KINETICS OF THE Fe(III) INITIATED DECOMPOSITION OF
HYDROGEN PEROXIDE: EXPERIMENTAL AND
MODEL RESULTS
by
Wai P. Kwan
Bachelor of Science, Chemistry & Engineering and Applied Science
California Institute of Technology, 1997
Submitted to the Department of Civil and Environmental Engineering
In Partial Fulfillment of the Requirements for the Degree of
MASTER OF SCIENCE
in Civil and Environmental Engineering
at the
Massachusetts Institute of Technology
September 1999
@ 1999 Massachusetts Institute of Technology
All rights reserved
Signature of the Author
Department of Civil and Environmental Engineering
August 3, 1999
Certified by
Bettina M. Voelker
Assistant Professor of Civil and Environmental Engineering
Thesis Supervisor
Accepted by
Daniele Veneziano, Chairman
MASSACHUSETTS INSTITUTE
OF
SE P 1t
BA
RE
BRARIES
Departmental Committee on Graduate Students
i"
KINETICS OF THE Fe(III) INITIATED DECOMPOSITION OF
HYDROGEN PEROXIDE: EXPERIMENTAL AND
MODEL RESULTS
by
Wai P. Kwan
Submitted to the Department of Civil and Environmental Engineering
on August 3, 1999
in partial fulfillment of the requirements for the Degree of Master of Science
in Civil and Environmental Engineering
ABSTRACT
Experimental data from the decomposition of hydrogen peroxide by the Fe(III) initiated
Fenton reaction at pH 3 were compared with model predictions. This model used only defined
chemical reactions, their published rate constants, the initial reactant concentrations, and no
fitting parameters. The initial concentration of hydrogen peroxide ranged from 0.1-1 millimolar,
and the amount of Fe(III) used varied from 4-325 micromolar. Differences between the data and
model results ranged from insignificant to about 20 percent of the initial concentration of
hydrogen peroxide. In the second set of experiments, 14C-labeled formic acid, a hydroxyl radical
probe, was added. Model results of hydrogen peroxide and 14C loss over time again compared
favorably with experimental data. The steady state concentration of hydroxyl radicals calculated
from the 14C-labeled formic acid agreed with those predicted by the model to within a factor of
two or better. These values were also compared with those derived from steady state
approximations. Furthermore, it was shown that the degradation rate of the 14 C-labeled formic
acid could be predicted from the decomposition rate of hydrogen peroxide.
Thesis Supervisor: Bettina M. Voelker
Title: Assistant Professor of Civil and Environmental Engineering
ACKNOWLEDGEMENTS
This research was funded in part by a Ralph Parsons Fellowship. I also want to thank
>
Tina Voelker - who improved this thesis immensely by requesting for clarifications and
details in numerous places
>
The Voelker group - for their help and camaraderie over the past two years
>
Rachel Adams - for caring
"A... Ayukawa." - Kasuga Kyousuke
TABLE OF CONTENTS
I.
Background
1.1
1.2
Introduction
11
Fenton Chemistry
12
1.2.1
1.2.2
1.3
2.
11
Overview
The Chain Reaction
12
16
Motivation
18
Methods
2.1
22
Materials and Analyses
2.1.1
2.1.2
2.1.3
2.1.4
22
Materials
Measurement of Hydrogen Peroxide
Measurement of Iron
Measurement of ' 4 C-labeled Formic Acid
2.2 Results and Discussion
2.2.1
Air Sparging Logistics
2.2.2
3.
24
24
DPM Measurements: Immediate versus Delayed
Experimental Setup
26
2.4
Modeling with Acuchem
27
Results
3.2
29
The Basic Fenton System
3.1.1
3.1.2
29
Effect of Initial Concentration of Hydrogen Peroxide
Effect of Total Amount of Fe(III)
The Basic Fenton System and
4
CH2 0 2
Discussions
29
34
43
46
4.1
The Basic Fenton System
4.2
The Basic Fenton System and
4.3
The Steady State Concentration of Hydroxyl Radicals
4.3.1
46
4
CH 2 0
2
57
61
61
4.3.2
[OH-]ss, measured
[OH-]L, model prediction
4.3.3
[OH-]ss,
63
equation prediction
4.4 Modeling Probe/Contaminant Loss
5.
25
2.3
3.1
4.
22
22
22
23
Conclusions
62
65
68
Bibliography
69
APPENDIX
75
LIST OF FIGURES
Figure 1.1.
14
Log C-pH diagram for Fe(II) at equilibrium with amorphous Fe(OH) 2 (s).
Figure 1.2. Log C-pH diagram for Fe(III) at equilibrium with amorphous Fe(OH) 3 (s).
14
Figure 1.3. A schematic diagram of reactions in the traditional Fenton system.
17
Figure 1.4. A schematic diagram of the chain reaction mechanism. Any reaction of OH. that
18
results in the formation of H0 2 /O - propagates the chain through another cycle.
Figure 2.1. DPM measurements from solutions containing 14 CH 2 0 2 and 1mM H2 0 2 at pH 3.
The data for "Stirred overnight" were obtained from a separate experiment. (Mean value
24
±2.1% error, as reported by the instrument; n = 2.)
Figure 2.2. Sample Acuchem input file.
27
Figure 3.1a. Measured and predicted hydrogen peroxide decomposition versus time with
[Fe(III)]T = 20 gM and [H2 0 2]o = A) 106 gM, B) 206 gM.
30
Figure 3.1b. Measured and predicted hydrogen peroxide decomposition versus time with
[Fe(III)]T = 20 pM and [H2 0 2]o = C) 315 gM, D) 417 pM, E) 514 gM, F) 606 gM.
31
Figure 3.1c. Measured and predicted hydrogen peroxide decomposition versus time with
[Fe(III)]T = 20 gM and [H2 0 2]o = G) 782 gM, H) 931 gM, 1) 1.00 mM, J) 1.06 mM.
-
32
Figure 3.2. The first half-life of hydrogen peroxide as a function of [H2 0 2]o with [Fe(III)]T= 20
33
piM.
Figure 3.3. Measured and predicted hydrogen peroxide decomposition versus time with
[Fe(III)]T = 4.3 jM.
35
Figure 3.4. Measured and predicted hydrogen peroxide decomposition versus time with
[Fe(III)]T = 5 pM.
36
Figure 3.5. Measured and predicted hydrogen peroxide decomposition versus time with
[Fe(III)]T = 20 pM.
37
Figure 3.6. Measured and predicted hydrogen peroxide decomposition versus time with
[Fe(III)]T= 67 pM.
38
Figure 3.7. Measured and predicted hydrogen peroxide decomposition versus time with
[Fe(III)]T= 325 4M.
39
Figure 3.8a. The first half-life of hydrogen peroxide as a function of [Fe(III)]T with [H2 0 2]o =
100 pM.
40
Figure 3.8b. The first half-life of hydrogen peroxide as a function of [Fe(III)]1 with [H2 0 2]o =
500 pM.
41
Figure 3.8c. The first half-life of hydrogen peroxide as a function of [Fe(III)]1 with [H2 0 2]o = 1
mM.
42
Figure 3.9. Measured and predicted hydrogen peroxide and 14CH 20 2 decomposition versus time
with [Fe(III)]T= 44 pM, [H 2 0 2]o = 454 gM, and [CH 2 0 2]o = 85.9 nM.
44
Figure 3.10. Measured and predicted hydrogen peroxide and 14CH 20 2 decomposition versus
time with [Fe(III)]T= 42 gM, [H2 0 2]o = 1.14 mM, and [CH 2 0 2]o = 89.4 nM.
45
Figure 4.1 a. Measured and predicted hydrogen peroxide decomposition versus time with k3
1.2 x 107 M- 1 s', [Fe(III)]T= 20 pM and [H 2 0 2]o = A) 106 gM, B) 206 pM.
=
48
Figure 4. 1b. Measured and predicted hydrogen peroxide decomposition versus time with k3 =
1.2 x 107 M-1 S-1, [Fe(III)]T= 20 gM and [H 2 0 2]o = C) 315 gM, D) 417 gM., E) 514 jiM, F)
606 pM.
49
Figure 4.1c. Measured and predicted hydrogen peroxide decomposition versus time with k3 =
1.2 x 107 M- S-1, [Fe(III)]T= 20 jM and [H 2 0 2]o = G) 782 pM, H) 931 pM, 1) 1.00 mM, J)
1.06 mM.
50
Figure 4.2. Measured and predicted hydrogen peroxide decomposition versus time with k3 = 1.2
x 10' M- s-1 and [Fe(lII)]T= A) 4.3 gM, B) 5 jiM, C) 67 RM, D) 325 pM.
51
Figu re 4.3. Measured and predicted hydrogen peroxide and 14CH 20 2 decomposition versus time
with k3 = 1.2 x 107 M-1 s-1, [Fe(III)]T= 44 gM, [H 2 0 2]o = 454 pM, and [CH 2 0 2]o = 85.9 nM.
52
Figure 4.4. Measured and predicted hydrogen peroxide and 14CH 20 2 decomposition versus time
with k3 = 1.2 x 107 M-1 s-, [Fe(III)]T= 42 [tM, [H 2 0 2]o = 1.14 mM, and [CH 2 0 2]o = 89.4
nM.
53
Figure 4.5. Measured and predicted hydrogen peroxide decomposition versus time with
[Fe(III)]T= 40 gM and [H2 0 2]o = 456 jM at pH 3. Notice that no hydrogen peroxide
decomposition was detected in the first four hours.
59
Figure 4.6. Measured and predicted hydrogen peroxide decomposition versus time with
[Fe(III)]T= 42 [LM and [H2 0 2]o = 1.13 mM at pH 3. The Milli-Q water was treated for about
30 seconds with a TOC reduction unit.
59
Figure 4.7. Measured and predicted hydrogen peroxide decomposition versus time with [H2 0 2]o
= 1 mM and A) [Fe(II)]o = 1 pM, [Fe]T = 44 pM, B) [Fe(II)]o = 3 gM, [Fe]T = 37 pM, C)
[Fe(II)]o = 6 gM, [Fe]1T = 43 pM, D) [Fe(II)]o = 9 jM, [Fe]T = 46 RM. All solutions were at
60
pH 3.
Figure 4.8.
Semi-log plot of
14 CH 2 0
2
from data presented in Figures 3.9 and 3.10. The solid
lines are the regression lines of the data set.
63
Figure 4.9. Comparison of [OH*]ss from three different methods.
64
Figure 4.10. Comparison between measured [CH202]1T and d[CH 20 2]/dt predicted from
d[H 2 0 2]/dt for [Fe(III)]T 40 jM and two concentrations of H2 0 2 . The lines are the
predictions.
67
LIST OF TABLES
Table 1.1.
Reactions and rate constants (at pH 3) of the Fenton system.
15
Table 1.2. Hydroxyl radical oxidation mechanisms.
15
Table 2.1.
25
The influence of air sparge time on DPM measurements.
Table 2.2a. [4CH202]T for [Fe(IIL)]T = 40 gM and [H2 0 2]
=
454 RM.
25
Table 2.2b. ["CH202]T for [Fe(III)]T = 40 tiM and [H2 0 2]o
=
1.14 mM.
26
Table 4.1. Iron speciation in reference solutions. An iron species was considered major if it was
greater than or equal to ten percent of the total amount of iron.
46
Table 4.2. The amount of hydrogen peroxide needed for either case I or case 11 to occur.
