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Critical Evaluation of Rate Constants and Equilibrium Constants
of Hydrogen Peroxide Photolysis in Acidic Aqueous
Solutions Containing Chloride Ionsa…
Xiao-Ying Yub…
Department of Chemistry, The University of Michigan, Ann Arbor, Michigan 48109-1055
共Received 9 August 2003; revised manuscript received 26 January 2004; accepted 2 February 2004; published online 13 August 2004兲
Equilibrium constants and rate constants involving Cl"共aq兲,Cl
⫺,Cl
2
⫺"(aq), HO",H
2O,
and H2O2(aq) determined at 297⫾2 K in the aqueous phase are updated and evaluated.
Most of the rate constants and equilibrium constants are obtained by either pulse radi-
olysis or laser flash photolysis. The recommended values of rate constants and equilib-
rium constants are achieved by un-weighted averaging of the reliable experimental mea-
surements. © 2004 American Institute of Physics. 关DOI: 10.1063/1.1695414兴
Key words: aqueous phase; chloride; chlorine; critical evaluation; dichlorine radical anion; equilibrium
constant; free radical; hydrogen peroxide; rate constant; room temperature.
Contents
1. Introduction................................ 747
2. General Methods........................... 749
3. Guide to the Data Sheets. . ................... 749
3.1. Conventions Concerning Rate Constants.. ... 750
3.2. Arrangement of Tables................... 750
3.3. Data Evaluation......................... 750
4. Data Sheets................................ 750
4.1. k2,HO"⫹H2O2→HO2"⫹H2O"........... 750
4.1.1. Direct Method.................... 750
4.1.2. Indirect Method................... 751
4.2. k3,HO"⫹Cl⫺→ClOH⫺"................ 751
4.2.1. Direct Method.................... 751
4.2.2. Indirect Method................... 752
4.3. K3and k⫺3, ClOH⫺"→Cl⫺⫹HO"........ 753
4.4. k4K3,HO"⫹Cl⫺⫹H⫹→Cl"⫹H2O........ 753
4.5. K4and k4, ClOH⫺"⫹H⫹→Cl"⫹H2O..... 754
4.6. k⫺4关H2O兴,Cl"⫹H2O→ClOH⫺"⫹H⫹...... 754
4.7. k5,k⫺5, and K5,Cl"⫹Cl⫺↔Cl2
⫺"........ 755
4.7.1. Forward Rate Constant k5.......... 755
4.7.2. Reverse Rate Constant k⫺5.......... 756
4.7.3. Equilibrium Constant K5........... 757
4.8. k6,Cl
2
⫺"⫹Cl2
⫺"→2Cl⫺⫹Cl2............. 757
4.9. k7,Cl"⫹Cl2
⫺"→Cl⫺⫹Cl2............... 759
4.10. k8关H2O兴,Cl
2
⫺"⫹H2O→ClOH⫺"⫹H⫹
⫹Cl⫺................................ 759
4.11. k9,Cl
2
⫺"⫹H2O2→HO2"⫹H⫹⫹Cl⫺....... 761
4.12. k10 ,Cl"⫹H2O2→H⫹⫹Cl⫺⫹HO2"........ 761
4.13. k11 ,Cl
2
⫺"⫹HO2"→O2⫹H⫹⫹2Cl⫺........ 761
5. Conclusions................................ 762
6. Acknowledgments.......................... 763
7. References................................. 763
List of Tables
1. The preferred values of kiand Kiin the
photochemical system of H2O2and Cl⫺in the
aqueous phase at room temperature. ........... 748
2. Rate constant data of k2by 共a兲direct
measurements and 共b兲competition kinetics. ..... 750
3. Rate constant data of k3by 共a兲direct
measurements and 共b兲competition kinetics. ..... 752
4. Rate constant data of k⫺3.................... 753
5. Rate constant data of k4K3by direct and
competition kinetics......................... 753
6. Data of K4and k4.......................... 754
7. Rate constant data of k⫺4关H2O兴............... 755
8. Rate constant data of k5by direct
measurements.............................. 755
9. Rate constant data of k⫺5by direct
measurements.............................. 756
10. Equilibrium constant data of K5............... 757
11. Rate constant data of k6...................... 758
12. Rate constant data of k7...................... 759
13. Rate constant data of k8关H2O兴................ 760
14. Rate constant data of k9...................... 761
15. Rate constant data of k10..................... 761
16. Rate constant data of k11..................... 761
1. Introduction
The photochemical system involving HO"共aq兲and Cl⫺in
the aqueous phase is of significant interest in the fundamen-
tal kinetics understanding and its application to atmospheric
and biological sciences. Overall there have been more than
a兲Dedicated to Professor John R. Barker, whose inspiration and advice made
this work possible.
b兲Current address: Dept. of Atmospheric Science, Colorado State University,
Fort Collins, CO 80523-1371; Electronic mail: yingybei@umich.edu or
xiao-ying.yu@colostate.edu
© 2004 American Institute of Physics.
0047-2689Õ2004Õ33„3…Õ747Õ17Õ$39.00 J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
747
70 independent research articles related to the chemical ki-
netics study of Cl2
⫺"(aq)/Cl"(aq) in the aqueous phase in the
past few decades. Although several previous reviews sum-
marized the rate coefficient of aqueous phase free radical
reactions,1–5 the most recent evaluations are dated in 1988.3,4
Since then, more research has been dedicated to the kinetics
of free radicals of interest in atmospheric water phase spe-
cifically investigating the Cl2
⫺"(aq)/Cl"(aq) mechanism. In
contrast, there is a lack of in-depth analysis and critical
evaluation of research findings relevant to the Cl⫺/H2O2/hv
system in the aqueous phase. Hence, a critical review of the
research papers in the past 40 yr is needed to recognize past
accomplishments, identify mistakes, refine rate constants and
equilibrium constants, verify the validity of previous cita-
tions, improve the creditability of future citations, and clarify
future research focus.
This review is the fourth paper of a series of papers des-
ignated to the kinetic and mechanistic investigation of the
Cl⫺/H2O2/hv and Cl⫺/S2O8
2⫺/hv systems. We recently
studied the chemical mechanism of the HO"共aq兲and Cl⫺
system6,7 in the aqueous phase and reported a series of reac-
tion rate constants and equilibrium constants involving
HO"共aq兲,Cl"共aq兲,Cl
⫺,H
2O2, and Cl2
⫺"(aq). The first three
papers deal with the kinetic and mechanistic analyses of our
experimental data, and this paper evaluates the rate constants
and equilibrium constants involved in the updated mecha-
nism. As a result of our experimental findings,6,8 the hydro-
gen extraction reaction Cl"(aq)⫹H2O2→HO2"(aq)⫹H⫹
⫹Cl⫺is added to the mechanism. In addition, the reaction
Cl"(aq)⫹Cl2
⫺"(aq)→Cl⫺⫹Cl2is confirmed to participate in
the second-order decay of Cl2
⫺"(aq). Although our recent re-
sults are in fairly good agreement with previous findings,
discrepancy still exists in certain rate constants and equilib-
rium constants. Therefore, it is necessary to evaluate the ex-
perimentally obtained kinetics data reported in the literature
to discuss and estimate the uncertainty.
The review of reaction rate coefficients and equilibrium
constants is focused on Cl"共aq兲related free radicals gener-
ated by photodissociation of hydrogen peroxide and its sub-
sequent reactions with Cl⫺at room temperature, i.e., reac-
tions 共2兲–共11兲. The preferred values of rate constant data and
equilibrium constant data are summarized in Table 1. The Ki
always refers to equilibrium constant for reaction i; and ki
refers to reaction rate constants for reaction i. The 共aq兲is
omitted in the following text for the simplicity of presenta-
tion. The numbering scheme of the reactions of interest is
consistent throughout the paper. Farhataziz and Ross1have
detailed evaluation of HO"and HO2"related reactions, i.e.,
reactions 共12兲–共16兲, which are included for completeness of
the mechanism. Most of the reaction rate constants were de-
termined by pulse radiolysis or flash photolysis. Values de-
termined by other techniques were included when they seem
reliable and when absolute rate constants could be derived
from their reports. Relative rates are not included as such.
All values presented in this paper were determined in aque-
ous or predominantly aqueous systems.
The equilibrium constant of reaction 共5兲,Cl"
⫹Cl⫺↔Cl2
⫺", has been the subject of several investigations.
Literature values of K5near 20°C scattered over about 4
orders of magnitude.9–12 However, the recent values obtained
by Buxton et al.12 and Yu and Barker6agree reasonably well
with that of Jayson et al.9Recent works appear to have
settled questions about the magnitude of this equilibrium
constant9–12 and led to a minor revision in the recommended
values with improved uncertainty. Although the reaction be-
tween chlorine atoms and hydrogen peroxide is well known
in the gas phase,13 it has only been determined in the aque-
ous phase recently.6We included this new measurement in
Table 1. The reaction Cl"(aq)⫹Cl2
⫺"(aq)→Cl⫺⫹Cl2was of-
ten missed in previous mechanisms. However, it plays an
important role in the second-order decay of Cl2
⫺"(aq), there-
fore it is included in the mechanism.
In this paper, we evaluate rate constants and equilibrium
constants determined in the previous two companion
papers6,7 and present the most reliable values of either rate
constants or equilibrium constants of aqueous phase free
radical reactions involving Cl",Cl
⫺,Cl
2
⫺",HO",H
2O, and
H2O2at room temperature. The tables in this paper include
the published rate constants as presented in their original
reports with some revisions where appropriate. The data in-
cluded are published from the 1960s to January 2004. An
update and critical evaluation of the recent and past works
are necessary for experimentalists as well as modelers for
future research in the Cl⫺/H2O2/hv aqueous system. Free
radicals, such as Cl",Cl
2
⫺", and HOCl⫺", are also basic
chemical species in the study of electron transfer theory. The
review of the kinetics study of the Cl⫺/H2O2/hv aqueous
TABLE 1. The preferred values of kiand Kiin the photochemical system of
H2O2and Cl⫺in the aqueous phase at room temperature
No. Reaction k
1H
2O2⫹h
→HO"⫹HO"a⌽HO"⫽1b
2HO"⫹H2O2→HO2"⫹H2Ok2⫽(3.2⫾1.5)⫻107M⫺1s⫺1
3HO"⫹Cl⫺→ClOH⫺"k3⫽(4.2⫾0.2)⫻109M⫺1s⫺1
⫺3 ClOH⫺"→HO"⫹Cl⫺k⫺3⫽(6.0⫾1.1)⫻109s⫺1
K3⫽0.70⫾0.13 M⫺1
4 ClOH⫺"⫹H⫹→Cl"⫹H2Ok4⫽(2.4⫾0.4)⫻1010 M⫺1s⫺1
⫺4Cl"⫹H2O→ClOH⫺"⫹H⫹k⫺4关H2O兴⫽(1.8⫾0.6)⫻105s⫺1
K4⫽(7.4⫾2.8)⫻106
5Cl"⫹Cl⫺→Cl2
⫺"k5⫽(7.8⫾0.8)⫻109M⫺1s⫺1
⫺5Cl2
⫺"→Cl"⫹Cl⫺k⫺5⫽(5.7⫾0.4)⫻104s⫺1
K5⫽(1.4⫾0.2)⫻105M⫺1
6Cl2
⫺"⫹Cl2
⫺"→2Cl⫺⫹Cl2k6⫽(3.5⫾2.7)⫻109M⫺1s⫺1
7Cl"⫹Cl2
⫺"→Cl⫺⫹Cl2k7⫽(1.4⫾1.0)⫻109M⫺1s⫺1
8Cl2
⫺"⫹H2O→ClOH⫺"⫹H⫹⫹Cl⫺k8关H2O兴⬍1300⫾100 s⫺1
9Cl2
⫺"⫹H2O2→HO2"⫹H⫹⫹2Cl⫺k9⫽(6.2⫾6.8)⫻106M⫺1s⫺1
10 Cl"⫹H2O2→H⫹⫹Cl⫺⫹HO2"k10⫽(2.0⫾0.3)⫻109M⫺1s⫺1
11 Cl2
⫺"⫹HO2"→O2⫹H⫹⫹2Cl⫺k11⫽(3.1⫾1.5)⫻109M⫺1s⫺1
12 HO2"⫹H2O2→H2O⫹O2⫹HO"
13 HO"⫹HO"→H2O2
14 HO"⫹HO"→H2O⫹O"—
15 HO2"⫹HO2"→H2O2⫹O2
16 HO"⫹HO2"→H2O⫹O2
aSee Faust et al.79
bSee Yu and Barker.7
748748 XIAO-YING YU
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
system provides an update of kinetics measurements as well
as the source of a self-consistent set of thermodynamic data
related to Cl"free radicals in the aqueous phase.14 Our main
objectives of this paper are to provide insight into future
research directions focused on halogen related free radical
systems, specifically chlorine, and to provide a concise ex-
planation and commentary of essential experimental kinetic
approaches to solving complicated fast multiple equilibria
problems.
