Free Radical Reactions Involving Cl(.), Cl2(-.), and SO4(-.) in the 248 nm Photolysis of Aqueous Solutions Containing S2O8(2-) and Cl(-)

Article abstract of DOI:10.1021/jp036211i

Rate constants and other properties are reported for photochemical reactions initiated by laser photolysis (248 nm) of S2O8(2-)(aq) in acidic solutions containing Cl(-)(aq) at 297 +/- 2 K. The absorption spectra of SO4(-.)(aq) and Cl2(-.)(aq) are measured and compared to literature values. Equilibrium constants and rate constants involving Cl(.) (aq), Cl2(-.)(aq), H2O, SO4(-.)(aq), and S2O8(2-)(aq) are determined by analyzing the formation and decay of Cl2(-.)(aq) and SO4(-.)(aq) in a self-consistent chemical mechanism. For the first time, the anticipated pH dependence is observed unambiguously in the pseudo-first-order decay rate constant of Cl2(-.). The rate constants for the reactions Cl(.)(aq) + Cl2(-.)(aq) -> Cl2(aq) + Cl(-)(aq) and Cl2(-.)(aq) + Cl2(-.)(aq) -> Cl2(aq) + 2Cl(-)(aq) are determined; rate constants for the latter are measured as a function of temperature and ionic strength. In addition, the ionic strength dependence of the reaction SO4(-.)(aq) + Cl(-)(aq) -> SO4(2-)(aq) + Cl(.)(aq) is reported. Rate constants for the reactions of Cl(.)(aq) and Cl2(-.)(aq) with S2O8(2-)(aq) are reported for the first time. The present and previous (when available) experimental results are generally in good agreement within the context of the comprehensive chemical mechanism for this system.

Full text of DOI:10.1021/jp036211i

J. Phys. Chem. A 2004, 108, 295-308
295
•
-•
-•
Free Radical Reactions Involving Cl , Cl2 , and SO4 in the 248 nm Photolysis of Aqueous
Solutions Containing S2O82 and Cl-
-
Xiao-Ying Yu,†,‡ Zhen-Chuan Bao,§,⊥ and John R. Barker*,†,§
Department of Chemistry, The UniVersity of Michigan, Ann Arbor, Michigan 48109-1055, and Department of
Atmospheric, Oceanic, and Space Sciences, The UniVersity of Michigan, Ann Arbor, Michigan 48109-2143
ReceiVed: July 29, 2003; In Final Form: October 30, 2003
Rate constants and other properties are reported for photochemical reactions initiated by laser photolysis
2
-
-
-•
(
248 nm) of S
O
2 8
(aq) in acidic solutions containing Cl (aq) at 297 ( 2 K. The absorption spectra of SO
4
(aq)
-•
and Cl
Cl (aq), Cl
2
(aq) are measured and compared to literature values. Equilibrium constants and rate constants involving
•
-•
-•
2-
2
(aq), H
2
O, SO
4
(aq), and S
2
O
8
(aq) are determined by analyzing the formation and decay of
(aq) in a self-consistent chemical mechanism. For the first time, the anticipated pH
-
•(aq) and SO
-•
Cl
dependence is observed unambiguously in the pseudo-first-order decay rate constant of Cl
2
4
-•
2
. The rate constants
•
-•
-
-•
-•
-
for the reactions Cl (aq) + Cl
are determined; rate constants for the latter are measured as a function of temperature and ionic strength. In
addition, the ionic strength dependence of the reaction SO
Rate constants for the reactions of Cl (aq) and Cl
2
(aq) f Cl
2
(aq) + Cl (aq) and Cl
2
(aq) + Cl
2 2
(aq) f Cl (aq) + 2Cl (aq)
-•
-
2-
•
4
(aq) + Cl (aq) f SO
4
(aq) + Cl (aq) is reported.
(aq) are reported for the first time. The
•
-•(aq) with S
2-
2
2
O
8
present and previous (when available) experimental results are generally in good agreement within the context
of the comprehensive chemical mechanism for this system.
1
. Introduction
summarized in Table 1. This mechanism is similar to the ones
found for the bromide and iodide systems.
1
2
13
Cloud-, fog-, and rainwater are known to scavenge soluble
species from the gas phase in the atmosphere.1-5 The dissolved
species can become highly concentrated when water from the
droplet evaporates. Subsequent chemical reactions in the droplet
are sometimes orders of magnitude faster than those in the gas
Sulfate radicals (SO4-•) are strong oxidants that react with
many species in aqueous systems. They are important precursor
radicals in the laboratory and important intermediate species in
1
the autoxidation of S(IV) to S(VI). Sulfate radicals also oxidize
-
•
-•
-•
and Cl2
6
chloride ions (Cl ) to chlorine atoms (Cl ). Both SO
4
phase and can have an important impact on atmospheric
chemical processes.1
,2,5-8
are of interest in the study of nitrate free radical chemistry,
•
because they are produced in cloudwater by dissolved NO3
Sea salt is a major source of dissolved halide ions in
atmospheric water droplets. In aqueous solution, chloride ions
react rapidly with dissolved free radicals such as OH , NO3 ,
Cl , and SO4 . (To simplify notation, the “aq” designation on
chemical species is omitted in the remainder of this paper.) The
present work (designated as Paper III) is one of a series of papers
3
radicals in reactions with other dissolved species. Free radical
•
•
reactions are important in the inorganic aerosol or raindrop
chemistry of nitrogen, sulfur, and the halogens.
•
-•
The reaction between sulfate radicals and chloride ions rapidly
14-24
produces solvated chlorine atoms.
Once chlorine atoms are
•
-•
describing the chemical mechanism and kinetics of Cl and Cl2
dichloride or dichlorine radical anion) in the aqueous phase.
formed, they quickly react with chloride ions and form an
-•
(
equilibrium with Cl2 , which absorbs strongly in the ultraviolet.
9
-•
Paper I focuses on the chemical mechanism of hydrogen
peroxide photolysis of acidic solutions containing chloride ions.
Paper II extends the knowledge of the chemical mechanism
and reports the primary quantum yield for production of
hydroxyl radicals in the photolysis of hydrogen peroxide, as
measured using chloride ions as a scavenger. Paper III (this
The bimolecular reaction between two Cl2 radicals produces
Cl2, which can be released as a gas in the atmosphere. The
photochemical reaction mechanism is shown schematically in
Figure 1. The goal of our research is to determine the
comprehensive reaction mechanism and rate constants in a self-
consistent system.
1
0
-
•
-•
work) deals with the chemical mechanism of Cl2 and SO4
In laboratory studies, persulfate ions (S2O82-) are often used
formation and decay. Paper IV11 reports evaluations of some
as a photochemical precursor for producing sulfate free radicals
-
•
of the important rate constants involved in the Cl2 formation
and decay. The chemical mechanism and rate constants are
-•
(
SO4 ) in solutions. The thermal, photochemical, and radiation-
induced decomposition of potassium persulfate has been studied
2
5-32
33
extensively.
The structure of the persulfate ion suggests
*
To whom correspondence should be addressed. E-mail: jrbarker@
-•
that it consists of two SO4 tetrahedra held together by a single
homopolar bond between oxygen atoms at one corner of each
of the two tetrahedra. Photolysis of S2O8 produces two SO4
radicals via a simple O-O bond scission.
efficiency of the photodissociation of persulfate ion has been
umich.edu.
†
‡
Department of Chemistry.
Present Address: Cloud Simulation and Aerosol Laboratory, Depart-
2-
-•
ment of Atmospheric Science, Colorado State University, Fort Collins,
Colorado 80523-1371.
29,31
The quantum
§
Department of Atmospheric, Oceanic, and Space Sciences.
Present Address: 22692 Liberty Oak Lane, Cupertino, California 95014.
⊥
27
26
found to be unity for acidic, neutral, and alkaline solutions.
1
0.1021/jp036211i CCC: $27.50 © 2004 American Chemical Society
Published on Web 12/16/2003

