Linking Thermodynamics to Pollutant Reduction Kinetics by Fe2+

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Characterization of Natural and Affected Environments

Linking Thermodynamics to Pollutant Reduction Kinetics by Fe Bound to Iron Oxides 2+

Sydney M. Stewart, Thomas B. Hofstetter, Prachi Joshi, and Christopher A. Gorski Environ. Sci. Technol., Just Accepted Manuscript • Publication Date (Web): 29 Mar 2018 Downloaded from http://pubs.acs.org on March 29, 2018

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Environmental Science & Technology

Linking Thermodynamics to Pollutant Reduction Kinetics by Fe2+ Bound to Iron Oxides Sydney M. Stewart,† Thomas B. Hofstetter,‡ Prachi Joshi,† and Christopher A. Gorski∗,† 1

†Department of Civil & Environmental Engineering, Pennsylvania State University, 212 Sackett Building, University Park, PA 16802 ‡Eawag, Swiss Federal Institute of Aquatic Science and Technology, CH-8600 D¨ ubendorf, Switzerland E-mail: [email protected] Phone: 814-865-5673. Fax: 814-863-7304

2

Abstract

3

Numerous studies have reported that pollutant reduction rates by ferrous iron (Fe2+ )

4

are substantially enhanced in the presence of an iron (oxyhydr)oxide mineral. Devel-

5

oping a thermodynamic framework to explain this phenomenon has been historically

6

difficult due to challenges in quantifying reduction potential (EH ) values for oxide-

7

bound Fe2+ species. Recently, our group demonstrated that EH values for hematite-

8

and goethite-bound Fe2+ can be accurately calculated using Gibbs free energy of for-

9

mation values. Here, we tested if calculated EH values for oxide-bound Fe2+ could be

10

used to develop a free energy relationship capable of describing variations in reduction

11

rate constants of substituted nitrobenzenes, a class of model pollutants that contain

12

reducible aromatic nitro groups, using data collected here and compiled from the lit-

13

erature. All the data could be described by a single linear relationship between the

1

ACS Paragon Plus Environment


14

logarithms of the surface-area-normalized rate constant (kSA ) values and EH and pH

15

values [log(kSA ) = −EH /0.059V − pH + 3.42]. This framework provides mechanistic

16

insights into how the thermodynamic favorability of electron transfer from oxide-bound

17

Fe2+ relates to redox reaction kinetics.

18

Introduction

19

Ferrous iron (Fe2+ ) bound to iron (oxyhydr)oxides reduces oxidized pollutants, 1–14 molecular

20

oxygen, 15–18 and nitrite 19 far more quickly than aqueous Fe2+ alone. Early work studying

21

this phenomenon proposed that Fe2+ forms surface complexes on iron oxide surfaces that

22

have higher electron densities than aqueous Fe2+ , due to surface hydroxyl ligands serving as

23

electron donors. 20,21 Consequently, oxide-bound Fe2+ was thought to have a more negative

24

reduction potential (EH ) value than aqueous Fe2+ in the same solution. 20,22–24 More recently,

25

however, two lines of reasoning have questioned the validity of this explanation. First,

26

spectroscopic and microscopic analyses demonstrated that an Fe2+ atom rarely forms a

27

stable adsorbed species on iron oxides, but rather it becomes oxidized to an Fe3+ atom

28

and donates an electron into the bulk semiconducting iron oxide lattice. 24–31 Second, the

29

explanation implicitly assumes that relevant solutions must be in a state of thermodynamic

30

disequilibrium, as all redox couples in a system at equilibrium have the same EH value. Using

31

electrochemical measurements, our group recently confirmed that suspensions containing

32

aqueous Fe2+ and goethite or hematite do reach thermodynamic equilibrium, 32 indicating

33

that oxide-bound Fe2+ and aqueous Fe2+ reached the same EH value.

34

An alternative hypothesis to explain this phenomenon is that the presence of an iron oxide

35

alters the Fe2+ oxidation product that forms and therefore the Gibbs free energy of the reac-

36

tion. 32–35 When aqueous Fe2+ oxidizes in the absence of an oxide, it produces an aqueous Fe3+

37

complex or a metastable iron oxide (e.g., ferrihydrite). 36 In contrast, when Fe2+ oxidizes in

38

the presence of a crystalline iron oxide surface, it commonly produces a thermodynamically-

39

stable iron oxide (e.g., goethite or hematite) via epitaxial growth. 15,37,38 Thermodynamically2


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40

stable iron oxides (e.g., goethite and hematite) have more negative Gibbs free energies of

41

formation than metastable iron oxides (e.g., ferrihydrite), and therefore the iron oxide is

42

thought to make Fe2+ oxidation and concomitant epitaxial oxide growth more exergonic

43

(i.e., thermodynamically favorable).

44

This hypothesis is consistent with characterizations of oxides made before and after pollu-

45

tant reduction reactions, 33,34,38 but it remains unclear if it can be invoked to quantitatively

46

explain trends in pollutant reduction kinetics. In theory, EH values of oxide-bound Fe2+

47

should relate to observed reaction rate constant (kobs ) values in a predictable manner if an

48

electron transfer event occurs during or before the rate-limiting step of the reaction. 39–42

49

The goal of this study was to test the validity of this argument for the reduction of a model

50

oxidized pollutant by oxide-bound Fe2+ . We characterized the free energy relationship that

51

exists between reaction rate constant values for nitrobenzene reduction as a function of the

52

EH values of oxide-bound Fe2+ and pH. We subsequently tested if the free energy relation-

53

ship could describe data compiled from the literature collected with other iron oxides and

54

substituted nitrobenzenes.

