Bromamine Decomposition Revisited: A Holistic Approach for

Oct 26, 2017 - The remaining three acid-catalysis constants for reaction 1 (HPO42–, H2CO3, and H3PO4) and four base-catalysis constants for reaction...
0 downloads 4 Views 591KB Size
Subscriber access provided by READING UNIV

Article

Bromamine decomposition revisited: A holistic approach for analyzing acid and base catalysis kinetics David G. Wahman, Gerald E. Speitel, and Lynn E. Katz Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b02661 • Publication Date (Web): 26 Oct 2017 Downloaded from http://pubs.acs.org on October 26, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Environmental Science & Technology is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 29

Environmental Science & Technology

1

Bromamine decomposition revisited: A holistic approach for analyzing acid

2

and base catalysis kinetics

3

David G. Wahman1*, Gerald E. Speitel Jr.2, and Lynn E. Katz2

4

1

United States Environmental Protection Agency, Office of Research and Development, Cincinnati, OH 45268

5

2

University of Texas at Austin, Department of Civil, Architectural and Environmental Engineering, Austin, TX

6 7 8

9

78712 *

Corresponding author, mailing address: USEPA, 26 W. Martin Luther King Dr., Cincinnati, OH 45268. Phone: (513) 569-7733. Fax: (513) 487-2543. E-mail: [email protected]

TOC/ABSTRACT ART

NH2Br + NH Br 2

NHBr2 + NH3

10 11 12

NHBr2 + H2O N2 + 3Br– + 3H+ + HOBr

Keywords: monobromamine; dibromamine; haloamines; brønsted; catalysis

1

ACS Paragon Plus Environment

Environmental Science & Technology

13 14

ABSTRACT Chloramine chemistry is complex, with a variety of reactions occurring in series and

15

parallel and many that are acid or base catalyzed, resulting in numerous rate constants. Bromide

16

presence increases system complexity even further with possible bromamine and

17

bromochloramine formation. Therefore, techniques for parameter estimation must address this

18

complexity through thoughtful experimental design and robust data analysis approaches. The

19

current research outlines a rational basis for constrained data fitting using Brønsted theory,

20

application of the microscopic reversibility principle to reversible acid or base catalyzed

21

reactions, and characterization of the relative significance of parallel reactions using fictive

22

product tracking. This holistic approach was used on a comprehensive and well-documented

23

data set for bromamine decomposition, allowing new interpretations of existing data by revealing

24

that a previously published reaction scheme was not robust; it was not able to describe

25

monobromamine or dibromamine decay outside of the conditions for which it was calibrated.

26

The current research’s simplified model (3 reactions, 17 constants) represented the experimental

27

data better than the previously published model (4 reactions, 28 constants). A final model

28

evaluation was conducted based on representative drinking water conditions to determine a

29

minimal model (3 reactions, 8 constants) applicable for drinking water conditions.

2

ACS Paragon Plus Environment

Page 2 of 29

Page 3 of 29

30

Environmental Science & Technology

INTRODUCTION

31

Free chlorine is a popular distribution system disinfectant choice in the United States

32

(US),1-4 but because of Stage 1 and Stage 2 Disinfectants and Disinfection Byproducts Rules

33

implementation, many US utilities now use combinations of chlorine and chloramines to avoid

34

excessive regulated disinfection by-product formation, including trihalomethanes and haloacetic

35

acids.3, 5

36

Chloramine chemistry is complex, with a variety of reactions taking place in series and

37

parallel. Some reactions are acid or base catalyzed, which greatly increases the number of rate

38

constants that must be estimated in mechanistic kinetic models of natural waters where carbonate

39

and phosphate are present. When bromide is present in significant concentrations, the system

40

complexity increases even further with possible bromamine and bromochloramine formation

41

under drinking water conditions.6 Therefore, it is impossible practically to generate enough

42

experimental data to estimate rate constants in kinetic models solely using data fitting techniques.

