Reduction potentials of so3·- , so5·- , and S4O6·3- radicals in aqueous solution

Article abstract of DOI:10.1021/jp9900234

Reduction potentials of the SC₃^·- , SO₅^·- , and S₄O₆^3·- radicals in aqueous solutions are measured by pulse radiolysis at 294 K. These radicals are produced by reaction of ^·OH or N₃^· radicals with sulfite, peroxymonosulfate, and thiosulfate anions, respectively. The potentials for the couples SO₃^·-/SO₃^2- and SO₅^·-/ SO₅^2- are determined from equilibrium constants with three reference couples of the phenoxyl/phenoxide type, i.e., those derived from phenol, 3-cresol, and tyrosine. The potential for PhO^·/PhO^- is redetermined against ClO₂^·/ClO₂^- and confirms the published value. The potentials for the other two phenols are determined against PhO^·/PhO^-. The potential for the SO₃^·-/SO₃^2- couple is found to be 0.73 ± 0.01 V vs^·NHE. The potential for SO₅^·-/SO₅^2- is found to be 0.81 ± 0.02 V. The reduction potential of the radical formed from the one-electron oxidation of thiosulfate, which exhibits a λ_max at 375 nm, is also determined. This radical was identified before as either the monomeric S₂O₃^·- or the dimeric S₄O₆^·3-. Equilibrium measurements for this species, using N₃^· and the 4-cyanophenoxyl radical as references, support the dimeric assignment and yield a value of 1.07 ± 0.03 V for the reduction potential for the couple S₄O₆^·3- /2S₂O₃^2-.

Full text of DOI:10.1021/jp9900234

J. Phys. Chem. A 1999, 103, 3581-3588
3581
•-
•-
•3-
Reduction Potentials of SO3 , SO5 , and S4O6 Radicals in Aqueous Solution
†
Tomi Nath Das, Robert E. Huie,* and P. Neta
Physical and Chemical Properties DiVision, National Institute of Standards and Technology,
Gaithersburg, Maryland 20899-8381
ReceiVed: January 4, 1999; In Final Form: March 1, 1999
•-, SO
•-, and S
O
•3-
radicals in aqueous solutions are measured by pulse
Reduction potentials of the SO
3
5
4
6
•
•
radiolysis at 294 K. These radicals are produced by reaction of OH or N
peroxymonosulfate, and thiosulfate anions, respectively. The potentials for the couples SO
SO are determined from equilibrium constants with three reference couples of the phenoxyl/phenoxide
type, i.e., those derived from phenol, 3-cresol, and tyrosine. The potential for PhO /PhO is redetermined
3
radicals with sulfite,
•-
2-
•-
3
/SO
3
5
and SO /
2-
5
•
-
•
-
2 2
against ClO /ClO and confirms the published value. The potentials for the other two phenols are determined
•
-
•-
2-
against PhO /PhO . The potential for the SO
3
/SO
is found to be 0.81 ( 0.02 V. The reduction potential of the radical formed from
the one-electron oxidation of thiosulfate, which exhibits a λmax at 375 nm, is also determined. This radical
3
couple is found to be 0.73 ( 0.01 V vs NHE. The
•
-
2-
potential for SO
5 5
/SO
•
-
•3-
was identified before as either the monomeric S
2
O
3
or the dimeric S
O
4 6
. Equilibrium measurements for
•
this species, using N and the 4-cyanophenoxyl radical as references, support the dimeric assignment and
yield a value of 1.07 ( 0.03 V for the reduction potential for the couple S
3
•
3-
2-
4
O
6
/2S
2
O
3
.
+
2-
•-
Introduction
X + SO f X + SO3
(1)
(2)
3
Radicals from Sulfite Autoxidation. One hundred years ago,
Bigelow presented an extensive study of the inhibitory effect
of various organic compounds on the autoxidation of sulfite
SO3•-+ O f SO
•-
5
2
Further, Connick and co-workers have suggested that the
autoxidation of sulfite in the absence of transition metal ions
involves the almost thermoneutral reaction
1
solutions. Subsequent work by Young, Lumi e` re, and Pinnow
confirmed and extended these observations,2 and a very
-4
17
important study by Titoff demonstrated the importance of trace
metal catalysis. Even earlier work by Jorissen had shown that
5
HSO5- + HSO3 f SO4•- + SO3 + H O
-
•-
(3)
2
the autoxidation of sulfite could induce the oxidation of other
6
7
In either case, the SO5•- and SO4•- radicals react further to
propagate the chain
substances, including transition metal ions. Matthews and co-
workers showed that the autoxidation reaction was accelerated
8
greatly by ultraviolet light, an effect that was inhibited by
SO5•- + X + H f X + HSO
+
+
-
(4)
(5a)
(5b)
(6)
organic substances in the same manner as autoxidation in the
5
dark.9 B a¨ ckstr o¨ m determined that the quantum yield of the
,10
SO5•- + SO3 + H f HSO + SO3
2-
+
-
•-
11
photoinduced oxidation of sulfite was quite large. He con-
cluded that the thermal reaction was very similar to the
photochemical reaction and, consequently, both reactions were
chain reactions.12 The autoxidation was also demonstrated to
be initiated by R particles in a similar manner. Haber then
built upon this earlier information to propose a free radical
mechanism, which has led us to that used today.14 This free
radical mechanism remained speculative until the early pulse
radiolysis and flash photolysis studies of Hayon and co-workers
that demonstrated the existence of the basic free radicals
5
SO5•- + SO3 f SO42- + SO4
2-
•-
1
3
SO4•- + SO3 f SO42- + SO3
2-
•-
SO5•- + SO5 f 2SO4•- + O2
•-
(7)
or participate in termination reactions
•
-
•-
SO5•- + SO5 f S O + O2
•-
2-
2 8
involved (SO3 and SO5 ) and began the process of unraveling
1
5,16
their chemistry.
