close

Вход

Забыли?

вход по аккаунту

?

acs.est.7b02661

код для вставкиСкачать
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: wahman.david@epa.gov
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
<=
<?=
<
<E
Reactions 1 and –1 equilibrium constant, K: =
Rate
Fictive
Product
Expression a
P1
k: NH Br
P–1
k B: NHBr NH P2
k NHBr P3
k NH BrNHBr <=
<?=
k: = k:,F + k:,G H D + k:,GH NHID + k:,JFE H CO + k:,JF?E HCOB
+ k:,E LFH H POI HPOB
+ k:,LFH? H POIB + k:,LF?
I
H
k B: = k B:,F + k B:,G H D + k B:,GH NHID + k B:,JFE H CO + k B:,JF?E HCOB + k B:,ELFH H POI HPOB
+ k B:,LFH? H POIB + k B:,LF?
I H
COB
H POIB k = k ,F + k ,F? OH B + k ,E NH + k ,JF?E HCOB + k ,JF?
+ k , LF?
H
E
B
B
HPOI + k ,LFE? POI + k ,LF?
H
H
COB
H POIB k = k ,F + k ,F? OH B + k ,E NH + k ,JF?E HCOB + k ,JF?
+ k , LF?
H
E
B
B
HPOI + k ,LFE? POI + k ,LF?
H
H
364
365
19
ACS Paragon Plus Environment
Environmental Science & Technology
366
367
368
369
Page 20 of 29
Table 2. Equilibrium constants at 25°C and ionic strength (I) = 0 M or I = 0.1 M. Ionic
strength adjustments made with the Davies equation16 from I = 0 M except for the
hypobromous acid (HOBr) and hypobromite ion (OBr–) equilibrium where adjustments
were made from I = 0.5 M, pKa = 8.80.17
Equilibrium
pKa (I = 0 M)
pKa (I = 0.1 M)
Reference
NH4+ ⇌ NH3 + H+
9.24
9.24
Smith, et al.18
H2CO3* ⇌HCO3– + H+
6.35
6.13
Plummer and
Busenberg19
H2CO3 ⇌HCO3– + H+
3.45
3.23
Adamczyk, et al.20
HCO3– ⇌CO32– + H+
10.33
9.88
Plummer and
Busenberg19
H3PO4 ⇌H2PO4– + H+
2.15
1.93
Smith, et al.18
H2PO4– ⇌HPO42– + H+
7.20
6.75
Smith, et al.18
HPO42– ⇌PO43– + H+
12.38
11.71
Smith, et al.18
HOCl ⇌OCl– + H+
7.54
7.32
Morris21
HOBr ⇌OBr– + H+
9.1
8.88
Troy and
Margerum17
Br2(aq) ⇌HOCl + Br– + H+
8.46
8.24
Beckwith, et al.22
H2O ⇌OH– + H+
14.00
13.78
Benjamin16
H3O+ ⇌H2O + H+
0.00
0.00
Benjamin16
O PQ ∗ Per Adamczyk, et al.20 and Plummer and Busenberg19, O PQE = 795
E
370
20
ACS Paragon Plus Environment
Page 21 of 29
371
372
373
374
Environmental Science & Technology
Table 3. Relative importance of acid catalysts for rate constants k1 and k–1 from Lei, et al.7
for selected experiments. Rate constants denoted as measured and predicted in Lei, et al.7
are designated as (M) and (P), respectively. Red numbers indicate contributions greater
than or equal to 5% of the total rate constant.