43

Thus, a rational basis for constraining the number of parameters that must be calibrated

44

simultaneously is needed. The current research outlines such a holistic approach using Brønsted

45

theory, application of the microscopic reversibility principle to reversible acid or base catalyzed

46

reactions, and characterization of the relative significance of parallel reactions using fictive

47

product tracking. The approach is demonstrated on a comprehensive and well-documented data

48

set for a relatively simple system examining bromamine decomposition.7, 8

49

The holistic approach allowed new interpretations of existing data, revealing that the

50

reaction scheme employed in previous research was not robust; it was not able to simulate

51

monobromamine (NH2Br) or dibromamine (NHBr2) decay outside of the conditions for which it 3

ACS Paragon Plus Environment

Environmental Science & Technology

52

was calibrated (e.g., Figure 1). Thus, a revised reaction scheme for bromamine decomposition

53

was developed that not only reduces the number of estimated parameters but is also robust in its

54

ability to describe data over a significant range of experimental conditions. As the goal of model

55

development is ultimately its practical application, the revised reaction scheme was further

56

evaluated to arrive at a minimal model applicable to drinking water practice. The revision of the

57

previously published bromamine decomposition reaction scheme and associated new

58

interpretations of existing data is important as the reaction scheme has already been incorporated

59

into models seeking to further extend bromamine chemistry.9

60

EXPERIMENTAL SECTION

61

Data Set

62

No new experimental data were generated. Rather, the data set was taken from stopped-

63

flow experiments conducted by Lei, et al.7 and Lei8. A summary of experimental initial

64

conditions is provided in supporting information (SI), Table S2, and the reader is directed to Lei,

65

et al.7 and Lei8 for further data set details.

66

Using absorbance values at 232 nm (A232) and 278 nm (A278) in Appendix A of Lei8,

67

NH2Br and NHBr2 concentrations were calculated from molar absorptivity (ε ,  = 82

68

M-1 cm-1; ε ,  = 425 M-1 cm-1; ε ,  = 2,000 M-1 cm-1; ε ,  = 715 M-1

69

cm-1)7 and Eq. 1 and Eq. 2 which are appropriate for a 1 cm absorbance cell path length: NHBr  =

A  ε ,  − A  ε,  (1) ε ,  ε ,  − ε ,  ε, 

NH Br =

A  − NHBr ε ,  (2) ε ,  4

ACS Paragon Plus Environment

Page 4 of 29

Page 5 of 29

70 71

Environmental Science & Technology

Model Reaction rate expressions and stoichiometry The bromamine decomposition model of Lei, et al.7 served as the starting point for the

72

current research (Table 1) along with the hypobromous acid (HOBr) and ammonia (NH3)

73

reaction to form NH2Br (HOBr + NH3  NH2Br; k = 7.5x107 M-1 s-1).10 The model is composed

74

of a general acid-catalyzed NH2Br disproportionation reaction (Table 1, reaction 1), the

75

associated general acid-catalyzed reverse of reaction 1 (Table 1, reaction -1), and two general

76

base-catalyzed bromamine decomposition reactions (Table 1, reactions 2 and 3). Equilibrium

77

constants of catalytic species were taken from published literature (Table 2) and adjusted to the

78

ionic strength used by Lei, et al.7 (0.1 M). Model reactions (Table 1) and required equilibrium

79

equations (Table 2) were implemented into Aquasim.11

80

Brønsted Theory

81 82

Brønsted relationship. Individual catalysis constants were related by the Brønsted relationship12 for acid (Eq. 3) and base (Eq. 4) catalysis: k! qK ) log  # = log G! + α log  # (3) p p k pK ) log  # = log G − β log  # (4) q q

83

In Eq. 3 and Eq. 4, kA and kB are rate constants for acid and base catalysis, Ka is the respective

84

acid dissociation constant, GA and α and GB and β are constants for a similar series of catalysts

85

where α and β have values between 0 and 1, and p and q are statistical correction factors that

86

represent the number of equally bound dissociable protons (p) and equivalent points where

87

protons can attach (q) and were calculated as outlined by Bell12. When developing the Brønsted

88

relationships, the carbonic acid (H2CO3) true concentration was used rather than the sum of 5

ACS Paragon Plus Environment

Environmental Science & Technology

89

dissolved carbon dioxide and carbonic acid (H2CO3*), whereas H2CO3* is implemented in the

90

Aquasim model.