Sulfite autoxidation is known to involve the SO3•-, SO4•-
SO3•- + SO3 f S O
•-
2-
(8)
,
2
6
•
-
and SO5 radicals as intermediates and to be catalyzed by
certain transition metal ions. The reaction may be initiated by
When X is a transition metal ion, it may react with peroxy-
-
the oxidation of sulfite by free radicals or transition metal ions
monosulfate, HSO5 , to branch the chain
+
(both represented here by X )
-
+
-
•-
4
X + HSO5 f X + OH + SO
(9)
*
To whom correspondence should be addressed.
On leave from the Chemistry Division, Bhabha Atomic Research
†
The generation of these free radicals during the autoxidation of
sulfite leads to many chemical and physiological conse-
Centre, Mumbai 400085, India.
1
0.1021/jp9900234 This article not subject to U.S. Copyright. Published 1999 by the American Chemical Society
Published on Web 04/22/1999

3582 J. Phys. Chem. A, Vol. 103, No. 18, 1999
Das et al.
quences.18,19 The rates of the reactions leading to these
consequences are dependent largely on the reduction potentials
of the various species involved. A recent study of DNA damage
associated with sulfite autoxidation demonstrated that the details
of the damage mechanisms depended intimately on the radical
reduction potentials.20 The SO4 radical is known to be a very
strong oxidant, with E° (SO4•-/SO42-) ) 2.43 V vs NHE and,
thus, can rapidly oxidize sulfite and many metal ions. The
same absorption feature in pulse radiolysis experiments, involv-
ing deaerated tetrathionate solutions containing formate, condi-
tions that would favor one-electron reduction reactions
eaq- (CO2•-) + S O f S O
2-
•3-
6
+ (CO2)
(13)
4
6
4
•-
21
Therefore, it was proposed that the absorption at 370 nm in the
photolysis and in the oxidation of thiosulfate arose from the
reaction of the thiosulfate radical with thiosulfate to generate
the dimer radical
•
-
2-
•-
2-
reduction potentials for SO3 /SO3 and for SO5 /SO5
,
however, are not well-established. A value for SO5•-/SO5 of
2-
1
.1 V was estimated from kinetic measurements and may
22
S2O3•- + S O a S O
2-
•3-
6
represent an upper limit. Two reported values derived from
(14)
2
3
4
•
-
2-
pulse radiolysis studies for the SO3 /SO3 couple differ by
almost 140 mV.2 In the first study, chlorpromazine was the
reference compound and there is some uncertainty in its
2,23
This interpretation was questioned by Mehnert and co-workers
who studied the pulse radiolysis of thiosulfate and tetrathionate
•
reduction potential. In the second study, ClO2 , which has a well-
27,32
with greater time resolution.
In these studies, a very short
established potential, was the reference. But in this case, there
is a question of whether the equilibrium involving sulfite and
chlorite at high pH is reached via electron transfer only or
whether it involves oxygen transfer as well.24 To avoid this
lived absorption was observed at 320 nm, ascribed to the OH-
thiosulfate adduct, which decays to another transient intermedi-
ate at 420 nm; this species is then transformed into the final
form of the radical, absorbing at 370 nm. The authors explain
these spectral changes by a reaction of the OH-thiosulfate
adduct with an additional thiosulfate to generate a dimer
absorbing at 420 nm. This dimer decomposes to the monomer
radical that absorbs at 370 nm. This identification was based
primarily on the ionic strength dependence of the self-reaction
of the species absorbing at 370 nm.
2-
complication, the equilibrium constant for the reaction of SO3
with the tetraamine(phenanthroline)ruthenium(III) cation was
derived from independent kinetic studies of the forward and
reverse rate constants, specifically taking into consideration
secondary reactions of SO3•
- 25
.
In that work, the value E° )
0
.72 V was derived.
•-
Because of these uncertainties in the potentials for SO3 and
To help resolve these discrepancies, we have reinvestigated
the properties of the species absorbing at 375 nm, including a
study leading to its reduction potential.
SO5• , we have redetermined these reduction potentials in the
-
present study. The reduction potentials were determined from
•
-
2-
equilibrium measurements, involving the SO3 /SO3 and
Experimental Section33
•-
2-
SO5 /SO5 couples with several phenoxyl/phenoxide couples.