__
57
11
1. Background
1.1 Introduction
Fenton chemistry has been known for over a century, but only in the last decade or so has
it been considered and used as an advanced oxidation process for wastewater treatment (Bigda,
1995). Fenton's reagent (Fe2++ H20 2 ) can successfully remediate contaminated water because it
produces hydroxyl radicals (OH-), which will oxidize almost every organic pollutant at very fast
rates at ambient temperatures. Other advantages of this technique include inexpensive reactants
and ease of use. The effectiveness of Fenton's reagent in destroying contaminants has been
demonstrated on aromatic amines, chlorinated hydrocarbons, and many others (Pignatello, 1992;
Potter and Roth, 1993; Venkatadri and Peters, 1993; Lipczynska-Kochany et al., 1995; Tang and
Huang, 1996; Casero et al., 1997). In most cases, the wastewater is mixed with high doses of a
ferrous salt, e.g., FeSO 4 , and hydrogen peroxide in large, well-stirred reactors. The destruction is
usually complete within a day, accompanied by mineralization of a substantial percentage of the
organic contaminant.
This success has spurred research and development in applying Fenton chemistry to
remediate contaminated soils and groundwater in situ (Watts et al., 1990; Aronstein et al., 1994;
Ravikumar and Gurol, 1994; Vigneri, 1994; Vigneri, 1996; Wilson, 1996; Ho et al., 1997; Li et
al., 1997; Wilson, 1997; Kong et al., 1998). For the most part, these investigators emulated the
methods used in wastewater treatment, i.e., remediate the contaminated soil and groundwater
with a solution of concentrated hydrogen peroxide and ferrous salt, and reported good results.
The use of natural iron oxides, e.g., goethite, hematite, and magnetite, instead of ferrous salts to
promote the Fenton reaction in situ has received more attention recently because they are
ubiquitous in nature (Watts et al., 1993; Khan and Watts, 1996; Lin and Gurol, 1996; Gurol et
al., 1997; Lin, 1997; Watts et al., 1997; Kong et al., 1998; Valentine and Wang, 1998). The
results are promising, with some showing more efficient use of H2 0 2 than systems that used
FeSO 4 . In conclusion, researchers have shown that Fenton chemistry can be a viable, fast, and
low-cost technique for the in situ remediation of contaminated aquifers.
However, we lack a thorough chemical understanding of Fenton chemistry in natural
settings. Only a few studies have been done on the effects that natural water constituents have on
the Fenton reaction, or on the kinetics and mechanisms of the catalytic decomposition of
12
hydrogen peroxide on iron oxides (Wells and Salam, 1967; Walling and Goosen, 1973;
Lipczynska-Kochany et al., 1995; Lin and Gurol, 1998). Such knowledge is necessary so that we
can optimize this technology, both in general and for particular sites.
1.2 Fenton Chemistry
1.2.1 Overview
In 1894, Henry J. H. Fenton reported the oxidation of tartaric acid in a solution of ferrous
ions and hydrogen peroxide (H 2 0 2 ). It was later shown that the combination of Fe2+ and H2 0 2
can oxidize many organic substrates, and this has been known as "Fenton chemistry," the
"Fenton reaction," or "Fenton's reagent." Since its discovery, numerous investigators in various
fields have continued to study it because of its oxidative potential and the ubiquitous nature of
both iron and hydrogen peroxide in the environment and living organisms (Moffett and Zika,
1987; Pignatello, 1992; Sawyer et al., 1996; Bauer and Fallmann, 1997).
It took a few decades before the mechanisms of the Fenton reaction was understood. In
1934, Haber and Weiss proposed that the Fenton reaction occurs as follows:
Fe(II) + H202
-
Fe(III) + OH. + OH~
(1-1)
Further studies by Barb et al. (195 1ab), Walling and Goosen (1973), and others have established
the generally accepted description of the Fenton system (Reactions 1-1 to 1-6):
Fe(III) + H2 0 2 -> Fe(II) + HO 2/0
H 20
2
+
+
H+
OHe -- H0 2 /O - + H 2 0
Fe(III) + H0 2/O - -> Fe(II)
+
(1-3)
02 + H*
(1-4)
Fe(II) + OHe -* Fe(III) + OH~
Fe(II) + HO 2/ 0 - + H*-+ Fe(III) + H 2 0
(1-2)
(1-5)
2
(1-6)
When hydrogen peroxide and Fe(II) are mixed together, Fe(II) is rapidly oxidized to Fe(III)
according to Reaction 1-1 until one of the reactants is exhausted. Reaction 1-1 is a fast reaction,
complete on a time scale of minutes. If sufficient hydrogen peroxide remains, Reaction 1-2
13
becomes dominant since most of the iron has been converted to the ferric form. The details of the
Fenton system, especially the one initiated by Fe(III), will be discussed more thoroughly in the
next section.
Some researchers dispute the existence of the hydroxyl radical in the Fenton reaction
(Bray and Gorin, 1932; Wink et al., 1994; Sawyer et al., 1996; Bossmann et al., 1998). They
instead invoke an intermediate ferryl radical FeO2+ or FeOH 3+, and the kinetics yield an
equivalent rate law for the loss of hydrogen peroxide. Walling (1998) believes it is unlikely that
the ferryl species would produce reactivities for a range of substrates that agree with the rates of
reaction of OHe measured by radiation chemists in metal-free systems. In addition, he had
reported that methanol and ferrous ion were oxidized at the same relative rates in solutions with
and without 0.5 M NaClO 4 (Walling et al., 1974). This supports the OHe intermediate theory due
to the Bronsted Bjerrum treatment of the effect of ionic strength: reactions between ions and
neutral species will be unaffected by ionic strength, but those between ions of like charge will be
accelerated. Although most researchers concur with Walling, the debate will persist until
conclusive results are demonstrated.
pH is an important factor to consider in the Fenton system because most of the reactions
involve H+ and OH-. Moreover, the solubility of Fe(II) and Fe(III) are also highly pH dependent.
Figures 1.1 and 1.2 were constructed using equilibrium constants from Morel and Hering (1993),
and they show that both Fe(II) and Fe(III) have the greatest solubility in strongly acidic
environments. It is also true that iron hydrolysis species react with rate constants different from
non-hydrolyzed ones (Millero et al., 1991). Therefore, partially to avoid the formation of iron
(hydr)oxides and partially to use reported rate constants, many of the experiments on Fenton
chemistry in the literature were done in acidic media, typically ranging from pH 1 to 4. The rate
constants of the Fenton system at pH 3 are summarized in Table 1.1; they have been adjusted for
acid/base reactions (the pKa of HO 2 is 4.9) and iron hydrolysis effects. These rate constants are
discussed in greater detail in Section 4.1.
14
14
12
10
8
6
4
0
2
0
-2
-4
-6
-8
-10
0
1
2
3
4
6
6
7
8
9
10
11
12
13
14
pH
Figure 1.1. Log C-pH diagram for Fe(II) at equilibrium with amorphous Fe(OH) 2 (s).
A
........................................................
........................................................
...............
................................
.......................................................
.........................................................
.........................................................
........................................................
........................................................
........................................................
.
......................................................
.......................................................
.......................................................
......................................................
.......................................................
....................................................
................... ....
2
. . . . . . . .
0-2
-
-4
U9
0)
-6
-
-8
-
. . . . . . . . .
. . .
. . . .........................
. . . . . . . . . . . . .. . . .. . . . . . . .3.- . . . . . . ........
....................................................
*................ ........ ....
'...................................................
'........... ..... ....
.*
...........................
. .......
........................................................ .. * *
...................................................
..................................................
..................................................
.................................................
. . . . . . . . . . . . . . . .I . . . . . . . . . . . I . . . . . . . . . . * * * * . . . . . .
.................................................
. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . * * * . . . . . .
................................................
................................................
...............................................
..............................................
. . . . I . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
...........................................
..........................................
........................................
.......................................
....................................
...................................
.........*..... ......
. . . . . . . . .. ..
......................
...........................
............................
. . . 1 1 . . .. . . . . . . . . . . . . . . . . .
........................
.......................
....................
...................
................
............
...........
-10 -12 -14 -
Fe 2 (OH)24+
Fe(OH)2+
3+
Fe(OH4FE)OH 2+
F%(OH),4 6+,,J9
---
0
Fe
V
1
2
3
I
4
I
5
I
6
I
7
I
8
I
9
I
10
I
11
I
12
I
13
I
14
pH
Figure 1.2. Log C-pH diagram for Fe(III) at equilibrium with amorphous Fe(OH) 3 (s).
15
No.
Reaction
Rate constant at pH 3 (M- s-)
Fe(II) + H2 O2 ---
(1-2)
Fe(III) + H 2 0 2
(1-3)
H 20 2
(1-4)
Fe(III) + HO2/ O -
(1-5)
Fe(II) + OH. -k.
> Fe(III) + OH-
(1-6)
Fe(II) + H0 2 / O
H+k
+
76
> Fe(III) + OHe + OH-
(1-1)
-k2
OHe -k->
2+
Fe(II) + HO 2 / O
2 H+1
10-3
X
a
4.5 x 107 b
HO 2 / O - + H2 0
k4L_
a
2.4 x 106
Fe(II) + 02+ H+
4.3 x
e
10 8 d
1.3 x 106 c
Fe(III) + H22
Table 1.1. Reactions and rate constants (at pH 3) of the Fenton system.
a Barb et al. (1951b)
b Ross and Ross (1977)
' Rush and Bielski (1985)
d Christensen and Sehested
(1981)
The hydroxyl radical (OHe) formed in Reaction 1-1 is a very powerful oxidant and is
responsible for the destruction of organic substrates observed in experiments. Its oxidation
potential is greater than singlet oxygen and second only to atomic fluorine (Bigda, 1995).
M' s 1) at
Furthermore, it reacts with many compounds at or near diffusion limited rates (~101W
ambient conditions (Ross and Ross, 1977; Buxton et al., 1988). The hydroxyl radical oxidizes a
molecule in one of three ways: hydrogen atom extraction, addition to a double bond, and electron
abstraction from a lone pair of electrons. These mechanisms are depicted below.
Hydrogen atom extraction.
C-
-
Addition to a double bond.
Electron abstraction from a lone pair of
H
e
.OH
Table 1.2. Hydroxyl radical oxidation mechanisms.
-
-
-
C * + H20
O_
*
ee
electrons.
OH
\
OH
1j/\
+
OH
16
Other metals, such as copper, cobalt, and manganese, can also react with hydrogen
peroxide in a manner similar to Reaction 1-1 (Wells and Mays, 1968; Moffett and Zika, 1987;
Luo et al., 1988; Goldstein et al., 1993; Wardman and Candeias, 1996; Leonard et al., 1998, and
references therein). It is also possible to replace hydrogen peroxide with other oxidants
(Wardman and Candeias, 1996). Thus, the most general form of the Fenton reaction is:
reduced metal + oxidant -+ oxidized metal + more powerful oxidant
(1-7)
Although these "Fenton-like" reactions are important in certain environments, they were not
considered in this study's models because neither iron nor hydrogen peroxide was substituted for
in any of the experiments.
1.2.2 The Chain Reaction
Reactions 1-1 and 1-2 show that both Fe(II) and Fe(III) can react with hydrogen
peroxide. Furthermore, Reaction 1-1 proceeds at a rate that is almost five orders of magnitude
faster than Reaction 1-2 at pH 3. This dramatic difference has a significant impact on the lifetime
of hydrogen peroxide and the rate at which hydroxyl radicals are generated.
If Fe(II) is used to initiate the Fenton reaction, OH- and Fe(III) will be quickly produced
according to Reaction 1-1. The Fe(III) may precipitate out of solution as an amorphous solid,
depending on how much is made and the solution composition, e.g., pH. The hydroxyl radicals
will react with almost any organic molecules, hydrogen peroxide, dissolved organic carbon
(DOC), or anything else in solution. Figure 1.3 shows these concepts pictorially (Baker, 1997).
Due to the fast reaction rate of Reaction 1-1, the "burst" of hydroxyl radicals does not last for
long because one of the reactants rapidly becomes depleted.