2. General Methods
The dichlorine radical anions (Cl2
⫺") were produced in
most cases by pulse radiolysis of aqueous solutions. The ra-
diolysis of water forms short-lived intermediates: hydrated
electrons, hydrogen atoms, and hydroxyl radicals, which re-
act rapidly with appropriate solute to yield the desired sec-
ondary radicals.3,4,15 In certain cases, these secondary radi-
cals exhibit sufficient optical absorption in the visible or
near-ultraviolet range that allows kinetic spectrophotometric
measurements of the formation and decay rates. By follow-
ing the decay rate as a function of added solute concentration
one can determine the absolute second-order rate constant for
the reaction of the radical with the added solute. In other
cases, when the radical does not exhibit intense absorption, it
is often possible to determine absolute rate constants by fol-
lowing the buildup of the species produced from the added
solute upon reaction with the radical.
When none of these methods is applicable, the rate con-
stants are determined by competition kinetics. In such cases,
a reaction with a known absolute rate constant is chosen as a
reference and the yield of the product of this reaction is
determined as a function of the ratio of concentrations of the
reference solute to other added solutes. From a plot of the
yield ratios versus the concentration ratios, one derives the
relative rate constants of the two competing reactions. Based
on the known rate constant for the reference reaction, one
then derives the rate constant for the unknown reaction. The
competition method assumes constant radiation yield in all
solutions examined and gives somewhat less precise results
than the direct method. However, it is a useful strategy in
many systems.
The results obtained from competition kinetics are not em-
phasized in this paper, because they intrinsically are affected
by the relative rate constant depending on what reference
solute is used. This evaluation focuses on rate constants and
equilibrium constants obtained from direct methods. When a
result obtained by competition kinetics is cited, the reference
rate constant is not evaluated.
3. Guide to the Data Sheets
Some symbols appear repeatedly in the following discus-
sions. A list of abbreviations and symbols used in the Data
Sheets section is summarized here.
aactivity coefficient
a distance of closest approach between two ions
ave. average
calc. calculated
Ddiameter
molar extinction coefficient 共base 10兲
Eaactivation energy
ESR electron spin resonance
EPR electron paramagnetic resonance
⌽quantum yield
Fenton Fenton reaction
FP flash photolysis
␥
-Rgamma radiolysis
Gradiation yield 共molecules per 100 eV or
1.60209⫻10⫺17 J兲
Iionic strength
Kequilibrium constant
krate constant
kfthe forward reaction rate constant
kobs the observed rate constant
krthe reverse reaction rate constant
wavelength 共nm兲
LFP laser flash photolysis
Mmol/L
N.A. not available
O.D. optical density
pH negative logarithm of the proton ions concentra-
tion, e.g., where pH⫽⫺log共关H⫹兴兲
pKanegative logarithm of the acid dissociation con-
stant, e.g., where AH⫹H2O→A⫺⫹H3O⫹
PR pulse radiolysis
sim. simulation
Zion charge
A list of chemical species appeared in the text is included in
the following:
t-BuOH tert-butyl alcohol 共2-methyl-2-propanol兲
Cl"chlorine atom
Cl⫺chloride ion
Cl2chlorine molecule
Cl2
⫺"dichloride radical anion, dichlorine anion radical
ClOH⫺"ClOH minus radical
EtOH ethanol
Fe2⫹Fe共II兲ion
HO"hydroxyl radical
HO2"hydroperoxyl radical
H2O2hydrogen peroxide
H2O water
MeOH methanol
RNO N, N-dimethyl-4-nitrosoaniline
SO4
⫺"sulfate radical
S2O8
2⫺persulfate ion
The data discussed here are only for the photochemical ki-
netic information.
749749CRITICAL EVALUATION OF RATE CONSTANTS
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
3.1. Conventions Concerning Rate Constants
All reactions listed in the tables are elementary processes.
Thus, the rate expression is derived from a statement of the
reaction, e.g.,
A⫹A→B⫹C共1兲
⫺1
2
d关A兴
dt⫽d关B兴
dt⫽d关C兴
dt⫽k关A兴2共I兲
Note that the stoichiometric coefficient for A, i.e., 2, appears
in the denominator before the rate of change of 关A兴共which is
equal to 2k关A兴2; the square brackets 关兴represent concentra-
tion of the species兲and as a power on the right hand side.
3.2. Arrangement of Tables
Tables 2–16 are arranged in the order of the occurrence of
the reaction in Table 1. The products of the reactions are
included when they are known reasonably well or when they
have been discussed in the paper reporting the data. In most
cases, the rate constant listed is kobs at the quoted pH. When
ionic strength conditions were specified or could be derived
from the description of the report, they are enclosed in the
data sheet. In some case kobs may be for a mixture of ionic
forms of the substrate.
The method of radical generation is given by symbols
such as PR 共pulse radiolysis兲and FP 共flash photolysis兲, iden-
tified in the list of abbreviations and symbols. Other details
of the determination and the system are described in the
notes. Temperature and pressure are assumed to be ambient;
otherwise the conditions will be noted. The references are
followed at the end of the article.
3.3. Data Evaluation
Rate data selected for inclusion in this paper are based on
the best available direct determination. Preference is given to
data derived from pulse radiolysis, flash photolysis, or other
kinetic or time-resolved methods capable of monitoring the
formation or decay of the transient species Cl2
⫺". High prior-
ity is given to entries derived from publications containing
the most comprehensive information concerning the experi-
mental methodology, errors, conditions, details of parameters
needed for the unambiguous identification and characteriza-
tion of the reactive species, and the nature of the reaction, as
well as factors influencing or controlling the reaction kinet-
ics.
The uncertainties of the preferred values are assigned us-
ing the standard deviation of all reliable direct measure-
ments. Therefore the uncertainties presented indicate the
range of the available rate constant or equilibrium constant
data. They are not determined by extensive statistical analy-
sis of the data, which is often not allowed due to the limited
data set or insufficient information.
4. Data Sheets
4.1.
k
2,HO"¿H2O2\HO2"¿H2O"
Both direct and indirect methods were used to measure
k2, which are discussed separately. The representative mea-
surements of pKaof HO"and HO2"are 11.916,17 and 4.88,18
respectively. The k2is not affected by the different pH en-
vironments reported.
4.1.1. Direct Method
Notes 关Table 2共a兲兴
aSchwarz 共1962兲,19 k2⫽4.5⫻107M⫺1s⫺1.
The variation of H2O2steady state was expressed as a
function of pulse period. The mathematical derivation of k2
is complicated. The k2was obtained by trial and error with
one intermediate parameter until a consistent value was
reached.
bFricke and Thomas 共1964兲,20 k2⫽1.2⫻107M⫺1s⫺1.
Studies of reactions in solutions of H2O2and O2provided
the absolute rate constants for a series of rate constants, one
TABLE 2. Rate constant data of k2by 共a兲direct measurements and 共b兲competition kinetics
k2⫻10⫺7共M⫺1s⫺1兲Method pH Reference Notes
共a兲4.5 PR N.A. 196219 a
1.2 PR 3 196420 b
2.7⫾0.3 PR 6.8–13.8 198221 c
2.7 ave. N.A. 199223 d
4.2⫾0.2 LFP 2 20036e
k2⫻10⫺7共M⫺1s⫺1兲Method Ratio pH Reference Notes
共b兲4.3 FP kHO"⫹Br⫺/k2⫽830 2.2 196324 a
2.25 PR k2/kHO"⫹I⫺⫽(2.2⫾0.7)⫻10⫺37 196525 b
8.8 PR k2/kHO"⫹HCO3
⫺⫽1.8 8.4 196926 c
5.9 PR kHO"⫹thymine /k2⫽72.4 1.0 196927 d
1.7 PR k2/kHO"⫹RNO⫽1.36⫻10⫺2N.A. 196929 e
1.7 FP k2/kHO"⫹RNO⫽1.36⫻10⫺27 197430 e
4.5
␥
-R k2/kHO"⫹RNO⫽3.6⫻10⫺35–10.5 197431 e
3.8 PR k2/kHO"⫹Luminol⫽4.25⫻10⫺37.7, 9.3, 11 198032 f
2.0 PR kHO"⫹SCN⫺/k2⫽550 7 198134 g
750750 XIAO-YING YU
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
of which is k2. With GH⫽3.3, GHO"⫽2.7, GH2⫽0.45, and
GH2O2⫽0.75, k2⫽1.2⫻107M⫺1s⫺1was obtained.
cChristensen et al. 共1982兲,21 k2⫽(2.7⫾0.3)
⫻107M⫺1s⫺1.
The value of k2was determined from the pH dependence
of kobs which is a mixed rate constant involving reactions
共2兲–共5兲. The k2was derived by computer simulation of the
following eight reactions that are involved with the observed
pH dependence:
HO"⫹H2O2→H2O⫹O2
⫺⫹H⫹共2兲
O⫺⫹H2O2→OH⫺⫹O2
⫺⫹H⫹共3兲
HO"⫹HO2
⫺
→OH⫺⫹O2
⫺⫹H⫹共4兲
O⫺⫹HO2
⫺
→OH⫺⫹O2
⫺共5兲
H2O2⫹OH⫺→HO2
⫺⫹H2O共6兲
HO2
⫺⫹H2O→H2O2⫹OH⫺共7兲
HO"⫹OH⫺→O⫺⫹H2O共8兲
O⫺⫹H2O→HO"⫹OH⫺共9兲
The rate constant of reaction 共3兲was considered negligible,
the rates of reactions 共4兲and 共5兲were known.22 The best fit
was generated by using k4⫽(7.5⫾1.0)⫻109M⫺1s⫺1and
k5⫽(4.0⫾0.5)⫻108M⫺1s⫺1. Although the experimental
technique is pulse radiolysis, k2was indeed determined by
computer simulations.
dElliot and Buxton 共1992兲,23 2.7⫻107M⫺1s⫺1.
This is a citation of the result of Christensen et al.21
eYu and Barker 共2003兲,6(4.2⫾0.2)⫻107M⫺1s⫺1.
The rise and decay of Cl2
⫺"was analyzed. The rise rate
constant of Cl2
⫺"could be expressed as kA⫽k2关H2O2兴
⫹k4K3关H⫹兴关Cl⫺兴. The k2was directly obtained from the
linear least squares analysis of kAversus 关H2O2兴. Whereas
the k4K3关H⫹兴was extracted from the subsequent linear least
squares analysis of the intercept from the kAversus 关H2O2兴
analysis plotted as a function of 关NaCl兴under constant pH
2.6
Preferred Values
k2⫽(3.2⫾1.5)⫻107M⫺1s⫺1
Comments on Preferred Values
The preferred value of k2is the unweighted average of the
four reported rate constants except Elliot and Buxton’s23 re-
sult, because it is a citation of Christensen et al.21
4.1.2. Indirect Method
The values of k2determined by competition kinetics meth-
ods are summarized below for completeness of comparison.