•
-
•-
Radicals from Thiosulfate. In addition to SO3 and SO5
,
Materials. Most of the compounds used were obtained from
Aldrich, Alfa, and Mallinckrodt in their highest available purity
(varying from 98% to >99%) and were used as received. Only
N,N-dimethylaniline (DMA) was purified by refluxing and
distilling over KOH under nitrogen. Sodium tetrathionate
(>99%) was obtained from Fluka, sodium chlorite (80%) from
Kodak, and potassium peroxymonosulfate as the triple salt
basic radicals of importance to sulfite oxidation, we have also
measured reduction potentials for a radical derived from another
oxyanion, thiosulfate S2O32 . Thiosulfate has been proposed as
-
26
an oxidation inhibitor in flue gas desulfurization processes and
as an additive in spray solutions in nuclear power reactors, where
27
it would react with volatile iodine. Further, since the unpaired
•
-
•
•
electron on the S2O3 radical is located on the terminal sulfur,
Oxone (2KHSO5 KHSO4 K2SO4) from Aldrich. The content of
KHSO5 in the Oxone product was determined by adding excess
2
-
there should be little structural difference between S2O3 and
•-
-
-
S2O3 , making this a convenient couple for studies of electron-
I and measuring the concentration of I3 from its absorbance
at 350 nm. It was found to correspond to 96% of the calculated
value based on the above formula. Water was purified by a
Millipore Super-Q system.
2
8
transfer reactions.
Adams and co-workers observed a transient spectrum centered
about 375 nm after the pulse radiolysis of aqueous solutions of
thiosulfate.29 This spectrum, with ꢀ ) 1720 L mol cm , was
-1
-1
Procedures. To minimize thermal oxidation of the phenolic
compounds by dissolved O2 at high pH, all solutions were first
saturated with N2O and then KOH was added to raise the pH
to the desired level. Studies with peroxymonosulfate solutions
indicate that this compound is thermally unstable at pH values
near its second pKa (9.3) and rapidly evolves oxygen, but at
•-
2-
ascribed to the S2O3 radical, formed by the oxidation of S2O3
•
by OH.
•
2-
-
•-
OH + S O3 f OH + S O
3
(10)
2
2
2
-
The generation of this absorption in the flash photolysis of
higher pH values the SO5 ion is only moderately unstable
15
thiosulfate solutions was observed also by Dogliotti and Hayon
and decomposes over a period of an hour (to ∼5% of the starting
34
value in the range of concentrations used in this study). In
S2O3 - + hν f S O3 + eaq
2
•-
-
(11)
2-
our experiments, the concentration of SO5 in the alkaline
2
solution was frequently checked by absorbance measurements
during the progress of the study (about 15 min) and the corrected
concentrations were used in the calculations. Additionally, to
A second photolysis channel was thought to result in the
•
•-
generation of OH and S2O2 but was demonstrated to be
2
-
avoid any thermal reaction between SO5 and other reactants,
these solutions were mixed just before entering the irradiation
cell and the prepulse contact time was e2 s; therefore, any
changes in the concentration of either reactant within this
duration could be neglected.
S2O3 - + hν f SO3 + S
2
•-
• -
(12)
in a subsequent ESR (electron spin resonance) study by Behar
and Fessenden.30
An absorption centered about 370 nm was also observed by
Sch o¨ nesh o¨ fer after the pulse radiolysis of N2O-saturated thio-
sulfate solutions. Additional experiments demonstrated the
The pulse radiolysis experiments were carried out in either
one of two independent facilities, one based on a Febetron 705
pulser providing single 50 ns pulses of 2 MeV electrons and
3
1

Reduction Potentials of SO3•-, SO5 , and S4O6•3-
•-
J. Phys. Chem. A, Vol. 103, No. 18, 1999 3583
•
-
•
-
TABLE 1: Measurement of the Equilibrium Constant for R + S a S + R
-
-
Ka
[
S ]
[R ]
added solute
(mol L )
S•
(mmol L-1)
R•
(mmol L-1)
pH
λ (nm)
-1
I
(mol L-1)
E°(I)0) (V)
b
•
•
C
TyrO
TyrO
6
H
5
O
2 to 14
ClO
2
100
10
50
66
100
11.5
11.3
11.3
13
400
410
410
410
400
0.120
0.076
0.600
0.100
0.180
213 ( 30
12.0 ( 1.2
11.5 ( 1.2
12.4 ( 1.2
69 ( 7
0.800 ( 0.005
0.736 ( 0.003
0.737 ( 0.004
0.736 ( 0.003
0.692 ( 0.003
•
•
-
-
•
•
•
•
1.7 to 5.1
2.8 to 9.0
3.3 to 10.0
Å0.25 to 0.75
C
C
C
C
6
6
6
6
H
H
H
H
5
5
5
5
O
O
O
O
N
N
3
- (0.05)
- (0.50)
3
3
-MeC
6
H
4
O•
•
+
DMA
12
glycol (2.7)
a
-
•
•
-
b
K ) ([R ][S ])/([R ][S ]). E at zero ionic strength as explained in the text.
the other on a Varian linear accelerator providing multiple pulses
of 5 MeV electrons with pulse duration of 50-500 ns. The
detection in both systems is based on optical absorption in the
UV and visible range. All measurements were carried out at
room temperature, 21 ( 2 °C. Other experimental details were
pulse intensity can be determined as the yield of phenoxyl
radicals, [PhO ]o, measured in the absence of added sulfite. In
the presence of added sulfite, the concentration of sulfite radicals
at equilibrium will be given by
•
•
•
3
5
as described.
