montmorillonite and an Fe-richnontronite, at two pH values (7.3 and 5.5) and a range ofXFe(II) values.

Previous work demonstrated that the bulk kinetics of Cr(VI) reduction by Fe(II/III)-bearing clays vary by orders ofmagnitude with XFe(II), suggesting that XFe(II) may alsogovern kinetic isotope effects (Joe-Wong et al., 2017).Changing XFe(II) of each clay changes the standard freeenergy (DGr�) of Cr(VI) reduction, whereby a more reducedclay (high XFe(II)) is a stronger reductant of Cr(VI), andDGr� of Cr(VI) reduction is more negative (Gorski et al.,2012a; Gorski et al., 2012b; Gorski et al., 2013). This sim-ulates variable environmental redox conditions, where aclay with a higher XFe(II) would be found in a more reduc-ing environment and vice versa. By systematically changingthe initial XFe(II) of each clay, we were able to observe a lin-ear free energy relationship that describes Cr isotope frac-tionation by both clays at both pH values. This linearfree energy relationship may allow quantitative modelingof Cr kinetic isotope effects in natural systems where Fe(II/III)-bearing clays are the primary reductant.

2. METHODS

2.1. Materials

Two clays were purchased from the Clay MineralsSociety (http://clays.org), a nontronite (NAu-2,

M0.72(Al0.34Fe3.54Mg0.05)(Si7.55Al0.16Fe0.29)O20(OH)4) (Gateset al., 2002) and a montmorillonite (SWy-2, Ca0.52Na0.14K0.01

(Al3.23Fe0.42Mg0.56)(Si7.89Al0.14)O20(OH)4) (Mermut andCano, 2001). To eliminate impurities, the clay mineralswere sonicated and size fractionated (<2 lm) (Keelinget al., 2000; Chipera and Bish, 2001). The clays were thenfurther size fractionated to eliminate particles smaller than0.2 lm so that the reaction could be quickly stopped by fil-tering out the clay. Both clay minerals were then saturatedwith Na+ by repeatedly suspending them in 1 M NaCl.Scanning electron microscopy and dynamic light scatteringwere used to verify the size fractionation, and X-ray diffrac-tion was used to verify that no Fe oxides or other impuritieswere present. A small amount of quartz remained in bothclays, but no other impurities were detected. The montmo-rillonite contains 2.3 wt.% Fe and the nontronite 23.7 wt.%Fe, as detected with X-ray fluorescence spectrometry, whichis consistent with literature results (Keeling et al., 2000;Taylor et al., 2000; Mermut and Cano, 2001; Bishopet al., 2014; Soltermann et al., 2014).

Almost all Fe in the clay minerals is present as Fe(III)(Bishop et al., 2014). To reduce this Fe(III), the clays wereabiotically reduced in an anaerobic glovebox (Russell et al.,1979; Stucki et al., 1984; Komadel et al., 1990; Ribeiroet al., 2009; Stucki, 2011; Stucki et al., 2014). In brief,sodium dithionite was added to each clay in a sodiumcitrate/bicarbonate buffer. The ratio of sodium dithionite:-clay and the temperature and duration of the reaction werevaried to produce different XFe(II) values. All solutions weremade with doubly deionized water that had been spargedwith N2 and allowed to equilibrate with the glovebox atmo-sphere for at least 1 day. All bottles were made of HDPEplastic and were washed with acid and allowed to equili-brate with the glovebox atmosphere for at least 1 day priorto use.

XFe(II) was determined for each clay using synchrotron-based Fe K-edge X-ray absorption near edge structure(XANES) spectroscopy (Table 1). XANES spectroscopywas conducted at beamline 11-2 at the Stanford Syn-chrotron Radiation Lightsource using a Si (2 2 0) crystalat / = 90�. Clay samples were partially dried and sand-wiched between Fe-free Kapton tape. The sample chamberwas purged with He at room temperature. To reduce signalnoise, Soller slits and a Mn filter were mounted outside thechamber. Sample fluorescence was measured with a Gearray detector, and spectra were collected in 0.2 eV incre-ments around the Fe absorption edge. No damage to thesamples was observed after repeated scans. An Fe metalstandard was measured simultaneously with every sample,and the first maximum of the first derivative of the standardspectrum was calibrated at 7112.0 eV. XANES scans werecalibrated and averaged in SixPack (Webb, 2005), and theywere normalized in Demeter by fitting a first-order polyno-mial to the pre-edge region and a second-order polynomialto the post-edge region (Ravel and Newville, 2005). XFe(II)

was determined through linear combination fitting, usingthe native (oxidized) and fully reduced spectra of each clayas references. Samples were also fit with a library of Festandards, but no other Fe species were detected in anysample.

Table 1Thermodynamic and kinetic properties of the montmorillonite (SWy-2) and nontronite (NAu-2). R2 values are for the linearized fit of Cr(VI)concentrations with time to a second-order rate law for each reactor. Rate constants for the most highly reduced nontronite (XFe(II) = 0.98)could not be accurately determined due to the speed of the reaction.

XFe(II) E�eff (V) Log(k) (M�1 s�1) (pH 7.3) R2 (pH 7.3) Log(k) (M�1 s�1) (pH 5.5) R2 (pH 5.5)

SWy-2 0.93 �0.13 0.59 0.96, 0.92 1.57 0.98, 0.980.84 �0.05 0.93 0.99, 0.99 1.84 0.99, 0.990.73 0.00 �0.23 0.93, 0.93 0.88 0.88, 0.890.54 0.07 0.51 0.99, 0.98 1.22 0.98, 0.98

NAu-2 0.98 �0.72 – – – –0.89 �0.38 1.74 0.96, 0.74 2.58 0.90, 0.930.77 �0.21 1.13 0.84, 0.89 1.92 0.98, 0.98. 0.940.44 0.09 1.46 0.96, 0.98 2.30 0.97, 0.970.26 0.27 �0.54 0.80, 0.81 0.05 0.76, 0.87

C. Joe-Wong et al. /Geochimica et Cosmochimica Acta 292 (2021) 235–253 237

2.2. Experimental Setup

All isotope experiments were conducted in constantlystirred batch reactors under dark conditions in an anaero-bic glovebox. Every experiment was replicated at least once.Reactors contained an ionic strength buffer of 10 mMsodium chloride and were buffered at pH 7.3. or 5.5 by0.5 mM sodium 4-(2-hydroxyethyl)-1-piperazineethanesulfonate (HEPES) or sodium acetate, respectively. Controlexperiments with Cr(VI) and each buffer showed that nei-ther buffer reacted with Cr(VI), and separate control exper-iments with Cr(VI), buffer, and each native, fully oxidizedclay showed that Cr(VI) does not adsorb on the oxidizedclay (Joe-Wong et al., 2017). A large excess of clay was pre-sent in each experiment in order to keep XFe(II) reasonablyconstant over the course of the reaction. Total Fe was keptconstant instead of Fe(II) so that the surface area of eachclay would be constant, allowing comparison of reactorswith different XFe(II) values. The starting molar Cr:Fe ratiowas 0.033 for the montmorillonite reactors and 0.017 forthe nontronite reactors. These Cr:Fe ratios correspond to0.73 g montmorillonite/L and 0.14 g nontronite/L (300and 600 lM Fe respectively) for 10 lM Cr(VI).