No preferred value is concluded from the indirect measure-
ment. Competition kinetics has been widely applied in deter-
mining k2using various scavengers. Relative rate ratios were
obtained as a result. The accuracy of k2depends on the rela-
tive rate constant as explained in Sec. 1.
Notes 关Table 2共b兲兴
aFerradini and Koulke
`s-Pujo 共1963兲,24 kHO"⫹Br⫺/k2
⫽830.
Bromide ions were used as the scavenger of hydroxyl radi-
cals. The ratio kHO"⫹Br⫺/k2⫽830 was obtained. By using
their value of kHO"⫹Br⫺⫽3.6⫻1010 M⫺1s⫺1,24 k2⫽4.3
⫻107M⫺1s⫺1was determined.
bThomas 共1965兲,25 k2/kHO"⫹I⫺⫽(2.2⫾0.7)⫻10⫺3.
The ratio k2/kHO"⫹I⫺⫽(2.2⫾0.7)⫻10⫺3was obtained by
using iodide ions as the HO"scavenger. With his own deter-
mination of kHO"⫹I⫺⫽(1.02⫾0.13)⫻1010 M⫺1s⫺1,25 k2
⫽2.25⫻107M⫺1s⫺1was derived.
cBuxton 共1961兲,26 k2/kHO"⫹HCO3
⫺⫽1.8.
The ratio of k2/kHO"⫹HCO3
⫺was measured. The k2⫽8.8
⫻107M⫺1s⫺1was determined by taking kHO"⫹HCO3
⫺⫽(4.9
⫾0.5)⫻107M⫺1s⫺1.26
dArmstrong 共1961兲,27 kHO"⫹thymine /k2⫽72.4.
The k2was corrected first in this work by using a compe-
tition scheme involving HO"and H2O2and HO"and thym-
ine. The k2⫽5.9⫻107M⫺1s⫺1was determined by taking
kHO"⫹thymine⫽(4.3⫾0.1)⫻109M⫺1s⫺1.28
eBaxendale and Khan 共1961兲,29 k2/kHO"⫹RNO⫽1.36
⫻10⫺2; Kachanova and Kozlov 共1974兲,30 k2/kHO"⫹RNO
⫽1.36⫻10⫺2; Hatada et al. 共1974兲,31 k2/kHO"⫹RNO⫽3.6
⫻10⫺3.
The above three used RNO 共p-nitrosodimethylaniline兲as
the competitor to study the HO"radical reaction. Baxendale29
and Kachanova30 obtained almost identical ratio, whereas
Hatada’s31 result differs by almost a factor of 4. It is unclear
what causes the discrepancy.
fMere
´nyi and Lind 共1980兲,32 k2/kHO"⫹Luminol⫽4.25
⫻10⫺3.
Luminol was the scavenger of hydroxyl radicals. The ratio
of k2/kHO"⫹Luminol⫽4.25⫻10⫺3was measured. Taking pre-
viously determined kHO"⫹Luminol⫽8.7⫻109M⫺1s⫺1,33 k2
⫽3.7⫻107M⫺1s⫺1was derived.
gGreenstock and Wiebe 共1981兲,34 kHO"⫹SCN⫺/k2⫽550.
The k2⫽2.0⫻107M⫺1s⫺1was derived using the ratio
kHO"⫹SCN⫺/k2⫽550 with kHO"⫹SCN⫺⫽1.1⫻1010 M⫺1s⫺1.35
Comments on Preferred Values
No preferred value is given based upon results from indi-
rect measurements.
4.2.
k
3,HO"¿ClÀ\ClOHÀ"
Similarly to k2,k3have been determined both using direct
and indirect methods. The following discussions of data are
organized according to the determination method.
4.2.1. Direct Method
Notes 关Table 3共a兲兴
aBurton and Kurien 共1959兲,36 k3⫽4.0⫻109M⫺1s⫺1.
The effect of halide ions in a system of hydrogen peroxide
and halide ions was found to reduce GH2O2. The plot of the
fraction of free hydroxyl radicals unscavenged by halide ions
versus a quantity, which is the product of the rate constant of
the radical scavenging reaction, the concentration of the
751751CRITICAL EVALUATION OF RATE CONSTANTS
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
scavenger solute, and the defined initial time characteristic of
the irradiation spur (to), followed the Ganguly–Magee rela-
tionship. With Ganguly and Magee to,k3is determined as
4⫻109M⫺1s⫺1.
bMattews and Sangster 共1965兲,37 very low.
The k3was measured at very high pH, i.e., alkaline con-
ditions, which resulted in a very slow rate constant.
cJayson et al. 共1973兲,9k3⫽(4.3⫾0.4)⫻109M⫺1s⫺1.
The observed rate constant of Cl2
⫺"rise, i.e., HO"disap-
pearance, was analyzed as a function of 关H⫹兴. Steady state
approximations of Cl", and ClOH⫺"were applied to derive
the expression for the pseudo-first-order rate constant. Linear
relationship was obtained: aCl⫺aH⫹/k⫽(1/k4K3)
⫹(aH⫹/k3). By plotting aCl⫺aH⫹/kversus aH⫹, the data
points yielded a straight line. The slope corresponded to
1/k3, and the intercept 1/k4K3.
dGrigore
´vet al. 共1987兲,38 k3⫽3.0⫻109M⫺1s⫺1.
The results range from (0.4– 3.0)⫻109M⫺1s⫺1with in-
creasing 关NaCl兴and unspecified pH. The details of their
analysis were not given.
Preferred Values
k3⫽(4.2⫾0.2)⫻109M⫺1s⫺1.
Comments on Preferred Values
Mattews and Sangste’s37 directly determined results were
obtained under high pH conditions that is unfavorable for
reactions 共3兲and 共4兲to proceed. Grigore
´vet al.’s results38
are not considered because they are in a wide range with no
reported analytical details. Therefore the preferred value
from directly determined measurements is obtained by the
unweighted average of the reported values from Burton and
Kurien36 and Jayson et al.9
4.2.2. Indirect Method
Notes 关Table 3共b兲兴
aAnbar and Thomas 共1964兲,39 k3/kHO"⫹Fe共CN兲6
4⫺⫽7.25
⫻10⫺3–0.169 and k3/kHO"⫹MeOH⫽9.9– 71.5⫻10⫺2.
This is one of the earliest reports using competition kinet-
ics to measure k3. Both methanol and potassium ferrocya-
nide were used under various pH. The k3was found in a
range of values depending on 关H⫹兴and 关Cl⫺兴.
bKraljı
´c and Trumbore 共1965兲,16 k3/kHO"⫹RNO⫽10⫺4.
The value of k3is very low under alkaline conditions.
cKraljı
´c共1967兲,40 k3/kHO"⫹RNO⫽4.2⫻10⫺2,(pH⫽2);
k3/kHO"⫹RNO⫽0.381, (pH⬃0.1).
A series of scavengers such as Br⫺,Cl
⫺, RNO, MeOH,
EtOH, and thymine was used to scavenge HO".
dArmstrong 共1969兲,27 k3/kHO"⫹H2O2⫽9.5.
A series of hydroxyl radical scavenger reactions was stud-
ied. The ratio of k3/k2was obtained. There could be a typo-
graphical error in the ratio k3/k2or k3in this paper. Since if
we use the reported k3/k2⫽9.5 and k2⫽5.9
⫻107M⫺1s⫺1,k3⫽5.6⫻108M⫺1s⫺1is derived, which is
different from what was reported in the paper, i.e., k3⫽5.6
⫻109M⫺1s⫺1. From the k2evaluation above, a ten times
difference in k2is unreasonable. However, it is unclear
whether k3/k2or k3was reported with a mistake. In Table
3共b兲, the value 5.6⫻109M⫺1s⫺1is listed, which is sus-
pected to be the determined parameter.
eHughes and Makada 共1969兲,41 k3/kHO"⫹MeOH⫽0.039 and
k3/kHO"⫹EeOH⫽0.020.
Both methanol and ethanol were used to scavenge HO",
and ratios were obtained first. The ratio of
kHO"⫹MeOH /k3/kHO"⫹EeOH⫽1.95 was then derived. No pH
dependence was mentioned. Hydrochloric acid was used to
provide chloride ions. Their values are smaller than Anbar
and Thomas’ results.39 No explanation was given why a dif-
ference exists using methanol and ethanol as the HO"
scavenger.39,41
fPramanick et al. 共1988兲,42 k3/kHO"⫹M⫽1.11⫻10⫺4.
The rate of HO"reacting with halide ions was determined
by entrapping the product radicals as polymer end groups
that have been detected and estimated by a sensitive dye
partition technique. The ratio of kHO"⫹X⫺to kMwhich is a
predetermined rate constant of HO"and a monomer, is equal
to the ratio of the counts of halogen end group to that of the
hydroxyl end group. Therefore, this method is essentially
TABLE 3. Rate constant data of k3by 共a兲direct measurements and 共b兲competition kinetics
共a兲k3⫻10⫺9(M⫺1s⫺1) Method pH Reference Notes
4
␥
-R 2 195936 a
very low
␥
-R 10 196537 b
4.3⫾0.4 PR ⬃21973
9c
0.4–3.0 PR N.A. 198738 d
共b兲k3⫻10⫺9(M⫺1s⫺1兲Method Ratio pH Reference Notes
0.089–0.64 PR k3/kMeOH⫽0.099– 0.715 1–2.5 196439 a
0.067–1.6 PR k3/kFe(CN)6
4⫺⫽7.25⫻10⫺3–0.169 1–2.7 196439 a
⬍1.25⫻10⫺3
␥
-R k3/kRNO⫽10⫺49 196516 b
0.52 PR k3/kRNO⫽0.042 2 196740 c
4.8 PR k3/kRNO⫽0.381 ⬃0.1 196740 c
5.6
␥
-R k3/k2⫽9.5 1 196927 d
0.035
␥
-R k3/kMeOH⫽0.031 1.1 196941 e
0.037
␥
-R k3/kEtOH⫽0.020 1.1 196941 e
1.32 PLY k3/kM⫽1.11 1 198842 f
752752 XIAO-YING YU
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
competition kinetics, because it relies upon the knowledge
and accuracy of kM. The initiator efficiency is an important
factor in the determination of k3.43
Comments on Preferred Values
No preferred value is given based upon the results from
indirect measurements.
4.3.
K
3and
k
À3, ClOHÀ"\ClÀ¿HO"
Notes 共Table 4兲
aJayson et al. 共1973兲,9K3⫽0.7⫾0.13 M⫺1;k3⫽(4.3
⫾0.4)⫻109M⫺1s⫺1;k3⫽(6.1⫾0.8)⫻109s⫺1.
The most widely used value of K3is 0.70⫾0.13 M⫺1.9It
was determined directly by using the linear relationship be-
tween the inverse of the difference of the optical density of
ClOH⫺"and 关HO"兴in saturated nitrous oxide solution and
saturated oxygen solution, respectively. The k3⫽(4.3⫾0.4)
⫻109M⫺1s⫺1is the directly determined value, k⫺3⫽(6.1
⫾0.8)⫻109s⫺1was derived based on K3and k3.
Preferred Values
k⫺3⫽(6.0⫾1.1)⫻109s⫺1.
Comments on Preferred Values
This is only report of K3.9The preferred k⫺3is derived
using the preferred value of k3and the only direct measure-
ment of K3. Since k⫺3is affiliated with K3and k3, the
recommended k⫺3is affected by k3.
4.4.
k
4
K
3,HO"¿ClÀ¿H¿\Cl"¿H2O
The global rate constant combining reactions 共3兲and 共4兲,
k4K3, was measured in many previous works. Using steady
state approximation, the third-order global rate constant can
be expressed as k4K3. The derivation and definition of the
global rate constant are detailed elsewhere.6
Notes 共Table 5兲
aAnbar and Thomas 共1964兲,39 k4K3⫽1.16–2.16
⫻1010 M⫺2s⫺1(pH⬃3) and 0.32–1.84⫻1010 M⫺2s⫺1
(pH 0–3兲.