17
Fe(II) + H 2 0 2
OH-
Fe(III)
OH
H20
sinks
2
DOC
Figure 1.3.
other
contaminants
A schematic diagram of reactions in the traditional Fenton system.
However, if only Fe(III) is present at the start, the slower Reaction 1-2 must occur and
initiates a chain reaction. The Fe(II) produced is then quickly oxidized by H 2 0 2 , and the chain
propagates via Reactions 1-3 and 1-4. Reactions 1-1, 1-3, and 1-4 form a cycle that makes one
OH*, consumes two molecules of H 2 0 2 , and sustains itself by regenerating Fe(II). This cycle,
instead of the initiation Reaction 1-2, can determine the lifetime of H 2 0
many molecules of H 2 0
2
2
since it can decompose
before it terminates. Reactions that will stop the chain include
Reactions 1-5, 1-6, and any reactions of OH- with solutes that do not produce HO 2/ 0
. This
also means that stoichiometrically unimportant reactions can control the number of cycles in the
chain reaction, that is, trace concentrations of terminators can cause a several fold decrease in the
number of cycles. The chain reaction mechanism is illustrated in Figure 1.4, with the termination
steps removed for simplicity (Baker, 1997). In contrast with the traditional Fenton system, the
chain reaction mechanism creates OH. at a slow and steady pace. This can also occur in the
traditional Fenton system if an excess of H 2 0 2 over Fe(II) is present initially. In that case, Fe(II)
will be rapidly converted to Fe(III), and further loss of H 2 0 2 is then due to the chain reaction.
18
Fe(III) + H 2 0
H2 0 2
Fe(II)
+
OH-
2
+ Fe(III)
HO2/O~
2
+ H202
contaminants, DOC,
and other sinks
Figure 1.4. A schematic diagram of the chain reaction mechanism. Any reaction of OHO that
results in the formation of H0 2 /O - propagates the chain through another cycle.
1.3 Motivation
We believe the current way of using Fenton chemistry to remediate groundwater in situ
can be improved upon with a better understanding of the chemical kinetics, sources, and sinks of
both hydrogen peroxide and the hydroxyl radical. H2 0 2 is important because it is the source of
hydroxyl radicals and its concentration is a parameter that can be readily changed. The hydroxyl
radical is the chief chemical species of interest in remediation technologies employing Fenton
chemistry since it is a highly reactive, powerful, and indiscriminate oxidant. Therefore,
knowledge of the factors that control the fate of hydrogen peroxide and hydroxyl radicals will
allow us to manipulate them to increase the efficiency of the remediation process.
We define the efficiency (i) of the Fenton remediation process as:
19
moles of Mi consumed
moles of H20 2 consumed
d[Mi]
d[H 2 0 2 ](
where M denotes a contaminant. Although this definition is intuitive, an alternate way of
calculating r is more instructive. The efficiency can also be expressed in terms of the yield of
hydroxyl radicals from hydrogen peroxide (Y) and the fraction of hydroxyl radicals that react
with the various contaminants (F).
moles of hydroxyl radicals produced
moles of H 2 0 2 consumed
moles of Mi consumed
moles of hydroxyl radicals produced
(1-9)
=YF
The efficiency rises if either Y or F increases. It is not easy to raise Y because it is a parameter
dictated by the chemical reactions of the system. Thus, we should examine F in greater detail.
In a well-mixed reactor, F can be computed from the concentrations of the chemical
species in solution and their second-order reaction rate constants with OHe.
F=
moles of M. consumed
moles of hydroxyl radicals produced
kM [M
(aq)(1-10)
km, [Mi ](aq) + kH2 O2 [H 2 0 2 ] +lksin[sink]
"sink" is all other forms of OH. sink besides H2O 2 and Mi, and k is the reaction rate constant of
OHe with the species in subscript. km is on the order of 1010 M 1 s-1 for many organic molecules,
and kH202 is the rate constant of Reaction 1-3. The concentrations and types of the other OHO
sinks depend on the environment, but a common one in groundwater is dissolved organic carbon,
which has a rate constant on the order of 3 x 104 S-1 (mg/l DOC)-' (Hoignd, Faust et al., 1989).
Equation 1-10 illustrates why, for hydrophobic contaminants, the system is most effective if the
aqueous concentrations of [Mi](aq) are kept near saturation. Moreover, if
lksink [sink] is
negligible, the value of F will increase if we lower the amount of hydrogen peroxide.
20
F, and therefore il, increases if we decrease the concentration of hydrogen peroxide
because H2 0 2 competes with the other solution constituents for the available hydroxyl radicals.
When the chain reaction is the dominant hydrogen peroxide decomposition mechanism, Reaction
1-3 is the chief way by which it propagates. However, Reaction 1-3 is also a sink reaction.
Therefore, there exists an optimal H2 0 2 concentration that will propagate the chain but does not
severely hamper the likelihood of OH. reacting with the pollutant. This optimal level is probably
below the dosages being used currently, which are on the order of one molar or higher. There are
other benefits to not using concentrated hydrogen peroxide besides increased efficiency.
Concentrated H2 0 2 is dangerous to transport, and upon injection into groundwater, can react
violently with many substances, e.g., ferrous ions, to evolve large amounts of gas and heat that
can lead to serious consequences.
The in situ Fenton remediation process may also be more effective if the lifetime of
hydrogen peroxide in the subsurface is increased; this is due to contaminant mass transfer
limitations and transport issues. For a given amount of H2 0 2 ,
TI
is at its maximum when the
aqueous concentration of the pollutant is at saturation. Although [pollutant](aq) in a contaminated
aquifer may be at saturation before the Fenton reagents are introduced, it will decrease as the
pollutant reacts with the hydroxyl radicals. A hydrophobic pollutant will desorb at a rate much
slower than its reaction rate constant with OH- and cause ri to drop over time. Hence, we want to
delay the decomposition rate of hydrogen peroxide so that aqueous concentration of the pollutant
can be replenished. Moreover, soil and sediment particles usually consist of aggregates of
individual solid phases (Schwarzenbach et al., 1993). Contaminants trapped in these aggregates
may be difficult to remediate because their destruction rates can be affected by their mass
transfer rates (Sedlak and Andren, 1994; Watts et al., 1994). Yet, these pollutants cannot be
ignored since they contribute to the rebound effect observed in pump-and-treat systems. The
third argument for increasing the lifetime of hydrogen peroxide is that it can then be carried
farther by groundwater via advection, dispersion, and diffusion. These transport processes are
slow, so fast decomposition of H 2 O2 will only cleanse the area surrounding the injection points.
One possible drawback to this idea is that the lifetime of hydrogen peroxide may eventually be
controlled by sink reactions that do not produce hydroxyl radicals. For example, the enzymes
catalase and peroxidase destroy hydrogen peroxide but do not create OH. or other products that
can propagate the chain.
21
2H 2 0
H202 +
2
NADH + H
catalase > 2H20+02
peroxidase> 2H 2 0 + NAD*
(1-11)
(1-12)
These enzymes are common to most microorganisms, so biological processes could play a key
role in determining the lifetime of hydrogen peroxide. Such problems must be dealt with on a
case-by-case basis.
We chose to study the chain reaction mechanism because its slow initiation step permits
hydrogen peroxide to decompose more slowly than in the traditional Fenton system. We want to
be able to model the chain reaction mechanism so that we can accurately predict the temporal
behavior of the Fenton system based on initial conditions, known chemical reactions and their
corresponding rates. Our approach to building this model is to start from the fundamental system,
i.e., Fe(III) and H202 only, and work toward solutions similar to that of groundwater. If the
natural waters are too complicated to model, we will focus our attention on the behavior of the
pollutant and how it is influenced by hydrogen peroxide.
22
2. Methods
2.1 Materials and Analyses
2.1.1 Materials
All glassware and containers were soaked in 1 N HC1 at least overnight before use. The
reagents are reagent grade and were used without further purification. The activity of the 14 Clabeled formic acid is 48.1 gCi/mmol. All solutions were prepared using 18 MQ Milli-Q water
from a Millipore
system. Peroxidase
(type II from horseradish)
and N,N-diethyl-p-
phenylenediamine (DPD) solutions were kept in the dark at 4 *C for not more than two weeks.
Stock solutions of Fe(Cl0 4 )3-9H 2 0 were made fresh daily and acidified with a few drops of
concentrated HClO 4. pH measurements were made using an Orion Model 420A benchtop meter
calibrated against standard buffers. All spectrophotometric measurements were done on an HP
8453 diode array spectrophotometer. 14 C measurements were done on a Beckman LS 6500 multipurpose scintillation counter.
2.1.2 Measurement of Hydrogen Peroxide
Hydrogen peroxide was measured using the DPD method (Bader et al., 1988) as modified
by Voelker and Sulzberger (1996) to minimize interference by Fe(II) and Fe(III). 1.5 ml of
sample was added to 0.3 ml of pH 6 phosphate buffer (0.5 M), 0.15 ml of 2,2'-dipyridyl
(bipyridine) (0.01 M bipyridine in 10-3 M HClO4), and 50 pl of EDTA (10-2 M Na 2EDTA).
Then, 25 R1 each of DPD (0.1 g in 10 ml of 0.1 N H2 SO 4 ) and peroxidase (10 mg diluted to 10
ml) were pipetted into the cuvette. Absorbance at 552 nm (F = 21,000±500 M-I cm') was
measured after 45, 75, and 135 seconds in a 1-cm pathlength cuvette. The detection limit is 100
nM.
2.1.3 Measurement of Iron
Total Fe was measured using the ferrozine method (Stookey, 1970) as modified by
Voelker and Sulzberger (1996). 0.3 ml of a reductant (20.8 g of NH 3ClOH and 40 ml 32% HCl
diluted to 100 ml) was added to 4-5 ml of sample and allowed to stand at least overnight. 1 ml of
4.9 mM ferrozine was mixed with 1.5 ml of the reduced sample before 0.5 ml of acetate buffer
23
(193 g of ammonium acetate and 170 ml 25% NH 4 0H diluted to 500 ml) was added. Absorbance
at 562 nm (P = 27,900 M-1 cm-1) was measured after 2 minutes in a 1-cm pathlength cuvette. The
detection limit is 45 nM.
2.1.4 Measurement of14 C-labeled Formic Acid
Molecular probes are often used to study reactive transients, both qualitatively and
quantitatively. OH* probes that have been cited in the literature include cumene, butyl chloride,
and methanol (Zafiriou et al., 1990). We chose a different probe, 14C-labeled formic acid, for two
main reasons. The first is that the reactions of formate and formic acid with OH. are fast (k = 3.4
x 109 M- s-1 and 1.6 x 10' M-' s- , respectively, at pH 2-5) and have been well characterized
(Ross and Ross, 1977).
OHe + HCOO
OHe +HCOOH
- H 2 0 > COO._
- H20>
COOH*
+02
2
> CO2+OCO 2 + O-
(2-1)
(2-2)
Both reactions, in essence, produce the same end products. Also, the carbon radicals create
almost no side products in an oxygenated environment because they react with oxygen at near
diffusion limited rates. The second is that low concentrations (-100 nM) can be used since the
detection limit is on the order of nanomolars. This allowed us to investigate the kinetics of the
system while causing minimal perturbations to the chain reaction (Section 1.2.2).
To measure the amount of 14 C-labeled formic acid in the reactor, a 4 ml aliquot was
transferred into a 15-ml polystyrene conical tube. It was subsequently air sparged vigorously
with house air using a gas dispersion tube with a fritted cylinder for at least 30 seconds to drive
out the
14C-labeled
carbon dioxide. 1 ml of the aliquot was then combined with 6 ml of
scintillation fluid in a 7-ml glass scintillation vial. The frit was washed with Milli-Q water and
wiped clean after each sparge. The vials were kept at room temperature and their 14C-content
measured en masse within one day.