91

Relative catalyst importance. Because catalysts are typically controlled at relatively

92

constant concentrations in experiments (i.e., buffer concentrations and pH), an analysis of

93

individual catalyst relative importance to the overall reaction rate constant can be made even for

94

complex models with parallel reaction pathways. Such an analysis distinguishes those catalytic

95

species that are likely to be important (and therefore likely estimated from the experimental data)

96

from those catalytic species that are better estimated from a Brønsted relationship. The

97

procedure and an example calculation for determining relative catalyst importance is provided in

98

the SI.

99

Microscopic Reversibility

100

Fast, reversible reactions are common when dealing with haloamine chemistry.

101

Application of the microscopic reversibility principle to general acid or base catalysis reactions

102

can substantially reduce the required number of estimated parameters (e.g., Table 1, reactions 1

103

and -1). Based on the microscopic reversibility principle,13 equilibrium constants are used along

104

with either the forward or reverse reaction rate constants to calculate the other rate constant.

105

Equilibrium constant incorporation into the model can be accomplished in at least two ways to

106

decrease the required number of parameters. First, published equilibrium constants determined

107

experimentally or from thermodynamic estimates can be directly used. For example, referring to

108

Table 1, K1 can be used along with k1 to calculate k-1, eliminating the need to estimate the

109

individual catalysis constants associated with k-1. Second, published equilibrium constants and

110

their associated uncertainty may be used to constrain the allowable range of equilibrium 6

ACS Paragon Plus Environment

Page 6 of 29

Page 7 of 29

Environmental Science & Technology

111

constants estimated through model fitting to experimental data. The latter method was applied in

112

the current research, using the equilibrium constant for reactions 1 and -1 (K1) proposed by

113

Trogolo and Arey14 (log K1 = -0.5 ± 1.2, K1 = 0.020-5.0) where the initial guess for K1 was set to

114

0.32 and its minimum and maximum allowable values were 0.020 and 5.0, respectively.

115

Fictive Products

116

Imaginary products, termed fictive products herein, were included in reaction

117

stoichiometry (Table 1). Fictive products allowed assessment of reaction pathways during

118

simulations by acting as reaction counters. The magnitude (i.e., concentration) of the fictive

119

product relates to the number of times a particular reaction has occurred in the reaction scheme,

120

allowing direct comparisons of parallel reaction pathway importance.

121

Fictive product analysis can be employed in at least two circumstances. First, using

122

published reaction rate constants, fictive products allow evaluation of which reactions will be

123

important under typical conditions (e.g., drinking water conditions). Using fictive products in

124

this manner allows selection of the minimal number of reactions required in the kinetic model.

125

Second, fictive products can be utilized after a proposed model has been developed to evaluate

126

whether all the reactions in the model are indeed required.

127

Parameter Estimation

128

To estimate parameters in this nonlinear system, an iterative procedure was utilized

129

between (i) Aquasim kinetic model parameter estimates from experimental data and (ii) Brønsted

130

relationship parameter estimates, which used Aquasim parameter estimates as inputs to estimate

131

additional parameters for subsequent use in the Aquasim kinetic model. Iteration continued until

132

the Aquasim parameter estimates converged. 7

ACS Paragon Plus Environment

Environmental Science & Technology

133

Aquasim. Parameter estimates were obtained in Aquasim using the parameter estimation

134

function (secant algorithm) which was configured to minimize residual sum of squares (RSS)

135

between measured and model simulated concentrations (Eq. 5): 8



-.. = /012345,6 − 16 7 (5) 69:

136

In Eq, 5, ymeas,i is the i-th measurement and yi is the model simulated concentration

137

corresponding to the i-th measurement.