Anbar and Thomas measured the appearance of Cl2
⫺".
Pseudo-first-order approximation was used to derive this rate
constant. The concentration of solute (关Cl⫺兴) was assumed
to be unchanged during the pulse radiolysis process, i.e.,
Cl2
⫺"lifetime. The change of optical density, the difference
between the optical density at time infinity, and that at any
time t, was plotted as a function of time. The slope of such
lines is the rate of the appearance of Cl2
⫺". A range of k4K3
was reported. Different ionic strength of the solution is con-
sidered to be the cause, since k4is affected by ionic strength.
bWard and Myers 共1965兲,44 k4K3⫽7.6⫻109M⫺2s⫺1.
The rate constant of Cl2
⫺"rise was measured. Both thym-
ine and ethanol were used. Thymine was used as a measur-
able double-bonded component, and ethanol as a measurable
saturated component. If both a double-bonded compound
and a saturated compound are present in the aqueous solu-
tion, chlorine atoms will react specifically with the former,
whereas hydroxyl free radicals will react with both. Oxygen
removes hydrogen atoms, hydrated electrons, and organic
radicals leaving HO"and Cl"the only effective attacking
species. The relative rate constant ratios of HO"and ethanol
or HO"and thymine were determined. G⫺thymine varied with
pH and 关Cl⫺兴. However, the ratio kHO"⫹thymine /kHO"⫹ethanol
remained constant. Their results showed that as pH increased
the Cl"involvement in the reactions decreased in aqueous
solutions containing thymine and ethanol. Chloride concen-
tration and pH of solutions were kept constant in their ex-
periments. The ratio of kHO"⫹thymine /kHO"⫹ethanol was useful in
determining GCl⫺⫹H⫹⫹HO"/Gthymine⫹HO". The plot of
GCl⫺⫹H⫹⫹HO"/Gthymine⫹HO"versus 关H⫹兴•关Cl⫺兴was fitted
with a linear relationship. The slope of such line is
kCl⫺⫹H⫹⫹HO"/kthymine⫹HO"⫽1.9⫾0.3 M⫺1. The k4K3⫽7.6
⫻109M⫺2s⫺1was derived by using kthymine⫹HO"⫽4
⫻109M⫺1s⫺1.45
cWard and Kuo 共1968兲,44 k4K3⫽1.5⫻1010 M⫺2s⫺1.
Ward and Kuo found that k4K3showed a first-order de-
pendence on 关H⫹兴and 关Cl⫺兴. A published relative rate con-
stant was used to obtain k4K3⫽1.5⫻1010 M⫺2s⫺1. How-
ever, the specific relative reaction and its rate constant were
not specified. Since Ward46 used thymine and HO"reaction
previously as the reference reaction, it is assumed that they
used the same relative reaction again in this slightly later
work. By using the same referenced value of the relative
TABLE 4. Rate constant data of k⫺3
k3⫻10⫺9共M⫺1s⫺1兲k⫺3⫻10⫺9共s⫺1兲K3共M⫺1兲Method pH Reference Notes
4.3⫾0.4 6.1⫾0.8 0.70⫾0.13 PR ⬍31973
9a
TABLE 5. Rate constant data of k4K3by direct and competition kinetics
k4K3⫻10⫺10 (M⫺2s⫺1) Method Ratio I共M兲pHReference Notes
1.16–2.16 PR ¯⬍0.15 1–3 196439 a
0.32–1.84 PR ¯1(NaClO4) 0–3 196439 a
0.76
␥
-R k4K3/kthymine⫽1.9 M⫺1⬍0.2 ⬃1–3 196546 b
1.5 PR k4K3/kthymine⫽3.75 M⫺1⬍0.2 0.8–3.4 196844 c
1.5⫾0.12 PR ¯⬍0.1 3 19739d
1.85 or 1.9 PR ¯0.05/0.06 2 197347 e
1.8⫾0.1 FP ¯⬃0.01 2 20036f
753753CRITICAL EVALUATION OF RATE CONSTANTS
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
reaction rate constant, a ratio of kCl⫺⫹H⫹⫹HO"/kthymine⫹HO"
⫽3.75 M⫺1was derived.
dJayson et al. 共1973兲,9k4K3⫽1.5⫻1010 M⫺2s⫺1.
The method of how Jayson et al. obtained k4K3has been
described in the section of k3evaluation. Essentially, the rate
constant of Cl2
⫺"appearance is expressed as a function of
both 关H⫹兴and 关Cl⫺兴.
eOgura and Hamill 共1973兲,47 k4K3⫽1.85 or 1.9
⫻1010 M⫺2s⫺1.
Ogura and Hamill used the same strategy as Anbar and
Thomas.39 The change of optical density was plotted against
time. The slope of such lines corresponds to the rate constant
of Cl2
⫺"appearance in either H2OorD
2O.
fYu and Barker 共2003兲,6k4K3⫽(1.8⫾0.1)
⫻1010 M⫺2s⫺1.
The rise and decay of Cl2
⫺"was analyzed. The global rate
constant k4K3关H⫹兴was derived using steady state approxi-
mation. More details are seen in Sec. 4.1.1.
Preferred Values
k4K3⫽(1.7⫾0.3)⫻1010 M⫺2s⫺1.
Comments on Preferred Values
The preferred value is the unweighted average of the re-
ported global rate constants except the result by Ward and
Myers,44 because it is suspected that there is a typographical
error in their reported value.
4.5.
K
4and
k
4, ClOHÀ"¿H¿\Cl"¿H2O
Notes 共Table 6兲
aJayson et al. 共1973兲,9k4⫽(2.1⫾0.7)⫻1010 M⫺1s⫺1.
Jayson et al. defined a standard absorbance of Cl2
⫺"at
关Cl⫺兴⫽0.01 M and 关H⫹兴⫽0.01 M. Then various absorben-
cies of Cl2
⫺"at different 关Cl⫺兴and 关H⫹兴conditions were
compared with the standard absorbance. The ratio was ex-
pressed as a function of both K3K4and K5, which were
solved for their most probable values. The preferred solu-
tions of K3K4and K5are 1.1⫻107and 1.9⫻105M⫺1from
a range of 7.5⫻106M⫺1–2.5⫻107M⫺1, and 1.4
⫻105–2.8⫻105, respectively. Then K3was determined di-
rectly by plotting the difference of optical density 共O.D.兲
versus aCl⫺following this relationship:
1
O.D.⫽1
5K3•aCl•关HO"兴o•Cl2
⫺⫹1
5关HO"兴o•Cl2
⫺
where the factor of 5 comes from the optical path length, and
关HO"兴ois the hydroxyl radical concentration introduced by
reaction of the hydrated electron with nitrous oxide with a
yield G⫽2.75. The value of K4could then be derived as
1.6⫻107M⫺1. The derivation of k4was not specified, how-
ever, since it has almost the identical numerical value as that
of k5, i.e., 2.1⫻1010 M⫺1s⫺1, it is suspected that it was
obtained by following the same diffusion controlled calcula-
tion. It is unclear why k4has a 30% error, whereas k5does
not.
bYu and Barker 共2003兲,6k4⫽(2.6⫾0.6)⫻1010 M⫺1s⫺1.
The k4K3⫽1.8⫻1010 M⫺2s⫺1was directly determined
共seen in Sec. 4.4.1兲, and k4⫽2.6⫻1010 M⫺1s⫺1was derived
using K3⫽0.70⫾0.13 M⫺1by Jayson et al.9The K4was
thereby (7.2⫾1.6)⫻106based on k⫺4关H2O兴⫽(2.0⫾0.2)
⫻105s⫺1.
Preferred Values
k4⫽(2.4⫾0.4)⫻1010 M⫺1s⫺1.
K4⫽(7.4⫾2.8)⫻106.
Comments on Preferred Values
The preferred k4is the unweighted average of the two
reported values. The difference in K4is caused by k4, since
the same K3was used to derive k4from k4K3. The preferred
value of K4is determined once k⫺4is evaluated.
4.6.
k
À4†H2O‡,Cl"¿H2O\ClOHÀ"¿H¿
The k⫺4is commonly reported as k⫺4关H2O兴in the litera-
ture. In order to avoid confusion, we compare k⫺4关H2O兴
here. Essentially, we should compare the ratio of
k⫺4关H2O兴/K5instead of k⫺4关H2O兴, because the latter is af-
fected by the K5value taken by different researchers. Al-
though Jayson et al.’s9K5has been widely used in the deri-
vation of other rate constants, it is not necessarily the most
accurate measurement. The uncertainty of K5reported in the
original paper is quite high, i.e., (1.4– 2.8)⫻105M⫺1. More
discussion on K5is detailed in the following section. When
justification is necessary, a 10% error is arbitrarily assigned
to K5. For convenience of comparison, the K5used to cal-
culate k⫺4关H2O兴/K5is listed in a separate column.
Notes 共Table 7兲
aJayson et al. 共1973兲,9k⫺4关H2O兴⫽7.2⫻104s⫺1.
The description of how Jayson et al. obtained k4and K4is
in Sec. 4.5. The value of k⫺4was derived based on k4and
K4. Since the equilibrium constant K4was in a range
(0.9– 4.4)⫻107and k4⫽(2.1⫾0.7)⫻1010 M⫺1s⫺1, the
k⫺4关H2O兴obtained falls in a range: (0.3– 3.0)
⫻103M⫺1s⫺1.
bKla
¨ning and Wolff 共1985兲,48 k⫺4关H2O兴⫽1.6⫻105s⫺1.
As noted in their paper, K5⫽1.9⫻105M⫺1was used. It is
postulated that k⫺4关H2O兴/K5was the quantity that was mea-
sured in their experiment. However, the details of analytical
method were not described.
cWine et al. 共1988兲,k⫺4关H2O兴⫽1⫻105s⫺1.
The detail of this result is not available. This is a confer-
ence presentation.
TABLE 6. Data of K4and k4
k⫺4关H2O兴⫻10⫺5共s⫺1兲k4⫻10⫺10 共M⫺1s⫺1兲K4(⫻10⫺6) Method pH Reference Notes
0.17–1.7 2.1⫾0.7 9– 44 PR ⬍3 19739a
2.0⫾0.2 2.6⫾0.6 7.2⫾1.6 FP 2 20036b
754754 XIAO-YING YU
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
dMcElroy 共1990兲,49 k⫺4关H2O兴⫽(2.5⫾0.2)⫻105s⫺1.
Although a different form of k⫺4关H2O兴expression was
used in McElroy’s analysis, the essence of the mathematical
relationship is the same as the above works. With the mea-
sured k⫺4关H2O兴⫽(1.3⫾0.1)⫻103s⫺1from the same work
and Jayson et al.’s K5, the most reliable estimate of
k⫺4关H2O兴was (2.5⫾0.2)⫻105s⫺1at 关Cl⫺兴⫽10⫺3M. In
order to make the error propagation of k⫺4关H2O兴/K5mean-
ingful, it is assumed that the error of K5is 10%. The justified
ratio of k⫺4关H2O兴/K5is therefore 1.3⫾0.2 M s⫺1from
McElroy’s original data.
eJacobi et al. 共1997兲,50 k⫺4关H2O兴⫽(2.3⫾0.6)
⫻105s⫺1.
The ratio of k⫺4关H2O兴/K5⫽1.2⫾0.3 M s⫺1was obtained
from the linear least squares fit of the observed first-order
decay rate constant of Cl2
⫺"versus 1/关Cl⫺兴. By taking Jayson
et al.’s equilibrium constant,9K5⫽1.9⫻105M⫺1,
k⫺4关H2O兴was derived.
fBuxton et al. 共1998兲,12 k⫺4关H2O兴⫽(2.5⫾0.3)
⫻105s⫺1.
Buxton et al. obtained k⫺4关H2O兴/k⫺5in their analysis.
With their k5⫽(8.5⫾0.7)⫻109M⫺1s⫺1and K5⫽k5/k⫺5,
k⫺4关H2O兴/K5was calculated with propagated uncertainty.