Each clay was suspended in the pH and ionic strengthbuffers overnight to allow equilibration. The reaction wasinitiated by adding a 200 lM sodium chromate stock tothe constantly stirred reactor to reach a final concentrationof 10 lM Cr(VI). The time for the reaction to reach com-pletion ranged from minutes to weeks (Tables 2–5). Ali-quots were taken at specified intervals and immediatelypassed through a 0.2 lm polyethersulfone (PES) syringe fil-ter to arrest the reaction. A subsample was taken from eachfiltered aliquot to determine the Cr(VI) concentration spec-trophotometrically with diphenylcarbazide (EnvironmentalProtection Agency, 1992) with reproducibility within 3%.Chromium(VI) concentrations and timestamps were usedto quantify reaction kinetics for all reactors except for themost highly reduced nontronite (XFe(II) = 0.98). For thisclay, all Cr(VI) was reduced in less than 2 minutes. Becausesampling and filtering an aliquot large enough for spec-trophotometric and isotopic analysis took �20 seconds,determining a precise timestamp was not possible. For allreactors, the rest of the aliquot was treated for isotopicanalysis.

2.3. Isotopic analysis

A double isotope spike solution (50Cr and 54Cr) wasadded to each sample to correct for isotopic fractionationfrom sample preparation and instrumental mass bias (Joe-Wong et al., 2019). In brief, 50Cr and 54Cr metals wereobtained from Isoflex (San Francisco, CA), gravimetricallycombined, and dissolved in a solution with a target50Cr/54Cr of approximately 1 (Rudge et al., 2009). The spikewas calibrated by combining it with the NIST SRM 979 Crstandard at various spike-sample ratios and measuring theresulting isotopic compositions. The isotopic compositionof the spike was determined using accepted values for NISTSRM 979, as detailed in Joe-Wong et al. (2019). For eachrun, a new batch of spike was oxidized to Cr(VI) with hydro-gen peroxide and ammonium hydroxide. The oxidized spikewas then added to each sample for a ratio of spike Cr:totalCr � 0.4. The spike was allowed to equilibrate overnightwith the sample. Samples were purified using standard proce-dures (Ellis et al., 2002; Basu and Johnson, 2012). In brief,samples were placed on anion exchange columns (AG1X8resin, 100–200 mesh, Eichrom). Cations were eluted, andadsorbed Cr(VI) was reduced to Cr(III), allowed to reactovernight, and eluted with 2 M nitric acid and hydrogen per-oxide. Column yields were approximately 70%.

Because the anion column did not remove all Fe fromthe sample, the sample was treated with hydrogen peroxideand ammonium hydroxide to oxidize the Cr(III) to Cr(VI)and precipitate Fe as an Fe(III) oxyhydroxide. The Cr(VI)was then dissolved in water, and the sample was filtered(0.2 lm, PES) to remove Fe. Finally, the sample wasreduced back to Cr(III), and organic residue from the resinwas destroyed by repeatedly treating the samples with 30wt.% hydrogen peroxide and 15 M nitric acid. The effectsof any remaining 54Fe on the 54Cr/52Cr ratio were itera-tively removed with the spike deconvolution algorithm asdescribed in the Electronic Annex.

All Cr isotopic ratios were measured on a multi-collectorinductively-coupled-plasma mass spectrometer (NeptunePlus, Thermo Fisher) at Lawrence Berkeley National Lab-oratory in medium resolution. Samples were dissolved in2% nitric acid to yield �0.2 lg 52Cr/mL. Isotopic composi-tions are reported in d notation as deviations from NISTSRM 979:

Table 2Chromium isotopic compositions of the remaining Cr(VI) during Cr(VI) reduction by montmorillonite at various values of XFe(II) and pH 7.3for replicate reactors.

XFe(II) Time (h) Fraction Cr(VI) remaining d53Cr(VI) (‰) Time (h) Fraction Cr(VI) remaining d53Cr(VI) (‰)

0.93 0.01 1 0.27 0.02 1 0.300.76 0.76 1.24 0.75 0.76 1.282.00 0.64 1.89 2.03 0.63 1.998.19 0.39 3.71 5.17 0.47 3.0311.25 0.32 4.34 7.78 0.40 3.7225.63 0.15 7.51 11.25 0.33 4.53

0.84 0.01 1 0.32 0.02 1 0.310.75 0.72 1.40 0.75 0.74 1.572.00 0.59 2.25 2.03 0.58 2.394.57 0.41 3.46 5.17 0.39 3.898.18 0.28 4.77 7.78 0.30 4.8811.25 0.21 5.85 11.25 0.24 6.2125.63 0.04 10.89 – – –

0.73 0.02 1 0.36 0.02 1 0.222.08 0.77 1.42 2.08 0.77 1.285.20 0.67 2.05 5.20 0.65 1.9211.27 0.55 2.92 11.27 0.54 2.7625.48 0.43 4.00 25.48 0.41 3.8756.22 0.29 5.57 56.22 0.28 5.5598.7 0.18 7.45 98.7 0.17 7.45

0.54 0.02 1 �0.01 0.02 1 0.022.08 0.67 1.41 2.08 0.70 1.2426 0.16 6.68 26 0.20 5.9133 0.08 8.23 33 0.12 7.88

Table 3Chromium isotopic compositions of the remaining Cr(VI) during Cr(VI) reduction by montmorillonite at various values of XFe(II) and pH 5.5for replicate reactors.