Catalyst Percent Contribution to k1 for Given Experiment
H2O
HPO42–
HCO3–
NH4+
H2PO4–
H+
H2CO3*
H3PO4
Experiment
(M)
(P)
(M)
(M)
(M)
(M)
(P)
(P)
NN–1–1
23.4
0.0
0.0
44.1
0.0
32.5
0.0
0.0
NN–1–2
16.1
0.0
0.0
62.5
0.0
21.3
0.0
0.0
NN–1–3
9.5
0.0
0.0
77.0
0.0
13.5
0.0
0.0
NN–1–4
7.0
0.0
0.0
83.7
0.0
9.3
0.0
0.0
NN–1–5
5.4
0.0
0.0
87.2
0.0
7.4
0.0
0.0
CN–2–1
11.8
0.0
50.2
30.0
0.0
5.7
2.3
0.0
7.7
0.0
65.7
19.8
0.0
3.8
3.0
0.0
CN–2–2
CN–2–3
4.6
0.0
78.0
11.7
0.0
2.2
3.5
0.0
CN–2–4
3.3
0.0
83.1
8.3
0.0
1.6
3.8
0.0
CN–2–5
2.5
0.0
85.9
6.4
0.0
1.2
3.9
0.0
Catalyst Percent Contribution to k–1 for Given Experiment
H2O
HPO42–
HCO3–
NH4+
H2PO4–
H+
H2CO3*
H3PO4
Experiment
(M)
(P)
(M)
(M)
(M)
(M)
(P)
(P)
NN–1–1
33.3
0.0
0.0
20.6
0.0
46.2
0.0
0.0
NN–1–2
27.8
0.0
0.0
35.4
0.0
36.8
0.0
0.0
19.7
0.0
0.0
52.3
0.0
28.0
0.0
0.0
NN–1–3
NN–1–4
16.0
0.0
0.0
62.8
0.0
21.2
0.0
0.0
NN–1–5
13.0
0.0
0.0
69.0
0.0
18.0
0.0
0.0
CN–2–1
32.4
0.0
22.9
26.9
0.0
15.6
2.3
0.0
CN–2–2
25.7
0.0
36.4
21.6
0.0
12.6
3.7
0.0
CN–2–3
18.4
0.0
52.1
15.3
0.0
8.9
5.2
0.0
CN–2–4
14.3
0.0
60.8
11.9
0.0
6.9
6.1
0.0
CN–2–5
11.7
0.0
66.3
9.7
0.0
5.6
6.6
0.0
375
376
21
ACS Paragon Plus Environment
Environmental Science & Technology
377
378
379
380
Table 4. Relative importance of base catalysts for rate constants k2 and k3 from Lei, et al.7
for selected experiments. Rate constants denoted as measured and predicted in Lei, et al.7
are designated as (M) and (P), respectively. Red numbers indicate contributions greater
than or equal to 5% of the total rate constant.
Catalyst Percent Contribution to k2 for Given Experiment
Experiment
OH– (P)
PO43– (P)
CO32– (P)
NH3 (P)
HPO42– (M)
H2O (M)
NN–1–1
83.1
0.0
0.0
15.4
0.0
1.5
NN–1–2
71.5
0.0
0.0
27.3
0.0
1.2
NN–1–3
55.2
0.0
0.0
43.8
0.0
1.0
NN–1–4
45.6
0.0
0.0
53.6
0.0
0.8
NN–1–5
38.3
0.0
0.0
61.0
0.0
0.7
CN–2–1
78.6
0.0
1.3
19.6
0.0
0.5
CN–2–2
77.4
0.0
2.6
19.5
0.0
0.5
75.7
0.0
5.0
18.8
0.0
0.5
CN–2–3
CN–2–4
73.8
0.0
7.3
18.4
0.0
0.5
CN–2–5
72.1
0.0
9.5
17.9
0.0
0.4
Catalyst Percent Contribution to k3 for Given Experiment
Experiment
OH– (M)
PO43– (P)
CO32– (M)
NH3 (P)
HPO42– (P)
H2O (M)
NN–1–1
11.0
0.0
0.0
20.8
0.0
68.2
NN–1–2
9.3
0.0
0.0
36.0
0.0
54.8
NN–1–3
6.5
0.0
0.0
52.4
0.0
41.1
NN–1–4
5.3
0.0
0.0
63.4
0.0
31.3
69.3
0.0
26.4
NN–1–5
4.3
0.0
0.0
CN–2–1
14.6
0.0
17.3
36.9
0.0
31.2
CN–2–2
12.3
0.0
29.3
31.5
0.0
26.9
CN–2–3
9.6
0.0
45.5
24.3
0.0
20.6
CN–2–4
7.8
0.0
55.6
19.8
0.0
16.8
6.6
0.0
62.6
16.7
0.0
14.1
CN–2–5
381
382
22
ACS Paragon Plus Environment
Page 22 of 29
Page 23 of 29
383
Environmental Science & Technology
Table 5. Reaction 1 summary of Brønsted plot and estimated parameters (25°C, I = 0.1 M).