24
2.2 Results and Discussion
2.2.1 Air SpargingLogistics
We had to devise a method to remove the aqueous 14CO 2 end product so that the loss of
14 CH 20 2
over time could be tracked accurately. A simple approach is to vigorously air sparge the
aliquot to promote the escape of aqueous 14 CO 2 . However, we had to be certain that this method,
and the simple act of stirring the solution, did not remove 14CH 2 0
2
from solution. The data
shown in Figure 2.1 confirmed that this was true.
6000
5000 4000 -
0L
Q
3000
2000
1000
*
0
Y
-
Stirred for 0 hours
Stirred for 3 hours
Stirred overnight
00
1
2
3
4
5
Minutes sparged
Figure 2.1. DPM measurements from solutions containing 14CH 20 2 and 1mM H 20 2 at pH 3.
The data for "Stirred overnight" were obtained from a separate experiment. (Mean value ±2.1%
error, as reported by the instrument; n = 2.)
After establishing that air sparging had no effect on 14CH 2 0 2, an experiment in which
4CH 2 0 2 was oxidized to 14CO 2 using 5 mM each of Fe(NH 4 ) 2 (SO 4 ) 2 -6H 2 0 and H 2 0 2 , adjusted
to pH 3 with HClO 4 , and 50 nM 14CH 2 0 2 was done to determine the amount of time needed to
air sparge a 5 ml aliquot. Fe(NH 4 ) 2 (SO 4 )2 -6H 2 0 is a source of Fe2+, so hydroxyl radicals will be
produced at a much faster rate than if Fe3 was used (see Reactions 1-1 and 1-2). Aliquots were
25
withdrawn about 2 hours after initiation of the Fenton reaction to ensure that all of the 14CH 2 0 2
was converted to 14 CO 2 . The disintegration per minute (DPM) data in Table 2.1 show that half a
minute of air sparging was sufficient to drive off the 14 CO 2 since background DPM is about 50.
Minutes sparged
DPM
0
269.97
0.5
63.34
1
64.13
3
63.83
66.96
5
Table 2.1. The influence of air sparge time on DPM measurements.
2.2.2 DPM Measurements:Immediate versus Delayed
Experiments were done to determine if the DPM of an aliquot measured immediately
after extraction differed from that measured a day later. As shown in Tables 2.2a and b, where
DPM has been converted to [14CH2O2]1T, no differences were detected. Therefore, we were able
to sample at a high frequency and do batch DPM measurements at a later, more convenient time.
Time after
Experiment began (hrs)
0.15
[14
CH202]T (nM)
[1 4CH202]T (nM)
(Meas ired immediately)
86.0
(Measured a day later)
85.8
0.43
0.73
1.15
86.0
85.6
86.7
85.2
87.3
1.77
2.27
2.93
3.53
4.27
5.27
79.7
81.1
57.6
27.0
80.6
79.3
57.0
12.3
6.3
12.4
6.1
6.33
2.9
2.8
7.23
9.68
1.9
1.0
1.8
0.9
87.8
Table 2.2a. [14CH202]1 for [Fe(III)]T = 40 gM and [H2 0 2 ]0 = 454 gM.
26.6
26
Time after
[14CH 202] (nM)
[14 CH 20 2] (nM)
Experiment began (hrs)
0.00
0.17
0.33
(Measure(dimmediately)
89.2
89.5
0.50
87.6
(Measured a day later)
89.6
89.2
89.2
89.3
0.75
87.0
1.05
85.1
82.8
1.30
1.55
1.88
2.12
2.45
90.1
87.3
84.7
81.5
84.6
84.2
86.1
85.5
65.5
66.4
82.2
3.02
70.2
27.4
3.55
13.7
3.95
4.23
10.2
4.72
6.0
3.4
5.25
5.95
2.1
Table 2.2b. [ 14 CH202]T for [Fe(III)]T= 40 RM and [H 2 O
82.4
69.6
27.0
13.7
10.4
6.1
3.4
2.1
2]
= 1.14 mM.
2.3 Experimental Setup
All of the experiments were done in 250-ml HDPE amber bottles (Nalgene) to exclude
light. During the course of an experiment, the bottles were loosely capped and the solutions
(initial volume ~ 200 ml) were stirred at room temperature (22±3 'C) by a magnetic stirrer. The
hydrogen peroxide solutions, including those with 14CH 2 0 2, were adjusted to pH 3 with HClO 4
(1.0 and 0.1 M) and/or NaOH (1.0 and 0.15 M) before addition of Fe3+ (in the form of
Fe(Cl0 4 ) 3 -9H 2 0). Only a small volume (typically 20-200
l) of the acidified ferric perchlorate
stock solution was added to avoid changing the solution pH dramatically. H2 0 2 and 14CH 2 0 2
measurements were taken at appropriate times. An aliquot for iron measurement was withdrawn
a few minutes after initiation of the Fenton reaction, and often, at the conclusion of an
experiment.
27
2.4 Modeling with Acuchem
All of the modeling results presented in this thesis were calculated with the computer
program Acuchem (Braun and Herron, 1986). The user creates a single text file containing a set
of chemical equations, their corresponding rate constants, initial concentrations of the reactants,
and the length of time to run the model. Afterwards, Acuchem solves the resulting system of
differential equations using a numerical approach and returns the concentrations of the chemical
species chosen by the user at discrete time steps. The user can then use these concentrations to
create model curves in a graphing or spreadsheet program.
The reactions and rate constants that were used in the model were those summarized in
Table 1.1. A sample Acuchem input file is shown below.
fenton
1011
1,Fe3+H2O2=Fe2+HO2,1e-3
2,Fe2+H202=Fe3+OH,76
3,HO2+Fe3=Fe2,2.4e6
4,OH+H202=HO2,4.5e7
5,OH+Fe2=Fe3,4.3e8
6,HO2+Fe2=Fe3+H202,1.3e6
end
Fe3,50e-6
H202, 1OOOe-6
end
.001
25200
Figure 2.2. Sample Acuchem input file.
Reactions 2-3 and 2-4 were added to the model to account for the reactions between the
hydroxyl radicals and both formic acid and formate; they were discussed earlier in Section 2.1.4.
OH + CH 2 0 2
ka"
> CO;- +H 20
CO;- + 02 -> CO2 + O-
The rate constant of Reaction 2-3, kapp, is equal to
(2-3)
(2-4)
28
kapp
=
[CHO2]T
[CH 2 0 2]T
kformate
+ [CH 2 0 2 ]
[CH 2 0 2 IT
(2-5)
kformic acid
where [CHO- ] and [CH 2 0 2] are the concentrations of formate and formic acid, respectively,
[CH20 2]T
=
[CH 20 2] + [CHOi ], kformate = 3.4 x 109 M-' s-1, and kformic
acid =
1.6 x 108 M- 1 S-1
(Ross and Ross, 1977). At pH 3, kapp = 6.5 x 108 M-' s-. kapp is necessary since, at pH 3, both
formate and formic acid are present in significant quantities (pKa = 3.745) and are oxidized
rapidly by OH-. The same approach was used to obtain the composite rate constants of reactions
of HO 2 and 0
with iron.
Reaction 2-4 was included for clarity and does not change the model results. Its rate
constant is 4.2 x 109 M- 1 s4 (Ilan and Rabani, 1976). Although CO'- can reduce other solutes,
Fe(III) for example,
CO;- + Fe(III) -+ CO 2 + Fe(II)
(2-6)
these side reactions are not important because the concentration of oxygen will be much greater
than the other reactants ([O2]sat = 258 IM at 25 'C (Wetzel, 1983)), and the rate constant of
Reaction 2-4 is already near the diffusion-controlled limit.
29
3. Results
Two sets of experiments were done to study the behavior of the Fenton system. In the
first set, the decomposition rate of hydrogen peroxide as a function of the concentration of iron
and H2 0 2 was observed. In the second set, a hydroxyl radical probe,
14C-labeled
formic acid, was
added and its loss, along with hydrogen peroxide, was observed. These data were compared
against results from a model comprised of defined chemical reactions and their published rate
constants (Table 1.1), and the initial reactant concentrations only, with no additional fitting
parameters.
3.1 The Basic Fenton System
The basic Fenton system consists of only iron and hydrogen peroxide. The details of the
experimental setup were described in Section 2.3. In all cases, the solution pH was not adjusted
because it remained at 3±0.20 for the entire experiment. Hydrogen peroxide measurement errors
were ±1%.
3.1.1 Effect of Initial Concentrationof Hydrogen Peroxide
The loss of hydrogen peroxide versus time for [H2 0 2]o
=
100-1000 gM and [Fe(III)]T=
20 pM are shown in Figures 3.1a-c. The differences between the model results and experimental
data ranged from a few to twenty percent of the initial amount of hydrogen peroxide. As [H2 0 2]o
increased, the percent difference decreased. However, those percentages actually reflect
deviations of about 20-50 gM of hydrogen peroxide after they have been multiplied by their
respective initial concentrations of H2 0 2 .
One way to analyze the data collectively is to determine their respective first half-life,
which is the amount of time needed to consume 50% of the initial amount of hydrogen peroxide.
To obtain this value, the data points were fitted to a function of the form y = Aexp(-Bt), where y
is the fraction of remaining hydrogen peroxide, A and B are fitting parameters, and t is time. All
of the R2 values were 0.9 or greater. The function was then evaluated at y = 0.5 to obtain t. The
time for the first half-life from the model results were obtained directly from the model output.
Figure 3.2 shows the first half-life of hydrogen peroxide versus [H2 0 2]o. The initial hydrogen
peroxide concentration influenced, although not greatly, the amount of time to reach the first
30
half-life. This demonstrates that the decomposition of H2 0 2 is approximately, but not exactly, a
first-order reaction. The reason for this behavior will become clear in Section 4.1, which deals
with the kinetics of the chain reaction.
A
B
0
0
N
C1
0
0
Nm
N~
I~
0
0
1
2
3
4
5
6
7
0
Days
Figure 3.la.
1
2
3
4
5
6
7
Days
Measured and predicted hydrogen peroxide decomposition versus time with
[Fe(III)]T= 20 RM and [H2 0 2]o = A) 106 pM, B) 206 jiM.
31
D
C
1.0
* Measured
- Predicted
08
0
0
C'j
0
-
06
. - -
- -
CmJ
Ci
CM
...
....
.....
...........
...-.
.. .....
......
...... ..
....
...
.......
......
-.
. ..
04-
...
..
...
..
....
..
..
..
....
....
..
.....
....
. ..
...
....
...
.....
...... ....
.
...
. . ..
.....
...
...
...
..
...
...
..
...
..
...
...
...
..
02-
1
0
4
3
2
5
7
6
0
1
2
3
4
5
6
7
4
5
6
7
Days
Days
F
E
140~1
-
-.
08-
* Measured
- Predicted
0
0
0
-
Q6-
-
Cl
CiJ
7'J
CI
.....
..*
..
......
Q2e
0O
0
1
2
3
Days
4
5
6
7
0
1
2
3
Days
Measured and predicted hydrogen peroxide decomposition versus time with
Figure 3. lb.
[Fe(III)]T= 20 gM and [H2 0 2]o = C) 315 gM, D) 417 gM, E) 514 jiM, F) 606 RM.
32
H
G
1.1
0
-
0 0.6 0.
-
-
-...
-....... 0'
IM
0
0
1
2
3
4
5
6
0
7
1
2
3
4
5
6
7
4
5
6
7
Days
Days
I
J
0
0
C\J
c\j
0
Ci
Iq
0'
04
0
1
2
3
Days
4
5
6
7
0
1
2
3
Days
Measured and predicted hydrogen peroxide decomposition versus time with
Figure 3.1 c.