XFe(II) Time (h) Fraction Cr(VI) remaining d53Cr(VI) (‰) Time (h) Fraction Cr(VI) remaining d53Cr(VI) (‰)

0.93 0.01 1 0.81 0.01 1 0.490.50 0.73 1.52 0.50 0.68 2.161.00 0.49 3.14 1.00 0.45 3.262.00 0.23 5.88 2.00 0.21 5.933.00 0.14 7.17 3.00 0.12 7.544.17 0.09 9.13 4.18 0.07 9.45

0.84 0.005 1 0.37 0.004 1 0.090.17 0.78 1.12 0.17 0.82 0.050.50 0.54 2.53 0.50 0.58 1.911.01 0.27 6.22 1.00 0.18 6.261.50 0.15 6.31 1.50 0.12 7.092.00 0.10 8.30 2.01 0.05 8.383.02 0.04 10.96 3.01 – –

0.73 0.02 1 0.58 0.02 1 0.242.10 0.33 4.54 2.10 0.32 5.114.98 0.19 6.38 4.98 0.18 6.647.62 0.14 7.84 7.62 0.13 8.0310.85 0.11 8.73 10.85 0.09 9.11

0.54 0.02 1 0.11 0.02 1 0.201.92 0.40 2.93 1.92 0.31 4.126.02 0.16 5.83 6.02 0.12 6.838.02 0.10 7.40 8.02 0.07 8.93

238 C. Joe-Wong et al. /Geochimica et Cosmochimica Acta 292 (2021) 235–253

Table 4Chromium isotopic compositions of the remaining Cr(VI) during Cr(VI) reduction by nontronite at various values of XFe(II) and pH 7.3 forreplicate reactors. Timestamps for the most highly reduced nontronite (XFe(II) = 0.98) could not be accurately determined due to the speed ofthe reaction, which reaches completion in less than 2 minutes.

XFe(II) Time Fraction Cr(VI) remaining d53Cr(VI) (‰) Time Fraction Cr(VI) remaining d53Cr(VI) (‰)

0.98 – 1 1.54 – 1 1.08– 0.52 2.57 – 0.69 1.70– 0.28 3.51 – 0.52 2.09– 0.14 4.21 – 0.43 2.56– 0.06 4.94 – 0.33 2.84– – – – 0.19 3.65

0.89 (min) (min)0.40 1 1.45 0.38 1 1.111.77 0.65 2.44 1.75 0.65 2.004.82 0.47 3.05 4.92 0.48 2.649.90 0.38 3.71 10.05 0.40 3.2019.95 0.29 4.28 20.33 0.31 3.7432.32 0.25 4.70 29.82 0.27 4.1160.72 0.17 5.42 67.40 0.19 4.95

0.77 (h) (h)0.01 1 1.36 0.01 1 1.350.03 0.79 2.06 0.03 0.71 2.320.08 0.69 2.43 0.08 0.57 2.960.25 0.55 3.17 0.25 0.40 4.120.49 0.45 3.77 0.50 0.30 5.001.00 0.38 4.33 1.00 0.21 6.172.82 0.27 5.63 2.82 0.10 7.785.23 0.20 6.97 – – –7.40 0.15 7.43 – – –

0.44 (d) (d)0.001 1 0.29 0.001 1 0.100.88 0.58 1.92 0.40 0.72 1.051.21 0.54 2.23 0.96 0.64 1.561.94 0.46 2.77 2.01 0.52 2.093.01 0.38 3.45 4.06 0.36 3.244.92 0.27 4.50 8.06 0.23 4.587.28 0.19 5.89 – – –

0.26 (d) (d)0.001 1 0.21 0.001 1.00 0.090.34 0.87 0.68 0.27 0.91 0.741.00 0.82 0.89 2.20 0.84 1.412.08 0.78 1.25 6.01 0.72 1.804.06 0.70 1.75 15.99 0.51 3.509.02 0.64 2.31 – – ––

C. Joe-Wong et al. /Geochimica et Cosmochimica Acta 292 (2021) 235–253 239

d53Cr ¼53Cr= 52Crð Þsample

53Cr= 52Crð Þ979� 1

!ð1Þ

Spiked standard NIST SRM 979 (d53Cr defined as 0‰)was measured between every three samples. Over tenmonths, the average d53Cr of the standard was 0.03± 0.07‰ (2S.D., n = 199), and an oxidized sample of NISTSRM 979 processed in parallel with samples had a statisti-cally indistinguishable d53Cr of 0.01‰. All measured d val-ues were corrected for sample preparation and instrumentalmass isotopic fractionation by deconvoluting the doublespike, as discussed further in the Electronic Annex(Rudge et al., 2009).

The isotopic fractionation factor for each experimentwas estimated from the linearized Rayleigh equation usinga weighted linear regression (York et al., 2004). Theweighted average was determined for isotopic fractionationfactors from replicate experiments, and reported uncertain-ties are two standard errors of this weighted average.

3. RESULTS

Chromium(VI) was removed from solution in all reac-tors. Adsorption of Cr(VI) on oxidized montmorilloniteand nontronite is minimal under the experimental condi-tions, so all lost Cr(VI) is assumed to have been reduced

Table 5Chromium isotopic compositions of the remaining Cr(VI) during Cr(VI) reduction by nontronite at various values of XFe(II) and pH 5.5 forreplicate reactors. Timestamps for the most highly reduced nontronite (XFe(II) = 0.98) could not be accurately determined due to the speed ofthe reaction, which reaches completion in less than 2 minutes.

XFe(II) Time Fraction Cr(VI) remaining d53Cr(VI) (‰) Time Fraction Cr(VI) remaining d53Cr(VI) (‰)

0.98 – 1 0.00 – 1 0.18– 0.77 0.30 – 0.56 0.88– 0.65 0.32 – 0.40 2.72– 0.49 0.75 – 0.23 4.72– 0.37 1.81 – – –– 0.23 3.05 – – –– 0.15 3.57 – – –

0.89 (min) (min)0.33 1 1.64 0.38 1 2.030.77 0.70 2.36 0.90 0.89 2.411.22 0.54 2.68 1.40 0.57 2.791.95 0.43 3.30 2.80 0.38 3.904.82 0.25 4.61 5.13 0.25 4.749.92 0.14 5.71 11.28 0.12 6.0615.32 0.10 6.49 15.80 0.08 6.82

0.77 (h) (h)0.005 1 2.15 0.007 1 1.350.03 0.72 2.97 0.03 0.75 1.880.08 0.54 4.01 0.08 0.54 2.730.25 0.31 4.85 0.25 0.34 4.100.50 0.18 6.19 0.49 0.18 5.871.00 0.04 8.52 0.99 0.05 8.19

0.77 (h) –0.01 1 1.48 – – –0.04 0.84 2.03 – – –0.09 0.70 2.63 – – –0.26 0.52 3.64 – – –0.51 0.40 4.25 – – –1.01 0.28 5.07 – – –1.51 0.19 6.18 – – –