55

We focused on substituted nitrobenzenes for three reasons. First, there are many studies

56

in which substituted nitrobenzenes have been reacted with oxide-bound Fe2+ , which provided

57

us with relevant data to reinterpret. 3,5,6,8,9,43 Second, the elementary steps in the reduction

58

reaction of nitrobenzene to aniline have been extensively characterized, 44–48 which allowed us

59

to interpret kobs values in the context of elementary reaction steps. Third, nitrobenzene does

60

not appreciably adsorb to iron oxides, which means that disappearance rate of nitrobenzene

61

can be assumed to be equal to the transformation rate. 3

62

Materials and Methods

63

All experiments were conducted under anaerobic conditions in a glovebox (MBraun Unilab

64

Workstation, 100% N2 , O2 < 0.1 ppm). All lab supplies that came in contact with Fe2+ were

3



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65

left under vacuum for at least 12 hours in the exchange chamber and allowed to equilibrate

66

with the N2 atmosphere before use. Deionized water (Millipore Milli-Q system, resistivity

67

>18 MΩ·cm) was used to make all aqueous solutions. All liquid solutions were purged

68

with N2 (99.99%) for at least three hours before being cycled into the glovebox, except

69

for nitrobenzene. Approximately 2 mL of reagent grade nitrobenzene (Sigma-Aldrich) was

70

cycled through the vacuum chamber in a small sealed container with little headspace and

71

was used to make 5 mM and 25 mM stock solutions in deoxygenated methanol. Ferrous

72

chloride (FeCl2 , Acros, anhydrous, 99%) from a sealed ampule was used to make Fe2+ stock

73

solutions that were kept acidic using HCl. All measurements of aqueous Fe2+ were done

74

using the 1,10-phenanthroline method. 49

75

All experiments were done in aqueous solutions containing 25 mM KCl (EM Science)

76

and 25 mM pH buffer. The pH buffer used at pH values 6.0 and 6.5 was MES (2-N-

77

morpholinoethanesulfonic acid acid monohydrate, pKA 6.1, Aresco, ≥99%), and the pH

78

buffer used at pH 7.0 was MOPS (3-N-morpholinopropanesulfonic acid, pKA 7.2, EMD

79

Chemicals Inc., 100%). Note that past works have argued that the buffers used here may

80

affect iron oxide–aqueous Fe2+ interactions. 50,51 This possibility was unfortunately unavoid-

81

able, as we needed to maintain a constant pH in the experiments. While carbonate has

82

been recommended as an alternative buffer, 51 our interpretation of published data (below)

83

suggests that carbonate dramatically inhibits nitrobenzene reduction rates by oxide-bound

84

Fe2+ .

85

Goethite Synthesis and Characterization

86

An established protocol was used to synthesize two batches of micron-scale goethite. 52 We

87

synthesized two batches of goethite because the first batch was exhausted prior to completing

88

all experiments. After synthesis, the goethite was freeze-dried (Labconco benchtop freeze-

89

drier), ground with a mortar and pestle, and sifted through a 200 mesh sieve (Humboldt).

90

The purities of the goethite batches were confirmed using cryogenic 4


57

Fe Mo¨ssbauer spec-

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91

troscopy. The BET surface area of the first goethite batch was 30.9±0.3 m2 /g (ASAP 2020

92

Automated Surface Area and Porosimetry System). The BET surface area of the second

93

batch was assumed to be equal to that of the first based on previous experience with this

94

synthesis procedure. Unfortunately, we exhausted the second batch of goethite before the

95

BET surface area was measured. Based on our experience, this synthesis method reliably

96

produces goethite with a specific surface area of ≈ 30 m2 /g.

97

Reduction Potential Measurements

98

We used mediated potentiometry to determine standard reduction potential (EH0 ) values for

99

each batch of goethite using a previously published protocol. 32 We prepared triplicate re-

100

actors with varied initial Fe2+ concentrations (100, 200, 400, 800, 1000, 1500 or 3000 µM)

101

and pH (6.0 or 7.0) values. After the addition of aqueous Fe2+ , the pH was readjusted to

102

the initial value using 1 N KOH and/or HCl stock solutions because the slight changes on

103

the order of approximately 0.1 pH units significantly affected measured and calculated EH

104

values. After measuring the initial Fe2+ concentration, we added goethite to the solutions

105

to achieve a mass loading of 1 or 2 g/L. Reactors were covered with aluminum foil to avoid

106

inadvertent photochemical reactions and mixed on a magnetic stir plate. After one hour of

107

mixing, a mediator compound (cyanomethyl viologen, EH0 = –0.14 V) 53,54 was added from a

108

10 mM stock solution to reach a final concentration between 10 and 20 µM. The reactors were

109

mixed for 24 hours, then a final aqueous Fe2+ measurement was made by filtering the solution

110

through a 0.45 µm nylon syringe filter. We then performed a potentiometric measurement

111

of the solution at two second intervals for one hour with a Pt ring combined redox electrode

112

(Metrohm) inside the glovebox. The EH value reported is the lowest value recorded during

113

the one hour measurement. Between measurements, the electrode was stored in 3 M KCl for

114

≥3 hours to ensure the internal KCl solution was not diluted. The electrode was cleaned pe-

115

riodically with 0.1 M HCl, and calibrated approximately monthly using quinhydrone buffers

116

prepared at pH 4.0 and 7.0 (Tokyo Chemical Industry Co., LTD). All measurements were 5



117

made in reference to Ag/AgCl, and were subsequently converted to values in reference to

118

the standard hydrogen electrode (SHE) based on the calibrations. To convert from con-

119

centrations to activities, activity coefficients for Fe2+ were calculated according to reactor

120

conditions using Visual MINTEQ, and values ranged from 0.48 to 0.52.

121

Nitrobenzene Reduction Experiments

122

We set up reactors containing aqueous Fe2+ and goethite using the same approach as de-

123

scribed for the reduction potential measurements, except that no mediator was added. In

124

the reactors, we varied the total initial Fe2+ concentration, goethite loading, and pH value.