Acid
Catalyst
pKa
K)q
p q log #
p
Model
Brønsted
Estimated
Estimated
k1 (M–2 s–1)
k:
log #
p
k:
log #
p
–2.0
Model
Brønsted
Implemented
Plot
k1 a ± 95% CI d
H2O
15.52 2 3
–15.34
1.1±0.095
2.0x10–2 b
HPO42–
11.71 1 4
–11.11
12
12
HCO3–
9.88
1 3
–9.40
200±6.6
200
2.3
NH4+
9.24
4 1
–9.84
98±14
98
1.4
H2PO4–
6.75
2 3
–6.57
(3.4±0.044)x105
3.4x105
5.2
H+
–1.74 3 2
1.56
(6.8±0.82)x108
6.8x108
8.4
H2CO3
3.23 e 2 2
–3.23
2.4x103
1.9x106 c
6.0
H3PO4
1.93
–2.11
1.4x107
1.4x107
6.7
3 2
K1
1.1
2.1±0.024
a
Model k1 values are in M–2 s–1 except H2O which is in M–1 s–1 and K1 which is the equilibrium
constant for reactions 1 and –1
b
Model k1 divided by 55.5 M to arrive at Brønsted k1
c
Model k1 is based on H2CO3*; therefore, model k1 value was multiplied by 795, O PQE , to
O PQ ∗ arrive at Brønsted k1
d
95% confidence interval (CI) provided for model estimated parameters only
e
pKa is for true H2CO3 concentration
384
385
23
ACS Paragon Plus Environment
E
Environmental Science & Technology
386
Page 24 of 29
Table 6. Reaction 2 Summary of Brønsted plot and estimated parameters (25°C, I = 0.1 M).
Base
Catalyst
pKa
p q log K)q
#
p
Model
Brønsted
Estimated
Estimated
k2 (M–2 s–1)
k
log #
q
log 6.1
Model
Brønsted
Implemented
Plot
k2 a ± 95% CI c
k
#
q
OH–
15.52
2 3
–15.34
(3.7±0.54)x106
3.7x106
PO43–
11.71
1 4
–11.11
1.2x105
1.2x105
CO32–
9.88
1 3
–9.40
(2.3±0.45)x104
2.3x104
NH3
9.24
4 1
–9.84
8.9x103
8.9x103
HPO42–
6.75
2 3
–6.57
(1.9±0.010)x103
1.9x103
2.8
H2O
–1.74
3 2
1.56
9.6±0.97
1.7x10–1 b
–1.1
HCO3–
3.23 d
2 2
–3.23
28
28
1.1
H2PO4–
1.93
3 2
–2.11
9.2
9.2
0.66
4.5
3.9
3.9
a
Model k1 values are in M–2 s–1 except H2O which is in M–1 s–1
b
Model k1 divided by 55.5 M to arrive at Brønsted k1
c
95% confidence interval (CI) provided for model estimated parameters only
d
pKa is for equilibrium with true H2CO3 concentration
387
24
ACS Paragon Plus Environment
Page 25 of 29
388
389
390
Environmental Science & Technology
Figure 1. Monobromamine (Panel A) and dibromamine (Panel B) simulations compared to
experimental data using the measured and predicted rate constants from Lei, et al.7 for
experiment set NN–1
A
4.0E-04
Monobromamine Concentration (M)
3.8E-04
3.6E-04
3.4E-04
3.2E-04
NN-1-1 Data
NN-1-2 Data
NN-1-3 Data
NN-1-4 Data
NN-1-5 Data
3.0E-04
NN-1-1 (Lei, et al.)
NN-1-2 (Lei, et al.)
NN-1-3 (Lei, et al.)
NN-1-4 (Lei, et al.)
NN-1-5 (Lei, et al.)
2.8E-04
0
20
40
60
80
100
120
140
160
180
200
Time (s)
391
B
3.0E-05
Dibromamine Concentration (M)
2.5E-05
2.0E-05
1.5E-05
1.0E-05
NN-1-1 Data
NN-1-2 Data
NN-1-3 Data
NN-1-4 Data
NN-1-5 Data
5.0E-06
NN-1-1 (Lei, et al.)