0.44 (d) (d)0.001 1 0.32 0.001 1 0.320.04 0.69 1.78 0.02 0.78 1.200.08 0.63 2.19 0.04 0.73 1.560.13 0.57 2.49 0.08 0.66 1.940.21 0.50 3.04 0.18 0.54 2.630.33 0.40 3.70 0.40 0.39 3.801.06 0.15 6.89 0.96 0.21 5.991.34 0.10 8.11 2.00 0.08 10.02

0.26 (d) (d)0.001 1 0.35 0.001 1 0.200.30 0.71 1.57 0.26 0.86 1.960.95 0.60 2.16 0.97 0.55 2.952.03 0.54 2.43 2.20 0.48 3.504.01 0.52 3.11 6.01 0.45 3.748.97 0.51 3.19 15.98 0.43 4.01

240 C. Joe-Wong et al. /Geochimica et Cosmochimica Acta 292 (2021) 235–253

to Cr(III) and removed by precipitation (Joe-Wong et al.,2017). The rate of removal is generally consistent with apreviously demonstrated second-order rate law (Joe-Wonget al., 2017) (Table 1):

d½Cr VIð Þ�dt

¼ �k½Cr VIð Þ� XFeðIIÞ � f Fe � dclay

MW Fe

� �ð2Þ

where k is the second-order rate constant (M�1 min�1), XFe

(II) is the fraction of Fe present as Fe(II), fFe is the weightfraction of Fe in the clay (g Fe/g clay), dclay is the clay min-eral suspension density (g clay/L), and MWFe is the molec-ular weight of Fe (g/mol). Thus, the term in parenthesesdenotes the effective concentration of Fe(II) as if it werean aqueous species. For some of the more highly reduced

C. Joe-Wong et al. /Geochimica et Cosmochimica Acta 292 (2021) 235–253 241

nontronite reactors, more Cr(VI) was lost in the �20 sec-onds prior to the first sampling point than predicted byEq. (2). This lost Cr(VI) may be reduced by a small fractionof Fe(II) sorbed to the clay surface that is an extremely fastreductant (Jaisi et al., 2008b). However, the rest of the reac-tion can be described with a single second-order rate con-stant under all reaction conditions, consistent with otherstudies of Cr(VI) and nitroaromatic reduction by clays(Neumann et al., 2008; Bishop et al., 2014; Joe-Wonget al., 2017).

Chromium(VI) reduction was accompanied in all reac-tors by isotopic fractionation that progressively enrichedthe remaining Cr(VI) in the heavier 53Cr isotope (Tables2–5). All isotopic fractionation is assumed to be kineticbecause isotopic exchange between aqueous Cr(VI) andsolid Cr(III) hydroxide, which is the major product ofreduction (Joe-Wong et al., 2017), takes place on the orderof years (Wang et al., 2015), and these experiments wereconducted over a much shorter timescale (<10 days). Iso-

Fig. 1. Isotopic fractionation during Cr(VI) reduction by montmorilloni

(II) = 0.84, (c) XFe(II) = 0.73, (d) XFe(II) = 0.54. Each plot shows the enricduplicate reactors in the filled and open symbols. Rayleigh curves baseddotted lines (open symbols). Vertical error bars (2 S.D.) are smaller thaTable 2.

topic fractionation in these experiments is also assumedto be primarily due to Cr(VI) reduction, not Cr(VI) adsorp-tion. Because Cr(VI) is reduced to Cr(III) immediately afteradsorption on the Fe(II/III)-bearing clays used in this studyand Cr(VI) does not adsorb on the fully oxidized, Fe(III)-bearing clays (Joe-Wong et al., 2017), directly measuringisotopic fractionation during Cr(VI) adsorption on clayswas not possible. However, in general, Cr(VI) adsorptionis believed to cause little isotopic fractionation, as discussedfurther in Section 4.3 (Ellis et al., 2004). Accordingly, eachexperiment was fit by a Rayleigh distillation model with asingle isotopic fractionation factor (e) (Figs. 1–4, Table 6):

d53Cr VIð Þ � d53Cr VIð Þ0 þ e ln½Cr VIð Þ�½Cr VIð Þ�0

� �� �ð3Þ

Thus, e is negative for all reactors because the remainingCr(VI) is enriched in the heavier 53Cr isotope. As discussedabove, in some reactors, more Cr(VI) is lost before the firstsampling point than accounted for by the second-order rate

te at pH 7.3 for various values of XFe(II): (a) XFe(II) = 0.93, (b) XFe

hment of 53Cr in the remaining Cr(VI) as the reaction progresses foron linear best fits are plotted as dashed lines (filled symbols) andn the symbols. The plotted data with timestamps are available in

Fig. 2. Isotopic fractionation during Cr(VI) reduction by montmorillonite at pH 5.5 for various values of XFe(II): (a) XFe(II) = 0.93, (b) XFe

(II) = 0.84, (c) XFe(II) = 0.73, (d) XFe(II) = 0.54. Each plot shows duplicate reactors in the filled and open symbols. Rayleigh curves based onlinear best fits are plotted as dashed lines (filled symbols) and dotted lines (open symbols). Vertical error bars (2 S.D.) are smaller than thesymbols. The plotted data with timestamps are available in Table 3.

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law. Because this lost Cr(VI) is likely not reduced by clay-bound Fe(II), it was not included in the Rayleigh model,and the concentration of Cr(VI) and d53Cr(VI) at the firstsampling point were taken as [Cr(VI)]0 and d53Cr(VI)0respectively. The R2 value for the linearized Rayleigh modelwas greater than 0.93 for all experiments and greater than0.995 for most experiments.

Isotopic fractionation is generally consistent betweenduplicate reactors. However, some variation in e is apparentbetween replicate experiments for the nontronite at highXFe(II) levels, where Cr(VI) reduction is fast (Figs. 3a and4a). These variations are likely caused by insufficient mix-ing. Although the reactors were constantly stirred, completeCr(VI) reduction by the highly reduced nontronite isachieved within a few minutes. For these fast reactors, Cr(VI) reduction that occurs immediately after the Cr(VI)stock is added to the reactor, before it fully mixes withthe clay suspension, can decrease the magnitude ofobserved isotopic fractionation due to diffusive limitations(Kitchen et al., 2012). Furthermore, because the reaction

is so fast, significant Cr(VI) reduction may occur duringthe �20 seconds it takes to sample and filter an aliquot,during which the aliquot in the syringe may not be com-pletely mixed.