125

After an equilibration period of 24 hours in which the goethite and Fe2+ reacted, a sample

126

was taken to measure the final aqueous Fe2+ concentration. Next, the reaction was started

127

by adding an aliquot of nitrobenzene stock solution to the reactor using a glass syringe

128

to reach an initial concentration of approximately 10 µM. The reactor was sealed with a

129

Teflon-lined septa and aluminum crimp cap. Samples were taken at pre-determined time

130

points using a needle and syringe and filtered through a 0.2 µM PTFE syringe filter into

131

amber sample vials with PTFE-lined screw caps. Nitrobenzene and aniline were measured

132

using high-pressure liquid chromatography (HPLC) with a Supelcosil LC-18 column using

133

established methods. 32

134

Derivation of Free Energy Relationship

135

We derived a rate expression to relate the disappearance of nitrobenzene to changes of re-

136

duction potential and pH using a quasi-equilibrium assumption, which assumes that the

137

reaction steps preceding the rate-limiting step reach equilibrium. 40,42,55 The reduction path-

138

way of nitrobenzene is shown in Scheme 1, with the relevant iron oxidation reactions shown

139

in Figure S1. The overall rate of nitrobenzene (compound 1 in Scheme 1) disappearance

6


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Page 7 of 35


NO2

NO

NH2

NHOH

+2e- +2H+

+2e- +2H+

+2e- +2H+

–H2O

–H2O

1 O

N

6 O

O

N

O

O

N

OH

O

+e–

+H+

+e–

–e–

–H+

–e–

1

3

2

N

OH

4

HO +H+ –H+

N

OH

O

N

– H2O 5

6

Scheme 1: Reaction scheme of nitrobenzene reduction. A. Overall steps of the reduction of nitrobenzene (1) to aniline. B. Elementary reaction steps of the reduction of nitrobenzene reduction to nitrosobenzene (6) that occurs through a series of electron and proton transfer reactions and ultimately a dehydration of N,N -dihydroxyaniline (5) to 6. 45,46 140

during a surface-catalyzed pseudo-first-order reduction reaction can be described by: −kobs · [1] d[1] = = −kSA · [1] dt A

141 142

(1)

143

1 ); A is the reactive where kobs is the observed pseudo-first-order reduction rate constant ( hr

144

surface area of an iron oxide ( mL ), which is calculated from the measured BET specific surface

145

area; and kSA is the surface-area-normalized reaction rate constant ( m2L·hr ).

2

146

Studies on the

15

N kinetic isotope effects 45–47 have indicated that the rate-limiting ele-

147

mentary step of the reduction of nitrobenzene (or substituted nitrobenzene) is the hydrolysis

148

of N,N -dihydroxyaniline (5) to nitrosobenzene (6) (5 → 6 in Scheme 1) when the reductant

149

is present in excess. If this is the case, the overall rate of nitrobenzene (1) disappearance

150

would depend on the rate constant for reaction 5 → 6, k5→6 , and the concentration of

151

N,N -dihydroxyaniline (5):

152 153

d[1] = −k5→6 · [5] dt

7


(2)


154

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Setting equations 1 and 2 equal to each other relates kSA to k5→6 :

kSA = k5→6 ·

155 156

[5] [1]

(3)

157

For this relationship to have practical utility, the concentration of 5 must be expressed as

158

a function of the concentration of 1. Using the quasi-equilibrium method, the concentration

159

of 5 could be mathematically derived based on the concentrations of species 1 to 4 using

160

equilibrium expressions for reactions sequence 1 * )2* )3* )4* ) 5 in Scheme 1 and the

161

oxidation of Fe2+ to goethite (KFe2+ * )αFeOOH in eq. 4e derived from the half reaction shown

162

in eq. 12 below): [2] [1]

(4a)

163

K1* )2 =

164

K2* )3 =

(4b)

165

K3* )4

(4c)

166

K4* )5

167

KFe2+ * )αFeOOH

168

[3] [2] · [H+ ] [4] = [2] [5] = [4] · [H+ ] [H+ ]3 = [Fe2+ ]

(4d) (4e)

169

Through a sequence of substitutions for transient species 1 to 4 for 5 and the assumption

170

that electrons come from the oxidation of Fe2+ to α−FeOOH, eq. 3 can be transformed to

8


Page 9 of 35

171

172


an interpretable relationship:

kSA · [1] = k5→6 · [5]

(5a)

173

+ = k5→6 · K4* )5 · [4] · [H ]

174

= k5→6 · K4* ) 5 · K3* )4 · KFe2+ * )αFeOOH · [3] ·

175

= k5→6 · K4* ) 5 · K3* )4 · KFe2+ * )3 · [2] · )αFeOOH · K2*

178

[Fe2+ ] [H+ ]2

(5c) [Fe2+ ] [H+ ]

[Fe2+ ]2 [H+ ]4 [Fe2+ ]2 2 = k5→6 · K4* ) · K · K · * * 2 3 1 2 ) 5 · K3* )4 · (KFe2+ * ) ) αFeOOH ) [H+ ]4 2 = k5→6 · K4* ) 5 · K3* )4 · (KFe2+ * ) 3 · K1* )2 · [1] · )αFeOOH ) · K2*

176

177

(5b)

kSA

(5d) (5e) (5f)

179

The observable reaction rate constant for nitrobenzene reduction will therefore depend on

180

the pH and Fe2+ concentration as well as the equilibrium constants for reactions 1 * ) 2, 2

181

* ) 3, 3 * ) 4, and 4 * ) 5.