296 J. Phys. Chem. A, Vol. 108, No. 2, 2004
Yu et al.
2-
and Cl- in the aqueous phase. Reaction numbers (from Table 1) are given
Figure 1. A schematic diagram of the reaction mechanism of S O
2 8
in parentheses.
2-
and Cl- in the Aqueous Phase
TABLE 1: The Chemical Mechanism of S
2
O
8
reaction
k
f
k
r
2
-
-•
-•
Φ
SO4 ) 232,37,50,92
-•
1
2
3
S
SO
2
O
8
+ hν f SO
4
+ SO
+ Cl
4
•
-
•
-
2-
8
-1 -1 a
-2 ) (2.1 ( 0.1) × 10 M s-1 24
8
-1
4
+ Cl T SO
4
k
2
) (3.2 ( 0.2) × 10 M
s
k
k
•
-
-•
9
-1 -1 9
4
-1 9
Cl + Cl T Cl
2
k
3
) (7.8 ( 0.8) × 10 M
s
-3 ) (5.7 ( 0.4) × 10 s
5
-1 9
K
3
) (1.4 ( 0.2) × 10 M
•
O T ClOH-• + H+
5
-1 a
10
4
5
Cl + H
2
k
1
4
[H
/K
2
O] ) (1.6 ( 0.2) × 10 s
) (7.2 ( 1.6) × 10
k
k
-4 ) (2.6 ( 0.6) × 10 M-1 s-1 9
6
a
4
ClOH-• T HO + Cl
•
-
k
) (6.1 ( 0.8) × 10 s
9
-1 16
-5 ) (4.3 ( 0.4) × 10 M s-1 16
9
-1
5
-
1 16
1
/K
5
) 0.70 ( 0.13 M
-
•
-•
+
-
-1 a,9
6
7
8
9
1
1
1
1
1
Cl
2
+ H
2
O f ClOH + H + Cl
f products
k
k
k
k
k
k
k
k
6
7
8
9
[H O] < 100 s
2
•
2-
) (8.8 ( 0.5) × 10 M s-1 a
6
-1
Cl + S
2
O
8
-
-
-
•
•
•
2-
4
-1 -1 a
Cl
Cl
Cl
SO
SO
SO
2
2
2
+ S
+ Cl
+ Cl f Cl
+ SO
2
O
8
f products
+ 2Cl
+ Cl
e 1 × 10 M
s
-•
-
8
-1 -1 a,9
2
f Cl
2
) (9 ( 1) × 10 M
s
-
9
-1 -1 a
0
1
2
3
4
2
10 ) (2.1 ( 0.05) × 10 M
s
-
-
-
•
-•
2-
2-
8
-1 -1 a
4
4
4
4
f S
2
O
8
11 ) (6.1 ( 0.15) × 10 M
s
•
•
2-
-•
5
-1 -1 a
+ S
+ H
2
O
8
T SO
4
+ S
+ HO
2
•
O
8
12 ) (5.5 ( 0.3) × 10 M
s
-
-1 a
-13 ) 6.9 × 10 M s-1 46
5
-1
2
O f HSO
4
2
13[H O] ) 460 ( 90 s
k
-
2-
+
-2
-1 117
HSO
4
T SO
4
+ H
K
14 ) 1.2 × 10
M
a
This work, errors are within (1σ.
Pulse radiolysis and flash photolysis techniques have been
of the predicted pH dependence. Most previous studies of the
-
• 9,18-20,23,73
used to study systems containing chloride ions and sulfate
second-order decay of Cl2
were carried out under
radicals.1
4-24
In our laboratory, sulfate radicals are generated
conditions of high Cl molar concentration, where reaction 9
-
-
-3
by laser flash photolysis of persulfate ions in aqueous solutions
via reaction 1 (see Table 1; in this paper, rate constants, ki, are
written in lower case, while equilibrium constants, Ki, are written
in upper case).
There has been considerable previous research investigating
the kinetics, as well as determining the absorption spectra, of
is dominant. At low Cl molar concentration (<1 × 10 M),
we have found that reaction 10 also contributes to the second-
-
•
•
-•
order loss of Cl2 . This is not surprising, since Cl and Cl2
-
• 74
form an equilibrium with Cl3
,
which can subsequently
-
54,75-77
dissociate into Cl2 and Cl .
-•
-•
Since Cl2 and SO4 were monitored simultaneously in this
-
•
-• 15,16,18-20,24,29,34-72
-•
Cl2 and SO4
.
Discrepancies in the peak
work, the rise and decay of SO4 was also investigated. Our
-
•
-•
molar extinction coefficients of Cl2 and SO4 still exist,
results for the pseudo-first-order rate constant and second-order
-
•
-•
however. Because of overlap between the spectra of Cl2 and
rate constant of SO4 decay are found to be consistent with
-
•
SO4 and because the spectra are broad and featureless, spectral
interference is always present. Thus, careful determinations of
the absorption spectra for the two species are reported here.
literature values.
In the following sections, we first present the chemical
mechanism and a discussion of the relevant literature. Afterward,
we briefly describe our experimental techniques and the
•
-•
9
•
Similar to the reactions of Cl and Cl2 with H2O2, Cl and
Cl2-• may react with S2O8 according to reactions 7 and 8
2-
determination of the absorption spectra of Cl2 and SO4 . We
then go on to explain how we tested the accuracy of the
mechanism and carried out measurements of rate constants.
Finally, we present the results and discuss them in relation to
the literature.
-•
-•
24
(
also see Buxton et al. ). The participation of reactions 3-5 in
-
•
the decay of Cl2 leads to the prediction of a pH dependence,
which has not been observed unambiguously in previous
experimental work. We report the first experimental observation

Free Radical Reactions Involving Cl , Cl2-•, SO4-•
•
J. Phys. Chem. A, Vol. 108, No. 2, 2004 297
2
. Chemical Mechanism (Table 1)
Milli-Q system (the water resistivity was g18 MΩ cm). All
reagents were of ACS grade. Sodium chloride (99.999%) and
anhydrous sodium perchlorate (98-102%) were purchased from
Alfa ÆSR and used without further purification. Perchloric acid
2
.1. Kinetics of Cl2-•. The photodissociation of persulfate
-
•
ions generates sulfate radicals (SO4 ) via reaction 1. Under
-
•
neutral and alkaline conditions, Cl2 is produced efficiently
(HClO4, 70%) was purchased from Aldrich. Potassium persulfate
by reaction 2, followed by reaction 3.1
4-24
Rate constant
(K2S2O8 g 99.0%) was obtained from Fisher Scientific. The
2
1,24
k-2 and equilibrium constant K2 have been reported.
The
concentration of K2S2O8 utilized in the experiments was usually
-
loss of Cl2 follows a mixed first- and second-order
-
3
∼
10 M. The pH (0-4) of all solutions was controlled by
mechanism.9
,19,60,78-81
Reactions 4 and 6 are for Cl and Cl2
•
-•
adding perchloric acid (HClO4) and measured with a Digital
Ionalyzer (Orion Research 501) calibrated with appropriate pH
buffer solutions (Fisher).
•
-•
with H2O; analogous reactions occur for Cl and Cl2 with
H2O2. We propose the similar reactions 7 and 8 for Cl and
Cl2 with S2O8
9
•
-
•
2-
.
All experiments were carried out at room temperature (297
Reaction -4 introduces a pH dependence into the mechanism.
(
2 K), except in the study of the k9 temperature dependence,
where the solution temperature was controlled in the range of
.8-51.6 °C by a constant-temperature water bath. The solutions
-•
Our present experiments on the pseudo-first-order decay of Cl2
+
show a dependence on H molar concentration, in contrast to
6
earlier experimental results1
9,44,82
yet supporting their theoretical
contained dissolved air, unless specifically mentioned otherwise.
In some experiments, the dissolved air was purged by bubbling
with argon gas (99.999%, Liquid Carbonic Corporation).
Dissolved air was found to have no detectable effect on the
kinetics of the system.
predictions.
-
Under relatively high Cl molar concentration, the second-
-•
9,18-20,23,73
order decay of Cl2 takes place mainly via reaction 9.
-
-3
At [Cl ] < 1 × 10 M, the present work (see below) shows
-
•
that reaction 10 contributes to the second-order loss of Cl2 to
-
54,75-77
•
-•
produce Cl2 and Cl
with Cl3
via the equilibrium of Cl and Cl2
-
• 74
.
4. Results
-
•
-•
2
.2. Kinetics of SO4 . The decay of SO4 follows mixed
4.1. Absorption Spectra of Cl2 and SO4-•. Interference
-
•
1
8,19,24,29,34-44
first- and second-order kinetics.
Sulfate radicals
-
•
-•
reacting with Cl , S2O82-, and H2O (reactions 2, 12, and 13)
-
between Cl2 and SO4 absorption has often been circum-
-
•
vented by detecting SO4 at a wavelength between 440 and
produce the pseudo-first-order contribution to the decay; reaction
1
included in the mechanism for completeness.
-
•
15,18,20,21,23
5
10 nm, where the Cl2 absorption is small,
while
1 makes the second-order contribution. Equilibrium 14 is
-
•
probing Cl2 around the peak of its absorption near 340
1
6,20-22,24,89
-•
nm,
where the SO4 absorption is small. To ensure
the quality of our kinetics results, we measured the absorption
spectra of both species. In analyzing the results to obtain
quantitative absorption coefficients, we assume that the quantum
3
. Experimental Section
.1. Apparatus. The experimental apparatus is similar to that
3
-•
yield of sulfate radical formation in reaction 1 is ΦSO ) 2, in
9,10,12,13,23,41,83
4
used in other work from this laboratory.
Briefly,
2
9,32,37,50
agreement with previous work.
This assumption is
a pulsed rare gas-halogen excimer laser was used to photolyze
solutions containing persulfate ions and chloride ions at 248
nm. The laser pulse energy was monitored by a diode detector
behind the reaction cell for all experiments run and calibrated
daily. The detailed experimental approach is published else-
where.10 A high-pressure xenon-mercury arc lamp provided a
continuous light source for monitoring transient species by
absorption. Dichloride radical anion (Cl2 ) was monitored by
its absorption at 364 nm, the wavelength of the strongest output
band of the xenon-mercury lamp in the vicinity of the Cl2
further supported by the virtually exact agreement of the results
-
• 53
obtained below with other recent determinations of ꢀSO
and
4
-
• 65,71
Cl2
ꢀ .
4
.1.1. The Absorption Spectrum of SO4-•. The absorption
spectrum of sulfate radicals was determined at 5 nm intervals
between 300 and 550 nm by laser flash photolysis of per-
sulfate ions at 248 nm. The relative absorption spectrum of
-
•
-
•
SO4 has been determined previously in our laboratory by
2
-
laser flash photolysis of S2O8 in a wide range of acidic
-
•
+
37,41
conditions, that is, 0 e [H ] e 2.0 M.
It was concluded
absorption maximum (∼340 nm). The absorption coefficient
-•
-
that SO4 radical and its protonated form HSO4 have the same
spectrum.
of the radicals is found in the present work (see below) to be
-
•
-1
-1
ꢀ
(Cl2 ,364 nm) ) 7000 ( 700 M cm (base 10). Under
The molar extinction coefficient of sulfate radical, ꢀSO -•, is
4
the experimental conditions used in this work, the concentration
•
expressed in eq Ia
of solvated Cl atoms is very low, and their light absorption
absorption coefficient84,85 ꢀ(Cl ,364 nm) ≈ 2000 M cm
•
-1
-1
(
(
A0(SO4-•)
-
•
base 10)) can be neglected compared to that of Cl2 (see
ꢀ
SO4-•
)
(Ia)
below). White cell optics were utilized to fold the optical path
in the cell to enhance detection sensitivity.86 A monochromator
equipped with a photomultiplier was used to monitor the
transmitted light. The photomultiplier tube output was amplified
and sent to a digital oscilloscope for signal averaging and thence
to a computer for data analysis. Least-squares fits of the
experimental data were carried out using KaleidaGraph
software, which utilizes the Levenberg-Marquardt nonlinear
least-squares algorithm. The fitting uncertainty is always within
2-
sΦSO4-•RS2O82-[S O ] F
0 λ
2
8
where A0(SO4 ) is the initial absorbance of SO4-•; s is the path
-•
length; ΦSO - is the quantum yield of SO4 in the photodis-
•
-•
4
sociation of S2O8 ; RS2O82- is the molar extinction coefficient
2
-
8
7
2-
2-
of S2O8
at the photolysis wavelength; [S2O8 ] is the
2
-
concentration of S2O8 ; and Fλ is the photolysis laser fluence.
88
The molar extinction coefficient of persulfate ions at 248 nm
2
-1
-1
15,27,37,39,90
5
% with R better than 0.98. The uncertainties for the recom-
is RS2O82- ) 25 M cm (base 10).
With the
2
9,32,37,50
an upper limit to ꢀSO4- can
mended values from this work correspond to (σ, obtained from
propagation of errors.
assumption that ΦSO4-• ) 2,
be obtained from measurements of the laser power, the
absorbance, and the other parameters in eq Ia. The spectrum of
3
.2. Reagents. All solutions were prepared immediately
-
•
before the experiments. The water was purified by a Milli-RO/
SO4 determined in this manner is shown in Figure 2.