[Fe(III)]T = 20 gM and [H2 0 2]o = G) 782 pM, H) 931 gM, 1) 1.00 mM, J) 1.06 mM.
33
3
-Data
Model
24-
0
200
400
600
800
1000
[H20 2]o (RM)
Figure 3.2. The first half-life of hydrogen peroxide as a function of [H2 0 2]o with [Fe(III)]T = 20
RM.
34
3.1.2 Effect of Total Amount of Fe(lII)
The decomposition of H2 0 2 at starting concentrations of 100, 500, and 1000 kM and
[Fe(III)]T= 4.3, 5, 20, 67 and 325 gM, are shown in Figures 3.3-3.7. The data in Figure 3.5 are
the same as those presented in the previous section. As the total Fe(III) increased, so did the
agreement between the data and the model results. Furthermore, deviations diminished when
[H20 2]o was increased; this was particularly evident in Figure 3.5.
The first half-life of hydrogen peroxide from these experiments, plotted in Figures 3.8a-c,
was again used as an evaluation tool. In general, agreement between the first half-life from
experimental data and model results was within a factor of two except for Fe(III) concentrations
less than or equal to 5 gM. In those cases, the first half-life from the experimental data was
greater than the prediction by at least a factor of two but not more than three. The figures show
that the length of the first half-life is related to the total amount of Fe(III). For example, in Figure
3.8b, raising [Fe(III)]T four-fold, from 5 gM to 20 gM, caused a six-fold decrease in the first
half-life, from 6.5 hours to 1.1 hours. This relationship will also be discussed in Section 4.1.
35
1.0
....
..
.0
- --
0.8 -
e
0
Expt 112gM H2O 2
.
o
Expt 1.13 mM H202
Model 112 gM H2 0 2
15
20
-
-020
_--
0 0
0
0.6
Cm
00
0.2
0.0
~.
0
.'.... ..
...
....
5
.
0.
10
25
Days
Measured and predicted hydrogen peroxide decomposition versus time with
Figure 3.3.
[Fe(III)]T = 4.3 M.
36
1.0
..-..
v
0
o2
--
C
0
0.6 -
I
o
-
Expt 12 M H 2 02
Expt 497 gM H2 0 2
Expt 1.03 mM H2 2
Model 102 pM H2 0 2
Model 497 gM H2 0 2
1.03 mM H2 0 2
-Model
\
0.2
0
5
10
15
20
Days
Measured and predicted hydrogen peroxide decomposition versus time with
Figure 3.4.
[Fe(III)]1 = 5 IM.
37
1.0
_
0.8
-
e
Expt 106 gM H 20
v
Expt 514 gM H2
Expt 1 mM H2 02
0
2
2
Model 106 pM H2 02
-.-Model 514 gM H2 O2
Model 1 mM H2 O2
\.
0.6 -
O 0.40.2
0
.0 -
0
..........
..
.....
V ........
1
2
4
3
5
6
7
Days
Measured and predicted hydrogen peroxide decomposition versus time with
Figure 3.5.
[Fe(III)]T= 20 gM.
38
1.0
_
0.8
...
. ..........
-
---
0.6 -
..
v
Expt 506 gM H2 02
E
Expt 999 pM H2 02
. .....
T
--
Model 102 jM 20
H2 O2
o
d
e
l
5
0
6
jiM
H
--- M
Model
506 pM H0
Model 999 gM H2 O2
--
--
0 .4 -
Expt 102 pM H2 O2
--
..
...
........................
......
.....
....
.... ... ............. . .....
... .. ....
o
*
0.2
0
1
2
3
4
5
6
Days
Measured and predicted hydrogen peroxide decomposition versus time with
Figure 3.6.
jM.
=
67
[Fe(III)]T
39
1.0
M
Expt 100 pM H2 0 2
*
v
0.8 -
......A
.
-.
....
........
.......-..
.........-..............
...........
-...............
...--..
.................
....
t --.-.--
0
0.6 I
-
.....
-..
..............
........
-.
I
0.4
-
n
i
-.
....
....-.
..
....
..
...
...
..
i
-
-
Expt 488 gM H2 0 2
Expt 961 gM H2 0 2
Model 100 gM H2 0
2
Model 488 gM H2 0 2
Model 961 gM H2 0 2
-
-.-.-
- -
- .. ....................... I,- - - ,................. ..............
0.2 -
0.0
0.0
0.5
1.0
1.5
I
2.0
Days
Measured and predicted hydrogen peroxide decomposition versus time with
Figure 3.7.
[Fe(III)]T = 325 gM.
40
8
7-
Data
Model
6S5 4-
(I)
LL
2
I
4.3
I
n
5
20
67
.I
325
[Fe(III)]T (M)
Figure 3.8a. The first half-life of hydrogen peroxide as a function of [Fe(III)]1 with [H2 0 2]o =
100 M.
41
7.
6 -
Data
Model
5 4 -
U,)
23-
1 -
01
__
5
I120
NHF]
-
67
325
m
[Fe(Ill)]T (M)
Figure 3.8b. The first half-life of hydrogen peroxide as a function of [Fe(III)]T with [H2 0 2 ]o =
500 gM.
42
7
6 '-3'
0
~'
Data
Model
5 -
4-
CD)
1-
0
T-
4.3
-
5
20
67
325
[Fe(Ill)]T (gM)
Figure 3.8c. The first half-life of hydrogen peroxide as a function of [Fe(III)]1 with [H2 0 2]o = 1
mM.
43
3.2 The Basic Fenton System and
4 CH
20 2
The details of the experimental setup were described in Section 2.3. The pH of the
solutions remained at 2.95±0.05 in all of the experiments. Hydrogen peroxide measurement
errors were ±1%. 14C measurement errors, as reported by the instrument, increased from ±1.5%
at the start to ±15% at the low activities towards the end of each experiment.
Figures 3.9 and 3.10 show the experimental data and predictions from the model for the
loss of hydrogen peroxide and
14 C-labeled
formic acid over time at [Fe(III)T ~ 40 gM. In both
cases, the concentration of 14C-labeled formic acid was low enough (on the order of tens of
nanomolars) that its effect on the kinetics of the system should be negligible. These experiments
were concluded much sooner than those in Section 3.1 because the main intent was to see if the
loss of 14C-labeled formic acid can be modeled correctly. Indeed, the model results for both
hydrogen peroxide and formic acid agreed with the data in the two experiments. However,
substantial deviations existed in the first three to four hours. We believe the 14CH 2 0 2 was not the
problem because a potential sink (or sinks) of hydroxyl radicals in the Milli-Q water was
discovered in later studies. The potential sink (or sinks) appeared to be completely consumed
after approximately three hours or so since the decomposition rates of 14CH 20 2 and H2 0 2 were
more in sync with the modeling results afterwards. This artifact will be discussed in detail in the
next chapter.
44
1.2
90
Measured H2 02
Measured CH2 0 2
Predicted H20 2
A
*
-
-
--
--
1.0
2 2
-
Predicted CH 202
60
0.8
2 -
-
oc
O
0.6
----
- ------
--- -
o
OI
0A~
30
0.4
i
.....
.............-..
........................ ...
.e..
......................
....
....
...........................
...
.........
...
....
..
...
......
....
T. .......
.....
...
....
....
......
..
.
0.2
...
...
...
..
...... .....
0.0
0
0
4
8
12
16
20
24
28
Hours
Figure 3.9. Measured and predicted hydrogen peroxide and 14 CH 20 2 decomposition versus time
with [Fe(III)]T= 44 gM, [H 2 0 2]o = 454 gM, and [CH 2 0 2]o = 85.9 nM.
----
45
90
1.2
1.0
0.8
60
o
0.6
0
0.4
30
0.2
0.0
0
0
4
8
12
16
20
24
Hours
Measured and predicted hydrogen peroxide and 14 CH 2 0 2 decomposition versus
time with [Fe(III)]T = 42 gM, [H 2 0 2]o = 1.14 mM, and [CH 2 0 2]o = 89.4 nM.
Figure 3.10.
46
4. Discussions
4.1 The Basic Fenton System
All of the modeling results were done using only defined chemical reactions and their
published rate constants (Table 1.1), the initial reactant concentrations, and no fitting parameters.
As previously stated (Sections 3.1.1 and 3.1.2), data and modeling results agreed to within a
factor of two. This is remarkably good, considering the range of values of some of the rate
constants found in published studies for the given experimental conditions. This variability is due
to several factors: instrument limitations, imprecision in the rate constant of the reference
reaction used in competition kinetics experiments, ionic strength effects, or possible differences
in Fe(II) and Fe(III) speciation due to anion complexation. Table 4.1 lists the major iron species,
calculated using MINEQL+ (Schecher, 1994), in the solutions used by the investigators to obtain
the rate constants cited in Table 1.1. To facilitate the calculations, some assumptions were made
based on information provided in the references.
Reaction
Solution conditions
Assumption.
Major Fe species at
pH 3
(1-1)
0.014 M NaCl
[Fe(II)]T << [Cl-I'
Fe 2+, FeCli
(1-2)
0.435 M NaNO 3
[Fe(III)]T = 0.8 mM
Fe3*, FeOH2+, FeOH +
(1-4)
[SO -] = [NH ] = 1mM
[Fe(III)]T = 1 mM
FeOH2+, FeOH +, FeSO*
Solution did not contain
Fe2+
(1-5)
(1-6)
N 2 0 saturated, [Fe 2+]
=
1 mM, pH 3
0.01 M NaC 2H 3 0 2, [FeSO
4]L = 0.1 mM,
1.25 x 10-4 M 02
complexing anions
2+
Fe
Table 4.1. Iron speciation in reference solutions. An iron species was considered major if it was
greater than or equal to ten percent of the total amount of iron.
It is important to know the iron speciation because we cannot presume that all of the
various iron species will have the same reactivity toward a particular chemical entity. Moreover,
a less prevalent iron species can dominate the kinetics if it has a very fast reaction rate. We
avoided creating extraneous anion complexes in our experiments by using only ferric
perchlorate, perchloric acid, and sodium hydroxide. Perchlorate does not complex iron, so our
47
solutions consisted of only ferrous and ferric ions and their hydrolysis species. Nevertheless, we
should not expect modeling results generated using rate constants obtained from solutions of
various compositions to match our data perfectly. Both Millero et al. (1991) and Rothschild and
Allen (1958) have reported different reactivities for the iron species of Reactions 1-1 and 1-4,
respectively. Rothschild and Allen believe that FeOH
HO 2 /0
-
is much more active toward reduction by
than FeSO'. The results from Rush and Bielski (1985), however, support their belief
that all of the Fe(III) species present in their study have the same reactivity toward HO 2/ 0
2
(Reaction 1-4). They showed a correlation between the speciation of HO 2/ 0 - and the rate of
reduction of ferric ions by HO 2/ 0 -. We agree with Rush and Bielski's conclusion as their
formula yielded reduction rate constants similar to those measured by Rothschild and Allen. In
addition, Voelker and Sedlak (1995) were able to successfully predict the effect of superoxide on
the fraction of reduced iron in seawater using the rate constants from Rush and Bielski.
The rate constants for reactions of charged ions are affected by the ionic strength of the
solution. Increasing the ionic strength accelerates the rate constant between ions of like charge
and decreases the rate constant between ions of opposite charge. Table 4.1 also lists the solution
conditions of the reference solutions, which were of various ionic strengths. Only Reactions 1-4
and 1-6 should show ionic strength effects, and their respective ionic strengths are 2.5 and 10
mM. As our experimental solutions were at pH 3 and contained only minute quantities of other
ions, their ionic strength were all equal to 1 mM. We then used the activity coefficients of the
reactants and the activated complex to evaluate the influence of ionic strength on reaction rates.