[SO3•-] ) [PhO ] - [PhO ]
(22)
eq
o
eq
Calculation of Transient Equilibrium Constants. In this
work, equilibrium constants are determined, which involve two
radicals that typically undergo subsequent radical-radical loss
processes. Therefore, the experiments must be designed to
establish the equilibrium among the reactants of interest on a
time scale that is short when compared to the decay time due
to radical-radical reactions. Further, it must be possible to
determine the concentrations of all of the species involved in
the equilibrium quantitatively. We will illustrate the procedures
employed in this study with the following example: the equi-
librium involving sulfite and a phenoxyl radical,
Also, in a pulse radiolysis experiment, the concentrations of
the nonradical species are typically far greater than the
concentrations of the radicals. Therefore, it is usually assumed
that the equilibrium concentrations of the nonradicals are equal
to the their initial concentrations. This assumption is not critical
since corrections can be made easily if necessary.
The phenoxyl radical concentration is measured by its optical
absorbance. In the absence of any sulfite, the absorbance is Ao;
at equilibrium and in the presence of sulfite, the absorbance is
Aeq. Since we are interested in the ratios of concentrations, the
absolute values of the radical concentrations can be replaced
by the phenoxyl radical absorbances. Thus:
•
2-
-
•-
PhO + SO3 a PhO + SO3
(15)
[PhO-]
Aeq
The equilibrium constant for this reactions is given by
o
)
Keq
(23)
SO32-]
PhO ][SO3•-]
-
[
Ao - Aeq
[
o
K )
(16)
eq
2
[
SO3 -][PhO•]
This equation shows that the equilibrium constant can be derived
from the slope of a plot of the ratio of the initial concentrations
of phenoxyl and sulfite against the ratio of the equilibrium
absorbance to the difference between the equilibrium absorbance
and the absorbance measured in the absence of sulfite.
which can be rearranged to:
PhO-]
[
[PhO•]
[SO3•-]
eq
eq
)
Keq
(17)
[
SO32-]
Results and Discussion
eq
eq
SO3 and SO5•-. All equilibria were measured in alkaline
solutions so that all the species are in their fully ionized forms.
These reactions are typically faster than the equivalent reactions
with neutral phenols, which also involve proton transfer.
Choosing these conditions helps in attaining a rapid electron-
transfer equilibrium at millimolar solute concentrations without
a significant loss of radicals via other reactions. We set out to
measure the equilibria for sulfite and peroxymonosulfate by
using more than one reference compound and, as often as
possible, by using the same reference compounds for both
radicals. In view of the reported reduction potentials and
following some preliminary measurements, we selected the three
phenoxyl radicals derived from phenol, 3-cresol, and tyrosine
as the most suitable for our purpose. The high self-exchange
rates of these phenoxyl radicals was of advantage in helping to
•-
The course of this reaction is followed by monitoring the
phenoxyl radical, which is the only species in the system that
absorbs in the visible portion of the spectrum (400 nm). In
radiolysis experiments, the concentration of radicals produced
is practically independent of the concentration of the solute,
for low solute concentrations. The radicals arise only from the
interaction of the radiation with the solvent.
•
-
+
H O -' OH + e + H
2
aq
•
(
+ small amounts of H , H , and H O ) (18)
2 2 2
In these studies, the hydrated electron is converted to additional
hydroxyl radicals by
eaq- + N O + H f OH + N
+
•
(19)
3
6
achieve rapid equilibration.
2
2
As a first step, we redetermined the reduction potential of
the phenoxyl/phenoxide couple against the well-accepted stan-
The initial phenoxyl and sulfite radicals then arise from the
•
-
2-
•
-
37
reactions of OH with C6H5O and SO3
dard ClO /ClO (E° ) 0.934 V vs NHE).
2
2
•
-
-
•
•
-
-
•
OH + C H O f OH + C H O
(20)
(21)
ClO + C H O a ClO + C H O
(24)
6
5
6
5
2
6
5
2
6
5
•
2-
-
•-
OH + SO3 f OH + SO3
These measurements were carried out in N2O saturated solutions
at pH 11.5, where >95% of the phenol is in the phenoxide form
and the equilibrium was determined at the selected solute
The total yield of radicals in any set of experiments at constant

3584 J. Phys. Chem. A, Vol. 103, No. 18, 1999
Das et al.
The results at two different ionic strengths, however, clearly
demonstrate (Table 1 and Figure 1) that the negative charge,
localized on the carboxyl group at the side chain, does not affect
significantly the reactivity of the radical center on the oxygen
and the ring. The measured K values are 12 at I ) 0.07 mol
-
1
-1
L
and 11.5 at I ) 0.6 mol L . On the basis of these obser-
vations, the reduction potential for the tyrosyl radical has been
assumed to be independent of ionic strength, E ) 0.736 V.