298 J. Phys. Chem. A, Vol. 108, No. 2, 2004
Yu et al.
Figure 3. The absorption spectrum of Cl
1σ) correspond to precision only.
2
-•. The error bars (propagated,
Figure 2. The absorption spectrum of SO -
gated, (1σ) correspond to precision only.
•. The error bars (propa-
4
(
TABLE 3: Comparison of the Molar Extinction Coefficient
TABLE 2: Comparison of the Molar Extinction Coefficient
-•
of Cl
2
at 340 nm
-
•
of SO
4
at 450 nm
Cl2-•, M- cm-1
1
ꢀ
SO4-•, M- cm-1
(
1
SO4-•ΦSO4-•
(base 10)
ꢀ
ꢀ
methoda
(base 10)
reference
base 10)
methoda
reference
196646
1
2500 ( 1000
PR
PR
PR
PR
PR
PR
PR
PR
PR
1964,57 1976103
1
1
1
1
1
1
1
1
1
050
100
100
600
600 ( 100
570 ( 130
630 ( 120
700 ( 150
630 ( 50
PR
PR
PR
PR
PR
PR
PR
PR
PR
60
75
62
89
8
9
8
8
8
800 ( 500
580 ( 100
1973
1973
1975
1976
b
47
1969
1972
1975
1990
1992
1992
1992
1996
3
1
3
4
4
4
5
6
5
9
0
0
0
3
700
600 b
1977, 1980,105 198766,119
118
100 c
67
1
2001
1989
1995
71
9
8
600
800 ( 650
91
2003
9
8
000
FP
FP
1972,120,121 198565
this work, 2003
3
2
4
4
4
50 ( 45
60 ( 25
FP
FP
FP
FP
FP
FP
1967
1967
1988
1988
1989
500 ( 500 d
9,35
c
c
d
37
50
18
a
PR, pulse radiolysis; FP, flash photolysis. b This measurement is
1
1
1
1
385 ( 140
385 ( 275
300 ( 300
2770 ( 280
2770 ( 550
done at 345 nm. c The maximum is assigned at 350 nm. The
d
uncertainty is propagated error with (1σ.
e
630 ( 10
3260 ( 20
this work, 2003
a
PR, pulse radiolysis; FP, flash photolysis. b Observed at 460 nm.
from 230 to 450 nm determined in this work is shown in Figure
c
Measured at 443 nm and derived with ΦSO4 ) 2 assumption. d The
-•
-•
3. The peak of the Cl2 absorption is found at 340 nm, where
e
conclusion is based upon ∼445 nm. The error was from fitting
-1
-1
the molar extinction coefficient is 8500 ( 500 M cm (base
uncertainty with error propagation ꢀSO -•
,450 nm ) 1630 ( 180 M cm
-1
-1
4
1
0). Values for ꢀCl2 at 340 nm are summarized in Table 3.
-•
(
base 10).
Our result is in excellent agreement with results from both pulse
54-64,40,65-72,91
radiolysis and flash photolysis,
assumption that ΦSO4-• is 2.
which supports the
The values for ꢀSO - at the absorption maximum (450 nm)
•
4
from the literature and from the present work are listed in Table
In our previous determination of quantum yield of the
hydroxyl radicals in the photolysis of aqueous hydrogen
•
-1
-1
2
. Our result of ꢀSO4- ) 1630 ( 180 M cm (base 10) is in
fair agreement with a previous laser flash photolysis measure-
1
0
-•
-•
peroxide, the absorption coefficient ꢀCl for Cl2 radicals
ment50 of ꢀSO4 ) 1385 M cm (assuming ΦSO4-• ) 2).
-•
-1
-1
2
-•
was required. The accuracy of ꢀCl depends on the validity of
2
However, it is in excellent agreement with recent pulse radiolysis
the assumption of ΦSO - ) 2. Ultimately, the quantum yield
•
4
measurements (see Table 2 where the assumption of ΦSO -
•
)
4
of hydroxyl radicals derived in that work is relative to that of
2
is not necessary), giving additional support to the conclusion
that ΦSO4 ) 2.
9
2
sulfate radicals.
.2. Absorbance Analysis. Since the spectra of Cl2 and of
SO4 overlap, caution is needed in analyzing the absorbance
data used to determine the reaction kinetics. In this work, SO4
was monitored at 450 nm (ꢀ(SO4 ,450 nm) ) 1630 M cm
base 10), this work), where the monitoring lamp has high
intensity and the Cl2 absorption is much weaker than that of
SO4 . Similarly, Cl2 was monitored at 364 nm, where the
-•
-•
4
4
.1.2. The Absorption Spectrum of Cl2-•. A scavenger method
-•
was used to determine ꢀCl2- using the mechanism in Table 1.
•
-•
-•
-•
With optimum scavenging, [SO4 ]0 ) [Cl2 ]0 and the expres-
-•
-1
-1
sion of ꢀCl2-• is given by eq Ib.
(
-
•
A0(Cl2-•)
-
•
-•
ꢀ
Cl2-•
)
(Ib)
-•
2-
radical anion has sufficiently strong absorption (ꢀ(Cl2 ,364 nm)
sΦSO4-•RS2O 2-[S O8 ] F
2
0
λ
-1
-1
8
) 7000 M cm (base 10), this work) and the monitoring
lamp is relatively bright.
The observed absorption is the sum of A(Cl2-•)t and A(SO4-•)t,
Atotal, expressed in eqs IIa and IIb corresponding to the sum of
Once again, ΦSO4-• ) 2 is assumed.
The dichloride anion radical, Cl2-•, was produced by laser
-
•
-•
flash photolysis of solutions containing 0.1 M NaCl and 3 ×
eqs III (A(Cl2 )t) and X (A(SO4 )t). The detailed derivation
-
3
-•
-•
9
-•
1
0
M K2S2O8. The spectrum of Cl2 at the interval of 5 nm
of A(Cl2 )t is presented in Paper I, and A(SO4 )t is readily