138

From the 65 experiments (Table S2), 11 were excluded. Six (Br-eff-1, Br-eff-2, Br-eff-3,

139

Br-eff-4, Br-eff-5, and Br-eff-6) were excluded (as in Lei, et al.7) because they studied the

140

impact of increased bromide, four (HN-1-1, HN-2-1, HN-3-1, and HN-3-2) were excluded

141

because simulated initial NH2Br and NHBr2 concentrations differed substantially from the

142

experimental data, and one (CN-1-1) was excluded because it disproportionately contributed to

143

the RSS. The remaining 54 experiments were simultaneously fit using absorbance resolved

144

NH2Br and NHBr2 concentrations (n = 9,971 data points).

145

Brønsted relationship. The Brønsted relationship was used to estimate parameters in

146

coordination with the Aquasim kinetic model. Typically, a Brønsted relationship is utilized as a

147

post-analysis assessment of estimated parameters and prediction of additional parameters unable

148

to be estimated from the experimental data. In the current research, the Brønsted relationship

149

was used as an active part of the parameter estimation procedure in an iterative process so that

150

the entire set of acid or base catalysts are included in Aquasim parameter estimation, assuring

151

self-consistent rate constant estimates are obtained from experimental data and the Brønsted

152

relationship.

8

ACS Paragon Plus Environment

Page 8 of 29

Page 9 of 29

Environmental Science & Technology

153

Aquasim parameter estimates provided inputs to generate Brønsted relationships.

154

Parameters unable to be obtained through Aquasim parameter estimation because of their lack of

155

sensitivity in the Aquasim model were resolved from the Brønsted relationship, representing a

156

full set of estimated parameters (i.e., Aquasim model and Brønsted relationship estimated

157

parameters). The Brønsted relationship estimated parameters were then entered as fixed

158

parameters into the Aquasim model and Aquasim parameter estimation was repeated. The entire

159

process iterated until Aquasim model estimated parameters no longer changed.

160

RESULTS AND DISCUSSION

161

Evaluation of Published Rate Constants

162

Upon review of the Lei, et al.7 results (e.g., Figure 1), limitations became apparent. Our

163

inability to accurately simulate the breadth of their data using their full model was attributed to

164

two factors associated with their data analysis approach. First, Lei, et al.7 made assumptions

165

regarding the importance of the two bromamine decomposition reactions (Table 1, reactions 2

166

and 3). For instance, when they used experiment sets NN-1 and NN-2 to determine ammonia

167

catalysis; HN-1, HN-2, and HN-3 to determine hydrogen ion catalysis; and CN-1 and CN-2 to

168

determine carbonate buffer catalysis, only reaction 3 for bromamine decomposition was assumed

169

important, and reaction 2 was ignored. Importantly, Lei, et al.7 never verified this assumption.

170

Second, Lei, et al.7 designated parameter estimates as either “measured” (determined from the

171

kinetic model using experimental data) or “predicted” (determined from Brønsted relationships),

172

and this terminology is used herein when describing their results. Lei, et al.7 only presented

173

simulations using their measured parameters, and no simulations were presented using both their 9

ACS Paragon Plus Environment

Environmental Science & Technology

174

measured and predicted parameters against their experimental data to evaluate the proposed

175

reaction scheme in its entirety as conducted herein. The impact of these limitations is

176

subsequently discussed.

177

Reaction importance assumptions. To evaluate the assumption that reaction 2 could be

178

ignored for experiment sets NN-1, NN-2, HN-1, HN-2, HN-3, CN-1, and CN-2, a fictive product

179

analysis was conducted using both measured and predicted parameters from Lei, et al.7 The

180

fictive product analysis allowed a calculation of the percentage of bromamine decomposition

181

associated with reaction 2 (Figures S1, S2, and S3). Overall, the analysis showed that between

182

53-75% of the bromamine decomposition was attributed to reaction 2 with the balance to

183

reaction 3. Therefore, the assumption that reaction 2 could be ignored was not supported by the

184

final model. Based on parameters estimated from their analysis, both reactions 2 and 3 were

185

required in any data fitting, and reaction 2 was more important for bromamine decomposition

186

than reaction 3. Also, Lei, et al.7 used a step-wise analysis for rate constant estimation (Figure

187

S4, Steps 1-4), allowing errors introduced in each estimation step to propagate throughout their

188

analysis.