•+
The radical cation of N,N-dimethylaniline (DMA ) was also
selected as a reference for our estimations. However, because
of the limited solubility of DMA in water, we used 2.7 mol
-
1
L
ethylene glycol solutions as the solvent matrix, where the
•
40
oxidizing radical is CH2CHO. At pH 12 and I ) 0.18 mol
-
1
L , the equilibrium constant with phenol (reaction 26)
•
-
•+
C H O + DMA a C H O + DMA
(26)
6
5
6
5
was K ) 69. Because the rate of the reverse reaction should be
dependent on ionic strength, we corrected the measured value
for the effect of ionic strength making use of an extended form
of the Debye-H u¨ ckel equation:
Figure 1. Measurement of the equilibrium constant for the reaction
•
2-
-
•-
1/2
1/2
C
in N
6
H
5
O + TyrO a C
2
6
H
5
O + TyrO at different ionic strengths, I,
log K ) log K ° + 2Az z I /(1 + I ) + âI (27)
eq eq 1 2
O saturated solutions at pH 11.3, absorbed dose ) 5.3 Gy per
-
1
-
-1
-
pulse. (•) I ) 0.6 mol L with [N
3
] ) 0.5 mol L , [C
6
H
5
O ] ) 50
where I is the ionic strength, Keq° is the equilibrium constant at
zero ionic strength, zi are the charges on the reactants, and A is
a collection of physical constants with the value of 0.509 at
298 K. The parameter â is specific for each system and is
normally obtained by experiment. Following Wardman, we
-
1
2-
-1
-1
mmol L , [TyrO ] ) 2.8-9.0 mmol L and (2) I ) 0.076 mol L
-
-1
-
-1
2-
with [N
3
6 5
] ) 0.05 mol L , [C H O ] ) 0.01 mol L , [TyrO ] )
-
1
1
.7-5.1 mmol L . Dashed line is the fit to the low ionic strength
4
1
data; solid line is the fit to the high ionic strength data.
42
concentrations (Table 1). From the equilibrium constant, K )
take â ) -0.02. The value of E thus corrected to zero ionic
strength for DMA /DMA is 0.69 V. The reduction potentials
2
13 ( 30, we calculate E° ) 0.80 ( 0.01 V vs NHE for the
•+
•
-
C6H5O /C6H5O couple, in excellent agreement with the value
of 0.79 V reported earlier.38 Our measured value is used as
reference for all subsequent measurements on the sulfite and
the peroxymonosulfate systems.
for all the organic compounds used as references for the
following studies are summarized in Table 1.
•-
2-
Reduction Potential of the SO3 /SO3 Couple. Equilib-
rium measurements for this couple with several reference
systems are summarized in Table 2 and the data for tyrosine
and cresol are shown in Figure 2. Studies with phenol were
carried out at different ionic strengths and are presented in Figure
The second step in this process was to determine the reduction
potentials of three other organic radicals against the phenoxyl/
phenoxide couple. The three chosen were 3-methylphenoxyl/
3
-methylphenoxide (m-cresol), tyrosyl/tyrosine, and N,N-
3
, where the effect of the ionic strength on equilibrium 1 is
clearly demonstrated. The K value decreases from 16.5 at I )
.067 mol L to 9.23 at I ) 0.86 mol L . After correction to
dimethylaniline radical cation/N,N-dimethylaniline. We measured
the reduction potential of the phenoxyl radical derived from
-1
-1
0
3
-cresol recently against phenol as the reference and found the
zero ionic strength, as described above, we calculated E ) 0.720
V. With tyrosine (Figure 2a), the measurements at different ionic
strengths once again confirmed that the negative charge on the
carboxyl does not affect the equilibrium as much as would be
predicted by the Debye-H u¨ ckel equation; the K value decreased
marginally with increasing ionic strength from 0.61 at I ) 0.105
mol L to 0.50 at I ) 0.3 mol L . The value of E° at zero
ionic strength is estimated to be 0.736 V. With 3-cresol, the K
value is 0.88 at I ) 0.08 mol L , giving E° ) 0.733 V at zero
ionic strength. Measurements against DMA were not possible
because of the limited solubility of this compound and the high
39
value to be 0.736 V. We include these results in Table 1. As
part of the present study, we measured the equilibrium constant
for the tyrosyl radical against phenol for subsequent use as
reference in this study.
•
2-
-
•-
-
1
-1
C H O + TyrO a C H O + TyrO
(25)
6
5
6
5
-
1
Tyrosine at pH 11.3 exists as the dianion; the tyrosyl radical is
a monoanion. Therefore, we expected that the reverse reaction
of equilibrium 25 would be dependent on ionic strength (I).