182

While the electron transfer reactions involving the oxidation of Fe2+ to an iron oxide

183

(in this case, goethite, α−FeOOH) can be expressed in terms of an equilibrium constant

184

(KFe2+ * )αFeOOH ), representing them in terms of EH values is more familiar and practical in

185

the context of redox reactions. The Nernst equation for the goethite-Fe2+ (aq) half reaction can

186

be written in the following form (see eqs. 12 and 13 below for more details):

EH = EH0 −

187 188

RT [Fe2+ ] ln + 3 F [H ]

(6)

189

The Nernst equation can be re-expressed in terms of KFe2+ * )αFeOOH , which is inverted because

190

the equilibrium constant is for the oxidation reaction:

191

192 193

RT 1 = ln F K 2+ * Fe )αFeOOH RT [Fe2+ ] RT 1 EH = ln − ln + 3 F KFe2+ * F [H ] )αFeOOH EH0

9


(7) (8)


194

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Solving for KFe2+ * )αFeOOH yields:

KFe2+ * )αFeOOH

195 196

F [H+ ]3 = exp − · EH · RT [Fe2+ ]

(9)

197

Substituting equation 9 into equation 5f yields a relationship in which kSA can be related to

198

EH : 2 F [Fe2+ ]2 [H+ ]3 = k5→6 · K4* exp − · K · E · K · · K · * * * 3)4 H 2)3 1)2 )5 RT [H+ ]4 [Fe2+ ] 2F = k5→6 · K4* · EH · [H+ ]2 ) 5 · K3* )4 · K2* )3 · K1* )2 · exp − RT

199

kSA

200

kSA

201

202

log (kSA ) = log (k5→6 · K4* · K2* )5 · K3* ) 3 · K1* )2 ) − {z )4 } |

2F · EH 2.303RT

− 2 · pH

(10c)

d

204

205

(10b)

Taking the log of both sides of the equation yields:

203

(10a)

which at room temperature (25◦ C) simplifies to:

log(kSA ) = −2 ·

206 207

EH − 2 · pH + d 0.059V

(11)

208

Note that this derivation can also be done in terms of the aqueous Fe3+ activity based on

209

the solubility of the iron oxide present. 32

210

Results and Discussion

211

0 Quantification of Goethite-Aqueous Fe2+ EH Values

212

We initially confirmed that EH values of suspensions containing goethite (α−FeOOH(s) ) and

213

aqueous Fe2+ (Fe2+ (aq) ) were consistent with the following half-reaction and corresponding

214

Nernst equation:

215

α−FeOOH(s) + e− + 3 H+ * ) Fe2+ (aq) + 2 H2 O 10


(12)

Page 11 of 35


EH = EH0 −

216

217

RT RT ln[Fe2+ ln[H+ ] (aq) ] + 3 F F

(13)

where brackets denote activities. At 25◦ C, eq. 13 simplifies to:

EH = EH0 − 0.059V · log[Fe2+ (aq) ] − 0.177V · pH

218

(14)

219

We measured EH values of goethite suspensions over a range of total Fe2+ concentrations

220

(100 to 3000 µM) at two pH values (6.0 and 7.0) using mediated potentiometry, a technique

221

in which a soluble redox mediator is used to facilitate redox equilibration between a solution

222

and a redox electrode performing a potentiometric measurement (Figure 1). Data for goethite

223

from our previous work using the same method is shown for reference. 32 We characterized

224

two goethite batches made using identical synthesis routes because the first goethite batch

225

was exhausted before all nitrobenzene experiments were completed. We fit the data for each

226

goethite batch according to eq. 14 by floating the EH0 value and slope terms for Fe2+ (aq) activity

227

and pH using a least-squares multiple linear regression (Igor Pro software v7, Wavemetrics).

228

The activity coefficient for Fe2+ (aq) was calculated according to reactor conditions. There

229

was good agreement between the theoretical slope terms in eq. 14 and those from the

230

fitted regression (Fe2+ (aq) term: theoretical: 0.059 V, batch 1: 0.071±0.008 (±σ) V, batch 2:

231

0.065±0.005 V; pH term: theoretical: 0.177 V, batch 1: 0.177±0.008 V, batch 2: 0.165±0.005

232

V), confirming that the half-reaction in eq. 12 accurately described the EH values of the

233

suspensions.

234

These data were fit to calculate EH0 values for each batch of goethite. Since the deviations

235

between the theoretical and measured slope terms were most likely due to experimental error,

236

we used the theoretical slope values in eq. 14 to fit the data using a linear regression. The fits,

237

shown as dashed lines in Figure 1, yielded EH0 values of 0.801±0.004 (±σ) V (r2 = 0.98) for

238

batch 1 and 0.800±0.003 V (r2 = 0.99) for batch 2, which were within the range of previously

239

reported values (0.72 to 0.84 V). 56,57 The EH0 values were both approximately 0.03 V higher

240

than the value measured in our previous work using the same technique (0.768±0.001 V), 32 11


Reduction potential, EH [V vs. SHE]


Page 12 of 35

0.0 pH = 6.0 -0.1

-0.2 pH = 7.0 Batch 1 Batch 2 Gorski et al., 2016

-0.3 4

6 8

100

2

4

6 8

1000

Aqueous Fe

2+

2

4

6

[µM]

Figure 1: Measured reduction potential values of the goethite-Fe2+ (aq) redox couple for the two goethite batches (red circles for batch 1, blue triangles for batch 2). Reduction potential values are shown as a function of solution pH and Fe2+ (aq) concentration after 24 hours of equilibration. Solution conditions: 25 mM buffer (MOPS for pH 7.0 and MES for pH 6.0), 25 mM KCl, 17 µM mediator (cyanomethyl viologen). Error bars show standard deviation between triplicate reactors and are contained within some markers. 241

which was likely due slight differences between the goethite batches used in this study and

242

our previous work. Since the EH0 values of the two goethite batches used here were identical

243

within error to each another, we could directly compare data collected for each batch. For all

244

subsequent nitrobenzene reduction experiments, we calculated EH values of each suspension

245

0 based on the pH, Fe2+ (aq) activity, and measured EH value (0.800 V) according to eq. 14.

246

Role of EH on Nitrobenzene Reduction Kinetics at pH 6.0

247

We initially performed nitrobenzene reduction experiments at a single pH value (6.0) to

248

simplify interpretation by eliminating pH-dependent effects on goethite-Fe2+ (aq) EH values (eq.