Isotopic fractionation factors for all experiments rangefrom �1.29 to �4.85‰ (Table 6). Variables that may controle include the rate of reaction, XFe(II), the total Fe content ofthe clay, and pH. Our results demonstrate that e is stronglylinearly correlated with log(k) (R2 = 0.82) (Fig. 5a). Fasterreactions have less isotopic fractionation, consistent with pre-vious qualitative observations for Cr(VI) reduction by unre-lated reductants (Sikora et al., 2008; Basu and Johnson,2012; Jamieson-Hanes et al., 2014) as well as quantitativeobservations for Cr(VI) reduction by aqueous Fe(II) com-plexes (Joe-Wong et al., 2019). Furthermore, the magnitudeof isotopic fractionation is generally smaller for more highlyreduced clays, although the relationship between e and XFe

(II) is non-linear (Fig. 5b).In contrast, the total Fe content of the clay and pH do

not strongly affect e. Although the range of e is smaller

Fig. 3. Isotopic fractionation during Cr(VI) reduction by nontronite at pH 7.3 for various values of XFe(II): (a) XFe(II) = 0.98, (b) XFe

(II) = 0.89, (c) XFe(II) = 0.77, (d) XFe(II) = 0.44, (e) XFe(II) = 0.26. Rayleigh curves based on linear best fits are plotted as dashed lines (filledsymbols) and dotted lines (open symbols). Vertical error bars (2 S.D.) are smaller than the symbols. The plotted data with timestamps areavailable in Table 4.

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for the Fe-poor montmorillonite (�3.16 to �4.15‰) thanfor the Fe-rich nontronite (�1.29 to �4.85‰), this is likelybecause the range of XFe(II) values tested in this study is

smaller for the montmorillonite (0.93–0.54, vs. 0.98–0.26for the nontronite) (Fig. 5b). The effect of pH on e is morecomplex. For the montmorillonite, pH has a slight but

Fig. 4. Isotopic fractionation during Cr(VI) reduction by nontronite at pH 5.5 for various values of XFe(II): (a) XFe(II) = 0.98, (b) XFe

(II) = 0.89, (c) XFe(II) = 0.77, (d) XFe(II) = 0.44, (e) XFe(II) = 0.26. Rayleigh curves based on linear best fits are plotted as dashed lines (filledsymbols), dotted lines (open symbols), and dashed-dotted lines (filled blue symbols). Vertical error bars (2 S.D.) are smaller than the symbols.The plotted data with timestamps are available in Table 5.

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significant effect: e is more negative at pH 7.3 than at pH5.5, with an average difference of 0.34 ± 0.07‰ (paired t-test, two-tail p = 0.02). For the nontronite, e does not fol-

low a consistent trend with pH. Although e varies by asmuch as 1‰ for reactors with the same XFe(II) but differentpH values, decreasing the pH from 7.3 to 5.5 does not

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consistently decrease the magnitude of e, or vice versa. Theeffects of pH are discussed further in Section 4.3.

4. DISCUSSION

4.1. Thermodynamic controls on isotopic fractionation

Changes in e are clearly associated with changes in XFe

(II), as well as log(k), but the relationship between e andXFe(II) is non-linear. To understand more quantitativelyhow XFe(II) affects kinetic isotopic fractionation, we consid-ered the effect of XFe(II) on the redox potential of the clays.

Electrochemical characterization of the electron-donating/accepting properties of Fe(II/III)-bearing clays

Table 6Isotopic fractionation factors for Cr(VI) reduction by montmorilloniteduplicate reactors for all conditions except for NAu-2, pH 5.5, XFe(II) =

Clay pH XFe

SWy-2 7.3 0.930.840.730.54

5.5 0.930.840.730.54

NAu-2 7.3 0.980.890.770.440.26

5.5 0.980.890.770.440.26

Fig. 5. Dependence of kinetic isotope fractionation factor on a) log of thfor Cr(VI) reduction by nontronite clay (NAu-2) and montmorillonite claarrows show the direction in which Cr(VI) reduction is more thermodyn

by Gorski et al. has shown that XFe(II) controls their stan-dard reduction potential (E�) (Gorski et al., 2012a, 2012b,2013). Iron occupies a variety of sites in the clay structure,and the relative favorability of occupancy by Fe(II) or Fe(III) differs for each site, depending on its coordination.Each site thus has a unique E�, and the effective standardreduction potential (E�eff) of the bulk clay depends on XFe

(II). If XFe(II) is high, then most Fe-bearing sites are occu-pied by Fe(II), even sites that would prefer occupancy by Fe(III). Reducing the few remaining Fe(III)-bearing sites isunfavorable, so E�eff of the clay is low and re-oxidation ofthe clay by Cr(VI) is favorable, resulting in a more negativeDGr� for Cr(VI) reduction. In contrast, if XFe(II) is low,then most Fe-bearing sites are occupied by Fe(III), except

(SWy-2) and nontronite (NAu-2) are the weighted averages of0.77 (triplicate reactors), as shown in Tables 2–5.

(II) e (‰) 2S.E.

�3.68 0.12�3.47 0.08�4.19 0.13�3.48 0.09�3.39 0.07�3.27 0.06�3.66 0.09�3.16 0.08

�1.29 0.05�2.32 0.09�3.06 0.08�3.22 0.12�4.9 0.5�2.33 0.09�1.98 0.05�2.20 0.04�3.58 0.08�4.1 0.3

e rate constant and b) the fraction of reduced iron (Fe(II)/Fe(total)y (SWy-2). Dotted curves show 95% confidence bounds. The blackamically favorable in the standard state, i.e. DGr� is more negative.

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for sites that strongly prefer occupancy by Fe(II). Reduc-tion of the clay is relatively favorable, so E�eff of the clayis high, and re-oxidation of the clay by Cr(VI) is unfavor-able, resulting in a less negative DGr� for Cr(VI) reduction.Gorski et al. (2013) demonstrate that the relationshipbetween XFe(II) and E�eff of each clay in this study can bequantitatively described with a modified Nernst equation:

E�eff ¼ E/ þ b

b� 1

� �0:059log

XFe IIð Þ1� XFe IIð Þ

� �ð4Þ

where E/ and b are clay-specific constants.The relationship between XFe(II) and E�eff allows us to

quantify the effect of XFe(II) on Cr(VI) reduction kineticswith a linear free energy relationship (Fig. 6). For the non-tronite, e is strongly linearly correlated with E�eff of thenontronite, which is a proxy for DGr�, at both pH values(Fig. 6a and b). The slope of the linear correlation at pH

Fig. 6. Linear relationship between kinetic isotopic fractionation factor anontronite clay (NAu-2) at pH 7.3, (b) nontronite clay at pH 5.5, and (c)curves show 95% confidence bounds. The black arrows show the directionthe standard state, i.e. DGr� is more negative.