TABLE 2: Measurement of E(SO •-
) from the Equilibria R + SO
•
2-
a SO
•-
+ R-
3
3
3
[
SO
3
2-]
[R ]
-
added solute
mmol L-1)
R•
(mmol L-1)
pH
λ (nm)
(mol L
-1
)
I
K (mol L-1
)
E(I ) 0) (V)
b
(
•
1
4
4
4
1
4
1
4
5 to 50
to 12
to 12
C
C
C
C
C
TyrO
TyrO
6
6
6
6
6
H
H
H
H
H
5
5
5
5
5
O
260
50
50
50
25
5 to 15
10
5 to 15
11.3
11.6
11.6
11.6
11.7
12
400
400
400
400
400
410
410
410
KCl (0.50)
KCl (0.25)
0.855
0.342
0.192
0.092
0.067
0.300
0.105
0.080
9.23 ( 1.00
9.9 ( 1.0
0.724 ( 0.002
0.724 ( 0.002
0.723 ( 0.003
0.724 ( 0.003
0.716 ( 0.005
0.736 ( 0.003
0.736 ( 0.003
0.737 ( 0.004
•
•
•
•
O
O
O
O
KCl (0.10)
10.6 ( 1.1
a
to 12
K
K
K
K
K
2
2
3
2
2
SO
4
11.6 ( 1.2
a
.5 to 6.0
0 to 60
0 to 30
0 to 60
SO
4
16.54 ( 1.70
0.50 ( 0.05
0.606 ( 0.035
0.88 ( 0.09
•
•
-
-
(0.20)
-
a
11.5
12
SO
SO
4
•
a
3-MeC6H4O
4
a
2-]maximum - [SO
2-]working
Added K
2
SO
4
concentration maintained such that [K
2
SO
4
] ) [SO
3
3
.

Reduction Potentials of SO3•-, SO5 , and S4O6•3-
•-
J. Phys. Chem. A, Vol. 103, No. 18, 1999 3585
Figure 4. Redox relationships among the various species considered
2
-
in this work in the derivation of the reduction potentials for SO
SO
3
and
-
5
. The numbers represent the reduction potential differences, going
2
left to right, between the redox pairs.
Figure 2. Measurement of the equilibrium constants for the reactions
•
2-
-
•-
•
2-
-
TyrO + SO
3
a TyrO + SO
3
and cresol + SO
3
a cresol +
•-
3
.
SO
•-/SO
2-
and SO
•-/SO
2-
as a
Figure 5. Reduction potentials for SO
3
3
5
5
function of the solution pH.
for SO5•-) in Figure 4. Our value for the reduction potential of
•
-
SO3 is slightly lower than the value of 0.76 V measured
2
3
against ClO2 and higher than the value of 0.63 V measured
22
against chlorpromazine, but in good agreement with the value
of 0.72 V derived from kinetic studies involving a ruthenium
2
5
complex.
From the value of E ) 0.73 V for SO3•-/SO32- at pH >11
we can calculate the reduction potential for the sulfite radical
at other pH value by using eq 28.
+
+ 2
+
•
O-
E ) E + 0.059 log(K K + K [H ] + [H ] )/(K + [H ])
0 1 2 1 r
Figure 3. Variation of K for the equilibrium between C
H O /C H
6 5 6 5
•
-
2-
3
and SO
3
/SO
in N
2
O-saturated solutions at different I values,
(28)
absorbed dose ∼5 Gy. The solution compositions for (•) I ) 67 mmol
-
-
1
1
-1
-1
L
L
, (9) I ) 92 mmol L , (2) I ) 192 mmol L , (1) I ) 342 mmol
where E0 is the reduction potential at pH 0. By taking the
-1
, and (() I ) 855 mmol L are listed in Table 2.
-2
dissociation constants for sulfurous acid as K1 ) 1.39 × 10
-
8
•-
concentrations required for achieving equilibrium with sulfite
before the radicals decay. From the three measurements sum-
and K2 ) 6.3 × 10 and assuming that the SO3 radical does
-2
not protonate at pH > 2 (Kr > 1 × 10 ), we calculate the
reduction potential at pH 7 to be E7 ) 0.75 V, at pH 4 E4 )
0.92 V, and at pH 2 E2 ) 1.04 V vs NHE (Figure 5).
•-
marized above, we calculate a reduction potential for the SO3
/
SO32 couple at zero ionic strength of 0.73 ( 0.01 V vs NHE,
where the estimated error limit represents the spread of the
individual experimental values. The measurements leading to
this value are summarized (along with similar measurements
-
•
-
2-
Reduction Potential of the SO5 /SO5 Couple. Equilib-
rium measurements for this couple were conducted at pH >11
since the rate of thermal decomposition of peroxymonosulfate

3586 J. Phys. Chem. A, Vol. 103, No. 18, 1999
Das et al.
TABLE 3: Measurement of E(SO •-
) from the Equilibria R + SO
•
2-
a SO
5
•-
+ R-
Ia
(mol L-1)
0.060
5
5
2-]
[R ]
-
λ
(nm)
[
SO
5
(
mmol L-1)
R•
O•
(mmol L-1)
pH
K
E°(I)0) (V)
1
5
5
1
0
0
0
C
6
H
5
1 to 6
0.95 to 3.8
1 to 6
11.3
11.4
11.4
11
400
410
410
450
0.284 ( 0.030
(3.7 ( 0.4) × 10
(2.1 ( 0.2) × 10
(3.7 ( 0.4) × 10
0.820 ( 0.005
0.806 ( 0.005
0.818 ( 0.005
0.836 ( 0.005
O•
0.382
0.400
0.090 to 0.140
-2
-2
-3
3-Me-C
6
H
4
•
TyrO
•
+
5 to 25
DMA
0.05 to 0.35
a
2 4 2 5
From K SO , equivalent of 1.5 times [K SO ] in the triple salt.