Free Radical Reactions Involving Cl , Cl2-•, SO4-•
•
J. Phys. Chem. A, Vol. 108, No. 2, 2004 299
-
•
Figure 5. Some typical time profiles of Cl
2
under various pH
conditions. The solid lines are nonlinear least-squares fits. The
-
•
-•
4
-3
Figure 4. Typical time profiles of Cl
2
and SO
monitored at 364
-4
experimental conditions are [NaCl] ) 4 × 10 M, [K
2
S
2
O
8
] ) 2 ×
4
2
-
-
and 450 nm, respectively, at [S
2
O
8
] ) 3 × 10 M, [Cl ] ) 5 ×
-3
10
M, and pH ) 1.72, 2.02, and 3.14 all controlled by adding HClO .
-
5
1
0
M, and pH ) 0. The solid lines are nonlinear least-squares fits.
-•
-
The insert is a time profile of Cl
2
observed at higher [Cl ] fit with
mixed first- and second-order kinetics for its decay.
obtained by using the expression for mixed first- and second-
order kinetics:
For [Cl ] < 1 × 10 M, the observed loss of Cl2-• is mainly
-
-3
Atotal ) ꢀCl2-•sC[e-kAt - e-kBt] +
first-order because the second-order contribution is insignificant
due to low Cl2 molar concentration. Therefore, analyses of
-•
-
1
-3
2
kSO4-•
2kSO4-•
the experimental data obtained for [NaCl] < 1 × 10 M were
I
1
exp(k -• t)
SO4
+
-
analyzed by solving the mechanism as pseudo-first-order
-
4
I
I
{
(
A(SO )
ꢀ
sk
)
ꢀ
sk
}
9,97
0
SO -• SO -•
SO -• SO -•
consecutive reactions.
The mixed first- and second-order
4
4
4
4
scheme was also used for comparison. From the mixed first-
and second-order analysis, it was found that the second-order
contribution is essentially negligible. Hence, the second-order
reactions are neglected in most of the following analysis of the
(
IIa)
where s is the optical path length, C is a constant (see Paper
9
I ), kA is the observed pseudo-first-order rate constant corre-
sponding to the rise of Cl2 , kB is the observed pseudo-first-
-
•
-•
-
rise and decay of Cl2 under low Cl molar concentration,
-
•
I
9
order rate constant corresponding to the decay of Cl2 , k -•
similar to the strategy adopted in Paper I.
At lower Cl molar concentration, reaction 10 contributes to
the second-order loss of Cl2 in addition to reaction 9.
SO4
is the pseudo-first-order rate constant of SO4-• decay, and kSO
-•
-
4
-
•
-•
is the observed second-order rate constant of SO4 decay.
-
•
-•
When SO4 molar concentration is low, the principal
Therefore, the most important reactions related to Cl2 in Table
-
•
decay routes of SO4 are pseudo-first-order via reactions 2,
2, and 13. The total absorption, Atotal, given by eq IIa reduces
to eq IIb:
1 are reactions (2, (3, (4, and 6-10. In the following analysis,
we obtain values for rate constants, equilibrium constants, or
both for most of these reactions under conditions that minimize
interferences and correlations in the least-squares analysis. We
do not apply any estimated adjustments for ionic strength in
the following analysis because the ionic strength is nearly
constant (∼0.01 M) in all of the experiments. Moreover, the
estimated effects are relatively small (∼20%), as described in
section 5.1 where we specifically investigate the effect of ionic
1
Atotal ) ꢀCl2-•sC[e- - e ]+ A(SO4 )0 exp(-k
kAt
-kBt
-•
I
t) (IIb)
SO4
-
Typical time profiles of Cl2-• and SO4-• monitored simulta-
neously at 364 and 450 nm, respectively, are shown in Figure
4
. The solid lines are nonlinear least-squares fits using eq IIb.
-•
-•
2 9
strength on k and k .
The analysis of Cl2 and SO4 data is explained in more detail
in the following sections.
Typical time profiles (normalized for ease of comparison)
-
•
-•
4
.3. Kinetics Analysis. The present system, involving SO4
of the rise and decay of Cl2 under various pH conditions at
-
•
-3
2-
and Cl , is similar in some ways to the system containing HO
and Cl . This is especially true of the rise and decay of Cl2
under conditions of low Cl molar concentration. The decay of
Cl2 is an important focus in this work. In the present work,
SO4 and Cl2 time profiles are monitored simultaneously,
and then the rise and decay of each radical is analyzed. We
report the analysis of Cl2 first and then that of SO4
.3.1. Strategy. The mechanism shown in Table 1 and
Figure 1 is complicated but can be simplified considerably
constant NaCl molar concentration (e10 M) and S2O8 molar
-
9
-•
concentration are shown in Figure 5. The solid lines are
nonlinear least-squares fits to eq III. The rise time of Cl2 molar
concentration corresponds to the faster step of Cl2 production
-
-•
-
•
-•
-
•
-•
and loss, whereas the fall time corresponds to the slower
9
,97,98
-•
step.
The rise time of the Cl2 absorption signals is very
-
•
-•
.
rapid, regardless of pH. In contrast, the rate of the signal decay
+
4
decreases as H molar concentration increases. Since the
-
•
+
formation of Cl2 does not involve H , the signal decay time
-
•
-•
under controlled experimental conditions. The Cl2 formation
corresponds to the loss of Cl2 . This pH dependence of the
Cl2 decay is examined in detail below. First, we investigate
the Cl2 rise and decay at constant pH.
The analytical solution for Cl2-• molar concentration at
constant pH is expressed by eq III, which is derived in a manner
-
•
takes place via reactions 1-3 as concluded by earlier
1
4-24,43,81,89,93-95
-•
research,
and its loss takes place via reac-
tions 4-10, hence, following mixed first- and second-order
9
,19,60,78,79,81,96
kinetics.

300 J. Phys. Chem. A, Vol. 108, No. 2, 2004
Yu et al.
TABLE 4: Summary of Results from k
Temperature
A
Analysis at Room
method
source
directly measured results
-
) (3.3 ( 0.2) × 10 M s-1
8
-1
k
A
-[Cl ] linear fit
slope
intercept
k
k
2
6
-1 -1
12 < 2.0 × 10 M
s
k2 ) (3.3 ( 0.2) × 10 M s-1 is obtained from the slope of
8
-1
the linear least-squares fit; the intercept depends on k12.
4
.3.3. Analysis Based on kB. First-Order Reaction. The loss
-
•
of Cl2 is assumed to follow mixed first- and second-order
kinetics.
by laser flash photolysis of Cl and S2O8 at constant pH and
detected at 364 nm is shown in the insert panel of Figure 5.
Reactions 4, 6, 7, and 8 contribute to the first-order loss of Cl2
The study of Cl2 loss as a function of S2O8 and Cl molar
concentrations was studied at constant pH to avoid the predicted
pH dependence. The predicted pH dependence of Cl2 loss was
investigated at constant S2O8 and Cl molar concentrations.
Dependence on S2O8
9
,19,60,78,79,81,96
-•
A typical time profile of Cl2 produced
-
2-
-•
.
-
•
2-
-
-•
-
Figure 6. Plots of k
fits. The circle is k
(1σ) are usually approximately the size of or smaller than the markers.
A
and k
B
vs [Cl ]. The solid lines are least-squares
2
-
-
-
1
A
B
, and the triangle is k (unit, s ). The error bars
2
-
-
(
and Cl Molar Concentrations.
Reactions 4 and 6 are thought to be the main routes for the
pseudo-first-order loss of Cl2 . In controlled experiments, it
-
•
exactly analogous to the derivation presented in the Appendix
9
of Paper I.
was found that as NaCl molar concentration increases, k
B
19,23,81
decreases, as observed previously.
In experiments in which
A(Cl2-•)t ) ꢀCl2-•sC[e-kAt - e-kBt]
(III)
2-
S2O8 molar concentration was varied, the NaCl molar concen-
tration was kept constant to exclude the effects of reactions 4
and 6. However, kB was found to change systematically as
The expressions for kA and kB are given by eqs IV and V,
respectively:
2
-
S2O8 molar concentration varied. The major impurity in all
available sources of K2S2O8 is sulfuric acid, which tends to
2
8
-
-
19
control the pH of K2S2O8 solutions. For example, McElroy
k ) k [S O ] + k [Cl ]
(IV)
(V)
A
12
2
2
reported that a 0.4 M solution of K2S2O8 had a pH of ∼4,
-
equivalent to a H2SO4 content of ∼0.2%. We find a similar
k [Cl ]â + R(k + â)
3
-3
18,81
effect in our experiments.
To eliminate the pH effect caused
kB )
-
k [Cl ] + k + R + â
by the impurity, the pH of all solutions was controlled by adding
HClO4. The pH in the experiments discussed here was fixed at
3
-3
where R ) k7[S2O82-] + k-4[H2O] and â ) k8[S2O82-] +
k6[H2O]. When equilibrium 3 is maintained, that is, when
19,99
2, which is much lower than the unadjusted pH.
Under conditions where both pH and NaCl molar concentra-
-
K3 ) k3/k-3, and k3[Cl ] + k-3 . R + â, kB reduces to
tion are held constant, kB was observed to increase as K2S2O8
-
•
eqs VIa and VIb:
molar concentration increased, which indicates that Cl2 or Cl
2
-
reacts with S2O8 on the experimental time scale. When
-
-
2-
equilibrium 3 is maintained with [S2O8 ] e 1 mM, the fitted
k K [Cl ] + k
k K [Cl ] + k
6
3
4
8
3
7
[S O82-] (VIa)
2-
kB )
[H O] +
rate constant kB varies linearly with S2O8 molar concentration
2
2
-
-
K [Cl ] + 1
K [Cl ] + 1
3
3
as shown in Figure 7. The solid lines are linear least-squares
-
fits to eq VI. When K3[Cl ] . 1 is satisfied, the slope (S) and
or
-
intercept (I) of each line in Figure 7 depend on Cl molar
concentration as follows:
k ) I + S[S O 2-]
(VIb)
B
2
8
k [H O]
SI
[Cl-]
4
2
I )
+ k [H O] )
+ II
(VIIa)
(VIIb)
Equation VI is very useful in the analysis of the experimental
data.
Rate constants kA and kB, which are functions of both S2O8
and Cl molar concentrations, can be determined from data such
as those shown in Figure 6. From the least-squares fit of a single
experiment, it is only possible to find two fitted rate constants,
and it is not possible to identify which rate constant corresponds
to kA and which kB. However, by carrying out experiments over
a range of Cl molar concentration (refer to eqs IV and V),
one can identify the rate constants: the one linearly proportional
to Cl molar concentration is identified as kA (in eq IV), and
the other is identified as kB (in eq V). This identification is
unambiguous, as is apparent from the representative data shown
in Figure 6.
.3.2. Analysis Based on kA. Fitted rate constant kA in eq IV
depends on rate constants k2 and k12. The directly measured
and derived results for k2 and k12 are summarized in Table 4. A
-
6
2
K [Cl ]
3
2-
k7
Ss
-
S )
+ k )
+ Is
8
-
[Cl-]
K [Cl ]
3
where SI ) k4[H2O]/K3, II ) k6[H2O], Ss ) k7/K3, and IS ) k8.
The slopes and intercepts are plotted vs 1/[NaCl] in Figure 8a,b,
and a linear least-squares analysis gives values for k7/K3, k8,
k4[H2O]/K3, and k6[H2O] summarized in Table 5.
-
-
-
Dependence on pH. At low Cl molar concentration, the
•
-•
-
contribution of Cl atom reactions to the overall loss of Cl2
becomes more important, due to reactions 4 and 7. When S2O82
molar concentration is held fixed, the variation of kB should be
caused solely by reactions 4 and -4, which are assumed to be
4
+
at equilibrium. As H molar concentration increases, the overall
-
•
first-order reaction rate of Cl2 loss becomes slower because
the rate of reaction -4 becomes larger. It is observed here that
-
plot of kA vs [Cl ] at pH 2 is shown in Figure 6. Rate constant