189

Validation of full model. Impacts of Lei, et al.7 not performing validation simulations

190

using both their measured and predicted rate constants were first accessed by calculating the

191

relative importance of catalysts for each reaction. If predicted rate constants are shown to be

192

important, then they should have been included in any simulations conducted. Results for this

193

analysis with experiment sets NN-1 and CN-2 are presented in Table 3 (acid-catalysis reactions 1

194

and -1) and Table 4 (base-catalysis reactions 2 and 3). For reactions 1 and -1, it appears

195

sufficient to only include the measured parameters as they are the only ones that are important to

196

the overall reaction rates based on a 5% threshold, except experiments CN-2-3, CN-2-4, and CN10

ACS Paragon Plus Environment

Page 10 of 29

Page 11 of 29

Environmental Science & Technology

197

2-5 where H2CO3* has minor (5.2-6.6%) importance to the overall rate constant. The same

198

cannot be said for reactions 2 and 3. For reaction 2, only the predicted rate constants (OH–,

199

CO32–, and NH3) are important; therefore, final simulations should have been conducted to

200

evaluate the reasonableness of their estimations. For reaction 3, the only predicted rate constant

201

that was important was NH3, but it contributes 17-69% to the overall rate constant; therefore, as

202

in the case of reaction 2, validation of its estimation from the Brønsted relationship was needed.

203

To further assess the implications of Lei, et al.7 not performing simulations including

204

both measured and predicted parameters, simulations using both the measured and predicted rate

205

constants for experiments sets NN-1 (Figure 1) and CN-2 (Figure 2) were conducted. It is

206

apparent from these simulations that the implementation of the complete published model for

207

bromamine decomposition provides a poor representation of their experimental data, and because

208

of the previously stated concerns regarding their kinetic analysis approach, a reanalysis of the

209

experimental data was justified. For reference, a comparison of the current analysis approach

210

versus that conducted by Lei, et al.7 is summarized in Figure S4.

211

Model evaluation and parameter determination

212

Comparison of various model simulations. An initial attempt was made to include

213

both bromamine decomposition reactions (Table 1, reactions 2 and 3) in the reaction scheme as

214

proposed by Lei, et al.7, but initial attempts were unsuccessful as the model would not converge

215

during simultaneous parameter estimation using the 54 experiments. Therefore, the initial

216

conclusion was that the model was overparameterized. To evaluate this initial conclusion, the

217

individual experiments of Lei, et al.7 were used to estimate individual rate constants for reactions

218

1, -1, 2, and 3. For individual experiments where rate constants for both reactions 2 and 3 could 11

ACS Paragon Plus Environment

Environmental Science & Technology

219

be estimated (i.e., k2 or k3 not estimated as zero), k2 and k3 were highly, negatively correlated (-

220

0.93 to -1.0), providing evidence of model overparameterization and that both reactions 2 and 3

221

were not needed.

222

To evaluate the impact of including only reaction 2 or 3, individual parameter estimates

223

were conducted for each experiment of Lei, et al.7 using two schemes: (i) Scheme 1 included

224

reactions 1, -1, and 2 and (ii) Scheme 2 included reactions 1, -1, and 3. A residual sum of

225

squares (RSS) comparison (Figure S5) showed no apparent advantage for either scheme. Further

226

evidence that either reaction scheme would adequately represent the experimental data is

227

presented in Figure 3 where simulations are presented for those experiments where selection of

228

Scheme 1 over Scheme 2 (Figure 3, Panel A) or selection of Scheme 2 over Scheme 1 (Figure 3,

229

Panel B) provided the greatest RSS reduction. It is evident that even for these worst-case

230

scenarios between schemes, either scheme adequately represented the data. Overall, it was

231

concluded that choice of either Scheme 1 or 2 would be adequate and that either, but not both,

232

reaction 2 or 3 was required in the reaction scheme as proposed by Lei, et al.7

233

Subsequently, three lines of reasoning supported selection of Scheme 1 over 2. First,

234

Cromer, et al.15 studied NHBr2 decomposition and proposed two pathways. The first pathway