There are different empirical formulas for computing activity coefficients; we chose the Davies
equation. Calculations based on ionic strengths of 10 and 1 mM yielded a difference in reaction
rates that was slightly more than 30%, which could have contributed to the variability.
A new set of model calculations using k3 = 1.2 x 10' M' s-1 (Ross and Ross, 1977) were
produced and compared with the experimental points to demonstrate how variability in a rate
constant can influence the modeling results (Figures 4.1-4.4). This rate constant, while almost
four times smaller than the corresponding one in Table 1.1, was also derived from experiments
performed at pH 3, and there is no a priori reason to reject it in favor of the constant from the
other study. Although the fits improved for [Fe(III)]T less than or equal to 20 ptM (especially at
20 gM) for all hydrogen peroxide levels, they worsened (in most cases by a factor of two) in
48
every other instance. This is because reducing k 3 decreases the decomposition rate of hydrogen
peroxide directly and indirectly -
it decreases the concentration of hydroxyl radicals by
increasing the importance of its other sink reactions. Hence, modeling results that overpredicted
the consumption rate of hydrogen peroxide now achieved better agreement with the data.
Unfortunately, because this phenomenon is universal, modeling results that did not deviate much
from the experimental points before, e.g., [Fe(III)]T= 67 gM and [H2 0 2]o = 506 AM, became less
accurate.
B
A
1.0
1.0
*
-
0
Measured
Predicted
08-
0.8-
00.6
Measured
Predicted
1
2
35
0
1Q6
00
02
0.
02
Days
Figure 4.1la.
Days
Measured and predicted hydrogen peroxide decomposition versus time with kc3 =
1.2 x 10 M sc, [Fe(III)]1= 20
and [H2 O2 ]o = A) 106 M, B) 206
.M
.M.
49
C
D
1.0
* Measured
-- Predicted
-
- -
-
Q8
- .....-....-. ....-..
0
0
I*
C\J
........-...
-............
02
n
0
1
2
4
3
5
6
2
1
0
7
4
3
5
7
6
Days
Days
F
E
1.04
* Measured
- Predicted
0
0
.
0'
-.
-
-.
-.
I~
(IQ4
CI
-
-
.
-
....
.-..
...
......
.- .........
.......
..
.......
........
.......
.............
......
.......
......
.......
......
.....
Q2
0.0
0
1
2
4
3
Days
5
6
7
0
1
2
3
4
5
6
7
Days
Figure 4. lb. Measured and predicted hydrogen peroxide decomposition versus time with k3 =
1.2 x 107 M' s-', [Fe(III)]T = 20 gM and [H2 02] = C) 315 pM, D) 417 gM., E) 514 pM, F) 606
gM.
50
G
H
0
0
O 0.6
c'j
0
0.4
0
1
2
4
3
5
6
0
7
1
2
3
4
5
6
7
Days
Days
I
J
1.0:
*
Measured
Predicted
-.
-
-
-.
0.80
- .-.
-
.
0
QL6
-
0'
--
0
-
0.6-
0
-.
0.2-
-
0n
.
0
1
2
3
4
Days
5
6
7
0
1
2
3
4
5
6
Days
Figure 4.1 c. Measured and predicted hydrogen peroxide decomposition versus time with k3 =
1.2 x 107 M-' s-1, [Fe(III)]I = 20 gM and [H 2 0 2]o = G) 782 lIM, H) 931 gM, 1) 1.00 mM, J) 1.06
mM.
7
51
B
A
1.04
--
0
Expt 497 gMH
* Expt 1.03 mM H2 0 2
- Model 102 mM H 0
2
2
2 O2
................................
.............................
Model 112 pM H2 02
Model 1.13mMH 2 2
0
Mk
(NJ
H2O2
3:
0
04j
Model 497 gM H2 0 2
-+-
06-
M
102 M H2 O2
v
.
o Expt 1.13 mM H202
-..-...
G8 -
* Expt
......................
101l
* Expt112laMH 2 0 2
04-
-0S
- ...
...
..
. -..
I
....................
........... -..
-..
...........
-.
..........
..................
02
Q0I
0
2
2)
15
10
5
0
5
10
15
Days
Days
D
C
1.0
1I
* Expt 102 gM H2 0 2
v Expt 506 M H2 02
- Expt 999
MH2 02
- -. .-- Model 102
MH2O2
08-.
___.
080
~+- Model 506 gM H20
2
06 -
--.
0
................................
............
..
....
.
..
..
.....
.
..
..
...
.......
.......
1
2
3
Days
-
Q2 -
-
.......
......
.....
........
00
0
N4 -
......
.........
-...--...
......-.....-..
-..
... -.....
..
-.....
- .........
Q2
Model 961 pM H2 0 2
--
- --..
...
..-.
...
.. .....
- Model 100 gM H 0
2
2
-.--- Model 488 pM H2 0 2
06 -
~~ Model 999 gM H2 0
2
I Q4 -
Expt100 iMH 2O2
Expt 488 gM H2 0 2
Expt 961 MH2 0 2
1
v
4
5
t
00 4-
6
00
05
1.0
1.5
20
Days
Figure 4.2. Measured and predicted hydrogen peroxide decomposition versus time with k3 = 1.2
x 107 M~ s-1 and [Fe(III)]T = A) 4.3 gM, B) 5 gM, C) 67 gM, D) 325 gM.
52
90
1.2
A
Measured H2O2
A
Measured CH2 0 2
1.0
Predicted H202
-A
~60
Predicted CH2 0 2
--
0.80o
2 2
O0.6
\
e
*
0 0
ej
- 0.2
-0.0
4
8
12
16
20
24
28
Hours
Figure 4.3. Measured and predicted hydrogen peroxide and 14CH 2 0 2 decomposition versus time
with k3 = 1.2 x I0 7 M- s-1, [Fe(ll)]T= 44 RM, [H202]o = 454 pM, and [CH 20 2]o = 85.9 nM.
53
90
1.2
A
A
Measured H2O2
*
Measured CH 20 2
Predicted H 202
- -_--
60
-
1.0
Predicted CH2 0 2
2 -
0.8
C
0
0.6
-
0
o
30
.........
..
................
0.4
...............
.................
................
.................
...
......... ......
0.2
E
.-
-
\
. .
..
.
.
.
.
0.0
0
0
4
8
12
16
20
24
Hours
Figure 4.4. Measured and predicted hydrogen peroxide and 14 CH 2 0 2 decomposition versus time
with k3 = 1.2 x 107 M-1 s-1, [Fe(III)]T = 42 gM, [H2 0 2]o = 1.14 mM, and [CH 20 2]o = 89.4 nM.
54
This example illustrates that uncertainties in rate constants can greatly influence how well
model results match the data. Therefore, we need to justify the rate constants that we chose to
use in the model. The rate constants for Reactions 1-1 and 1-2 were interpolated from data in the
reference and are consistent with the values listed in other publications. As we have just pointed
out, there are two possible rate constants that we could have picked for Reaction 1-3. We decided
to use the one listed in Table 1.1 because the modeling results generated by it corresponded very
well to the data from solutions containing "C-labeled formic acid (Figures 3.9 and 3.10). The
effective rate constants at pH 3 for Reactions 1-4 and 1-6 were calculated from formulas in the
reference. Lastly, we used the reported rate constant for Reaction 1-5 because the experimental
condition in the reference was similar to ours.
One possible explanation for the poorer fit of the model results at low hydrogen peroxide
and low Fe(III) levels (using k 3 = 1.2 x 107 M-I s-1) using is due to differences in experimental
conditions. The investigators used concentrations of H2 0 2 and iron that were typically greater
than those used in the experiments in this thesis. It is known that Fe3+ reacts with H 20
2
to form
Fe(III)-hydroperoxy complexes (Evans et al. 1949), and diperoxo complexes may exist at very
high concentrations of hydrogen peroxide (Jones et al. 1959; Haggett et al. 1960; Lewis et al.
1963). These intermediates do not react at the same rate as uncomplexed Fe(III) (defined as Fe 3+
and its hydrolysis species). Hence, kinetic data for Fe(III) reactions obtained from experiments at
high concentrations of H2 0 2 may not be indicative of the rate constants of the uncomplexed
Fe(III). The experimental setups used by the investigators also overlook competing minor
reactions, e.g., sink reactions, that can be important at low levels of hydrogen peroxide or iron.
It was stated in Section 3.1.1 that the decomposition of hydrogen peroxide is
approximately, but not exactly, a first-order reaction. We will now examine this behavior in
more detail. In the chain reaction mechanism (Figure 1.4), H2 0 2 is consumed by the initiation
reaction plus two reactions within the cycle. If the chain propagates for many cycles before it
terminates, then it is the dominant pathway for hydrogen peroxide decomposition. Since
Reaction 1-1 is the slowest propagation step, and thus, the rate-determining step, we can write
the following rate law:
d[IH
20 2]
d[H202_
= 2k,[Fe(II)]ss [H20 2 ]
dt
(4-1)
55
The factor of two accounts for the two moles of hydrogen peroxide that are consumed in each
turn of the cycle.
A rate law is more useful if it is composed of only terms that are readily measurable, so
we need to substitute for [Fe(II)]ss in Equation 4-1. To determine [Fe(II)]ss, we started with the
reactions that make up the basic Fenton system (Table 1.1) and derived the equations for the time
derivatives of the transients, OH+, HO 2/ 0 - , and Fe(II).
d[OH.]
= k1[Fe(II)][H 2 0 2] - k3 [H2 0 2][OH*] - ks[Fe(II)] [OHe]
dt
(4-2)
d[H0 2]1T = k2[Fe(III)][H 20 2] + k3[H 20 2][OH.] - k4[Fe(III)][H02]T
- k6 [Fe(II)][H0 2]T
dt
(4-3)
d[Fe(II)]
= -
ki[Fe(II)][H 2 0 2] + k2[Fe(III)][H 20 2] + k [Fe(III)][HO2]T - ks[Fe(II)][OH.]
4
- k6[Fe(II)][HO2]T
dt
(4-4)
We then applied the steady state assumption.
k [Fe(II)]s [H202]
(4-5)
k 2 [Fe(III)]IH 2 0 2 ]+ k3 [H2 0 2 ][OH.]""
k 4 [Fe(III)] + k6 [Fe(II)],s
(4-6)
k2 [Fe(III)][H 2O2 ] +k 4 [Fe(III)][H0 2 ]ss
k,[H 20 2 ]+ k5 [OH.],s + k6[HO 2]ss
(4-7)
[OH*]ss =
[O
H *ss =k3[H 20 2]+ k5[Fe(II)]ss
[HO 2]ss =
[Fe(II)]ss =
Using the above three equations, and making some simplifying approximations (see
Appendix), it is possible to express [Fe(II)]ss as:
[Fe(II)]ss =
k2 k3k 4 [Fe(III)] 2 [H20
2
]
kk 4k[Fe(III)]+ kk kJ[H2 0 2 ]
(4-8)
56
This expression can be further simplified if either of the quantities in the denominator is much
greater than the other one. There are two possibilities:
I)
If kik 4ks[Fe(III)] >> k1k 3 k6[H 2 02), then [Fe(II)]ss =
d[H 202 ]
dt
II)
k~k2k
I
k5
3
k2 k3 [Fe(III)][H 2 0 2 ]
k1k5
v
Y
[Fe(III)]'2[H 2 0 2 ]2
If k 1k4 k 5[Fe(III)] << kk 3 k6[H 20 2], then [Fe(II)]ss =
k 2k
24
k k~
ko6
,and
(4.9)
[Fe(III)], and
d[H2]
_ 4kik
4 1 2 k4 [Fe(II)][H 2 0 2 ]
2 02]
dt
k6
(4-10)
Both rate laws can be considered as a function of hydrogen peroxide only since the concentration
of Fe(III) does not fluctuate with time. However, their dependence on hydrogen peroxide and
Fe(I) differ slightly. In case I, the loss of hydrogen peroxide depends on the ratio of k3 to k5 ,
which are the rate constants for the propagation and termination steps involving OH-,
respectively. Case II shows a dependence on the ratio between k4 and k6 , which are, respectively,
the rate constants for the propagation and termination steps involving superoxide and its
protonated form. The different dependencies are reasonable. In case I, the amount of hydrogen
peroxide is low enough, compared to Fe(III), that it will limit how fast the cycle propagates.