7 (�3.7 ± 2) (Fig. 6a) is greater than at pH 5 (�2.1 ± 1.7)(Fig. 6b), but the difference is not statistically significant.For the montmorillonite, e does not vary significantly withE�eff of the clay. However, e values for the montmorilloniteare consistent with the those predicted by the linear rela-tionship between e and E�eff of the nontronite (R2 = 0.76)(Fig. 6c). From these linear free energy relationships andEq. (4), model curves for the relationship between e andXFe(II) can be back-calculated (Fig. 7).

4.2. Marcus theory and redox-driven kinetic isotope effects

The empirical linear correlation between e and E�eff canbe understood using Marcus electron transfer theory. Mar-cus theory describes the kinetics of electron transfer reac-tions in terms of thermodynamic parameters such as DGr�(Marcus, 1964; Marcus and Sutin, 1985). Specifically, the

nd effective standard reduction potential for Cr(VI) reduction by (a)nontronite and montmorillonite (SWy-2) at pH 7.3 and 5.5. Dottedin which Cr(VI) reduction is more thermodynamically favorable in

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activation energy (Ea) and thus the rate constant (k) of elec-tron transfer can be written as a function of DGr� and thereorganization energy (k), which is defined as the hypothet-ical energy necessary for the spatial transformations duringthe electron transfer (e.g., changes in bond lengths) to occurwithout the electron transferring. For a set of related redoxreactions, Marcus theory generally predicts a log-linearrelationship between the rate constant (k) of electron trans-fer and DGr�: redox reactions with more negative DGr� val-ues, which are more thermodynamically favorable in thestandard state, are typically faster by orders of magnitude(Fig. 8a).

The log(k)-DGr� linear relationship predicted by Marcustheory has been validated for many geochemical systems,including Cr(VI) reduction by aqueous Fe(II) species(Buerge and Hug, 1997; Buerge and Hug, 1998) and Cr(VI) reduction by Fe(II/III)-bearing clay minerals (Joe-

Fig. 7. Dependence of kinetic isotope fractionation factor on the fractireduction by (a) nontronite clay (NAu-2) at pH 7.3, (b) nontronite clay atand 5.5. Black lines show the linear best fit for the relationship betwereduction potential. The black arrows show the direction in which Cr(Vstate, i.e. DGr� is more negative.

Wong et al., 2017). In this study, we were unable to repli-cate the linear free energy relationship observed in Joe-Wong et al. (2017), likely due to the difficulty collectingkinetic and isotopic data for the same experiment. In orderto get samples that contained enough Cr(VI) at a suffi-ciently high concentration compared to the other ions pre-sent from the buffers and clay dissolution that they could bepurified for isotopic analysis, reactors were designed to besampled only until the fraction of remaining Cr(VI) was�0.1–0.2 (Tables 2–5). In contrast, in previous kinetics-only experiments, reactors were sampled until the fractionof remaining Cr(VI) was less than 0.01, and the greaterrange allowed k to be determined more accurately and pre-cisely (Joe-Wong et al., 2017). Additionally, for the non-tronite at XFe(II) = 0.98, the reaction was too fast toestimate k, which eliminates an endmember for the putativelinear free energy relationship. Other possible

on of reduced iron (Fe(II)/Fe(total)) for Cr(VI) reduction Cr(VI)pH 5.5, and (c) nontronite and montmorillonite (SWy-2) at pH 7.3en the kinetic isotope fractionation factor and effective standardI) reduction is more thermodynamically favorable in the standard

Fig. 8. Marcus theory predicts quasi-linear relationships between (a) log of the rate constant and standard free energy of reaction, (b) kineticisotope fractionation factor and standard free energy of reaction, and (c) kinetic isotope fractionation factor and log of the rate constant. Thekinetic isotope fractionation factor is assumed to be negative in these plots.

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complications in these experiments include differences insurface area between clay stocks of different vintages. Ulti-mately, we assume that the linear log(k)-DGr� relationshippreviously observed is valid and justifies the applicationof Marcus theory to kinetic isotope fractionation in thisstudy (Joe-Wong et al., 2017).

Marcus theory has more recently been extended to pre-dict that the kinetic isotope fractionation factor for electrontransfer also follows a linear free energy relationship,whereby more favorable redox reactions with increasinglynegative DGr� values induce less kinetic isotope fractiona-tion (Kavner et al., 2005; Joe-Wong and Maher, 2020). Inbrief, the kinetic isotope fractionation factor (ekin) is definedas the ratio of the rates of reaction for each isotopologue,and the equilibrium isotope fractionation factor (eeq) isdefined in terms of the difference between DGr� for each iso-topologue. Because Marcus theory writes k in terms of DGr�and k, the kinetic isotope fractionation factor can be writ-ten as a function of eeq, DGr�, and k (Marcus, 1965;Kavner et al., 2005; Joe-Wong and Maher, 2020):

ekin � DG�r eeq2k

þ eeq2

ð5Þ

For related reactions where eeq and k are expected to besimilar, ekin follows a linear free energy relationship anddecreases in magnitude as DGr� decreases and the reactionbecomes more thermodynamically favorable (Fig. 8b). Thisis consistent with the empirical linear correlation between eand E�eff observed in this study, where E�eff of the clay is aproxy for DGr� (Fig. 7). Such a linear free energy relation-ship has also been observed for a variety of geochemicallyrelevant reactions, including electrochemical reactions(Kavner et al., 2005; Kavner et al., 2008), nitroaromaticreduction by magnetite (Gorski et al., 2010), and Cr(VI)reduction by aqueous Fe(II) species (Joe-Wong et al.,2019).

Finally, because log(k) and ekin are both linearly corre-lated with DGr�, Marcus theory predicts as a corollary thatlog(k) and ekin should be linearly correlated with each other,whereby a more thermodynamically favorable reaction is

both faster and accompanied by less kinetic isotope frac-tionation (Fig. 8c). This is shown for Cr(VI) reduction byFe(II/III)-bearing clays in Fig. 5a.

4.3. Secondary effects on isotopic fractionation

The empirical linear free energy relationship accountsfor most of the variation in e for both clays. Because efor the montmorillonite can be predicted from the linearfree energy relationship for the nontronite (Fig. 6c), totalFe content and any consequent differences in the reactionmechanism of Cr(VI) reduction evidently does not signifi-cantly change e. However, pH may be a secondary influenceon e because electrostatic interactions between Cr(VI) andthe clay adsorption site depend on pH.