12


Page 13 of 35


249

14) and nitrobenzene reduction kinetics. To determine the relationship between kobs values

250

and initial EH values of the goethite-Fe2+ (aq) redox couple, we measured nitrobenzene reduction

251

rate constants as a function of goethite concentration (0.5 to 4.0 g/L) and total Fe2+ (aq) con-

252

centration (100 to 5000 µM). All the nitrobenzene reduction experiments could initially be

253

described using a pseudo-first-order kinetic model (eq. 1), confirming that the reaction was

254

first-order with respect to nitrobenzene (example data shown in Figure S2). In experiments

255

that had relatively low initial Fe2+ (aq) concentrations, reaction kinetics eventually deviated

256

from what could be fit with a pseudo-first-order kinetic model, and therefore reported kobs

257

values were fit using only the portion of the data that yielded a linear fit between ln(kobs )

258

vs. time. In the experiments that went to completion, the mass balance of nitrobenzene

259

reduced to aniline produced ranged from 98 to 120% (average = 107±5%), and the molar

260

ratio of Fe2+ (aq) lost from solution to nitrobenzene reduced was 6.2(±2.8):1 (data shown in

261

Figure S3), consistent with the expected ratio of 6:1 from the electron balance of the overall

262

reaction (i.e., six electrons are needed to reduce one aromatic NO2 group to an NH2 group).

263

The kobs values among experiments were surface-area-normalized to account for differences

264

in goethite loadings among experiments according to eq. 1, as previously described in the

265

literature. 3,5,6

266

We plotted a free energy relationship in which log(kSA ) was related to the reaction’s

267

thermodynamic driving force (i.e., the Gibbs free energy of the reaction, ∆Grxn ). For redox

268

reactions, ∆Grxn is typically expressed in terms of EH . 41,58,59 Here, we used the EH values of

269

◦ the goethite-Fe2+ (aq) redox couple divided by 0.059 V (i.e., by 2.303 · RT /F when T =25 C).

270

The data, shown in Figure 2 and tabulated in Table S1, exhibited a linear relationship (r2 =

271

0.96) with a slope of –0.99±0.06. Note that EH /0.059 V scales with log{Fe2+ (aq) } in a 1:1 ratio

272

(eq. 14), and therefore a slope of ≈ −1 indicated that nitrobenzene reduction was first-order

273

with respect to the Fe2+ (aq) activity:

274

kSA = kFe · [Fe2+ (aq) ]

13


(15)


Page 14 of 35

-1.5

-1

-2

log([kSA/L·hr ·m ])

-1.0

-2.0 -2.5 -3.0 -1.5

-1.0 -0.5 EH/0.059 V

0.0

Figure 2: Log transformed surface-area-normalized reaction rate coefficient [log(kSA )] values vs. EH values divided by 0.059 V of the goethite-Fe2+ (aq) redox couple at pH 6.0. The black line shows the linear fit with slope = −0.99 ± 0.06, intercept = −2.79 ± 0.06, r2 = 0.96. 275

More generally, the fact that the slope was not zero was consistent with an electron

276

transfer step being involved in the rate-limiting step(s) of nitrobenzene reduction. 40,42 The

277

mechanistic implications of the slope value are discussed below. The practical significance of

278

the slope is that EH values of the goethite-Fe2+ (aq) redox couple may be used as a parameter

279

to predict trends in reduction rate constants of nitrobenzene, and likely other nitroaromatic

280

compounds, for a single pH value. To understand if this relationship of kSA with reaction

281

free energy trend was also valid at different pH values, we performed additional experiments.

282

Effect of pH on Nitrobenzene Reduction Rates

283

We measured nitrobenzene reduction kinetics at pH values of 6.5 and 7.0 for a subset of

284

the reactor conditions tested at pH 6.0 (goethite concentrations of 1 and 2 g/L; total Fe2+ (aq) 14


Page 15 of 35


285

concentrations of 100 to 1000 µM; data tabulated in Table S1). Since the pH value influences

286

both the EH value of the goethite-Fe2+ (aq) redox couple (eq. 14) and the thermodynamic driving

287

force dependence of nitrobenzene reduction rate constants, which involves proton transfer

288

steps, we expected that log(kSA ) values would vary as a function of both EH and pH:

289

log(kSA ) = a ·

EH + b · pH + c 0.059V

(16)

290

where a, b, and c are constants. Since eq. 16 contains two independent variables, its ability

291

to describe the data cannot be easily visualized in a 2-dimensional plot. We fit the data

292

using a multiple linear regression according to eq. 16 while floating b and c and holding a

293

equal to –1 (based on the results in Figure 2). The least-squares fit generated a pH slope

294

term (b) of –1.06±0.09 and an intercept term (c) of 3.6±0.6 (χ2 = 0.67; n = 23). The b value

295

was ≈ −1, which was the value that we used in subsequent analyses. To visually represent

296

the quality of this fit, we plotted log(kSA ) versus a · EH /0.059V + b · pH with a = −1 and

297

b = −1 (Figure 3, c = 3.12 ± 0.05, r2 = 0.96). The observation that the data was best

298

described with a pH slope term that differed from 0 indicated that nitrobenzene reduction

299

kinetics by goethite-bound Fe2+ were indeed pH-dependent, consistent with the reduction

300

pathway of nitroaromatic compounds and the Fe2+ oxidation reaction. 45,46

301

Note that representing the data this way masks the actual pH-dependency of log(kSA ),

302

since EH is itself a function of 3 · pH (eqs. 13 and 14). When the EH term is written out

303

according to eq. 14 and substituted into eq. 16 with a and b equal to –1, it is clear that the

304

reaction is second-order with respect to pH:

305

log(kSA ) = −

EH0 + log[Fe2+ (aq) ] + 2 · pH 0.059V

(17)

306

The mechanistic significance that can be drawn from the pH-dependency is discussed below.