Using K5⫽1.4⫻105M⫺1determined in the same study,
k⫺4关H2O兴was derived.
gYu and Barker 共2003兲,6k⫺4关H2O兴⫽(2.0⫾0.2)
⫻105s⫺1.
The rise and decay of Cl2
⫺"was analyzed and the rise and
decay rate constants of Cl2
⫺"were obtained. The
k⫺4关H2O兴/K5was extracted by linear least squares fitting of
the intercept data from the linear least squares fits of the
decay rate constant of Cl2
⫺"as a function of 关H2O2兴. This is
essentially the same approach as Jacobi et al.50 With the rec-
ommended K5⫽(1.4⫾0.2)⫻105M⫺1共discussion in Sec.
4.7兲,k⫺4关H2O兴was derived.
hYu et al. 共2004兲,8k⫺4关H2O兴⫽(1.6⫾0.2)⫻105s⫺1.
Similar to Yu and Barker’s previous work, the
k⫺4关H2O兴/K5was extracted by linear least squares fitting of
the intercept data from the linear least squares fits of the
decay rate constant of Cl2
⫺"as a function of 关S2O8
2⫺兴. With
K5⫽(1.4⫾0.2)⫻105M⫺1,k⫺4关H2O兴was derived.
Preferred Values
k⫺4关H2O兴/K5⫽1.3⫾0.3 Ms⫺1.
k⫺4关H2O兴⫽(1.8⫾0.6)⫻105s⫺1.
K4⫽(7.4⫾2.8)⫻106.
Comments on Preferred Values
The preferred ratio k⫺4关H2O兴/K5was evaluated first by
using the unweighted average of the available values. The
preferred k4关H2O兴was given based upon the recommended
value of K5⫽(1.4⫾0.2)⫻105M⫺1. The preferred value of
K4was derived based on the preferred k4and k⫺4关H2O兴
using K4⫽k4/k⫺4.
4.7.
k
5,
k
À5, and
K
5,Cl"¿ClÀ^Cl2
À"
4.7.1. Forward Rate Constant
k
5
The value of k5has been determined in several previous
studies.9,12,48,51–53
Notes 共Table 8兲
aJayson et al. 共1973兲,9k5⫽2.1⫻1010 M⫺1s⫺1and 4.1
⫻109M⫺1s⫺1.
The k5⫽2.1⫻1010 M⫺1s⫺1was not determined experi-
mentally; instead it was calculated by assuming diffusion
control. In fact, they reported a single measured pseudo-first-
TABLE 7. Rate constant data of k⫺4关H2O兴
k⫺4关H2O兴⫻10⫺5(s⫺1)k⫺4关H2O兴/K5共Ms
⫺1兲K5⫻10⫺5(M⫺1)Method pH Reference Notes
0.17–1.7 1.4–2.8 PR ⬍3 19739a
1.6 0.84 1.9 N.A. ⬎11 198548 b
1.0 1.9 FP 1988 c
2.5⫾0.2 1.3⫾0.2 1.9 PR 2–4 199049 d
2.3⫾0.6 1.2⫾0.3 1.9 FP 4 199750 e
2.5⫾0.3 1.8⫾0.6 1.4⫾0.1 PR 5–6 199812 f
2.0⫾0.2 1.4⫾0.1 1.4⫾0.2 FP 2 20036g
1.6⫾0.2 1.1⫾0.1 1.4⫾0.2 FP 2 20048h
TABLE 8. Rate constant data of k5by direct measurements
k5⫻10⫺9共M⫺1s⫺1兲Method Photolysis
共nm兲
Probe
共nm兲pH Reference Notes
4.1 PR N.A. 340 0 19739a
21 estimated — 340 0 19739a
6.5⫾0.9 LFP 308 360 10.0 198548 b
8.0⫾0.8 LFP 248 340 ⬃3.5 198551 c
8 LFP N.A. 340 ⬍5.5 198652 d
19.2 LFP 193 340 N.A. 199353 e
8.5⫾0.7 LFP 193 340 N.A. 199812 f
7.8⫾0.8 ave. — — — 20036g
755755CRITICAL EVALUATION OF RATE CONSTANTS
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
order rate constant of 4.1⫻106s⫺1when the concentrations
of hydrogen ions and chloride ions were 1 and 10⫺3M,
respectively.9The corresponding value for k5⫽4.1
⫻109M⫺1s⫺1is only ⬃20% of the diffusion limit. No ex-
planation was given why the assumed diffusion controlled
rate constant was preferred to their experimental value.
bKla
¨ning and Wolff 共1985兲,48 k5⫽6.5⫻109M⫺1s⫺1.
The k5was directly measured by generating Cl2
⫺"by laser
flash photolysis of ClO⫺and Cl⫺under alkaline conditions
at 308 nm, and monitoring the optical density of Cl2
⫺"at 360
nm. Under their conditions, the formation of Cl2
⫺"is in com-
petition with several other reactions. From a least squares
analysis of their data, k5was determined with no reported
uncertainty.
cNagaranjan and Fessenden 共1985兲,51 k5⫽(8.0⫾0.8)
⫻109M⫺1s⫺1.
Nagaranjan and Fessenden51 generated Cl2
⫺"by laser flash
photolysis of aqueous Cl⫺and S2O8
2⫺at 248 nm and then
used a subsequent photolysis pulse at 355 nm or 337 nm to
photodissociate Cl2
⫺". The dissociation of the Cl2
⫺"共moni-
tored at 340 nm兲results in a ‘‘bleach’’ and a subsequent
exponential recovery back to the original absorption level.
The plot of the recovery rate of Cl2
⫺"versus 关Cl⫺兴was ana-
lyzed by least squares analysis to determine k5⫽(8.0⫾0.8)
⫻109M⫺1s⫺1. An estimated 10% error was reported.
dWagner et al. 共1986兲,52 k5⫽8.0⫻109M⫺1s⫺1.
Wagner et al.52 also used a delayed second laser to photo-
lyze Cl2
⫺"and monitor its relaxation, but they gave no ex-
perimental details. Their result agrees exactly with Nagaran-
jan and Fessenden,51 but no associated uncertainty was
reported.
eIwata and Yamanaka 共1993兲,53 k5⫽1.92
⫻1010 M⫺1s⫺1.
Iwata and Yamanaka53 used laser flash photolysis of Cl⫺
solution at 193 nm to generate Cl2
⫺". The absorption signal
obtained at 340 nm was the sum of contributions from both
Cl"and Cl2
⫺". Since the time constant of Cl"is much faster
than the detection limit in their experiments, they assumed
that the rate of production of Cl"was proportional to the
time-dependent laser fluence during the laser pulse. Under
these assumptions they fitted the experimental data to obtain
the quantum yield of Cl", the formation rate of Cl2
⫺", and the
molar extinction coefficients of Cl"and Cl2
⫺". They found
k5⫽1.92⫻1010 M⫺1s⫺1, but did not report uncertainties.53
fBuxton et al. 共1998兲,12 k5⫽(8.5⫾0.7)⫻109M⫺1s⫺1.
Buxton et al.12 determined k5directly by using laser flash
photolysis of Cl⫺at 193 nm and monitoring the growth of
Cl2
⫺"at 340 nm. Since there were no competing reactions,
the rate of Cl2
⫺"growth followed pseudo-first-order kinetics
and gave k5⫽(8.5⫾0.7)⫻109M⫺1s⫺1.12 The uncertainty
reported is most likely the statistical precision obtained in the
least squares fits. Note that Iwata et al.53 and Buxton et al.12
employed virtually identical methods, but obtained results
that differ by a factor of two. Buxton et al.’s measurement is
in good agreement with the others described above.
gYu and Barker 共2003兲,6k5⫽(7.8⫾0.8)⫻109M⫺1s⫺1.
This is an unweighted average of experimental values
from notes b, c, d, and f.
Preferred Values
k5⫽(7.8⫾0.8)⫻109M⫺1s⫺1.
Comments on Preferred Values
The direct laser flash photolysis of Cl⫺is probably the
best way to determine k5. First, the chemical system does
not contain species that compete with reaction 共5兲. Second
the pseudo-first-order fit of the observed formation rate con-
stant requires few parameters and therefore there is less po-
tential correlation among fitted parameters. On the basis of
these considerations, we recommend the unweighted average
of the direct determinations by Kla
¨ning and Wolff,48 Nagar-
anjan and Fessenden,51 Wagner et al.,52 and Buxton et al.:12
k5⫽(7.8⫾0.8)⫻109M⫺1s⫺1.
4.7.2. Reverse Rate Constant
k
À5
There are only a few available results of k⫺5.
Notes 共Table 9兲
aJayson et al. 共1973兲,9k⫺5⫽(1.1⫾0.4)⫻105s⫺1.
The earliest value reported for k⫺5was by Jayson et al.,9
who obtained k⫺5indirectly from their assumed diffusion
controlled value for k5and their experimentally determined
K5. Their method for determining K5is described below.
The actual experimental uncertainty in their value of K5
ranges from 1.4⫻105to 2.8⫻105M⫺1, which seriously af-
fects the accuracy of k⫺5.
bZansokhova et al. 共1977兲,54 k⫺5⫽7.6⫻105s⫺1.
In a pulse radiolysis experiment, Zansokhova et al.54 re-
ported k⫺5⫽7.6⫻105M⫺1and 2k6⫽1.7⫻1010 M⫺1s⫺1as
the best combination of the modeled and experimental rela-
tionship between 关Cl2
⫺"兴max and dose per pulse. The accuracy
of k⫺5is correlated with that of 2k6. Zansokhova et al. ob-
tained a value for 2k6that is substantially larger than what
was found in recent measurements.6,8,49,55,56 It is possible
that the high result is due to correlations in the numerical
analysis of their data. Therefore, it is likely that the accuracy
of k⫺5is affected by the high value for 2k6.
cBuxton et al. 共1998兲,12 k⫺5⫽(6.0⫾0.5)⫻104s⫺1.
Buxton et al.12 determined k⫺5by examining the decay of
Cl2
⫺"by pulse radiolysis of an aqueous solution containing
1⫻10⫺3MNa
2S2O8, chloride ions (关Cl⫺兴⭓1⫻10⫺3M)
and t-BuOH. Chlorine atom and Cl2
⫺"readily react with the
hydroxyl group of t-BuOH. These reactions compete with
the reactions of Cl"and Cl2
⫺"with H2O. Buxton et al. found
that the observed pseudo-first-order decay rate constant of
Cl2
⫺"departed from linearity as the concentration of t-BuOH
increased due to the finite rate of reaction 共5兲in competition
TABLE 9. Rate constant data of k⫺5by direct measurements
k⫺5共s⫺1兲Method pH Reference Notes
(1.1⫾0.4)⫻105Indirect 0 19739a
7.6⫻105sim. 7 197754 b
(6.0⫾0.5)⫻104PR 5–6 199812 c
(5.2⫾0.3)⫻104LFP 2 20036d
(5.7⫾0.4)⫻104ave. — 20036d
756756 XIAO-YING YU
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
with the reactions with t-BuOH.12 By using their measured
value of k5in a least-squares procedure, they determined
k⫺5⫽(6.0⫾0.5)⫻104s⫺1.
dYu and Barker 共2003兲,6k⫺5⫽(5.2⫾0.3)⫻104s⫺1.
The pseudo-first-order decay rate constant of Cl2
⫺"was
analyzed as a nonlinear function of 关H2O2兴in the range of
0–0.01 M. The result obtained, k⫺5⫽(5.2⫾0.3)⫻104s⫺1,
is not sensitive to the value of k5. The analysis used is vir-
tually the same as that by Buxton et al., although the refer-
ence reactions were different.
Preferred Values
k⫺5⫽(5.7⫾0.4)⫻104s⫺1.