NN-1-2 (Lei, et al.)
NN-1-3 (Lei, et al.)
NN-1-4 (Lei, et al.)
NN-1-5 (Lei, et al.)
0.0E+00
0
392
20
40
60
80
100
120
140
Time (s)
25
ACS Paragon Plus Environment
160
180
200
Environmental Science & Technology
393
394
395
Page 26 of 29
Figure 2. Monobromamine (Panel A) and dibromamine (Panel B) simulations compared to
experimental data using the measured and predicted rate constants from Lei, et al.7 for
experiment set CN–2
A
4.5E-04
Monobromamine Concentration (M)
4.0E-04
3.5E-04
3.0E-04
2.5E-04
CN-2-1 Data
CN-2-2 Data
CN-2-3 Data
CN-2-4 Data
CN-2-5 Data
2.0E-04
CN-2-1 (Lei, et al.)
CN-2-2 (Lei, et al.)
CN-2-3 (Lei, et al.)
CN-2-4 (Lei, et al.)
CN-2-5 (Lei, et al.)
1.5E-04
0
20
40
60
80
100
120
140
160
180
200
Time (s)
396
B
3.0E-05
Dibromamine Concentration (M)
2.5E-05
2.0E-05
1.5E-05
1.0E-05
CN-2-1 Data
CN-2-2 Data
CN-2-3 Data
CN-2-4 Data
CN-2-5 Data
5.0E-06
CN-2-1 (Lei, et al.)
CN-2-2 (Lei, et al.)
CN-2-3 (Lei, et al.)
CN-2-4 (Lei, et al.)
CN-2-5 (Lei, et al.)
0.0E+00
0
397
20
40
60
80
100
120
140
Time (s)
26
ACS Paragon Plus Environment
160
180
200
Page 27 of 29
398
399
400
401
Environmental Science & Technology
Figure 3. Model simulation comparisons with experimental data for parameter estimation
conducted with selected individual experiments. Experiments HN–3–5 (Panel A) and NP–1
(Panel B) represent the greatest residual sum of squares (RSS) improvement for selecting
reaction Scheme 1 versus 2 or reaction Scheme 2 versus 1, respectively.
6.E-04
Monobromamine Data (HN-3-5)
Dibromamine Data (HN-3-5)
Monobromamine Model (Scheme 1: R1, R-1, and R2)
Dibromamine Model (Scheme 1: R1, R-1, and R2)
Monobromamine Model (Scheme 2: R1, R-1, and R3)
Dibromamine Model (Scheme 2: R1, R-1, and R3)
A
5.E-04
Concentration (M)
4.E-04
3.E-04
2.E-04
1.E-04
0.E+00
0
20
40
60
80
402
100
Time (s)
120
140
160
180
200
B
4.5E-04
4.0E-04
Monobromamine Data (NP-1)
Dibromamine Data (NP-1)
Monobromamine Model (Scheme 1: R1, R-1, and R2)
Dibromamine Model (Scheme 1: R1, R-1, and R2)
Monobromamine Model (Scheme 2: R1, R-1, and R3)
Dibromamine Model (Scheme 2: R1, R-1, and R3)
3.5E-04
Concentration (M)
3.0E-04
2.5E-04
2.0E-04
1.5E-04
1.0E-04
5.0E-05
0.0E+00
0
403
10
20
30
40
50
Time (s)
60
27
ACS Paragon Plus Environment
70
80
90
100
Environmental Science & Technology
404
Page 28 of 29
Figure 4. Brønsted plots for Reaction 1 (Panel A) and Reaction 2 (Panel B)
10
A
y = 0.62x + 7.98
R² = 0.96
8
log (k1/p)
6
H+
H3PO4
H2CO3
H2PO4–
4
HCO3–
2
HPO42–
NH4+
0
-2
Model estimated
H2O
Brønsted estimated
-4
-20
-15
405
-10
-5
log (Kaq/p)
0
5
B
7
OH–
6
5
PO43–
NH3
log (k2/q)
4
y = -0.42x - 0.23
R² = 0.99
CO32–
3
HPO42–
2
1
HCO3–
0
H2PO4–
Model estimated
-1
H2O
Brønsted estimated
-2
-20
406
-15
-10
-5
log (Kaq/p)
28
ACS Paragon Plus Environment
0
5
Page 29 of 29
407
408
409
410
Environmental Science & Technology
Figure 5. Monobromamine and dibromamine experimental data and simulations using
estimated parameters from the current research compared to using the measured and
predicted rate constants from Lei, et al.7 for experiments NN–1–3 (Panel A), NN–1–5
(Panel B), CN–2–3 (Panel C), CN–2–5 (Panel D), NP–3 (Panel E), and NP–5 (Panel F).