The mechanism of Cr(VI) reduction by Fe(II/III)-bearing clays has been well-studied (Bishop et al., 2014;Joe-Wong et al., 2017; Bishop et al., 2019). First, Cr(VI)adsorbs as an outer-sphere complex onto the clay edge orbasal plane. It is then reduced by Fe(II) in the clay structureand finally precipitated as a Cr(III) hydroxide. Chromiumisotope fractionation during adsorption is generally muchsmaller than isotopic fractionation during Cr(VI) reduction(Ellis et al., 2004). Nevertheless, because adsorption is thefirst step in Cr(VI) reduction, even slight isotopic fraction-ation during adsorption would carry over to the finalobserved fractionation, and so would any pH effects on iso-topic fractionation during adsorption (Schauble, 2004).Any isotopic fractionation during adsorption would beexpected to be kinetic, because adsorbed Cr(VI) is quicklyreduced to Cr(III) (Joe-Wong et al., 2017), and hence neg-ative, because lighter isotopes generally have a lower activa-tion energy barrier than heavier isotopes for non-electron-transfer reactions (Bigeleisen and Mayer, 1947).

Previous work has shown that Cr(VI) adsorbs to theclays in this study as an outer-sphere complex, likely at acombination of clay edge sites and basal plane sites(Bishop et al., 2014; Joe-Wong et al., 2017; Liu et al.,2018; Bishop et al., 2019). For both clays, the charge onthe basal plane does not depend on pH, but the edge is

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negatively charged at pH 7.3 and positively charged at pH5.5 (Tombacz and Szekeres, 2004; Jaisi et al., 2008b). Thus,adsorption of the Cr(VI) anion should be less favorable atpH 7.3, where the negatively charged Cr(VI) and negativelycharged clay edge electrostatically repel each other, than atpH 5.5, where the negatively charged Cr(VI) and positivelycharged clay edge electrostatically attract each other. Thisdifference makes it plausible that there may be a smallkinetic isotope effect during adsorption that is more nega-tive at the higher pH: because adsorption is less favorableat pH 7.3 than 5.5, adsorption likely has a larger kineticbarrier at pH 7.3. If the kinetic barrier is larger at pH7.3, then kinetic isotopic fractionation should also be largerin magnitude. Thus, the overall isotopic fractionationshould be more negative at pH 7.3 at 5.5, which wasobserved for the montmorillonite (Fig. 5, Table 6). Itremains unclear why pH does not consistently affect e forthe nontronite at different XFe(II) values. A potential expla-nation is that iron occupies most of the octahedral sites inthe nontronite (Keeling et al., 2000), so changing XFe(II)

induces more structural changes than for the montmoril-lonite. These structural changes in the nontronite may causethe edge structure of the nontronite at different XFe(II) val-ues to respond differently to changes in pH, and thus theeffect of pH on kinetic isotopic fractionation during Cr(VI) adsorption is inconsistent across different XFe(II) val-ues for the nontronite.

4.4. Implications for Cr as an isotopic proxy

This work reveals a strong thermodynamic trend inkinetic isotope fractionation during Cr(VI) reduction in alaboratory system. In natural systems, such a simple linearcorrelation is unlikely because isotopic fractionation due tophysical transport will modulate observed isotopic fraction-ation and equilibrium isotope fractionation is potentiallyimportant over long timescales (i.e., years) (Wang et al.,2015). Redox cycling, which would repeatedly enrich theremaining Cr(VI) in heavier Cr isotopes, may make it diffi-cult to even determine underlying values of e, althoughredox cycling would not directly alter e. Nevertheless, thethermodynamic dependence of kinetic isotope fractionationpredicted by Marcus theory may be an important compo-nent in a broader model of environmental isotopic fraction-ation that also incorporates reactive transport (Rolle et al.,2010; Druhan and Maher, 2016) and mixed kinetic andequilibrium isotope fractionation (DePaolo, 2011).

Another potential complication in natural environmentsis the multitude of possible reductants with different reac-tion mechanisms. Chromium(VI) reduction is a multistepprocess involving three electron transfers as well as achange from tetrahedral to octahedral coordination, andall steps up to and including the rate-determining step affectthe net kinetic isotope effect (Schauble, 2004). Unsurpris-ingly, the reaction mechanism and rate-determining stepfor Cr(VI) reduction vary with the reductant. For Cr(VI)reduction by Fe(II/III)-bearing clays, adsorbed Cr(VI)may be reduced by three distinct Fe(II) sites in the clay thatare in reasonably close proximity to the adsorbed Cr(VI)(Joe-Wong et al., 2017). Alternatively, adsorbed Cr(VI)

may be reduced by the single closest Fe(II) site, and oncethat site is oxidized to Fe(III), semiconductor-like intra-clay electron hopping from Fe(III) sites further away mayregenerate Fe(II) at that site, allowing subsequent electrontransfers to Cr(V) and Cr(IV). Chromium(V) and Cr(IV)intermediates may also disproportionate to form Cr(III)and re-form Cr(VI). The rate-determining step for Cr(VI)reduction by Fe(II/III)-bearing clays is likely after the firstelectron transfer because the slope of the linear correlationbetween log(k) and E�eff is smaller than expected for a singleelectron transfer (Joe-Wong et al., 2017). This reactionmechanism contrasts with Cr(VI) reduction by aqueousFe(II), for which the large slope of the linear correlationbetween log(k) and E� suggests that the first electron trans-fer (Cr(VI) ? Cr(V)) is rate-determining (Buerge and Hug,1997; Buerge and Hug, 1998). Marcus theory describeskinetic isotope fractionation during any electron transfer,so a linear free energy relationship would be expected forreductants that have the same mechanism and rate-determining step as well as similar values of DG�r and k(Joe-Wong and Maher, 2020). However, if the reactionmechanisms for two reductants are different, and differentelectron transfer reactions contribute to the observedkinetic isotope effect, a linear free energy relationship wouldnot necessarily apply.