Therefore, how quickly the hydroxyl radical sinks react with OH-, which is just Fe(II) in this
scenario, will impact the decomposition rate of hydrogen peroxide. It is the opposite situation in
case II, where the concentration of Fe(III) is low compared to hydrogen peroxide. As H02/0reacts with Fe(III) to propagate the chain, its sinks, which in this scenario is also just Fe(II), will
influence d[H 20 2]/dt.
Table 4.2 lists the six Fe(III) concentrations used in our experiments and how much
hydrogen peroxide would be necessary to fulfill the requirement of case I or case II. The
inequality k 1k4k 5[Fe(III)] >> kik 3k6[H 20 2] is satisfied if the former quantity is at least ten times
57
greater than the latter. By inserting the values of the rate constants from Table 1.1, we see that
case I is true if [H20 2] < 2[Fe(III)]T, and case II is true if [H20 2] > 200[Fe(III)]T.
[Fe(III)]T (pM)
Case I is true if [H 2 0 2] is less than
Case II is true if [H 2 0 2 ] is greater than
4.3
8.6 gM
860 gM
5
10 gM
1 mM
20
40 gM
4.0 mM
43
86 gM
8.6 mM
67
130 gM
13 mM
325
650 gM
65 mM
Table 4.2. The amount of hydrogen peroxide needed for either case I or case II to occur.
In all of our experiments, the concentration of hydrogen peroxide was always less than or
equal to 1 mM, so case II did not occur. Case I, with the exception of [Fe(III)]1= 325 gM, was
also never satisfied. Hence, d[H 2 O2 ]/dt in our experiments cannot be adequately described by
either Equation 4-9 or 4-10 because both terms in the denominator of Equation 4-8 are important.
Instead, its behavior lies somewhere in between. This shows why the first half-life of hydrogen
peroxide was affected to some extent by its initial concentration (Figure 3.2), and also why it was
roughly proportional to the total concentration of Fe(III) (Figures 3.8a-c).
It was observed that adding Reaction 4-11 to the model did not change the kinetics in any
significant manner (comparisons not shown). This was most likely due to the low concentrations
of HO 2 and 0 - during the course of the experiments. The same reasoning justifies neglecting the
recombination of hydroxyl radicals in the model. For completeness, Reaction 4-11 was left in the
model.
H0 2/0 - + H02/0 - -> H202+02
4.2
The Basic Fenton System and
14CH
(4-11)
20 2
Hydrogen peroxide and formic acid loss in the first three to four hours was much slower
than predicted. This unexpected behavior was not detected in earlier experiments since hydrogen
58
peroxide measurements at that point were done on a less frequent basis. It is clear from Figure
4.5 that this phenomenon was not caused by the 14C-labeled formic acid. We suspected an
unknown organic hydroxyl radical sink (or sinks) was in the Milli-Q water and tested this
hypothesis in two ways. We treated Milli-Q water with a TOC (total organic carbon) reduction
unit (Aquafine) for about 30 seconds before using it in our experiment. As shown in Figure 4.6,
H20 2 decomposition was detected after approximately two hours in the treated Milli-Q water, in
contrast to about three hours in the control. This indicated that an organic contaminant was in the
Milli-Q water. In a different series of experiments, small quantities of Fe(NH 4 )2 (SO 4 ) 2 06H 2 0, a
ferrous salt, was added to the hydrogen peroxide solution about one minute before the ferric
perchlorate was introduced. (The half-life of Fe(II) at pH 3 in the Fenton reaction, with [H2 0 2]o =
1 mM and assuming pseudo-first order kinetics, is 9.1 seconds.) The reason we used ferrous salt
is that it reacts with H2 0 2 to produce OH* rapidly and therefore, should quickly consume the
unknown sink. The results in Figure 4.7 demonstrate that the unknown sink was successfully
removed, even with just a few micromolars of Fe(II), because the concentration of hydrogen
peroxide agreed closely with the expected value throughout the experiments.
We can make a rough estimate of the concentration of the unknown sink in the Milli-Q
water by using the data from the ferrous salt experiments. In the Fenton reaction, one mole of
OH. is produced for every mole of Fe(II) that is oxidized. If the unknown sink consumed all of
the hydroxyl radicals, then its concentration is about one micromolar. In reality, a large fraction
of the OH- must have reacted with hydrogen peroxide. If we assume that the following
relationship is a good approximation,
100 ksink [sink] = k 3 [H 2 0 2]
(4-12)
and ksink is on the order of 1010 M- s-1, k3 = 4.5 x 107 M- s-1, [H 20 2] = 1 mm, then the unknown
hydroxyl radical sink concentration is on the order of tens of nanomolars. This level of
contamination is not unlikely.
59
1.1
-
-
-
- -
S0.8-
0.7 --0.6
0.5
2
o
6
4
10
8
H ours
Measured and predicted hydrogen peroxide decomposition versus time with
Figure 4.5.
[Fe(III)]T = 40 p.M and [H2 O2]o, = 456 pM at pH 3. Notice that no hydrogen peroxide
decomposition was detected in the first four hours.
00
1.1
Measured
0
Predicted
*-
*
1.0
0.8--9
-
0.8
0.6 - -
e
--
0.5
0
1
2
3
4
5
6
7
Hours
Measured and predicted hydrogen peroxide decomposition versus time with
Figure 4.6.
[Fe(III)]T = 42 pM and [H 2 02]o = 1.13 mM at pH 3. The Milli-Q water was treated for about 30
seconds with a TOC reduction unit.
60
B
A
1.1
1.0
0.Q9
0
-- 0.8
C\J
M
0.7
0.6
0.5
1
0
2
3
4
5
6
0
7
1
2
3
4
5
6
7
5
6
7
Hours
Hours
D
C
1.1
0
0
C\l
0
C\j
04J
I~
I~
0'
IM
0
1
2
3
4
Hours
5
6
7
0
1
2
3
4
Hours
Figure 4.7. Measured and predicted hydrogen peroxide decomposition versus time with [H20 2]o
= 1 mM and A) [Fe(II)]o = 1 gM, [Fe]T = 44 gM, B) [Fe(II)]o = 3 gM, [Fe]1T = 37 gM, C)
[Fe(II)]o = 6 pM, [Fe]T = 43 gM, D) [Fe(II)]o = 9 gM, [Fe]T = 46 gM. All solutions were at pH
3.
61
4.3 The Steady State Concentration of Hydroxyl Radicals
It is important to know the concentration of hydroxyl radicals in solution because it is the
species of interest for remediation purposes. "C-labeled formic acid was used as a molecular
probe to determine [OHe],s in each solution. Those values were then compared with ones from
the model and from kinetics calculations.
4.3.1 [OH]ss,measured
Haag and Hoign6 (1985)
presented a method for estimating the steady state
concentrations of hydroxyl radicals in natural waters. Although the hydroxyl radicals in their
study were produced by photolysis, their theoretical treatment is equally appropriate for the
experiments in this thesis. Their scheme is given by Reactions 4-13 and 4-14:
r = km [M] [OH-]
d[A]
dt
dt
A
p
rformation
bP Mexi
(4-13)
h'Soxid
(4-14)
OHe
E-i
r =I ki [Si][OH*]
rconsumption
km and ki are the second-order rate constants for the reactions of OH* with M and Si,
respectively. A is a precursor molecule that produces hydroxyl radicals, M represents a
microprobe substance or a specified micropollutant, while Si denotes any major sink of hydroxyl
radicals, e.g., H2 0 2 , DOC, etc. (See Section 1.3). If M is to serve as a microprobe molecule, then
it cannot be the dominant OH. sink. This condition is expressed mathematically as:
kM[M] << Xki[S,]
The loss of M at any time is given by:
(4-15)
62
d[IM]
= km[M][OH*]
dt
(4-16)
If both rformation and rconsumption remain constant during the reaction, then so will [OH-], i.e.,
[OH.] = [OH-]s,. In this case, the loss of M is described by first-order kinetics:
- In [M] = km[OH]sst = kexpt
[M]0
(4-17)
Here, kexp is a pseudo first-order rate constant that is extrapolated from the data. It is then
used to obtain the steady state concentration of OH..
[OH-]ss =
kexp
kM
(4-18)
In accordance with Equation 4-17, the experimental data plotted in Figure 4.8 are
approximately linear with respect to time. Data gathered in the first three hours of the experiment
were not used due to the previously mentioned artifact. km for CHO -/CH 20 2 at pH 3 is 6.5 x 108
M-1
s-I, as previously stated. The steady state concentrations of hydroxyl radicals measured in
these experiments, [OH-]ss,
measured,
were calculated using Equation 4-18 and are presented in
Figure 4.9.
4.3.2 [OH]ss,model prediction
[OHe]ss,
model prediction
was calculated by averaging the concentration of hydroxyl radicals
computed by Acuchem over the time interval coinciding with the data points used to determine
[OH-]ss, measured (Figure 4.9).
63
1
o
Expt 454 gM H2 O2
v
y =-0.71x + 1.20,R = 0.99
Expt 1.14 mM H2 O2
2
y =-0.96x + 1.86,R = 0.99
-2
C\i
V
00
-4.
3
4
5
6
7
8
Hours
Figure 4.8. Semi-log plot of 14 CH 2 0 2 from data presented in Figures 3.9 and 3.10. The solid
lines are the regression lines of the data set.
4.3.3 [OH]ss,equation prediction
To determine [OHe]ss,
equation prediction,
we began with Equation 4-5, the expression for
[OH.]ss in the basic Fenton system. We then replaced [Fe(II)]ss with Equation 4-8 and assumed
that k3[H20 2] >> ks[Fe(II)]ss. This is justified even though k3 is an order of magnitude smaller
than k5 because [H 2 0 2] is at least 100 times greater than [Fe(II)]ss. Hence,
k
[OH*]ss = 1 [Fe(II)]ss
k3
(4-19)
64
As an aside, Equation 4-6 can be simplified to Equation 4-20 because k4 and k 6 are of the same
order of magnitude and [Fe(III)] >> [Fe(II)]ss.
[HO 2]ss =
k2[Fe(III)][f
2O2 ]+
k,[Fe(II)],s [H20 2 ]
k4 [Fe(HI)]
(4-20)
Equation 4-19 shows that the steady state concentration of OH- can be estimated using
just the known rate constants and the concentrations of Fe(III) and H2 0 2 as a function of time.
Since only a small amount of Fe(III) is converted to Fe(II) during the reaction, we can assume
that [Fe(I)] ~ [Fe(III)]T. The concentration of hydrogen peroxide may be computed from actual
measurements or an average value may be used. The [OHe]ss,
equation prediction
shown in Figure 4.9
were computed using an average hydrogen peroxide concentration over the time interval used to
determine [OH]ss, measured (Figure 4.8).
4.0e-13 -
[OHe]s,
measured
[O He]ss, model prediction
[O He]ss, equation prediction
3.0e-13 -
Co
Co
0
I
0
2.0e-13 -
1.0e-13
0.0
-
-
454
1140
[H 2 0 2]o (9M)
Figure 4.9. Comparison of [OH-]ss from three different methods.