307

To test the robustness of this free energy relationship, we plotted previously reported

308

log(kSA ) values for the reduction of nitrobenzene or substituted nitrobenzene compounds 15



Page 16 of 35

-1

-2


0

-1

-2 pH 7.0 pH 6.5 pH 6.0

-3 -6

-5

-4

-3

-EH/0.059 V - pH Figure 3: Relationship between log(kSA ), pH, and EH of the goethite-Fe2+ (aq) redox couple. The line shown is the fit with only the y-intercept term floated (c in eq. 16 = 3.12±0.05, r2 = 0.96). 309

by Fe2+ bound to goethite (Figure 4). 3,6,8,43,60 Since the rate of substituted nitrobenzene

310

compounds depends on the substituent groups present, we normalized EH values using a

311

published linear trend between log(kobs ) values and the compounds’ EH values for the first

312

electron transfer step (i.e., EH1 ). 59 The difference in EH1 values between nitrobenzene and

313

the substituted nitrobenzenes (i.e., ∆EH1 ) was calculated as:

0

0

0

0

314

0

0

∆EH1 = EH1 (nitrobenzene) − EH1 (substituted nitrobenzene)

(18)

0

315

The reported correlation between log(kobs ) and ∆EH1 used to normalize the data was: 59 0

316

log(kSA ) = 0.53 · ∆EH1 + c0

16


(19)

Page 17 of 35


0

-1

-2


1

This study Strehlau et al., 2017 (nano-goethite) Fan et al., 2016 Jones et al., 2016 (nano-goethite) Jones et al., 2016 Colón et al, 2006 Elsner et al., 2004

-1 -2 -3 -4 -6

-5

-4

-3

-EH/0.059 V - pH Figure 4: log(kobs ) values as a function of pH and the calculated EH value of the goethite3,5,6,8,43 Fe2+ The method used to cal(aq) redox couple for data compiled from the literature. culate EH values is provided in Section S2. Reactor conditions varied between reported experiments: total Fe2+ (aq) ranged between 0.375 and 1.24 mM, goethite loading ranged between 0.025 and 1.54 g/L, BET specific surface areas of goethite ranged between 16.2 and 51 m2 /g, and pH values range between 6.1 and 7.97. The line shown is the fit from Figure 3. 317

where c0 is the y-intercept. The calculated EH values were corrected for this factor prior to

318

plotting them (data in Table S2).

319

Remarkably, virtually all the data complied from these studies performed by five different

320

groups of research teams between 2004 and 2016 fell upon the line derived from this work.

321

The observation that this simple free energy relationship could explain data collected for

322

goethite with different substituted nitrobenzene concentrations was particularly compelling

323

given the fact that the studies used different goethite batches prepared with a variety of

324

synthesis routes.

325

Interestingly, the two outlier points in Figure 3 were collected using carbonate as a pH

17



Page 18 of 35

326

buffer, 43 whereas all the other studies including ours used Good’s buffers. Note that we

327

accounted for the fact that a portion (∼7%) of the Fe2+ (aq) was complexed with carbonate

328

(FeHCO3+ ) when calculating the activity of free Fe2+ (aq) from their data (Visual MINTEQ).

329

Carbonate is known to decrease the amount of available reactive surface area on an iron

330

2+ oxide and decrease the extent of Fe2+ uptake (aq) uptake. Since nitrobenzene reduction by Fe

331

is a surface-catalyzed reaction, the presence of carbonate explains the significantly lower

332

log(kSA ) values observed in this study.

333

Free Energy Relationship for Nitrobenzene Reduction

334

by Fe2+ and Different Iron Oxides

335

The consistent trend between log(kobs ) values and pH and EH values for goethite compelled us

336

to explore the extent to which this relationship could be applied to reported data collected for

337

other iron oxides, including hematite, 3,60 lepidocrocite, 3,8,60 ferrihydrite, 3,8 and magnetite. 9

338

Note that since the Gibbs free energy of formation of each oxide differs, the EH0 values for

339

2+ each oxide-Fe2+ (aq) redox couple also differs. We calculated EH of the oxide-Fe(aq) redox couples

340

according to the following half reactions and their corresponding Nernst equations:

341

Hematite :

3 1 α−Fe2 O3(s) + 3H+ + e− * ) Fe2+ (aq) + H2 O 2 2

(20a)

342

Lepidocrocite :

α−FeOOH(s) + 3H+ + e− * ) Fe2+ (aq) + 2H2 O

(20b)

343

Ferrihydrite :

Fe(OH)3(s) + 3H+ + e− * ) Fe2+ (aq) + 3H2 O

(20c)

Magnetite :

1 3 * Fe2+ Fe3 O4(s) + 4H+ + e− ) + 2H2 O 2 2 (aq)

(20d)

344 345

346

The Nernst equations for all these reactions, except magnetite, are identical to the one in

347

eq. 13. The Nernst equation for the magnetite half-reaction is:

348

EH = EH0 −

3 RT RT ln[Fe2+ ln[H+ ] (aq) ] + 4 2 F F 18


(21)

Page 19 of 35


349

32 We previously measured the EH0 value for the hematite-Fe2+ (aq) half reaction (0.768±0.002 V).

350

We calculated EH0 values for the half reactions containing lepidocrocite (0.846 V), ferrihydrite

351

(0.937 V), and magnetite (1.067 V) using existing thermodynamic data. 61,62 While solutions

352

containing lepidocrocite and ferrihydrite are not at thermodynamic equilibrium (i.e., the ox-

353

ides should transform to more stable phases), the EH0 values can be useful approximations if

354

the oxides remain stable over the course of the reaction. Values of EH were calculated accord-

355

0 ing to Fe2+ (aq) activity, pH, and EH values (data in Tables S2 and S3). Calculated EH values

356

were also corrected to account for differences of reactivities of the substituted nitrobenzenes

357

by normalizing reaction rate constants according to their EH1 values to nitrobenzene using

358

eq. 19.