Comments on Preferred Values
Because the errors from the results of Buxton et al.12 and
Yu and Barker6are likely to be of the same magnitude, we
conclude that the best unbiased recommendation of k⫺5is
the unweighted average of Buxton et al.12 and Yu and
Barker.6
4.7.3. Equilibrium Constant
K
5
Notes 共Table 10兲
aJayson et al. 共1973兲,9K5⫽(1.1⫾0.4)⫻105M⫺1.
Jayson et al.9assumed that the optical absorption due to
Cl2
⫺"had reached its maximum possible value when
关NaCl兴⫽0.01 M and 关HClO4兴⫽0.01 M. They then mea-
sured the absorption due to Cl2
⫺"under various other condi-
tions of 关NaCl兴and 关HClO4兴and expressed the results as
functions of equilibrium constants K3,K4, and K5. From
among a range of algebraic solutions that described their
data, they reported K3K4⫽1.1⫻107M⫺1and K5⫽1.9
⫻105M⫺1.9When all of the algebraic solutions are consid-
ered, K5falls in a rather wide range, i.e., 1.4⫻105–2.8
⫻105M⫺1. However, Jayson et al.9did not explain how
they arrived at their preferred value.
bWu et al. 共1980兲,10 K5⫽17.7 M⫺1.
The temperature dependence of Cl2
⫺"kinetics was studied.
The Cl2
⫺"decay kinetics was analyzed by analogy with the
I2
⫺"mechanism. Only second-order decay processes were
considered in the Cl2
⫺"disappearance. The global second-
order decay constant was found to vary with R
⫽1/K5关Cl⫺兴, a parameter defined by them. By varying
关Cl⫺兴,Rapproaches three categories: close to 0, 0, and
much larger than 1. The values of k6,k7, and that of Cl"and
Cl"recombination reactions were obtained, respectively. The
problem of this analysis is that only second-order decay was
considered, which is inappropriate for the lower chloride
conditions used in their experiments. A mixed first- and
second-order decay mechanism is more suitable to describe
Cl2
⫺"under low chloride concentration as supported by many
recent findings.6,49,56
cAdams et al. 共1995兲,11 K5⫽(4.7⫾0.4)⫻103M⫺1.
This experiment assumed that Cl2
⫺"was the only absorb-
ing species in a system containing S2O8
2⫺,Cl
⫺, and
(CH3)3COH by pulse radiolysis. The K5was obtained by
fitting the variance of Cl2
⫺"absorbance as a function of
1/关Cl⫺兴. This approach may oversimplify the complicated
Cl2
⫺"/Cl"mechanism by assuming that the maximum absor-
bance is when all Cl"are present as Cl2
⫺".
dBuxton et al. 共1998兲,12 K5⫽(1.4⫾0.1)⫻105M⫺1.
Buxton et al.12 directly determined k5and k⫺5共discus-
sions seen in Secs. 4.7.1 and 4.7.2兲. By using their experi-
mental values of k5and k⫺5,K5was derived.
eYu and Barker 共2003兲,6K5⫽(1.4⫾0.2)⫻105M⫺1.
The equilibrium constant was obtained from the ratio of
forward and reverse rate constants. The recommended values
of k5and k⫺5are (7.8⫾0.8)⫻109M⫺1s⫺1and (5.7⫾0.4)
⫻104s⫺1, respectively. The ratio of these values gives K5
⫽(1.4⫾0.2)⫻105M⫺1, where the uncertainty was obtained
by error propagation.
Preferred Values
K5⫽(1.4⫾0.2)⫻105M⫺1.
Comments on Preferred Values
The result of Yu and Barker6result is in good agreement
with that of Buxton et al.,12 both of which agree with the
result of Jayson et al.9The unweighted average of results
from Buxton et al.12 and Yu and Barker6is recommended as
the best unbiased estimate of K5. Although this numerical
value is not much different from that of Jayson et al.,9the
uncertainty of K5is much improved. With the recommended
K5and the standard reduction potential E(Cl"/Cl⫺)
⫽2.41 V,57 the standard reduction potential E(Cl2
⫺"/2Cl⫺)
⫽2.11 V is obtained, which differs only slightly from the
value obtained using the equilibrium constant from Jayson
et al.9(E(Cl2
⫺"/2Cl⫺)⫽2.09 V) as expected.
4.8.
k
6,Cl
2
À"¿Cl2
À"\2ClÀ¿Cl2
Since various extinction coefficients of Cl2
⫺"were taken
due to differences in monitor wavelength and arbitrary deci-
sions, more attention should be directed to the ratio 2k6/
instead of the derived value k6itself. The 2k6/falls into a
fair range, i.e., from 1.1⫻104to 1.4⫻106cms⫺1. Most of
the previous studies of Cl2
⫺"decay consider it primarily a
second-order process. When a more complicated kinetics
scheme was applied, it is noted in the comment.
Notes 共Table 11兲
aLangmuir and Hayon 共1967兲,58 k6⫽(0.75⫾0.05)
⫻1010 M⫺1s⫺1(pH⫽6) and (0.69⫾0.1)⫻1010 M⫺1s⫺1
(pH⫽1.1).
The k6was obtained by flash photolysis of NaCl, HgCl2,
and HgCl4
2⫺, respectively. The authors considered their k6
values the same within experimental error. In Table 11, the
unweighted average of the reported values from their work is
listed.
TABLE 10. Equilibrium constant data of K5
K5共M⫺1兲Method pH Reference Notes
(1.1⫾0.4)⫻105PR 0 19739a
17.7 FP N.A. 198010 b
(4.7⫾0.4)⫻103PR neutral 199511 c
(1.4⫾0.1)⫻105PR 5–6 199812 d
(1.4⫾0.2)⫻105ave. — 20036e
757757CRITICAL EVALUATION OF RATE CONSTANTS
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
bWard and Kuo 共1968兲,44 k6⫽(0.7⫾0.15)
⫻1010 M⫺1s⫺1.
No pH dependence of k6was found between pH 0.9 and
3.2.
cPatterson et al. 共1972兲,59 k6⫽(0.6⫾0.15)
⫻1010 M⫺1s⫺1.
In the presence of pyrimidine, the Cl2
⫺"self-reaction rate
was determined. It was suggested that Cl2
⫺"oxidized the py-
rimidine molecule.
dThornton and Laurence 共1973兲,60 k6⫽0.52
⫻1010 M⫺1s⫺1.
The Cl2
⫺was formed by complex FeCl2⫹dissociation and
the subsequent reaction between one of the dissociation
products Cl"and Cl⫺.
eZhestkova and Pikaev 共1974兲,61 k6⫽(0.75⫾0.05)
⫻1010 M⫺1s⫺1.
This value was obtained at high ionic strength, i.e.,
关Cl⫺兴⬎10 M. Because when 关Cl⫺兴⬍1 M, the signal to
noise ratio was high and the yield of Cl2
⫺"was low.
fWoods et al. 共1975兲,62 k6⫽(2.7⫾0.5)⫻1010 M⫺1s⫺1.
The ratio 2k6/was found to vary very little over the
range of concentrations studied, i.e., 1.5 M⬍关NaCl兴
⬍14 M.
gBroszkiewicz 共1976兲,63 k6⫽(0.65⫾0.25)
⫻1010 M⫺1s⫺1.
Only second-order decay of Cl2
⫺"was considered.
hZansokhova et al. 共1977兲,54 k6⫽0.85⫻1010 M⫺1s⫺1.
Both k6⫽0.85⫻1010 M⫺1s⫺1and k⫺5⫽7.6
⫻105M⫺1s⫺1were obtained by computer calculated de-
pendence of 关Cl2
⫺"兴max on dose per pulse with the best con-
vergence.
iWu et al. 共1980兲,10 k6⫽3.85⫻109M⫺1s⫺1.
The second-order component of Cl2
⫺"was considered as a
function of 关Cl⫺兴.
jNavaratnam et al. 共1980兲,64 k6⫽(2.0⫾0.2)
⫻109M⫺1s⫺1,
The rate constants of reactions 共6兲and 共11兲were simulta-
neously determined from the theoretical log–linear plots cal-
culated for various combinations of rate constants of reac-
tions 共6兲and 共11兲.
kGogolev et al. 共1980兲,65 k6⫽(1.0– 1.85)
⫻109M⫺1s⫺1.
A range of k6was obtained under concentrated HCl con-
ditions. The observed second-order rate constant was consid-
ered the sum of rate constants of reactions 共6兲and 共11兲.
lWagner et al. 共1986兲,52 k6⫽1.15⫻109M⫺1s⫺1共calcu-
lated兲and k6⫽(0.7⫾0.35)⫻108M⫺1s⫺1共simulated兲.Two
results were reported. One was calculated assuming diffusion
control between two identical ions 关Z⫽⫺1, D⫽0.7
⫻10⫺5cm⫺2s⫺1共estimated兲and a distance of closest ap-
proach a⫽3.5⫻1010 m], the other was obtained by simula-
tion of a mechanism containing 30 reactions, some of which
are listed in the discussion of k8关H2O兴below.
mSlama-Schwok and Rabani 共1986兲,66 k6⫽0.6
⫻1010 M⫺1s⫺1.
The k6⫽0.6⫻1010 M⫺1s⫺1was obtained by the Cl2
⫺"de-
cay generated by the complex 关Ir(C3,N⬘-Hbpy)(bpy)2)]4⫹
TABLE 11. Rate constant data of k6
k6⫻10⫺9
共M⫺1s⫺1兲I共M兲pH(2k6/)⫻10⫺5
(cms⫺1)
共M⫺1cm⫺1兲
共nm兲Method Reference Notes
7.05⫾0.6 0.5 1.1–6.0 11.3⫾1.0 12 500 360 FP 196758 a
7⫾1.5 N.A. 0.9–3.2 7 10 000 360 PR 196844 b
6⫾1.5 0.1 1.9 N.A. N.A. 340 PR 197259 c
5.2 0.2 0.3–1 8.4 12 500 340 FP 197360 d
7.5⫾0.5 ⬎10 ⬃7 12.1⫾0.8 12 400 340 PR 197461 e
2.7⫾0.5 1.5–14 7 6.2 8700 340 PR 197562 f
6.5⫾2.5 N.A. N.A. 10.5⫾4.1 12 400 340 PR 197663 g
8.5 N.A. N.A. 13.7 12 400 340 PR 197754 h
3.85 ⭐2 N.A. 6.6 12 000 340 PR 198010 i
2.0⫾0.2 0.2 ⬃2 4.54⫾0.45 8800 340 PR 198064 j
1.0–1.85 1–12 ⬍0 2.5–4.6 8000 360 PR 198465 k
1.15 — — — — — calc. 198652 l
0.07⫾0.035 — — 0.11⫾0.05 12 500 340 sim. 198652 l
6⫾2 N.A. N.A. 9.6⫾3.2 12 500 340 FP 198666 m
2.25⫾0.1 1 3 5.56⫾0.25 8100 340 PR 198767 n
5.5⫾3.5 0.25 5.5 8.8⫾5.6 12 500 340 FP 198168 o
1.55⫾0.05 0.13 2.2 3.65⫾0.12 8800 340 PR 199049 p
0.7⫾0.1 0 N.A. 1.6 8800 340 LFP 199049 p
1.3 0 N.A. 2.96 8800 340 LFP 199055 q
0.69⫾0.005 0 N.A. 1.57⫾0.01 8800 340 LFP 199769 r
1.8⫾0.1 0 4 4.24⫾0.24 8300 325 LFP 199956 s
0.61 0 2.05–3.0 1.27 9600 364 LFP 200070 t
0.65⫾0.14 0 N.A. 350 LFP 200271 u
0.72⫾0.08 0 2 2.06⫾0.27 7000 340 LFP 20036,2004
8v
2.0⫾0.3 N.A. N.A. 4.55⫾0.76 8800 340 PR 200372 w
758758 XIAO-YING YU
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
reacting with Cl⫺identified to be a mixed first- and second-
order process. However, the above result was obtained ignor-
ing the first-order component.
nLierse et al. 共1987兲,67 k6⫽(2.25⫾0.1)⫻109M⫺1s⫺1.