235

was a tribromamine (NBr3) and NHBr2 reaction which is excluded because Lei, et al.7 found that

236

NBr3 was below detection limits. The second proposed pathway was a bimolecular NHBr2

237

reaction consistent with current reaction 2 (Scheme 1). Second, a lower correlation was found

238

between estimated parameters for Scheme 1 than 2. Specifically, and for the majority of

239

experiments (Figure S6), k-1 was less correlated with the bromamine decomposition reaction in

240

Scheme 1 (k2, R = -0.31 to 0.57) than Scheme 2 (k3, R = -0.83 to 0.59). Third, based on parallels

12

ACS Paragon Plus Environment

Page 12 of 29

Page 13 of 29

Environmental Science & Technology

241

with chloramine chemistry, NHBr2 disproportionation (Scheme 1) should occur faster than a

242

reaction of NH2Br and NHBr2 (Scheme 2). Based on these three reasons, Scheme 1 was selected.

243

Model parameter estimation summary. As described previously, an iterative fitting

244

procedure between the Aquasim kinetic model and the Brønsted relationships was used for

245

parameter estimation. Through this approach, five acid-catalysis constants for reaction 1 (H2O,

246

HCO3–, NH4+, H2PO4–, and H+), the equilibrium constant for reactions 1 and -1 (K1), and four

247

base-catalysis constants for reaction 2 (OH–, CO32–, HPO42–, and H2O) were estimated in

248

Aquasim. The remaining three acid-catalysis constants for reaction 1 (HPO42–, H2CO3, and

249

H3PO4) and four base-catalysis constants for reaction 2 (PO43–, NH3, HCO3–, and H2PO4–) were

250

estimated from Brønsted relationships. An estimated parameter summary is provided in Table 5

251

(reaction 1) and Table 6 (reaction 2) with corresponding Brønsted plots in Figure 4, showing

252

excellent R2 values of 0.96 and 0.99 for reactions 1 and 2, respectively.

253

The relative catalyst importance of the individual constants for each experiment is

254

summarized in Table S3 (reaction 1) and Table S4 (reaction 2). For reactions 1 and 2, all the

255

important constants were directly estimated in Aquasim, except NH3 for reaction 2. Even though

256

the NH3 rate constant for reaction 2 was not estimated in Aquasim, directly including the

257

parameters from the Brønsted relationships ensures consistency between parameters estimated

258

from the experimental data and those estimated from Brønsted relationships.

259

The equilibrium constant estimate for reactions 1 and -1 (K1 = 2.1±0.024) compares

260

favorably to the thermodynamic estimate (log K1 = -0.5 ± 1.2, K1 = 0.020-5.0). Because of the

261

limitations previously stated for the Lei, et al.7 analysis, a direct comparison to the parameters

262

determined in the current research must be done with caution. Regardless, parameters

263

determined for reactions 1 and 2 (Table S5) in this research compare favorably to the previously 13

ACS Paragon Plus Environment

Environmental Science & Technology

264

determined parameters from Lei, et al.7, indicating this research offered an improved approach

265

for estimating the kinetic parameters but for the most part did not alter the relative significance

266

of the catalytic species for these two reactions. Importantly however, the current reaction scheme

267

does not include reaction 3 as in the model of Lei, et al.7

268

Simulation summary. Final simulations with the current model and with the measured

269

and predicted parameters from Lei, et al.7 were conducted (Figure S7) and RSS summarized

270

(Figure S8) for each experiment. Based on the total RSS for each experiment (Figure S8, Panel

271

C), the model of Lei, et al.7 marginally reduced the RSS for 9 (PP-1 through PP-5 and HP-1-2

272

through HP 1-5) of the 54 experiments compared to the current model. Whereas, the simplified,

273

current model (3 reactions, 17 constants) represented the experimental data substantially better

274

than that proposed by Lei, et al.7 (4 reactions, 28 constants) in 45 of the 54 experiments as

275

demonstrated by an almost order of magnitude (8 x 10-7 vs. 64 x 10-7) reduction in total RSS for

276

the data set (Figure S8, Panel C). To highlight the improvement with the current model, Figure 5

277

provides simulations and experimental data for experiments selected to investigate the impact of

278

ammonia (NN-1-3 and NN-1-5), carbonate (CN-2-3 and CN-2-5), and phosphate (NP-3 and NP-

279

5) concentrations. Clearly, the current model provides a better experimental data representation

280

along with a reduced RSS. Furthermore, the holistic approach outlined in this research is general

281

in nature and can be applied to kinetic analyses involving acid and base catalysis over a wide

282

variety of conditions.