Free Radical Reactions Involving Cl , Cl2-•, SO4-•
•
J. Phys. Chem. A, Vol. 108, No. 2, 2004 301
2
-
-
Figure 7. The k
are linear least-squares fits to eq VI. The pH of all experiments shown
was 2 controlled by adding HClO . The circle is 0.1 mM NaCl, triangle
.2 mM NaCl, diamond 0.4 mM NaCl, square 0.6 mM NaCl, and
B
dependence on [S
2
O
8
] and [Cl ]. The solid lines
4
0
inverse triangle 1.0 mM NaCl. The error bars ((1σ) are usually
approximately the size of or smaller than the markers.
kB depends on pH when S2O82- and Cl molar concentrations
-
are held constant, as shown in Figure 5. When equilibria 2 and
3
are maintained, kB can be expressed by eq VIII (derived in
Appendix A):
1
kB )
×
-
K [Cl ]
3
k [H O]
2
8
-
4
2
k [H O] + k [S O ] -
(VIII)
4
2
7
2
+
{
}
1
+ k /(k [H ])
x
-4
where kx ) k5a[Cl ] + k5b[Cl] + k5c[SO4 ] + k5d[S2O82-] +
-
-•
+
k5′. The dependence of kB on H molar concentration at constant
-
-
[
S2O82 ] ) 2 mM and Cl molar concentration is shown in
Figure 8. The plots of (a) S and (b) I vs 1/[NaCl]. The solid line is
linear least-squares fit. The error bars ((1σ) are usually approximately
the size of or smaller than the markers.
Figure 9.
The solid lines in Figure 9 are nonlinear least-squares fits
using eq VIII. Three fitting parameters are obtained directly
+
TABLE 5: Summary of Directly Measured and Derived
from the nonlinear least-squares fits of kB vs H molar concen-
2-
-
Results from k
B
Dependence on S
2
O
8
and Cl Molar
-
2-
-
tration: c1 ) k4[H2O]/(K3[Cl ]), c2 ) k7[S2O8 ]/(K3[Cl ]), and
c3 ) kx/k-4 (Table 6). The first two parameters are simply
Concentrations at pH 2
directly measured results
k [H O]/K ) 1.2 ( 0.1 M s
derived results
-
linearly dependent on the inverse of Cl molar concentration.
By plotting the fitted values of c1 and c2 with respect to 1/[Cl ]
-
1
5 -1
-
k [H O] ) (1.7 ( 0.1) × 10 s
4
6
7
8
2
2
3
4
2
-
1
k
k
k
[H
/K
O] e 100 s
) 65 ( 8 s
-1
and using linear least-squares fits to analyze the result, we
-
1
) (9.1 ( 1.1) × 10 M s-1
6
-1
3
k
7
-
1
2-
obtain k4[H2O]/K3 ) 1.1 ( 0.1 M s and k7[S2O8 ]/K3 )
e 1 × 10 M s-1
4
-
1
0
.12 ( 0.01 M s . These two parameters were also obtained
in the analysis of kB dependence on S2O8 and Cl molar
concentrations at a constant pH as listed in Table 5.
2-
-
TABLE 6: Summary of Directly Measured and Derived
2
-
Results from k
B
Dependence on pH at [S
2
O
8
] ) 2 mM and
-
Constant Cl Molar Concentration
The analysis of c3 ) kx/k-4 is more complicated, because it
-•
is associated with the loss of ClOH via the following reactions:
directly measured results
derived results
O] ) (1.5 ( 0.1) × 10 s
) 1.1 ( 0.1 M s-
]/K
1
k
k
k
[H
) (8.4 ( 0.7) × 10 M
5 -1
5
-1
k
k
k
4
7
[H
[S
2
O]/K
3
4
7
2
ClOH-• f OH + Cl
-
•
(5′)
2
-
-1
6
-1 -1
2
O
8
3
) 0.12 ( 0.01 M s
s
-
5
5′/k-4 ) (1.0 ( 0.8) × 10
M
5′ ) (2.7 ( 2.2) × 10 s
ClOH-• + Cl f OH + Cl
-
-
-•
2
(5a)
counteracts the forward reaction 5, making it an inefficient path
ClOH-• + Cl f HO + Cl
•
•
-•
(5b)
(5c)
2
-•
for ClOH decay.
-
ClOH-• + SO4 f Cl + HSO5
-•
-
-
Rate constant kx is given by kx ) k5a[Cl ] + k5b[Cl] +
-•
2-
k5c[SO4 ] + k5d[S2O8 ] + k5′. When the third fitting parameter
ClOH-• + S O8 f Cl + HSO5 + SO4
2-
•
-
-•
(5d)
-
is plotted as a function of Cl molar concentration, no
2
dependence is observed. Therefore, it is concluded that reaction
5a is not important. The importance of reactions 5b, 5c, and 5d
cannot be determined by the present data analysis. Assuming
-
-•
Because Cl molar concentration is much larger than ClOH
molar concentration in this system, the reverse reaction -5

302 J. Phys. Chem. A, Vol. 108, No. 2, 2004
Yu et al.
-
•
Figure 11. Some typical time profiles of SO
4
under various pH
+
Figure 9. The k
B
dependence on [H ]. The solid lines are nonlinear
conditions. The solid lines are nonlinear least-squares fits. The pH of
least-squares fits by eq VIII. The circle is 0.1 mM NaCl, triangle 0.4
mM NaCl, and diamond 1.0 mM NaCl. The error bars ((1σ) are usually
approximately the size of or smaller than the markers.
solutions is controlled by adding HClO
4
. The experimental conditions
] ) 2 × 10 M.
-4
-3
are [NaCl] ) 4 × 10 M and [K
2
S
2
O
8
Debye-H u¨ ckel theory does not provide a good description of
the observed behavior.
.3.4. SO4 Analysis. Some typical time profiles of SO4-•
-
•
4
absorption observed at 450 nm under various conditions are
shown in Figure 11. Equation X for mixed first- and second-
19,41
order kinetics
was used in a nonlinear least-squares analysis
to obtain the rate constants.
A(t) ) ꢀ
s[SO4-•] )
SO4-•
x
-
1
2
k11
2k11
I
1
exp(k t)
+
-
(X)
I
I
{
[
A
0
ꢀ
sk
]
ꢀ
sk
}
SO -•
SO -•
4
4
-
•
The rise of SO4 molar concentration is faster than the
instrument response. The pseudo-first-order component of the
mixed kinetics is due to reactions 2, 12, and 13, and the second-
I
-
order component is due to reaction 11, that is, k -• ) k2[Cl ]
SO4
2
-
II
+
k12[S2O8 ] + k13[H2O] and k ) 2k11/ꢀSO4-•.
II
Several rate constants are obtained from the analysis of the
pseudo-first-order component of the SO4 decay. A plot of
Figure 10. The dependence of kCl2
-
on [NaCl]. The solid line is
-•
global linear least-squares fit. The filled circle is 0.5 mM K
triangle 1.0 mM K , open circle 2.0 mM K , open square 3.0
mM K , and diamond 5.0 mM K . The error bars ((1σ) are
2 2 8
S O ,
I
-
2-
2
S
2
O
8
2
S
2
O
8
k
-• vs [Cl ] at constant pH and S2O8 molar concentration
SO4
2
S
2
O
8
2 2 8
S O
is shown in Figure 12. The slope obtained from the linear least-
usually approximately the size of or smaller than the markers.
squares fit corresponds to k2, and the intercept corresponds to
2
-
k12[S2O8 ] + k13[H2O]. The value of k11 is obtained directly
from the mixed first- and second-order analysis, and the results
are reported in Table 7.
that these three reactions are much slower than reaction 5′, kx
5
-1 11
is equal to k5′ and we obtain k5′ ) (2.7 ( 2.2) × 10 s .
Second-Order Reaction. When the chloride concentration
is relatively high, Cl2-• molar concentration is relatively
large and the second-order contribution to the overall loss
5
. Discussion
-
•
of Cl2 becomes more important. Most previous studies
5.1. Ionic Strength Effects. Rate constants for reactions
taking place in the aqueous phase are affected by the ionic
-
•
of the second-order decay of Cl2 are focused on reaction
9
,17,19,20,23,58,62,66,73,79,82,100-106
II
Cl2
-
strength of the medium. The Debye-H u¨ ckel-Bronsted-Davies
9
.
We find that k -• varies as Cl
41,107-110
semiempirical theory
gives a good description of many
molar concentration changes. When equilibrium 3 is maintained,
-
•
ionic strength effects:
reaction 10 is assumed to be important. Free radicals Cl2 and
•
-•
Cl are in equilibrium with Cl3 , which subsequently dissociates
-
54,75-77
II
kµ
1/2
into Cl and Cl2.
The expression for k -• is given by eq
µ
Cl2
log10 ) 2Z Z A
- bµ
(XI)
1
2
{
}
IX (derived in Appendix B).
1/2
k0
1 + µ
4
k10
II
Cl2
k
-• ) 2k +
/ꢀCl2-•
(IX)
where kµ and k0 are the rate constants at ionic strength µ and 0,
respectively, Z1 and Z2 are the ion charges, A is the Debye-
H u¨ ckel constant (A ) 0.509 for water at 298 K), and b is an
empirical constant in the range ∼0.2-0.3 for the few systems
9
-
(
)
K [Cl ]
3
II
Cl2
-
Rate constant k -• is observed to depend on Cl molar
1
09,110
concentration at constant pH, as shown in Figure 10. The
for which it has been measured.