The k6⫽(2.25⫾0.1)⫻109M⫺1s⫺1was obtained by
pulse radiolysis of UO2(ClO2)2containing NaCl at pH3.
The reactions between Cl2
⫺"and UO2
⫹and Cl2
⫺"and H were
considered insignificant compared to the Cl2
⫺"self reaction.
oHynes and Wine 共1988兲,68 k6⫽(5.5⫾2)
⫻109M⫺1s⫺1.
The k6⫽(5.5⫾2)⫻109M⫺1s⫺1was solved on the basis
of a pure second-order kinetics.
pMcElroy 共1990兲,49 k6⫽(0.7⫾0.1)⫻109M⫺1s⫺1(I
⫽0 M) and (1.55⫾0.05)⫻109M⫺1s⫺1(I⫽0.13 M).
McElroy reported two values of k6. One is the average
with no ionic strength justification, k6⫽(1.55⫾0.05)
⫻109M⫺1s⫺1. The other is k6⫽(0.7⫾0.1)⫻109M⫺1s⫺1
by extrapolating data to infinite dilution.
qHuie and Clifton 共1990兲,55 k6⫽1.3⫻109M⫺1s⫺1.
This result is an average of a set of results on k6corrected
to zero ionic strength.
rBao 共1997兲,69 k6⫽(0.69⫾0.005)⫻109M⫺1s⫺1.
The ionic strength dependence of k6was investigated by
adding NaClO4to vary the ionic strength of the solution.
This result was justified to zero ionic strength.
sJacobi et al. 共1991兲,56 k6⫽(1.8⫾0.1)⫻109M⫺1s⫺1.
The details of this measurement were not available except
that k6was corrected to zero ionic strength. The 2k6/is
derived based upon the reported value and the molar extinc-
tion coefficient used in the same work.
tAlegre et al. 共2000兲,70 k6⫽0.61⫻109M⫺1s⫺1.
The Debye–Hu
¨ckle relationship was observed up to 0.5 M
ionic strength.
uChristian and Chovelon 共2002兲,71 k6⫽(0.65⫾0.14)
⫻109M⫺1s⫺1.
This second-order rate constant is obtained under condi-
tions favoring second-order decay of Cl2
⫺", and it is adjusted
to zero ionic strength. The uncertainty is calculated within
⫾2
. The extinction coefficient of Cl2
⫺"used to derive k6is
not mentioned.
vYu and Barker 共2003兲6and Yu et al. 共2004兲,8k6⫽(0.72
⫾0.08)⫻109M⫺1s⫺1.
The 2k6/was obtained by mixed first- and second-order
analysis of the decay trace of Cl2
⫺"in the photolysis of acidic
solutions containing Cl⫺and H2O26and Cl⫺and K2S2O8,8
respectively. The ionic strength of all experiments was ap-
proximately 0.01 M or lower. Under such conditions, k6
⫽(0.9⫾0.05)⫻109M⫺1s⫺1was obtained using Cl2
⫺,364 nm
⫽7000 M⫺1cm⫺1.8When adjusted by infinite dilution, k6
⫽(0.72⫾0.08)⫻109M⫺1s⫺1was obtained. The tempera-
ture dependence of k6in the range of 6.8–51.6 °C is re-
ported.
wPoskrevbyshev et al. 共2003兲,72 k6⫽(2.0⫾0.3)
⫻109M⫺1s⫺1.
The Cl2
⫺"was generated by pulse radiolysis of solutions
containing Cl⫺and HNO3. The Cl2
⫺"follows a second-order
rate law with increased 关Cl⫺兴.
Preferred Values
2k6/⫽(6.5⫾2.5)⫻105cms⫺1(340 nm).
2k6/⫽(5.0⫾3.7)⫻105cms⫺1(⬃360 nm).
k6⫽(3.5⫾2.7)⫻109M⫺1s⫺1.
Comments on Preferred Values
The preferred values of 2k6/are categorized in two
groups considering the probe wavelength of Cl2
⫺", i.e., 340
and ⬃360 nm. They are both unweighted average of reported
results. The unweighted average of k6is obtained from all
reported values except the very low value from Wagner
et al., because it is an outlier compared to other reports. Val-
ues are taken as reported with no further ionic strength cor-
rection.
4.9.
k
7,Cl"¿Cl2
À"\ClÀ¿Cl2
The rate constant data of k7is in Table 12.
Notes 共Table 12兲
aWu et al. 共1980兲,10 k7⫽0.625⫻109M⫺1s⫺1.
Wu et al. studied the second-order dependence of Cl2
⫺"as
a function of 关Cl⫺兴. Detailed description of this analysis is
in Sec. 4.7.3.
bYu and Barker 共2004兲,8k7⫽(2.1⫾0.05)
⫻109M⫺1s⫺1.
The second-order decay rate constant of Cl2
⫺"was found to
depend on 关Cl⫺兴. The 2k6/and 4k7/were obtained from
the linear least squares fit of the Cl2
⫺"second-order decay
rate constant as a function of 1/关Cl⫺兴.8
Preferred Values
k7⫽(1.4⫾1.0)⫻109M⫺1s⫺1.
Comments on Preferred Values
The preferred value is the unweighted average of the two
reported values.
4.10.
k
8†H2O‡,Cl
2
À"¿H2O\ClOHÀ"¿H¿¿ClÀ
Similar to k⫺4, most of the literature reported k8关H2O兴.
The rate constant data of k8关H2O兴is in Table 13.
Notes 共Table 13兲
aWagner et al. 共1986兲,52 k8关H2O兴⫽7.2⫻103s⫺1.
TABLE 12. Rate constant data of k7
k7⫻10⫺9
共M⫺1s⫺1兲pH(2k7/)⫻10⫺5
共cm s⫺1兲
共nm兲
共M⫺1cm⫺1兲Method Reference Notes
0.625 N.A. 1.04 340 12 000 PR 198010 a
2.1⫾0.05 2 2.54⫾0.16 364 7000 LFP 20036b
759759CRITICAL EVALUATION OF RATE CONSTANTS
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
The experimental technique is to measure the change of
conductivity caused by the change of charge of certain radi-
cal products after photolysis of chloride ions in acidic solu-
tions. A system containing the following reactions:
Cl"⫹Cl⫺↔Cl2
⫺",共10兲
e⫺⫹H⫹→H",共11兲
H"⫹H"→H2,共12兲
e⫺⫹Cl2
⫺"→2Cl⫺,共13兲
HO"⫹H"→H2O, 共14兲
Cl2
⫺"⫹H"→H⫹⫹2Cl⫺,共15兲
HO"⫹HO"→H2O2,共16兲
Cl2
⫺"⫹Cl2
⫺"→Cl2⫹2Cl⫺,共17兲
Cl2⫹H2O↔HOCl⫹H⫹⫹Cl⫺,共18兲
Cl2
⫺"⫹H2O↔HO"⫹H⫹⫹2Cl⫺,共19兲
Cl2
⫺"⫹HO"→HOCl⫹Cl⫺,共20兲
was used to simulate experimental data. The k8关H2O兴was
obtained from the best set of rate constants fitting the experi-
mental results, i.e., k15 ,k17 ,k19 ,k20 ,k22 ,k23 . The system is
complex. The whole system was integrated using a fourth-
order Runge–Kutta method.
bMcElroy 共1990兲,49 k8关H2O兴⫽(1.3⫾0.1)⫻103s⫺1.
McElroy considered the following reactions for the
pseudo-first-order decay of Cl2
⫺".
Cl2
⫺"↔Cl"⫹Cl⫺,共21兲
Cl"⫹H2O↔H⫹⫹ClOH⫺",共22兲
ClOH⫺"↔HO"⫹Cl⫺,共23兲
and the overall process was described by reaction 共24兲
Cl2
⫺"⫹H2O↔HO"⫹H⫹⫹2Cl⫺.共24兲
The k8关H2O兴⫽(1.3⫾0.1)⫻103s⫺1was determined as a
lower limit of the observed decay rate constant of Cl2
⫺"when
关Cl⫺兴⬎1⫻10⫺2M, because kobs increases markedly under
conditions of 关Cl⫺兴⬍1⫻10⫺3M. Essentially, the analytical
strategy is the same as in the recent work by Yu and Barker,6
albeit the mathematical function was written in a different
form.
cJacobi et al. 共1997兲,50 k8关H2O兴⬍610 s⫺1.
Jacobi et al.50 has compared their results by photolysis of
chloride ions and persulfate ions with the earlier results
共notes a and b兲49,52 and given possible explanation on this
discrepancy. The decay of Cl2
⫺"was considered to include
Cl"⫹H2O, Cl2
⫺"⫹H2O, and Cl2
⫺"⫹Cl2
⫺". The equilibrium of
Cl"⫹Cl⫺↔Cl2
⫺"was assumed to be maintained. The
k8关H2O兴and k4关H2O兴/K5were obtained from the linear
least squares fit to the observed pseudo-first-order rate con-
stant.
dBuxton et al. 共1998兲,12 k8关H2O兴⫽(1.3⫾0.1)⫻103s⫺1.
Pulse radiolysis of Cl⫺and S2O8
2⫺was used to form Cl2
⫺".
The system contains t-BuOH, therefore, the decay of Cl2
⫺"
included Cl"⫹H2O, Cl"⫹t-BuOH, Cl2
⫺"⫹H2O, and Cl2
⫺"
⫹t-BuOH. The pseudo-first-order decay rate constant was
analyzed as a function of 关H2O兴and 关t-BuOH兴. The linear
part of this function generated two other relationships, i.e.,
intercept and slope. The k⫺4关H2O兴/K5and k8关H2O兴were
obtained from the linear least squares fit of the slopes from
kobs versus 关t-BuOH兴analysis with respect to 1/关Cl⫺兴.
eYu and Barker 共2003兲,6k8关H2O兴⬍100 s⫺1.
Laser flash photolysis of H2O2and Cl⫺under acidic con-
ditions was studied. The Cl2
⫺"decay consists of Cl"⫹H2O,
Cl"⫹H2O2,Cl
2
⫺"⫹H2O, and Cl2
⫺"⫹H2O2. An analysis
similar to that of Buxton et al.12 was applied. The
k⫺4关H2O兴K5and k8关H2O兴were obtained from linear least
squares fit of the slopes of the kobs versus 关H2O2兴analysis
with respect to 1/关Cl⫺兴.
fYu and Barker 共2004兲,8k8关H2O兴⬍100 s⫺1.
Laser flash photolysis of S2O8
2⫺and Cl⫺under acidic con-
ditions was used. The Cl2
⫺"decay consists of Cl"⫹H2O,
Cl"⫹S2O8
2⫺,Cl
2
⫺"⫹H2O, and Cl2
⫺"⫹S2O8
2⫺. The
k⫺4关H2O兴/K5and k8关H2O兴were obtained from linear least
squares fit of the slopes of the kobs versus 关S2O8
2⫺兴analysis
with respect to 1/关Cl⫺兴.
Preferred Values
k8关H2O兴⬍(1.3⫾0.1)⫻103s⫺1.
Comments on Preferred Values
Previous measurements of this rate constant are higher
than the recent ones. Yu and Barker’s result is consistent with
what Jacobi et al.50 found by using similar experimental
technique and analytical method. The result of Buxton
et al.12 is astonishingly close to that of McElroy.49 It is un-
clear why such a discrepancy exists between the results ob-
tained by laser flash photolysis and pulse radiolysis. The re-
action of Cl"and H2O was not included in the chemical
mechanism of Wagner et al.’s analysis.52 As to the result of
McElroy,49 Jacobi et al.50 believed that the second-order rate
constant (3.1⫾0.1)⫻109M⫺1s⫺1used by McElroy49
should influence the measured rate constant, because the de-
cay profile of Cl2
⫺"was considered a mixed first- and second-
order procedure. Jacobi et al.50 also suggested that k8关H2O兴
is slower than previously thought. They estimated the Gibbs
free energy of the intermediate species to explain their re-
sults. Here the range of k8关H2O兴is given as the preferred
value, because reaction 共8兲is rather slow despite the differ-
ences in reported values.