A
4.0E-04
4.0E-04
3.5E-04
3.5E-04
3.0E-04
3.0E-04
2.5E-04
Residual Sum of Squares
Current Research = 5.0 x 10–9
Lei, et al. = 1.9 x 10–8
2.0E-04
1.5E-04
1.0E-04
Dibromamine (Data)
Monobromamine (Current Research)
Dibromamine (Current Research)
Monobromamine (Lei, et al.)
Dibromamine (Lei, et al.)
40
60
80
100
Time (s)
120
140
160
180
0
Dibromamine (Current Research)
Monobromamine (Lei, et al.)
Dibromamine (Lei, et al.)
4.0E-04
4.0E-04
3.5E-04
3.5E-04
3.0E-04
3.0E-04
2.5E-04
Residual Sum of Squares
Current Research = 7.5 x 10–9
Lei, et al. = 3.6 x 10–7
1.0E-04
20
Dibromamine (Data)
Monobromamine (Current Research)
Dibromamine (Current Research)
Monobromamine (Lei, et al.)
Dibromamine (Lei, et al.)
60
80
100
Time (s)
120
140
160
180
2.5E-04
Residual Sum of Squares
Current Research = 9.5 x 10–9
Lei, et al. = 6.6 x 10–7
2.0E-04
1.0E-04
5.0E-05
200
D
1.5E-04
Monobromamine (Data)
40
4.5E-04
Concentration (M)
Concentration (M)
200
C
1.5E-04
Monobromamine (Data)
Dibromamine (Data)
Monobromamine (Current Research)
Dibromamine (Current Research)
Monobromamine (Lei, et al.)
Dibromamine (Lei, et al.)
5.0E-05
0.0E+00
0.0E+00
0
20
40
60
80
100
Time (s)
120
140
160
180
200
0
E
4.5E-04
4.0E-04
3.5E-04
3.0E-04
Monobromamine (Data)
Dibromamine (Data)
Monobromamine (Current Research)
Dibromamine (Current Research)
Monobromamine (Lei, et al.)
Dibromamine (Lei, et al.)
40
60
80
100
Time (s)
120
140
160
180
200
F
4.0E-04
Monobromamine (Data)
Dibromamine (Data)
Monobromamine (Current Research)
Dibromamine (Current Research)
Monobromamine (Lei, et al.)
Dibromamine (Lei, et al.)
3.5E-04
Residual Sum of Squares
Current Research = 1.3 x 10–9
Lei, et al. = 2.1 x 10–7
3.0E-04
Residual Sum of Squares
Current Research = 1.3 x 10–9
Lei, et al. = 1.1 x 10–7
2.5E-04
20
4.5E-04
Concentration (M)
Concentration (M)
Dibromamine (Data)
Monobromamine (Current Research)
0.0E+00
20
4.5E-04
412
Monobromamine (Data)
5.0E-05
0
2.0E-04
Residual Sum of Squares
Current Research = 5.8 x 10–9
Lei, et al. = 6.0 x 10–8
2.0E-04
1.0E-04
0.0E+00
2.0E-04
2.5E-04
2.0E-04
1.5E-04
1.5E-04
1.0E-04
1.0E-04
5.0E-05
5.0E-05
0.0E+00
413
2.5E-04
1.5E-04
Monobromamine (Data)
5.0E-05
411
B
4.5E-04
Concentration (M)
Concentration (M)
4.5E-04
0.0E+00
0
10
20
30
40
50
Time (s)
60
70
80
90
100
0
10
20
29
ACS Paragon Plus Environment
30
40
50
Time (s)
60
70
80
90
100
Документ
Категория
Без категории
Просмотров
5
Размер файла
591 Кб
Теги
acs, est, 7b02661
1/--страниц
Пожаловаться на содержимое документа