Free Radical Reactions Involving Cl , Cl2-•, SO4-•
•
J. Phys. Chem. A, Vol. 108, No. 2, 2004 303
I
-
Figure 12. The k -• dependence on [Cl ] at constant pH and
SO4
2-
[S O ]. The solid line is linear least-squares fit. The pH is 2 by adding
2 8
-
3
HClO
4
; [K
S O
2 2 8
] ) 2 × 10 M. The error bars ((1σ) are usually
approximately the size of or smaller than the markers.
Rate constants in the limit of low ionic strength were
0
estimated by using eq XI with b ) 0: k ) (2.65 ( 0.16) ×
2
8
-1 -1
-•
0
1
7
1
M
0 M
s
(from the Cl2 analysis), k ) (4.9 ( 0.1) × 10
1
-
1
-1
0
1
5 -1 -1
s , and k ) (3.5 ( 0.2) × 10 M s . Rate constant
2
9
k-4 is discussed in Paper I. Since almost all of the present
experiments were carried out with [NaCl] < 1 mM and pH )
2
, the ionic strength of the solutions (∼0.01 M) did not vary
significantly. Except for reactions 2 and 9, the reaction rate
constants are not affected significantly by the ionic strength,
because the corresponding reactants do not include two ions.
The effect of ionic strength on k2 and k9 was investigated
systematically by carrying out experiments of varying ionic
strength up to 0.25 and 1 M, respectively, by adding NaClO4.
1/2
1/2
Plots of k2 and k9 vs µ /(1 + µ ) at 296 K are presented in
Figure 13a,b. The ionic strength dependence of k2 agrees well
with the Debye-H u¨ ckel theory prediction, whereas the ionic
strength dependence of k9 deviates from it.
2
Figure 13. The ionic strength dependence (a) of k at 296 K. The
solid line is the linear least-squares fit to the Debye-H u¨ ckel equation.
The error bars ((1σ) are usually approximately the size of or smaller
than the markers. Panel b shows the comparison of ionic strength
A comparison of the present findings with those by Huie et
al.20 and McElroy is shown in Figure 13b. Although all three
investigations were carried out with care, there is little agreement
among them regarding either the magnitudes of the rate
constants or how they depend on ionic strength. The reason for
this striking lack of agreement is not known, but we speculate
that it may be due to trace impurities present at varying
concentrations in different batches of the reagent NaClO4 used
to control the ionic strength. This lack of agreement and the
wide range of k9 values reported in the literature show that more
work is needed.
9
dependence of k data reported by Huie et al. (2), McElroy et al. ([)
19
and this work (b). The dotted lines are least-squares fits of the
experimental data to the Debye-H u¨ ckel equation with the slope as an
adjustable parameter. The solid line is a nonlinear least-squares fit using
an ion-pair model.23
the influence of an energy barrier. This is reasonable because
both reactants are negatively charged and energy is needed to
overcome the Coulombic potential and bring them from infinity
to the distance corresponding to the activated complex.
5
.3. Rate Constant Values. We determined a series of rate
constants and rate constant to equilibrium constant ratios from
the above kinetics analyses. In the following, we compare our
experimental results with previous literature values. The com-
parison and discussion are arranged in the order of how the
5
.2. Temperature Effects. Most of the previous measure-
ments of k9 were carried out at room temperature. In the present
work, the temperature dependence of k9 was investigated over
the range from 6.8 to 51.6 °C, as shown in Figure 14. The solid
line is a nonlinear least-squares fit to the Arrhenius expression:
-
•
rate constants were determined, that is, from Cl2 first-order,
-
•
-•
-•
Cl2 second-order, SO4 first-order, and SO4 second-order
analyses. When the rate constants are determined from two
different approaches, both results are discussed together. Since
critical reviews of the relevant kinetics data are lacking, we have
assembled tables of the most relevant measurements.
k ) (5.6 ( 0.5) ×
9
1
2
-1
-1
1
0 exp(-16.5 ( 0.2 kJ mol /(RT)) M s-1 (XII)
The Cl2-• disproportionation reaction 9 is exothermic (∆G )
5.3.1. Rate Constant k2. Several methods have been used to
determine k2. The first method is to monitor and analyze the
-
1
-
32.1 kJ mol ), and therefore, the activation energy indicates

304 J. Phys. Chem. A, Vol. 108, No. 2, 2004
Yu et al.
-
•
TABLE 7: Summary of Directly Measured and Derived Results from Analysis of the SO
Second-Order Decay
4
Decay by Mixed First- and
source
method
parameter
directly measured results
derived results
I
-
) (3.1 ( 0.1) × 10 M s-1
8
-1
first-order
k
-[Cl ] linear fit
slope
intercept
k
k
k
2
SO4
-
2-
3
-1
12[S
2
O
8
] + k13[H
2
O] ) (2.1 ( 0.1) × 10 s
-
1
5
-1 -1
first-order
second-order
13[H
2
O] ) 460 ( 90 s
k
k
12 ) (5.5 ( 0.3) × 10 M
s
5
-1
11 ) (6.1 ( 0.15) × 10 M s-1
8
-1
2k11/ꢀSO - ) (7.7 ( 0.2) × 10 cm s
4
-
•
+ Cl- f SO
2-
+ Cl•,
TABLE 8: Comparison of k
2
, SO
4
4
et al. may be caused by the ionic strength of 0.3 M used in
Determined at Room Temperature
41,107-110
their experiment. Using Debye-H u¨ ckel theory,
we
k
M
2
,
extrapolated Buxton et al.’s result to infinite dilution, where it
is found to be in excellent agreement with our results at zero
ionic strength (Table 1).
method a
FP
species
RNO
I, M b ×10-8
-1
s-1
reference
197014
very low
5
.3.2. Rate Constants from First-Order Cl2-• Decay. Two
-
-
-
-
-
-
-
-
•
•
•
•
•
•
•
•
17
15
18
20
21
22
23
PR
SO
4
4
4
4
4
4
4
4
0.195
0.007
f0
2.0 ( 0.4
3.1
1986
1975
1989
1990
1991
1996
1997
values for the ratio k4[H2O]/K3 were obtained: 1.2 ( 0.1 and
FP-ESR SO
-1
-
2-
FP
FP
FP
FP
FP
FP
SO
SO
SO
SO
SO
SO
2.6
1.1 ( 0.1 M s from kB vs [Cl ] and [S2O8 ] and kB vs pH,
f0
0.1
2.47 ( 0.09
respectively. These results are also reasonably consistent with
the value 1.4 ( 0.1 M s
4.7
-1
9,72
5
from Paper I.
With the
f0
f0
f0
3.3 ( 0.5
2.49 ( 0.06
2.49 ( 0.08
-1
recommended value of K3 ) (1.4 ( 0.2) × 10 M , two
5
-1
values for k4[H2O] are obtained: (1.7 ( 0.1) × 10 s and
this work, 2003
5
-1
(
1.5 ( 0.1) × 10
s . The unweighted average of these
-
-
-
-
-
•
•
•
•
•
197689
PR
PR
FP
FP
FP
Cl
2
Cl
2
Cl
2
Cl
2
Cl
2
5.05
0.056
f0
4.1
1.3
9
,19,60,72,81,96
16,89
two values is consistent with literature values
and
1976
1990
1996
19
22
reported in Table 1 as k4[H2O].
2.7 ( 0.4
3.0 ( 0.9
2.65 ( 0.16
19
-•
•
f0
f0
McElroy pointed out that when [Cl2 ]/[Cl ] g 10, the
•
this work, 2003
absorption due to Cl atoms is negligible compared to that due
-
-
•
•
-•
-•
24
-•
5
-1
9
FP
FP
SO
SO
4
and Cl
and Cl
2
2
0.3
f0
6.1 ( 0.2
1999
1999
to Cl2 , considering K3 ) (1.4 ( 0.2) × 10 M (Paper I ),
- •
-1 -1 -1 -1 63,85
ꢀ
24
4
2.47
Cl2 ,364nm ) 7000 M cm , ꢀCl ,364nm ≈ 3000 M cm ,
-
•
-1
-1 60
a
and ꢀClOH ,364nm ≈ 3200 M
cm . The contribution of
PR, pulse radiolysis; FP, flash photolysis; ESR, electron spin
resonance. f0: ionic strength is extrapolated to 0 M.
-
•
-
b
ClOH is also expected to be minimal. At high Cl molar
concentration, an equilibrium between dichloride anion radicals
and chlorine atoms is rapidly achieved. Based upon reactions
•
-•
+
Cl + H2O T HOClH and HOClH T ClOH + H postulated
1
11
by Buxton et al. (essentially reactions 4 and -4 in Table 1),
-
the first-order rate constant for Cl decay should show an
inverse dependence on the chloride ion concentration due to
reactions 3 and 4. The observed first-order decay rate constant
-
kB was found to increase markedly when [Cl ] < 1 mM; rate
-
constant kB reaches a lower limit at [Cl ] ) 0.01 M. However,
-
-1
81
kB is not proportional to [Cl ] . Later, Jacobi et al. found
-
-1
-
kB ∝ [Cl ] in experiments with [Cl ] > 0.3 mM. In the
present work, kB ∝ [Cl ] is found over a relatively wide
range of [Cl ] g 0.1 mM corresponding to [Cl ] , [Cl2 ] and
-
-1
-
•
-•
-
K3[Cl ] . 1.
Although it had been proposed19,111 that kB should be
dependent on pH due to equilibrium 4, previous experimental
1
9,82,111
82
data showed inconsistent results.
Wagner et al. did not
-
•
include reaction -4 in their Cl2 mechanism. In deaerated
solutions at high pH, the decrease in conductivity due to the
difference in mobility of the electron and the Cl2 may have
been too small to detect with their equipment, which may
explain why they did not observe a pH dependence.
-
•
Figure 14. The Arrhenius plot of k
9
(points) and nonlinear least-squares
8
2
fit (line). The error bars ((1σ) are usually approximately the size of
or smaller than the markers.
19
-•
SO4-• decay, the second is to analyze the Cl2-• rise, and the
third is to combine the first two methods. The value of k2 )
McElroy attributed reactions -3, 4, and 5 to the Cl2 decay,
and described the overall process by reaction 15.
8
-1 -1
-•
(
3.1 ( 0.1) × 10 M
s
obtained from SO4 decay analysis
-
•
+
-
•
-
•
is consistent within error limits with that from the Cl2 molar
concentration growth analysis in this work. The unweighted
Cl
2
+ H
2
O T H + 2Cl + HO
(15)
8
-1
•
average of the above two results, k2 ) (3.2 ( 0.2) × 10 M
The equilibrium Cl + H2O T H2OCl was postulated to explain
-
1
•
-•
s , is reported in Table 1. Despite differences in analytical
methods, the present results are in agreement with previous
the lack of the pH dependence on the decay rate of Cl /Cl2
over the pH range of 2.2-3.9. Since McElroy used HCl to
14-24,43,81,89,93-95
19
-
measurements (see Table 8).
control the pH, it is likely that the combined effects of Cl
Herrmann et al.2 presented their self-consistent results from
2
and H molar concentrations on kB confounded the interpreta-
tion.
+
-
•
-•
24
the decay of SO4 and the growth of Cl2 . Buxton et al.
added SO42 to the system of SO4 and Cl to study
-
-•
-
Buxton et al.111 used photolysis of CH3COCH2Cl to generate
•
-
-•
equilibrium 2. Both k2 and k-2 were obtained by analyzing the
Cl , which subsequently reacts with Cl to form Cl2 . The
-•
-•
•
SO4 decay and Cl2 growth. The higher value of k2 by Buxton
reactions of Cl with water and chloroacetone in the pH range