283

Practical implications

284 285

A final evaluation of the current model was conducted based on representative drinking water conditions to evaluate the minimal model applicable to drinking water. Ten conditions 14

ACS Paragon Plus Environment

Page 14 of 29

Page 15 of 29

Environmental Science & Technology

286

(Table S6) were selected, including five pHs (6, 7, 8, 9, and 10), a maximum total free ammonia

287

concentration (0.1 mM = 1.4 mg N L-1), a maximum phosphate concentration (0.15 mM = 4.7

288

mg P L-1), and a low (1 mM = 12 mg C L-1) and high (10 mM = 120 mg C L-1) total carbonate

289

concentration. Individual catalyst relative importance to the overall reaction rates is summarized

290

in Table S7 (reaction 1) and Table S8 (reaction 2). Based on excluding species that contribute

291

less than 5% to the overall rate constant of reactions 1 or 2, a model intended for drinking water

292

applications could consist of only a total of eight parameters: (i) four parameters (H2O, HCO3–,

293

H2PO4–, and H+) for reaction 1, (ii) equilibrium constant for reactions 1 and -1, and (iii) three

294

parameters (OH–, CO32–, and H2O) for reaction 2. Validation of the minimal model is an avenue

295

of future research.

296

ASSOCIATED CONTENT

297

Supporting Information Available. Supporting information consists of 53 pages with a

298

section describing the calculation of relative catalyst importance, 8 tables, 8 figures, and

299

associated references. Supporting information is available free of charge at http://pubs.acs.org/.

300

ACKNOWLEDGMENT

301

The USEPA collaborated in the research described herein. It has been subjected to the

302

Agency’s peer and administrative review and has been approved for external publication. Any

303

opinions expressed are those of the authors and do not necessarily reflect the views of the

304

Agency; therefore, no official endorsement should be inferred. Any mention of trade names or

305

commercial products does not constitute endorsement or recommendation for use.

306 15

ACS Paragon Plus Environment

Environmental Science & Technology

307

REFERENCES

308

1.

AWWA Water Quality and Technology Division Disinfection Systems Committee,

309

Committee report: Disinfection at small systems. J. Am. Water Works Ass. 2000, 92, (5),

310

24-31.

311

2.

AWWA Water Quality and Technology Division Disinfection Systems Committee,

312

Committee report: Disinfection at large and medium-size systems. J. Am. Water Works

313

Ass. 2000, 92, (5), 32-43.

314

3.

AWWA Water Quality and Technology Division Disinfection Systems Committee,

315

Committee report: disinfection survey, part 2 - alternatives, experiences, and future plans.

316

J. Am. Water Works Ass. 2008, 100, (11), 110-124.

317

4.

AWWA Water Quality and Technology Division Disinfection Systems Committee,

318

Committee report: disinfection survey, part 1 - recent changes, current practices, and

319

water quality. J. Am. Water Works Ass. 2008, 100, (10), 76-90.

320

5.

321 322

Seidel, C. J.; McGuire, M. J.; Summers, R. S.; Via, S., Have utilities switched to chloramines? J. Am. Water Works Ass. 2005, 97, (10), 87-97.

6.

Heeb, M. B.; Criquet, J.; Zimmermann-Steffens, S. G.; von Gunten, U., Oxidative

323

treatment of bromide-containing waters: Formation of bromine and its reactions with

324

inorganic and organic compounds - A critical review. Water Res. 2014, 48, 15-42.

325 326

7.

Lei, H.; Marinas, B. J.; Minear, R. A., Bromamine decomposition kinetics in aqueous solutions. Environ. Sci. Technol. 2004, 38, (7), 2111-2119.