In a recent pulse radiolysis study, the oxidation of Mn2 and
+
-
its sulfite complexes by SO5‚ radicals at pH 3 was reported to
8
10
take place with a rate constant between 2 × 10 and 2 × 10
-
1
-1
L mol
s
and to depend on the nature of the species being
44
3+
2+
oxidized. The standard reduction potential for the Mn /Mn
couple is 1.56 V vs NHE in strongly acidic solutions, where
45
3+
both ions are in their aquo form. The aquo Mn ion is known
to undergo stepwise deprotonation of its water molecules to form
2
+
2+
Mn(OH) and then Mn(OH) , with pKa values of -0.4 and
.3. Therefore, at pH 3 the Mn(III) ion will exist as Mn(OH) .
45
2+
0
From the pKa values and the reduction potential at high acidity,
2
+
we estimate E° (Mn(III)/Mn ) at pH 3 to be 1.19 V. From our
•
-
2-
results, E° (SO5 /SO5 ) at pH 3 is 1.183 V. From this
comparison of the reduction potentials it may be suggested that
-
oxidation of Mn(II) at pH 3 by SO5‚ radicals will have a
relatively low rate constant. Since it is known that the nature
of the complexing anion strongly affects the reduction potential
of the Mn(III)/Mn(II) couple, we suggest that the high rate
4
4
constants reported earlier are probably due to reaction with
the sulfite complex rather than with the aquo complex.
Thiosulfate Radicals. In our initial studies, we used the
•
•
-
•
primary OH/ O radicals (pKa ) 11.9) and the secondary N3
radicals to react with thiosulfate. We observed symmetrical,
broad absorption bands, an early one centered at λmax 420 nm
and a later one centered at λmax 375 nm, in agreement with the
absorption features reported in the literature. We then measured
2
-
the rate constants for the oxidation of S2O3 by several
•-
oxidizing radicals and found that while Br2 reacts rapidly, with
8
-1 -1
•-
Figure 6. Measurement of the equilibrium constants for the reactions
k ) (4.4 ( 0.3) × 10 L mol s , the reaction with CO3 is
•
2-
-
•-
+•
2-
5
PhO + SO
5
a PhO + SO
5
and DMA + SO
a DMA +
7
slower by an order of magnitude, k ) (3.1 ( 0.5) × 10 L
•
-
SO
5
.
-1 -1
•-
6
-1
mol s , and I2 is even less reactive, with k e 10 L mol
-
1
•
is maximal near the second pKa value of 9.3 but is much slower
s . When N was used as the oxidant, it was observed that
3
at higher pH.3
4,43
The results obtained with the four reference
the maximum absorbance at 375 nm decreased with increasing
-
couples are summarized in Table 3. The K value obtained with
N3 concentration. This suggests that the reaction goes to
-
1
phenol as reference (Figure 6) was 0.284 at I ) 0.06 mol L .
After correcting for the effect of ionic strength, we calculate E
equilibrium. Therefore, a systematic study was undertaken of
this reaction. To achieve significant change in the yield of the
-
2
-
)
0.820 V. With tyrosine as reference, K ) 2.1 × 10 at I )
thiosulfate radical, very high concentration ratios of [N ]/
3
-
1
2-
0
.40 mol L , and the value of E at zero ionic strength is 0.818
[S O ] were necessary. Thus, while the thiosulfate concentra-
2
3
-
2
-1
V. With 3-cresol, K ) 3.7 × 10 at I ) 0.382 mol L , and
tion was maintained in the range of several millimolar, the azide
concentration was required to be in the range of several hundred
millimolar. At these high azide concentrations, we had to take
into account the dimerization equilibrium,
the corrected E is 0.806 V. With DMA as the reference (Figure
-
1
-3
6
), for I between 0.09 and 0.14 mol L , K was 3.7 × 10 and
E ) 0.836 V. The higher value in the latter case, as compared
to the average value of E° ) 0.81 ( 0.02 V obtained with the
three phenoxyl type references, is probably due to incomplete
dissolution of the DMA added to the solutions containing
Oxone. Therefore, the higher E value of 0.836 is considered to
be less certain and is not used in the final analysis, but the error
limit quoted above has been expanded to include this value.
The various measurements leading to the reduction potential
N + N a N6•-
•
-
(29)
3
3
for which K ) 0.3 L mol-1 has been reported.46,47
The reaction was monitored at 375 nm, with a small
•-
correction for the absorbance due to N6 . The results were
•-
plotted by assuming an equilibrium involving S2O3
•
-
of SO5 are summarized in Figure 4.
From the average value of E° ) 0.81 V for SO5•-/SO52- at
high pH and the pKa values for H2SO5 (1.0 and 9.3) and
N + S O a N3- + S O
•
2-
•-
(30)
(31)
3
2
3
2
3
-
assuming that the SO5 radical does not protonate at pH > 2,
or one involving the dimeric species.
we calculate from eq 28 a reduction potential of E7 ) 0.95 V
•
-
-
for SO5 /HSO5 at pH 7, E4 ) 1.12 V at pH 4, and E2 ) 1.24
N + 2S O a N3- + (S O )
•
3
2-
•3-
3 2
V at pH 2 (Figure 5).