Free Radical Reactions Involving Cl , Cl2-•, SO4-•
•
J. Phys. Chem. A, Vol. 108, No. 2, 2004 305
2
, Determined at Room Temperature
-
•
-•
-
TABLE 9: Comparison of k
9
, Cl
2
+ Cl
2
f 2Cl + Cl
(2k /ꢀ),
-•
k
M
9
,
9
-5
ꢀ(Cl ),
M
2
10-
9
-1
s-1
I, M
0.25
×10 cm s
8.8 ( 5.6
-1
-1
cm
-1
λ, nm
methoda
reference
×
5
1
0
1
0
1
0
2
0
0
.5 ( 3.5
12500
8800
8800
8800
8800
8300
9600
8800
7000
7000
340
340
340
340
340
325
340
340
364
364
LFP
LFP
LFP
PR
LFP
LFP
FP
PR
LFP
LFP
19893
2,50
19902
0
.3
0
0
0.13
0
0
0
2.96
1.6
3.65 ( 0.12
1.57 ( 0.11
4.24 ( 0.24
19
.7 ( 0.1
1990
19901
9
.55 ( 0.05
.69 ( 0.005
.8 ( 0.1
.61
23
1997
19997
3
112
2000
.0 ( 0.3
.9 ( 0.05
.72 ( 0.08
<1
4.55 ( 0.76
2.54 ( 0.16
2.06 ( 0.27
200391
this work and 2003
this work, 2003
4
9
<10
0
a
PR, pulse radiolysis; LFP, laser flash photolysis.
TABLE 10: Comparison of k11, SO -•
+ SO
-•
2 8
f S O
2-, Determined at Room Temperature
4
4
ꢀ
SO4
-1
-
,
2k11/ꢀSO4
-5
-
,
11
k ,
M
methoda
I, M
λ, nm
cm
450
1600
M
-1
×10 cm s
-1
×10
8.1
-8
-1
s-1
reference
19871
22
PR
PR
4
450
450
36
4.75
0
concd
3.8 ( 0.5
19924
34
FP
FP
FP
FP
FP
FP
FP
FP
FP
FP
FP
FP
FP
0.06
0.03
455
455
450 ( 45
460 ( 25
18.6b
4.2b
1967
1967
1967
1973
8.0 ( 0.7b
3.7 ( 0.3
b,c
b,c
29
35
∼3
6.1 ( 1.1
113
12
450
450
d
450
450
450
d
d
454
450
1050
460
6.05e
18
123
0.03, 0.13, 1
7.74c
1.78
2.5
2.7
19771
24
d
0
0
d
d
1978
1988
37
1385 ( 140
1600
1385
3.9 ( 0.6
5.5
3.2
d
19903
19931
9
4.45 ( 0.15
2.2 ( 0.15
0.55
-
4
52
d1 .5 × 10
16
d
d
d
1993
-
4
b
114
e1.5 × 10
d
1.6
19954
1
.0
2.5 ( 0.2
7.7 ( 0.2
d
1996
e0.25
1630 ( 10
6.1 ( 0.15
this work, 2003
a
PR, pulse radiolysis; FP, flash photolysis Original reported as k11/ꢀSO4 or k11. c Averaged results of measurements reported in the same
b
-•
d
e
paper. Not available. Based on 2.38 cm path length.
•
1
-6 were studied, where pH was adjusted by addition of either
bonded to a Cl atom. More research is needed to determine
+
HClO4 or NaOH. Little dependence of kB on H molar
concentration was observed. Buxton et al. also disagreed with
McElroy about the necessity of using the equilibrium of Cl
the products of reactions 7 and 8.
111
The ratio k7[S2O82-]/K3 ) (0.12 ( 0.01) M-1 s-1 is
directly obtained from the analysis of pH dependence of kB at
1
9
•
H2O T H2OCl, because their calculations suggested that Cl•
[S2O8 ] ) 2 mM. The value k7 ) (8.4 ( 0.7) × 10 M
2-
6
-1 -1
s
+
5
-1 9,72
and H2OCl are not different species. Although not discussed,
many possible radical reactions could be involved in the system
studied by Buxton et al. For example, the products produced
is derived on the basis of K3 ) 1.4 × 10 M ,
and it is
-
consistent with that obtained from the kB vs 1/[Cl ] analysis in
this work. The unweighted average of these two values is
reported in Table 1.
•
by Cl reacting with CH3COCH2Cl were not identified. More
research is needed to determine the possible factors in the
photolysis of chloroacetone that may affect the pH dependence.
5.3.3. Rate Constants from Cl2-• Second-Order Analy-
sis. Recent values of k9 obtained from this and previ-
9,19,72,81,82
9,19,20,23,32,73,91,112
Reaction 6 is slow, as concluded elsewhere.
The
ous
work are summarized in Table 9. Our result
-
1
value k6[H2O] < 100 s is determined in the present work
is consistent with the most recent measurements. The parameter
determined directly by experiments is 2k9/ꢀCl . The final result
for k9 depends on the value of ꢀCl2 . Reaction 10 is quite fast,
which is consistent with the previous result by Wu et al.
5.3.4. Rate Constants from SO4 First-Order Analysis. The
second-order component of SO4 decay is obtained directly
from the mixed first- and second-order analysis of SO4 . The
values of k11 are listed in Table 10. The experimentally measured
directly from kB vs [S2O82 ] and 1/[Cl ] analyses, in agreement
-
-
-
2
with previous measurements.9
,19,60,72,81,96
-•
79
As shown in the data analysis section, kB depends not only
-
2-
-•
on Cl molar concentration, but also on S2O8 molar concen-
tration via reactions 7 and 8. Here, values of k7 and k8 are
reported for the first time. Buxton et al. carried out pulse
radiolysis experiments on a system containing tert-butyl alcohol,
-
•
-
•
-
-3
2-
-•
-•
[Cl ] ) 10 M, and [S2O8 ] e 0.1 M but did not detect these
quantity is 2k11/ꢀSO4 ; thus ꢀSO4 affects the deduced k11. As
shown in Table 10, our result is consistent with the many
previous measurements of 2k11/ꢀSO4-
7
2
reactions, possibly because reaction 7 is not very important
at this chloride concentration and reaction 8 is very slow. The
• 18,24,29,34-44,52,94,113,114
.
It is
6
-1 -1
-•
value k7 ) (9.1 ( 0.1) × 10 M
s
is obtained on the basis
found in this work that 2k11/ꢀSO4 is affected by ionic
5
-1 9,72
37,39,41
of K3 ) 1.4 × 10 M . Since the fitting uncertainty of k8 is
strength.
The value reported here is higher than a previous
measurement in this laboratory obtained at almost zero ionic
strength. Our present result is in good agreement with Tang et
al. obtained at a similar ionic strength. The recommendation
for k11 extrapolated to zero ionic strength is listed in Table 13.
4
41
quite large, only a limiting value is obtained: k8 < 1 × 10
-1
-1
M
s . Reaction 7 is relatively fast, possibly due to the high
•
37
reactivity of Cl in the aqueous phase. The possible products of
reactions 7 and 8 include ClSO4 , SO4 , and SO4 . We
0
-
-•
2-
-
-•
-•
speculate that the structure of ClSO4 is similar to that of SO4
5.3.5. Second-Order Rate Constants from SO4 Analysis.
Table 11 summarizes values for k12, which fall into two distinct
except that one terminal oxygen in the SO4-• tetrahedron is