0

359

All the reduction rate constants compiled from the literature for goethite, hematite,

360

lepidocrocite, and ferrihydrite exhibited a clear linear trend consistent with the linear free

361

energy relationship developed for goethite (Figure 5). In the case of magnetite, the data

362

initially did not fall on the line when we calculated EH values according to eq. 21. This

363

was likely due to the incorrect assumption that magnetite was the oxidation product that

364

formed. A recent study that characterized the Fe2+ oxidation product that formed when

365

4-chloro-nitrobenzene was reduced by suspensions containing magnetite and Fe2+ (aq) observed

366

the formation of lepidocrocite, not magnetite, as the dominant oxidation product. 38 When we

367

calculated EH values assuming that lepidocrocite was the oxidation product, the magnetite

368

data fell in line with the data for the other oxides (Figure 5).

369

Fitting all the data with a line yielded a slope of 0.76, a y-intercept of –3.57, and an

370

r2 value of 0.68 (n = 74, fit not shown). Excluding three outlier points, which are denoted

371

with asterisks inside the markers, significantly improved the fit (r2 = 0.92, n = 71) and

372

yielded a slope of 1.02±0.03 and a y-intercept of 3.42±0.17 (line shown in Figure 5). Two

373

of the outliers were points collected using a carbonate pH buffer, 43 as discussed above. The

374

third outlier point was excluded because it clearly deviated from the overall trend, although

375

we could not identify an explanation as to why. 60 The 95% prediction band (encompassed

19



0

-1

-2


1

-1

Page 20 of 35

This study Elsner et al., 2004 Jones et al., 2016 Colón et al., 2006 Fan et al., 2016 Strehlau et al., 2016 Klausen et al., 1995 Goethite Hematite Lepidocrocite Ferrihydrite Magnetite

* *

-2 -3

*

-4 -7

-6

-5

-4

-3

-2

-EH/0.059 V - pH Figure 5: Compilation of log(kobs ) values as a function of pH and the calculated EH values for the reduction of nitrobenzene by Fe2+ in the presence of goethite, hematite, lepidocrocite, ferrihydrite, and magnetite. The solid line is the least-squares linear regression excluding the three outlier points (denoted with asterisks). The fit yielded a slope of 1.02±0.03, a y-intercept of 3.42±0.17, and an r2 value of 0.92 (n = 71; 24 from this study, 47 from the literature, 3 outlier points excluded). The shaded area represents the 95% confidence band, and the dashed lines encompass the 95% prediction band. Data were taken from refs. 3,6,8,9,43,60. 376

by the dashed lines in Figure 5) was approximately ±1 log unit on the y-axis, indicating

377

that 95% of the reported kSA values were within an order of magnitude of the values that

378

would be predicted by the free energy relationship. Some of the scatter among the datasets

379

was likely due to variations in the buffer type and concentrations used in each study. Prior

380

work found that commonly used pH buffers caused iron oxide particle aggregation, which

381

influenced kSA values by up to 0.5 log units. 51 This ability for the free energy relationship

382

to describe the literature data indicates that pH values and EH values for oxide-Fe2+ (aq) redox

383

couples can be used to estimate nitrobenzene, and likely nitroaromatic, transformation rate

20


Page 21 of 35

384


constants within an order of magnitude.

385

A critical assumption implicit to this approach is that Fe2+ oxidation results in homoepi-

386

taxial growth of the underlying oxide (e.g., goethite grows on goethite), with the exception

387

of magnetite. In the case of goethite, several studies have indeed found that Fe2+ oxida-

388

tion leads to goethite particle growth. 37,38,43 Ferrihydrite, hematite, and lepidocrocite are

389

more complicated. In the case of hematite, Fe2+ oxidation can lead to both the growth of

390

hematite and the nucleation of goethite particles. 38 Interestingly, this does not influence the

391

thermodynamic calculations because the half reactions for the oxidation of Fe2+ to hematite

392

or goethite have virtually identical EH0 values and identical Nernst equations. 32 Very little

393

work has examined what Fe2+ oxidation products form in the presence of lepidocrocite or

394

ferrihydrite. 8 Both oxides are known to undergo secondary mineralization reactions to more

395

63–67 stable phases in the presence of aqueous Fe2+ It is therefore (aq) at circumneutral pH values.

396

likely that Fe2+ may oxidize to form oxides other than original phase, which could explain

397

why the ferrihydrite and lepidocrocite points in Figure 5 are generally higher than those

398

of goethite and hematite. With this caveat in mind, assuming that nitrobenzene reduction

399

is coupled to homoepitaxial oxide growth works from a practical perspective for all oxides

400

except magnetite.

401

Two recent works have reported similar free energy relationships in which the authors

402

plotted log(kSA ) versus EH /0.059 V values for multiple iron oxides and substituted nitroben-

403

zene compounds at a single pH value. 6,8 The studies differed from the present work in that

404

the authors measured EH values for suspensions by preparing parallel reactors. In both

405

studies, the fitted slope values (0.16 8 or 0.49±0.15 6 ) were significantly smaller than the one

406

reported here (i.e., ≈1). In the study that observed a slope of 0.16, a portion of the reactors

407

contained dissolved Si that blocked iron oxide surface sites and therefore affected calculated

408

kSA values. 8 In the other study, the authors speculated that measured EH values may have

409

contained experimental artifacts, as the measurements depended on the concentrations of

410

Fe2+ and iron oxide in a way that deviated from the Nernst equation. 6 Note that data taken

21



411

from both these studies fell on the trend line in Figure 5 when we calculated EH values based

412

on the pH and Fe2+ (aq) activity and that the calculated values significantly differed from the

413

measured ones in most cases. We are unsure as to why the calculated and measured EH

414

values from these studies differed.