16

ACS Paragon Plus Environment

Page 16 of 29

Page 17 of 29

327

Environmental Science & Technology

8.

Lei, H. Bromamine decomposition and cyanogen bromide formation in drinking water

328

from monobromamine and formaldehyde. University of Illinois at Urbana-Champaign,

329

Urbana, IL, 2003.

330

9.

331 332

Environ. Sci. Technol. 2014, 48, (5), 2843-2852. 10.

333 334

Luh, J.; Mariñas, B. J., Kinetics of Bromochloramine Formation and Decomposition.

Wajon, J. E.; Morris, J. C., Rates of Formation of N-Bromo Amines in Aqueous Solution. Inorg. Chem. 1982, 21, (12), 4258-4263.

11.

335

Reichert, P., AQUASIM - a tool for simulation and data analysis of aquatic systems. Water Sci. Technol. 1994, 30, (2), 21-30.

336

12.

Bell, R. P., The Proton in Chemistry. Cornell University Press: Ithaca, NY, 1973.

337

13.

Krupka, R. M.; Kaplan, H.; Laidler, K. J., Kinetic consequences of the principle of

338 339

microscopic reversibility. Transactions of the Faraday Society 1966, 62, (0), 2754-2759. 14.

340 341

Trogolo, D.; Arey, J. S., Equilibria and Speciation of Chloramines, Bromamines, and Bromochloramines in Water. Environ. Sci. Technol. 2017, 51, (1), 128-140.

15.

Cromer, J. L.; Inman, G. W. J.; Johnson, J. D., Dibromamine Decomposition Kinetics. In

342

Chemistry of Wastewater Technology, Rubin, A. J., Ed. Ann Arbor Science Publishers,

343

Inc.: Ann Arbor, MI, 1978; pp 213-225.

344

16.

Benjamin, M. M., Water Chemistry. 1st ed.; McGraw-Hill: New York, NY, 2002.

345

17.

Troy, R. C.; Margerum, D. W., Nonmetal redox kinetics - hypobromite and hypobromous

346

acid reactions with iodide and with sulfite and the hydrolysis of bromosulfate. Inorg.

347

Chem. 1991, 30, (18), 3538-3543.

17

ACS Paragon Plus Environment

Environmental Science & Technology

348

18.

Smith, R. M.; Martell, A. E.; Motekaitis, R. J., Critical Stability Constants of Metal

349

Complexes Database (NIST Standard Reference Database 46, Version 3.0). National

350

Institute of Techology and Standards: Gaithersburg, MD, 1996.

351

19.

Plummer, L. N.; Busenberg, E., The solubilities of calcite, aragonite and vaterite in CO2-

352

H2O solutions between 0 and 90°C, and an evaluation of the aqueous model for the

353

system CaCO3-CO2-H2O. Geochim. Cosmochim. Acta 1982, 46, (6), 1011-1040.

354

20.

Adamczyk, K.; Premont-Schwarz, M.; Pines, D.; Pines, E.; Nibbering, E. T. J., Real-

355

Time Observation of Carbonic Acid Formation in Aqueous Solution. Science 2009, 326,

356

(5960), 1690-1694.

357

21.

358 359 360

Morris, J. C., The acid ionization constant of HOCl from 5 to 35C. The Journal of Physical Chemistry 1966, 70, (12), 3798-3805.

22.

Beckwith, R. C.; Wang, T. X.; Margerum, D. W., Equilibrium and kinetics of bromine hydrolysis. Inorg. Chem. 1996, 35, (4), 995-1000.

361 362

18

ACS Paragon Plus Environment

Page 18 of 29

Page 19 of 29

363

Environmental Science & Technology

Table 1. Kinetic model reactions for bromamine decomposition.

a

Current

Lei et al.7

Reaction

Reaction

Number

Number

1

1

2NH Br → NHBr + NH

–1

–1

NHBr + NH @A 2NH Br

2

10

2NHBr + H O → HOBr + N + 3Br B + 3H D

3

9

NH Br + NHBr → N + 3Br B + 3H D

Reaction Stoichiometry