306 J. Phys. Chem. A, Vol. 108, No. 2, 2004
Yu et al.
-
•
2-
2-
TABLE 11: Comparison of k12, SO
4
+ S
2
O
8
f SO
4
+
value is obtained when the pH ≈ 4. This suggests that the
apparent pH dependence of k12 may be due to contributions from
reaction 14, in addition to reactions 2, 12, -12, and 13. More
work is needed to identify the source of this behavior.
-
•
2 8
S O , Determined at Room Temperature
methoda
I, M
k
12, M-1 s-1
reference
6
122
PR
FP
PR
FP
FP
FP
FP
b
1.2 × 10
1987
1990
1992
1994
1995
1996
this work, 2003
198837
1997
1999
-
3
5
5
39
40
94
114
42
The value of k13 has been determined several times in the
3 × 10
(6.1 ( 0.6) × 10
(6.6 ( 2.7) × 10
c
36,37,39-41,114
concd
past.
In this work, laser flash photolysis of solutions
5
b
e5 × 10
2-
containing S2O8 with or without pH control give k13[H2O] )
-
4
5
5
b( 0.5-5) × 10
e0.25
(6.6 ( 0.4) × 10
-1
4
60 ( 90 s . Our value for k13 is compared with previous
5
6.3 × 10
determinations in Table 12. All of the measurements indicate
that reaction 13 is slow.
(5.5 ( 0.3) × 10
not observed
PR
FP
FP
FP
FP
e0.12
4
41
0.28-6.1
e10
6
. Conclusions
(3 × 10-4)-3
slow
<1500
115
2
4
The present work results in a more complete, self-consistent
0.3
1999
this work, 2003
-•
-•
e0.25
580 ( 90
mechanism describing the kinetics of Cl2 and SO4 (see Table
). Our results are consistent with literature values, where
1
a
PR, pulse radiolysis; FP, flash photolysis. b Not available. c concd,
SO
available, supporting the general correctness of the reaction
mechanism summarized in Table 1. In addition, the absorption
concentrated H
2
4
.
-
•
•
-•
-•
TABLE 12: Comparison of k13, SO
4
+ Ha
2
O f HO +
spectra of SO4 and Cl2 have been redetermined, and the
results are in excellent agreement with previous work. The
-
HSO
4
, Determined at Room Temperature
O], s-
1
reference
-•
method
I, M
NA
0.3
pH
>7
∼6
k
13[H
2
pseudo-first-order decay rate constant of Cl2 is, for the first
197236
time, shown to depend on pH as expected from the effects of
reaction -4. The temperature and ionic strength dependences
of k9 are measured, as is the ionic strength dependence of k2.
The results for k9 show that the ionic strength dependence is
still far from certain and should be the subject of future work,
because application to real systems will require large corrections
for ionic strength. The observed pseudo-first-order decay rate
PR
PR
FP
FP
FP
FP
FP
FP
FP
<3000
690 ( 120
1.5-5.4 410 ( 40
1.5-5.4 360 ( 90
199924
3
3
b
37
∼3 × 10
1988
1988
1990
c
37
∼3 × 10
d
39
f0
f0
4.9
5.0
NA
500 ( 60
660 ( 40
660
d
114
19954
2
NA
0.28-6.1
e0.25
1996
199741
4.8-5.8 440 ( 50
2-5 460 ( 90
-
•
this work, 2003
constant of SO4 appears to depend on pH and further work is
also needed to determine this aspect of the mechanism.
a
NA, not available; PR, pulse radiolysis; FP, flash photolysis. b In
SO , HClO
, or HAc. Assuming the first-order component from reactions
the absence of large concentrations of additives, H
2
4
4
,
Acknowledgment. We thank NASA (Upper Atmospheric
Research Program) and NSF (Atmospheric Chemistry Division)
for financial support of this work. We also thank Robert Huie,
Paul Wine, and Anthony Hynes for helpful discussions. (This
material is based upon work supported by the National Science
Foundation under Grant No. 9812680. Any opinions, findings,
and conclusions or recommendations expressed in this material
are those of the author(s) and do not necessarily reflect the views
of the National Science Foundation.)
c
NaClO
is 50 ( 50 s
4
-
1 d
.
f0: Ionic strength is extrapolated to 0 M.
groups. One is in the range of 10 M-1 s ,
5
-1 39,40,42,94,114
and the
In the
other is about an order of magnitude lower.2
4,37,41,115,116
present work, we obtain values that fall in both groups, raising
an interesting question about k12.
The high value of k12 obtained in this work corresponds to
pH ) 2, controlled by the addition of HClO4, while the low
TABLE 13: Summary of Results and Recommendations for Rate Constantsa
reaction
results (this paper)
recommendations
reference
this work
21, 24
9
1
2
k ) (2.57 ( 0.11) × 10 M s-1
0
2
8
-1
k ) (2.57 ( 0.11) × 10 M s-1
0
2
8
-1
-2 ) (2.1 ( 0.1) × 10 M s-1
8
-1
-
2
3
3
k
k
k
) (7.8 ( 0.8) × 10 M s-1
9
-1
3
4
-1
-1
-
-3 ) (5.3 ( 0.3) × 10 s
9
9
5
K
3
) (1.4 ( 0.2) ×10 M
5
-1
5
-1
4
4
4
k [H
2
O] ) (1.6 ( 0.2) × 10 s
k
k
4
0
[H
2
O] ) (1.7 ( 0.3) × 10 s
this work and ref 9
9
this work and ref 9
60
60
9
this work and ref 9
this work
this work
this work and ref 9
this work
this work
this work
this work and ref 41
46
10
-1
s-1
-
-
) (3.3 ( 0.9) × 10
M
-
4
0
4
7
1
/K ) (8.8 ( 2.2) × 10
9
-1
5
5
k
k
1
5
) (6.1 ( 0.8) × 10 s
-5 ) (4.3 ( 0.4) × 10 M s-1
9
-1
-
1
/K
5
) 0.70 ( 0.13 M
O] < 100 s-
1
k
k
k
[H
O] < 100 s
-1
6
7
8
9
0
1
2
3
k
k
k
6
[H
2
6
2
) (8.8 ( 0.5) × 10 M s-1
6
-1
) (8.8 ( 0.5) × 10 M s-1
6
-1
7
7
4
-1 -1
4
-1 -1
8
0
< 1 × 10 M
s
8
0
9
< 1 × 10 M
s
k ) (7.2 ( 0.8) × 10 M s-1
8
-1
k ) (7.2 ( 0.8) × 10 M s-1
8
-1
9
9
-1 -1
9
-1 -1
1
1
1
1
k
k
k
k
10 ) (2.1 ( 0.1) × 10 M
s
-1
k
k
k
k
k
K
10 ) (2.1 ( 0.1) × 10 M
s
0
1
0
) (4.91 ( 0.08) × 10 M s-1
8
0
) (4.91 ( 0.08) × 10 M s-1
8
-1
1
11
) (3.5 ( 0.2) × 10 M s-1
5
-1
0
) (3.5 ( 0.2) × 10 M s-1
5
-1
1
2
12
-
1
-1
13[H
2
O] ) 460 ( 90 s
13[H
2
O] ) 460 ( 90 s
-13 ) 6.9 × 10 M s-1
5
-1
-
1
13
4
-
2
-1
14 ) 1.2 × 10
M
117
a
This paper; uncertainties ((1σ) were obtained from error propagation; ionic strength µ ≈ 0.01 M unless otherwise noted by a superscript “0”
on rate constants that have been adjusted to µ ) 0.

Free Radical Reactions Involving Cl , Cl2-•, SO4-•
•
J. Phys. Chem. A, Vol. 108, No. 2, 2004 307
-
•
Appendix A. The kB Dependence on pH
When equilibrium 3 is maintained and k3[Cl ][Cl ] .
-
•
•
2
k10[Cl2 ][Cl ],
•
-•
The rate law expressions of Cl and ClOH are
d[Cl
-•] d[Cl•]
d[Cl•]
2
• 2
k2[SO4-•][Cl ] - [Cl ]{k [SO ] - k [Cl ] +
-
•
2-
-
-
(
+
)
) 2kCl2-•[Cl2-
]
(B.4)
(B.5)
)
-2
4
3
dt
dt
dt
k [H O] + k [S O ]} + k [ClOH ][H ] - k [Cl -•]
2-
-•
+
which leads to
4
2
7
2
8
-4
-3
2
(A.1)
4
k10
II
Cl2
-
•
k
-• ) 2k +
/ꢀCl2-•
9
-
d[ClOH ]
(
)
•
-•
+
K [Cl ]
3
)
k [Cl ][H O]- [ClOH ](k [H ] + k ) (A.2)
4
2
-4
x
dt
References and Notes
where kx ) k5a[Cl ] + k5b[Cl ] + k5c[SO4-•] + k5d[S2O82-] +
k5′. Due to the presence of Cl in the system, k5 is negligible.
By steady-state approximation, [ClOH ]ss is expressed as
-
•
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•
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(
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•
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4
2
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[
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(A.3)
ss
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x
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When equilibria 2 and 3 are maintained and Cl- and S2O82-
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(
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4
•
(
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•
(11) Yu, X.-Y. J. Phys. Chem. Ref. Data, submitted for publication,
)
(A.4)
B
2
2003.
dt
(
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and
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8
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4
2
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4
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7
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