415

Interpretation of the Slope Terms in the Free Energy Relationship

416

The trends between log(kSA ) and EH and pH (i.e., the slope terms a and b in eq. 16)

417

provide insights into the rate limiting step(s) in the reduction of reducible aromatic nitro

418

groups by oxide-bound Fe2+ . To interpret these trends, we briefly discuss the current state

419

of knowledge regarding the reduction pathway of nitroaromatics, using nitrobenzene as a

420

surrogate (Scheme 1). The reduction of nitrobenzene (species 1 in Scheme 1) to aniline is

421

initiated by a series of two proton and two electron transfer steps before nitrosobenzene (6) is

422

formed as first measurable product through a dehydration step, which controls the rate of ni-

423

trobenzene disappearance. Since the reaction from 1 to 6 is irreversible under environmental

424

conditions, 41 we can confine the kinetic interpretation of the free energy relationship to these

425

steps. Early studies examining the reduction of nitroaromatic compounds by oxide-bound

426

Fe2+ observed linear correlations between log(kobs ) and the one-electron reduction poten-

427

tial values of nitroaromatic compounds, EH1 . 3,7,9,41 These observations led to the hypothesis

428

that the first electron transfer step to nitrobenzene, 1 * ) 2, was a suitable descriptor of the

429

relative reduction rates and potentially the rate-limiting step of reactions 1 to 6 (Scheme

430

1B). 41,58 More recent evidence from large

431

duction of substituted nitrobenzenes 45–47,68 implied, however, that the dehydration step of

432

the N,N -dihydroxyaniline (5 → 6) was the rate-liming step, consistent with electrochemical

433

experiments examining the reduction of aromatic NO2 groups. 69,70

0

15

N kinetic isotope effect associated with the re-

434

We examined if the free energy relationship observed here was consistent with (i) reaction

435

5 → 6 being the rate-limiting step and (ii) one-electron reduction potentials being used as

436

descriptors for variations in reduction rate constants. We derived a rate expression for the 22


Page 22 of 35

Page 23 of 35


437

reduction of nitrobenzene by Fe2+ assuming that 5 → 6 was rate-limiting with the quasi-

438

equilibrium method, which assumes that the preceding reaction steps are in equilibrium (the

439

derivation is in the subsection “Derivation of Free Energy Relationship” above). 40,42,55 This

440

method is thought to be valid if the rate constant of the rate-limiting step is at least 100

441

times smaller than those of the preceding steps. 42 With eq. 11, we are able to reconcile

442

potentially contradicting views with regard to the rate-limiting step of aromatic NO2 group

443

reduction. Note that even though we assume that reaction 5 → 6 is rate-limiting, log(kSA )

444

scales linearly with changes of EH1 /0.059 V in constant d, as shown in the derivation.

0

445

The derived slope terms (a for the EH /0.059 term and b for the pH term) in eq. 11 are

446

both –2. Note that the b term does not reflect the overall pH-dependency of the reaction

447

since the EH value is itself pH-dependent. The derived equation can also be expressed in

448

terms of equilibrium constants instead of EH , in which case the derived rate expression

449

indicates that reaction kinetics would be second-order with respect to [Fe2+ ] and forth-order

450

with respect to 1/[H+ ] (eq. 5f). Clearly, the derived a and b terms differed from the observed

451

terms, which were both ≈ –1. The observed values instead indicate that the reduction rate

452

constants depend only on the free energy changes associated with transferring two protons

453

and one electron. There are two possible explanations for the discrepancy. The first is that

454

the quasi-equilibrium assumption used to derive the theoretical relationship is invalid for this

455

system because the preceding reaction steps do not reach equilibrium. Such a case can arise

456

when rate constants have similar orders of magnitude. 55 The second possibility is that the

457

second electron transfer step (3 * ) 4) and second proton transfer step (4 * ) 5) in Scheme

458

1B have sufficiently lower activation free energies than the preceding ones, making the steps

459

kinetically irrelevant. In either case, this exercise demonstrates that free energy relationship

460

for log(kSA ) depends on the transfer of one proton and one electron, not two of each.

23



461

Environmental Implications

462

In this work, we observed that EH values of oxide-bound Fe2+ could be used to accurately

463

describe variations in nitrobenzene reduction rates. This finding is significant because it

464

validates the use of thermodynamic data for oxide-bound Fe2+ to explain trends in nitroaro-

465

matic reduction rates. The data indicates that it is unnecessary to describe “adsorbed Fe2+ ”

466

as a discrete species when explaining trends in pollutant transformation rates. Instead, the

467

61,62 EH of Fe2+ can (aq) , which can be calculated from readily available thermodynamic data,

468

be used effectively. The extent to which this free energy relationship can be applied to other

469

classes of pollutants containing different reducible functional groups remains unclear at this

470

point due simply to the lack of data, but it seems highly probable that that EH values

471

will be useful if the reaction is completely or partially rate-limited by one or more electron

472

transfer steps. Of course, in real environmental systems, pollutant reduction rates will also

473

be affected by other species, such as carbonate, natural organic matter, and silicate, which

474

compete for reactive sites and/or passivate iron oxide surfaces.

475

The findings from this work can also explain a puzzling observation. Past works found

476

negligible reduction of nitrite, molecular oxygen, and nitrobenzene occurred when an iron

477

2+ 2+ oxide was exposed to Fe2+ (aq) and either the residual Fe(aq) was removed or most of the Fe(aq)

478

was taken up the oxide. 16,19,29 This observation was difficult to reconcile with the hypothesis

479

that oxide-bound Fe2+ is a strong reductant. 21 The observation can, however, be explained

480

based on the observations from this study. Removing Fe2+ (aq) from the system makes the EH

481

2+ values of both Fe2+ more positive. This suggests that the concen(aq) and oxide-bound Fe

482

tration of Fe2+ (aq) in groundwater systems can be used an important predictive parameter for

483

pollutant fate, as it is a proxy for oxide-bound Fe2+ EH values in the presence of iron oxides.

24


Page 24 of 35

Page 25 of 35


484

Acknowledgement

485

This work was supported by the U.S. National Science Foundation (grant EAR-1451593 to

486

CAG) and by the Swiss National Science Foundation (grant 200021 149283 to TBH). We

487

thank William Burgos for reviewing the manuscript prior to submission.

488

Supporting Information Available

489

Example kinetic data of nitrobenzene reduction and tabulated experimental and literature

490

data.

25



Graphical TOC entry This study Literature log(kSA)

491

1.02 1

-EH/0.059 V - pH

26


Page 26 of 35

Page 27 of 35

492


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