65
Figure 4.9 shows that all three methods yielded estimates of steady state concentration of
hydroxyl radicals that are within a factor of two. Moreover, the values from the equation
prediction are nearly the same as those from the model, demonstrating that the assumptions used
to formulate Equations 4-8 and 4-19 were valid.
4.4 Modeling Probe/Contaminant Loss
We want to formulate a simplified kinetic model that can predict the loss of a probe or a
pollutant using the decomposition rate of hydrogen peroxide, a readily determinable parameter.
This concept is worth pursuing because some systems may not be easily modeled due to
insufficient knowledge about some of their parts, such as rate constants or reactions that affect
the kinetics of the chain reaction.
We can estimate the degradation rate of the probe or contaminant using the simplified
kinetic model if we understand the main sink reactions that dictate the fate of OHe. Assuming a
well-mixed reactor, the fraction of OHe that reacts with chemical species, Mi, can be described
with Equation 1-10. A generalized form of it is,
kM [Mi ](aq)
ki [Si]I
where Si denotes any constituent i that will react with OH., such as Fe(II) or hydrogen peroxide.
H2 0 2 is most likely to be the dominant S in Fenton-like systems where it is present at
concentrations of hundreds of micromolar or greater. In this case, F for a particular M can be
approximated as:
F
kMIM](aq)
[H 2 0 2]
kH202
Substituting Equation 4-22 for F in Equation 1-9 gives:
(4-22)
66
=[ Y
d[H 2 0 2 ]
kmI](4-23)
kH2O2[H
2
0
2
]
(The subscript "(aq)" was dropped for simplicity.) Equation 4-23 is a differential equation that
can be solved in the following manner:
fd[ TM = Y
[M]
fd[H202]
kH202
(4-24)
[H202]
Evaluating both integrals from an initial concentration to that at some time t results in:
ln[M]t - ln[M]. = Y
kM
(ln[H 20 2]t - ln[H 2 0 2]o)
[M][ =
(4-25)
['M
H 202]o
where y = Y
kM
"
. Equation 4-25 shows the possibility of predicting the loss of M over time
kH20
using the decomposition rate of hydrogen peroxide.
The destruction of "C-labeled formic acid over time was modeled using Equation 4-25
with Y = 0.5. This value was chosen because in the chain reaction mechanism (Figure 1.4),
approximately two molecules of hydrogen peroxide are consumed to produce one OHe. (This
assumes that H 2 0 2 is the major sink of hydroxyl radicals and that its loss is primarily due to the
chain reaction.) The data used for this comparison were the same as those shown in Figures 3.9
and 3.10. It was mentioned before that an artifact affected data gathered in the first three hours.
Hence, the values of [H 2 0 2] 0 and [CH 2 0 2]o used were those three hours into the experiment
(obtained from interpolating between the two data points closest to three hours), not their starting
concentrations. [H2O2]t was obtained from regression fits to the data gathered between the third
and eighth hours into the experiment, assuming the loss could be modeled as a pseudo first-order
67
reaction. The [CH 2O 2]t data and the calculated curves are plotted in Figure 4.10, and good
agreement is seen between the predicted decay curves and the data points.
50x1 0-9
40x1 0-9
I-
30x1 0-9
O~
0
20x1 0-9
1Ox1 0-9
0
3
4
5
6
7
8
Hours
Comparison between measured [CH202]1T and d[CH 2 0 2]/dt predicted from
Figure 4.10.
d[H 20 2]/dt for [Fe(IUI)]T~ 40 gM and two concentrations of H2 0 2 . The lines are the predictions.
68
5. Conclusions
Experiments were done to understand the kinetics of the Fe(III) initiated decomposition
of hydrogen peroxide at pH 3 using various concentrations of ferric perchlorate, hydrogen
peroxide, and in some cases, 14C-labeled formic acid. Using a model consisting of only known
chemical reactions, their corresponding rate constants, and the initial amount of reactants, we
were able to predict to within a factor of two or better the decomposition rate of hydrogen
peroxide and formic acid, and the steady state concentration of hydroxyl radicals. The loss of
hydrogen peroxide over time was affected by both its starting concentration and the total amount
of iron. This behavior agreed with the rate law we derived from a theoretical treatment of the
Fenton system using steady state approximations. We also derived a simple expression relating
the decomposition rates of a chemical species and hydrogen peroxide. Its validity was tested and
shown with comparisons to data from the experiments that included
14 C-labeled
formic acid.
This relationship is useful because it is straightforward, its assumptions are satisfied in many
Fenton and Fenton-like systems, and the necessary parameters are easily obtained via
experimental methods. It allows us to estimate, even in complex systems that we do not
understand completely, how much time will be needed to oxidize the chemical species. It and the
model are two valuable tools for investigators because they will facilitate research exploring the
use of Fenton chemistry as an advanced oxidation technology to treat contaminated groundwater.
As mentioned earlier in the introduction, only in the last few years have investigators
conducted experiments to explore the ability of iron oxides to promote Fenton chemistry, and
more work is needed to elucidate the heterogeneous reactions and mechanisms that are involved.
Proper interpretation of data in which surfaces are also present depends on an understanding of
what happens in the homogeneous phase. Hence, the results in this thesis will also aid future
studies on Fenton-like reactions initiated by iron oxides.
69
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75
APPENDIX
DERIVATION OF [Fe(II)]ss
An expression for [Fe(II)]ss was presented in Chapter 4 and was derived in the following way. After formulating Equations 4-5
to 4-7, substitute Equation 4-5 into Equations 4-6 and 4-7.
k 2 [Fe(III)][H 20 2]+ k3 [H 2 0 2 ]
[H1O2]ss
[H021s
=
k,11 2 0 2 ]±
-k3[H202]+
k
k4[Fe(III)]+ k6[Fe(II)],,
[
k5[Fe(II)]ss
k 2k5 [Fe(II)]s, [Fe(III)] [H202] + k 2k 3 [Fe(III)][H202 ]2 + klk 3 [Fe(II)]ss [H 2 0 2 ]2
k5 k6 [Fe(II)]2 + k 3k 6 [Fe(II)]s [H202]+ k4k5 [Fe(II)]ss [Fe(II)]+ k3k4 [Fe(III)] 1[H202]
[Fe(II)],,
=
k2 [Fe(III)] [H202]+ k4 [Fe(III)] [H02]ss
k, [H202]+k5k, k[Fe(II)],ss[H2O2]
+k
)+
S k3 [H 2 0 2 ]+ k 5 [Fe(II)]
_
(A-1)
[HO2]ss
k2 k3 [Fe(III)][H202 ]2 + k2 k5 [Fe(II)]ss [Fe(III)] [H202] + k 3k4 [Fe(III)][1102 Iss[H202]+ k4 k5 [Fe(II)]s, [Fe(III)] [H02]ss
kIk 3 [H202 ]2 + 2kjk 5 [Fe(II)]s [H22]+ k3 k6 [HO2]ss [H202]+ k5 k6 [Fe(II)]ss [H02]ss
(A-2)
Multiply both sides of Equation A-2 by the denominator and collect all of the [H02]ss terms on one side.
2kik 5[Fe(II)]
-
2
[H20 2] + kik 3[Fe(II)]s,[H 202]2 - k2k,[Fe(II)]ss[Fe(III)][H 20 2) - k2k3[Fe(III)][H 20 2]2 = [HO 2]ss(k 4k 5[Fe(II)]ss[Fe(III)] + k3k4[Fe(III)][H 20 2]
k5k6[Fe(II)] S2- k3k6[Fe(II)]ss[H 2O2])
(A-3)
Substitute for [H02]ss in Equation A-3 with Equation A-1. Bring the denominator of Equation A-1 to the left-hand side of
Equation A-3, divide by 2[H202], and then collect the terms according to the powers of [Fe(II)]ss.
(ksk[Fe(II)] ' + kak 6[Fe(II)]ss[H 2O2] + k4k5[Fe(II)]ss[Fe(III)] + k3k4[Fe(II)][H 202])(2kiks[Fe(II)] 2 + kik 3[Fe(II)]ss[H 2O 2] - k2ks[Fe(II)].[Fe(III)]
- k2k3[Fe(III)][H 2 02]) = (k 2k5[Fe(II)]ss[Fe(III)] + k2k3[Fe(III)][H 20 2] + kik3[Fe(II)]ss[H 20 2 ])(k 4ks[Fe(II)]ss[Fe(III)] + k3k4[Fe(III)][H 20 2] - k5k6[Fe(II)] 2s
- k3 k6[Fe(II)]ss[H 2 O2])
(kik 2 k6 )
[Fe(II)]'
+ [Fe(II)] 3
(2kik 3k5k6[H 20 2] + kik 4 k 2 [Fe(III)]) + [Fe(II)]
2
- [Fe(II)]ss(2k 2k3k4ks[Fe(III)]2[H 20 2]) - k2k k4[Fe(III)]2[H 2 0 2]
2
(kik 3k4 ks[Fe(III)][H 20 2] + kik 2
2
k6 [H 20 2 ] - k 2k4k
[Fe(II)] 2 )
(A-4)
=0
Equation A-4 can be made more tractable by applying some simplifications. Given that [Fe(II)]ss << [Fe(III)], we can assume
that [Fe(lI)]ss < 0.01 [Fe(III)] and evaluate each of the terms in Equation A-4 using the values of the rate constants in Table 1.1.
[Fe(I)]
4
(A-5)
(kik k6) < 2 x 10[Fe(III)] 4
[Fe(II)] s (2kik 3k 5k6[H 20 2] + kik 4k5[Fe(III)])
[Fe(II)]
S (k 1k 3k4 ks[Fe(III)][H 20 2] + k 1k 3
4 x 101 8[Fe(III)] 3 [H 20 2] + 3 x 10'9[Fe(I)] 4
2
k6 [H 2 0 2] - k2k 4k 5 [Fe(III)]
[Fe(II)]ss(2k 2k3k 4ks[Fe(III)]2 [H 2 0 2 ])
2
)
4
2
9
4 x 1020 [Fe(III)][H 20 2] + 2 x 10' [Fe(III)]2[H 20 2] -4 x 1016[Fe(III)]
1 x 1018[Fe(II)]3[H 2 0 2]
k2k 2 k4[Fe(III)]2 [H 2 0 2 ]2 < 5 x 101"[Fe(IllI)]2 [H 2 0 2 ]2
(A-6)
(A-7)
(A-8)
(A-9)
[H 2 0 2] was greater than [Fe(III)] throughout most of our experiments, often by an order of magnitude or more. This implied
the following inequality:
4
[Fe(III)] 2[H 2 0 2]2 > [Fe(III)] [H 20 2] > [Fe(III)]
(A-10)
We now conclude that:
00
1) The quartic term is insignificant compared to the cubic terms.
2) [Fe(II)] 2 k2k4k 2 [Fe(III)] 2 is much smaller than the other quadratic terms.
3) The cubic terms are insignificant compared to [Fe(II)]
2
(k1k3k4 ks[Fe(III)][H 2 0 2] + kik k 6 [H 2 0 2 ] 2) since 4 x 1018 [Fe(III)]3[H 2 0 2 ] is
much smaller than 4 x 1020 [Fe(III)]3 [H20 2] and 3 x 1019[Fe(III)]4 is also much less than 2 x 10 9[Fe(III)]2 [H2 0 2 ]2
4) [Fe(II)]ss(2k 2k3k4ks[Fe(III)] 2[H 2 0 2]) is insignificant compared to [Fe(II)] ' (k1k 3k4k 5[Fe(III)][H20 2] + kik k6 [H2 0 2 ]2).
Thus,
[Fe(II)] s (kik 3k4 k5 [Fe(III)][H 20 2] + kik~k[H20 2]2 ) - k 2k k4[Fe(III)] 2 [H2 O2 ]2 = 0
The solution is Equation 4-8.
(A-11)