An initial test to determine whether Marcus theory canpredict Cr(VI) reduction rates or kinetic isotope effectsfor a variety of reductants and reaction mechanisms is tocompare Cr(VI) reduction by Fe(II/III)-bearing clays andby aqueous Fe(II) species. These reductants are in differentphases and have different reaction mechanisms with differ-ent rate-determining steps. Comparing log(k) for both typesof reductants demonstrates that across overlapping rangesof E� (�0.7 to 0.3 V for Fe(II/III)-bearing clays; �0.1 to0.4 V for aqueous Fe(II)), Fe(II/III)-bearing clays areorders of magnitude slower reductants than aqueous Fe(II) species and have a much weaker dependence on E�(Fig. 9a). Thus, the linear free energy relationship betweenlog(k) and E� does not allow even qualitative prediction ofk in an environmental system where the overall redoxpotential (E�) is known but multiple reductants are present.In contrast, not only is e of similar magnitude for Fe(II/III)-bearing clays and aqueous Fe(II), but the linear corre-lation between e and E� of the reductant accounts for up to40% of observed variations in e across both types of reduc-tants (Fig. 9b). The correlation between e and E� does notallow quantitative prediction of e from E� if the actualreductant is unknown but nevertheless may provide a usefulrule of thumb. Further work is needed to determinewhether the correlation holds across other types of reduc-tants, especially biotic reductants, and whether e and E�are more strongly correlated for reductants that are in thesame phase or share other similarities. Even if no suchbroader correlation exists, both aqueous Fe(II) and Fe(II/III)-bearing clays are dominant reductants of Cr(VI) inmany natural systems (Fendorf et al., 2000; Joe-Wonget al., 2017; Bishop et al., 2019).

Iron(II/III)-bearing clays are ubiquitous in soils, includ-ing Cr(VI)-contaminated sites such as Hanford, Washing-ton, USA (Qafoku et al., 2017; Bishop et al., 2019), and

Fig. 9. Linear relationships between (a) log of the rate constant and standard reduction potential and (b) kinetic isotope fractionation factorand standard reduction potential for Cr(VI) reduction by both clays (nontronite, NAu-2, and montmorillonite, SWy-2) and by aqueous iron(II) complexes. Rate constants for aqueous Fe(II) are from Buerge and Hug (1997), and rate constants for both clays are from this paper andJoe-Wong et al. (2017). Fractionation factors for aqueous iron(II) complexes are from Joe-Wong et al. (2019) and Kitchen et al. (2012).Dotted curves show 95% confidence bounds. The black arrows show the direction in which Cr(VI) reduction is more thermodynamicallyfavorable in the standard state, i.e. DGr� is more negative.

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may also be relevant to marine sediments (Lau et al., 2018).Although Fe(II/III)-bearing clays are often slow reductantsof Cr(VI) and other contaminants, in situ remediation ispossible (Qafoku et al., 2017; Bishop et al., 2019). If Fe(II/III)-bearing clays are the primary reductant, then therate constant and kinetic isotope fractionation can be pre-dicted from XFe(II) and experimental parameters for con-verting XFe(II) to E� using a modified Nernst equation(Eq. (3)) and the slope and intercept of the linear relation-ship between e and E�. Taking Hanford as an example,XFe(II) in the clay fraction of Hanford sediments naturallyvaries with depth from approximately 5–22% (Qafokuet al., 2017), which would correspond to a change in E�effof 0.3 V for the montmorillonite tested in this study(Gorski et al., 2013). Such a change in E�eff would causek to change by over an order of magnitude for Cr(VI)reduction by the montmorillonite (Joe-Wong et al., 2017),and based on the linear correlation between e and E�efffor both clays in this study, such a change in E�eff wouldinduce a nearly 1‰ change in e from �4.7‰ for the lessreduced clay at shallow depths to �3.9‰ for the morereduced clay deeper in the sediments.

Ultimately, the ability to directly link the large change ine to changes in both the thermodynamics and kinetics of Cr(VI) reduction may allow tracking of natural attenuation orreductive remediation efforts. In a highly reduced zone,Marcus theory predicts that Cr(VI) reduction should bemost thermodynamically favorable, fast, and induce smallkinetic isotope effects. In a less reduced zone, Cr(VI) reduc-tion should become less thermodynamically favorable,slower, and induce larger kinetic isotope effects. In naturalsystems where Fe(II/III)-bearing clays are the primaryreductant of Cr(VI), the linear free energy relationships pre-sented in this paper may permit quantitative correlationsbetween the rate, extent, and kinetic isotope fractionationof Cr(VI) reduction.

5. CONCLUSIONS

The linear free energy relationships presented in thisstudy may allow both kinetic isotope effects and rates ofCr(VI) reduction to be predicted in environmentally rele-vant conditions, potentially without direct knowledge ofthe reductant. As conditions become more reducing, reduc-tion is expected to be faster but induce less kinetic isotopefractionation. Our results demonstrate that for Cr(VI)reduction by Fe(II/III)-bearing clays, e can be predictedfrom XFe(II) of each clay, which is a relatively straightfor-ward parameter to measure. Alternatively, assuming thatthe clays are in redox equilibrium with their surroundings,e can be predicted solely from Eh of a geochemical systembecause neither the total Fe content of the clay nor pHhas a large effect on e. Marcus theory provides a theoreticalframework to validate these linear free energy relationships.

To date, Cr is the only isotope system shown to followMarcus theory isotope effects over a broad range of envi-ronmental redox conditions and redox partners. However,further work may elucidate similar trends for other key iso-tope systems, potentially including N, Se, and U (Johnson,2004; Gorski et al., 2010; Zhu et al., 2014; Stueken, 2017;Brown et al., 2018; Joe-Wong et al., 2019). Determiningthe applicability of Marcus theory to other isotope systemswill require carefully designed laboratory experiments toexplore the linear free energy relationships predicted forboth chemical kinetics (i.e., log(k) vs. DG�) and isotopickinetics (i.e., e vs. DG�). In natural environments, observedisotopic fractionation is unlikely to follow a straightfor-ward linear free energy relationship because physical trans-port and reduction by other species would affect isotopicfractionation. Nevertheless, by integrating laboratory-based linear free energy relationships into a larger frame-work that includes reactive transport and other sources ofisotopic fractionation, Marcus theory may improve

C. Joe-Wong et al. /Geochimica et Cosmochimica Acta 292 (2021) 235–253 251

quantitative modeling of isotopic signatures in naturalenvironments.

Declaration of Competing Interest

The authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper.

ACKNOWLEDGEMENTS

This work was supported by a National Science FoundationCareer Award (EAR-1254156) to K.M. C.J.-W. was funded bythe United States Department of Defense through a NationalDefense Science & Engineering Graduate Fellowship and by aStanford Graduate Fellowship. S.T.B. was funded by the U.S.Department of Energy, Office of Basic Energy Sciences (DE-AC02-05CH11231).

APPENDIX A. SUPPLEMENTARY MATERIAL

Supplementary data to this article can be found online athttps://doi.org/10.1016/j.gca.2020.09.034.

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Associate editor: Mark Rehkamper