TABLE 13. Rate constant data of k8关H2O兴
k8关H2O兴共s⫺1兲Method I, M pHReference Notes
(7.20⫾1.44)⫻103FP N.A. N.A. 198652 a
(1.3⫾0.1)⫻103PR 0.13 ⬃4 199049 b
⬍610 LFP ⬃0.1 4 199750 c
(1.3⫾0.1)⫻103PR N.A. 5–6 199812 d
⬍100 LFP N.A. 2 20036e
⬍100 LFP N.A. 2 20048f
760760 XIAO-YING YU
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
4.11.
k
9,Cl
2
À"¿H2O2\HO2"¿H¿¿ClÀ
Notes 共Table 14兲
aHasegawa and Neta 共1978兲,73 k9⫽(1.4⫾0.3)
⫻105M⫺1s⫺1.
Hasegawa and Neta73 monitored the decay of Cl2
⫺"both in
the absence and presence of at least four various concentra-
tions of H2O2. From the plot of the pseudo-first-order rate
constants of Cl2
⫺"decay versus 关H2O2兴,k9was derived with
20% uncertainty. The system contains S2O8
2⫺and Cl⫺to
generate Cl2
⫺"in the absence of H2O2. When H2O2was
added, it was suggested that more reactions among H2O2,
Cl",HO",SO
4
⫺",Cl
2
⫺", and S2O8
2⫺take place. It was unclear
whether these reactions were taken into account in the
pseudo-first-order derivation. The complicated interference
of other reactions might be the explanation of the discrep-
ancy between their result and that by Yu and Barker.6
bElliot 共1989兲,74 k9⫽4.1⫻104M⫺1s⫺1.
This result is even smaller than that of Hasegawa and
Neta.73 The first-order decay of Cl2
⫺"was mainly contributed
to the reaction of Cl2
⫺"with the impurity of perchloric acid,
whereas the reaction of Cl2
⫺"and H2O2was only a minor
component. The k9was measured in deoxygenated solution
containing 1 M hydrochloric acid and 1 or 2 M hydrogen
peroxide. Presumably, this value was obtained by fitting the
Cl2
⫺"profile by least squares regression.
cJacobi et al. 共1996兲,75 k9⫽3.2⫻105M⫺1s⫺1.
It was not explained how k9was measured. From the plot
of lg(k) versus bond dissociation energy 共BDE兲,lgk9⫽5.5
was reported with no uncertainty. The k9⫽3.2
⫻105M⫺1s⫺1was derived thereafter. However, Warneck76
most recently cited this rate constant as 7.0⫻105M⫺1s⫺1.
It is unclear why the value shown on the original graph was
not taken.
dYu and Barker 共2003兲,6k9⫽1.4⫻106M⫺1s⫺1.
The Cl2
⫺"decay consists of Cl"⫹H2O, Cl"⫹H2O2,Cl
2
⫺"
⫹H2O, and Cl2
⫺"⫹H2O2. The k10 /K5and k9were obtained
from the linear least squares fit of the intercepts of the kobs
versus 关H2O2兴analysis with respect to 1/关Cl⫺兴.6
Preferred Values
k9⫽(6.2⫾6.8)⫻105M⫺1s⫺1.
Comments on Preferred Values
Elliot’s result is not considered in the unweighted average
of k9, since no analysis detail was given.
4.12.
k
10 ,Cl"¿H2O2\H¿¿ClÀ¿HO2"
Notes 共Table 15兲
aYu and Barker 共2003兲,6k10⫽(2.0⫾0.1)⫻109M⫺1s⫺1.
The reported value of k10 is the first experimentally deter-
mined rate constant of the Cl extraction reaction with H2O2.
The Cl2
⫺"decay is considered to include Cl"⫹H2O, Cl"
⫹H2O2,Cl
2
⫺"⫹H2O, and Cl2
⫺"⫹H2O2. The k10 /K5and k9
were obtained from the linear least squares fit of the inter-
cepts of the kobs versus 关H2O2兴analysis with respect to
1/关Cl⫺兴.6
Preferred Values
k10⫽(2.0⫾0.1)⫻109M⫺1s⫺1.
Comments on Preferred Values
This is the first directly determined rate constant of Cl and
H2O2reaction in the aqueous phase. The same reaction tak-
ing place in the gas is almost ten times slower.13 The recom-
mended K5⫽(1.4⫾0.2)⫻105M⫺1is used to derive this re-
sult.
4.13.
k
11 ,Cl
2
À"¿HO2"\O2¿H¿¿2ClÀ
Notes 共Table 16兲
aGilbert et al. 共1977兲,77 k11⫽(4.5⫾0.5)⫻109M⫺1s⫺1.
The effect of dose per pulse on the yield of ferric ions
obtained from air-saturated solutions of ferrous ions contain-
ing various concentrations of chloride ions was investigated.
From a computer based analysis of the following 21 occur-
ring reactions:
H"⫹O2→HO2"
2⫻1010 M⫺1s⫺1,共25兲
H"⫹H"→H2
1.1⫻1010 M⫺1s⫺1,共26兲
H"⫹HO"→H2O
1.5⫻1010 M⫺1s⫺1,共27兲
H"⫹HO2"→H2O2
1.3⫻1010 M⫺1s⫺1,共28兲
HO"⫹HO2"→H2O3
1.18⫻1010 M⫺1s⫺1,共29兲
HO"⫹HO"→H2O2
1.3⫻1010 M⫺1s⫺1,共30兲
TABLE 14. Rate constant data of k9
k9共M⫺1s⫺1兲Method pH Reference Notes
(1.4⫾0.3)⫻105PR 1–3 197873 a
4.1⫻104PR 0 198974 b
7.0⫻105N.A. N.A. 199675 c
(1.4⫾0.2)⫻106LFP 2 20036d
TABLE 15. Rate constant data of k10
k10 /K5共s⫺1兲k10 共M⫺1s⫺1兲Method pH Reference Notes
1.4⫾0.2 (2.0⫾0.3)⫻109LFP 2 20036a
TABLE 16. Rate constant data of k11
k11⫻10⫺9(M⫺1s⫺1) Method I, M pHReference Notes
4.5⫾0.5 PR 0.2 ⬃0.4 197777 a
1.0⫾0.1 PR N.A. ⬃1 198064 b
⬃3 PR 1–12 ⬍2 198778 c
761761CRITICAL EVALUATION OF RATE CONSTANTS
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
HO"⫹Fe2⫹⫹H⫹→H2O⫹Fe3⫹
2.3⫻108M⫺1s⫺1,共31兲
HO2"⫹HO2"→H2O⫹H2O2
1.05⫻106M⫺1s⫺1,共32兲
HO2"⫹Fe3⫹⫹H⫹→H2O2⫹Fe3⫹
1.0⫻106M⫺1s⫺1,共33兲
H2O3⫹2Fe2⫹⫹2H⫹→2H2O⫹2Fe2⫹
slow, 共34兲
H2O3⫹4Fe2⫹⫹4H⫹→3H2O⫹4Fe2⫹
slow, 共35兲
Cl2⫹Fe2⫹→2Cl⫺⫹2Fe3⫹
slow, 共36兲
HO"⫹Cl⫺→OH⫺⫹Cl"
4.3⫻109M⫺1s⫺1,共37兲
Cl"⫹Cl⫺→Cl2
⫺"
2.1⫻109M⫺1s⫺1,共38兲
Cl2
⫺"→Cl"⫹Cl⫺
1.1⫻105M⫺1s⫺1,共39兲
Cl"⫹Fe2⫹→Cl⫺⫹Fe3⫹
5.9⫻109M⫺1s⫺1,共40兲
Cl2
⫺"⫹Fe2⫹→2Cl⫺⫹Fe3⫹
7.4⫻106M⫺1s⫺1,共41兲
Cl2
⫺"⫹Cl2
⫺"→2Cl⫺⫹Cl2
2.1⫻109M⫺1s⫺1,共42兲
Cl2
⫺"⫹HO2"→2Cl⫺⫹H⫹⫹O2
4.5⫻109M⫺1s⫺1,共43兲
Cl2
⫺"⫹H⫹→2Cl⫺⫹H⫹,共44兲
Cl"⫹H"→Cl⫺⫹H⫹.共45兲
The best rate constant k11⫽(4.5⫾0.5)⫻109M⫺1s⫺1was
obtained at high dosage.
bNavaratnam et al. 共1980兲,64 k11⫽(1.0⫾0.1)
⫻109M⫺1s⫺1.
Single pulses were delivered to oxygen-saturated solutions
containing 0.05 M sodium chloride and 0.15 M HClO4, the
disappearance of Cl2
⫺"was followed at 340 nm. Three reac-
tions were considered: Cl2
⫺"⫹HO2",Cl
2
⫺"⫹Cl2
⫺", and HO2"
⫹HO2". The reaction rate of Cl2
⫺"⫹HO2"was found insen-
sitive to the whole mechanism. The theoretical log plot of
关Cl2
⫺"兴versus time was fitted with various combinations of
possible values of k11 ,2k6, and k5.9The rate constants
k11⫽(1.0⫾0.1)⫻109M⫺1s⫺1and k6⫽(2.0⫾0.2)
⫻109M⫺1s⫺1were determined, respectively. The discrep-
ancy between this value and the result of Gilbert et al.77 was
attributed to the complexity of reactions taking place in the
system. However, a quantitative revision of such a scheme
was not offered.
cGogolev et al. 共1984兲,78 k11⫽3⫻109⫺4
⫻109M⫺1s⫺1.
The second-order decay of Cl2
⫺"was considered to include
reactions 共6兲and 共11兲, i.e., kobs
II ⫽2k6⫹k11关HO2"兴/关Cl2
⫺兴.
When 关HO2"兴⫽关Cl2
⫺"兴,kobs
II ⫽2k6⫹k11 was reached. When
2k6was subtracted from kobs
II ,k11 was obtained. The accu-
racy of k6is crucial in determining k11 . The k6determined
in the same work ranged from 1.0⫻109to 1.85
⫻109M⫺1s⫺1.
Preferred Values
k11⫽(3.1⫾1.5)⫻109M⫺1s⫺1.
Comments on Preferred Values
The preferred value is the unweighted average of all three
previous measurements.
5. Conclusions
A series of rate constants and equilibrium constants in-
volving Cl"related free radicals in aqueous solutions ob-
tained in three companion papers6–8 are evaluated in relation
to literatures. The numerical values shown in Table 1 may
not seem too appealing because some of them have quite
large uncertainties. However, they reflect the most reliable
range of the kor Kdetermined in the past 40 yrs or so.
The purpose of this evaluation is to point out what has
been accomplished and what needs to be done in the future.
Some of the rate constants and equilibrium constants need
more investigation, for instance, k4,K4,K3, and k10 , since
there is only one reported value of these specific rate con-
stants or equilibrium constants. The same applies to the rate
constants k2,k9, and k11 , because they have a fair range of
reported values. In contrast, K5is better defined by recent
works. The values of k⫺4,k5,k⫺5, and k8are well estab-
lished by past and current results. The k6is well studied,
however, the ionic strength effect on k6still needs clarifica-
tion.
It is biased to reject or prefer certain results when a range
of results were reported and not too much information was
disclosed on some of the key analyses. The main strategy
used in this paper is to consider experimentally directly de-
termined results unless there were serious doubts on the ac-
curacy of them and take the unweighted average of the data
as the recommended value. The commentary of the experi-
mental approaches also serves as a brief guidance for future
investigation on fast multiple equilibria systems similar to
the system reviewed here.
762762 XIAO-YING YU
J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
6. Acknowledgments
Thanks go to NASA 共Upper Atmospheric Research Pro-
gram兲and NSF 共Atmospheric Chemistry Division兲for finan-
cial support of this work.
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J. Phys. Chem. Ref. Data, Vol. 33, No. 3, 2004