2
3
2

Reduction Potentials of SO3•-, SO5 , and S4O6•3-
•-
J. Phys. Chem. A, Vol. 103, No. 18, 1999 3587
•
3-
•
2-
•3-
+ R-
TABLE 4: Measurement of E(S
4
O
6
) from the Equilibria R + 2S
2
O
3
2
a (S O
3
)
2
2
-] (mmol L-1
R•
-
[R ] (mmol L-1]
Ia (mol L-1
[S O
2 3
)
pH
λ (nm)
)
K
E° (I ) 0)
•
•
4
4
8
6
3
to 20
to 16
0 to 60
N
N
3
800
400
20
8.8
8.8
12
375
375
375
0.850
0.440
0.280
(2.0 ( 0.2) × 10
(1.9 ( 0.2) × 10
2.2 ( 0.2
1.054 ( 0.003
1.060 ( 0.004
1.084 ( 0.003
3
4-CNC
6
H
4
O•
a
2-]maximum - [S
2-]working
.
Added K
2
SO
4
concentration maintained such that [K
2
SO
4
] ) [S
2
O
3
O
2 3
these studies. From this reduction potential and the estimated
•
-
49
potential for the thiosulfate radical, S2O3 , of E° ) 1.30 V,
-
4
-1
we calculate Keq ) 1.3 × 10 L mol for the reaction
•
3-
•-
2-
3
(
S O )
a S O + S O
(33)
2
3 2
2
3
2
In an attempt to resolve the discrepancies in the assignment
of the thiosulfate radical, we repeated some of the earlier
experiments and compared the species formed by oxidation of
•
•
thiosulfate with OH or N3 radicals with that formed by
-
reduction of tetrathionate with eaq . With solute concentrations
-
1
above 5 mmol L , both oxidation reactions with thiosulfate
lead to the very rapid formation of a species with λmax at 420
-
1
-1
nm and with ꢀ ) 4200 ( 250 L mol cm . This species decays
6
-1
by first-order kinetics (kobs ) (2 ( 0.4) × 10 s ), independent
of pH, solute concentration, dissolved O2, or dose per pulse, to
form the species absorbing with λmax 375 nm. These results are
2
7
in agreement with those of Mehnert et al., except we did not
observe the very short lived absorption at 320 nm under our
conditions. The same 420 nm absorption is observed in the
-
reduction of tetrathionate by eaq , again in agreement with
Mehnert et al. and supporting the identification of the absorption
•
3-
as from S4O6 . In the oxidation reactions, this dimer results
2
-
from the rapid reaction of excess S2O3 with the initial
•
-
oxidation product, possibly S2O3
.
This leaves the question of the identity of the species
absorbing at 375 nm. We find it difficult to accept that the
dimeric species would rapidly decompose to its monomeric
components, as suggested by Mehnert et al., since S2O3•
radicals have been suggested to bind strongly to various other
anions. Moreover, our equilibrium measurements are in
agreement with a dimeric structure for the radical absorbing at
a λmax of 375 nm, not with a monomer. To rationalize these
results, we suggest that the dimeric species absorbing at 420
nm, in which the binding involves four sulfur atoms in a row
Figure 7. Equilibrium plots assuming monomeric and dimeric radicals
2-
from the oxidation of S
2
O
3
in N
2
O-saturated solutions, absorbed dose
‚ as
5
-10 Gy. Solution compositions are presented in Table 4, (a) N
3
-
•
6 4
the oxidant and (b) 4-CNC H O as the oxidant.
5
0
The plots (Figure 7) indicate that if equilibrium 30 is assumed,
the plot is strongly curved, whereas if equilibrium 31 is assumed
to be valid, a straight line passing through the origin is obtained.
For the latter case, the plot involves the square of the thiosulfate
2
1
concentration, i.e.
-
- •-
as in tetrathionate, i.e., ( O3S-S-S-SO3
)
rearranges rapidly
N ][(S O ) 3-]
-
[
to another dimeric species, possibly by breaking the central
-S-S-) structure and forming an S-O bond instead, i.e.,
to form ( O3S-S-O-SO2-S ) . This rearrangement may take
place via a four-centered cyclic intermediate. This suggested
scheme satisfies the reaction kinetics reported earlier and those
observed in our study. The absorption at 420 nm for the ( O3S-
S-S-SO3 ) intermediate is similar to that of organic (RS-
SR) species. These species are known to be in equilibrium
with their monomeric components and to monomerize at lower
pH. The absorption at 375 nm suggested for the rearranged
3 2 3 2
K )
(32)
•-
(
•
2- 2
[
N ][S O
]
-
• 2-
3
2
3
4
-1
From the values K ) 2.0 × 10 (Table 4) at I ) 0.85 mol L
4
-1
and K ) 1.9 × 10 at I ) 0.4 mol L and taking E ) 1.35 V
-
•
- 48
for N3 /N3
,
we calculate E ) 1.057 V for the reduction
-
•-
•
3-
potential of the (S2O3)2 radical at zero ionic strength.
The value obtained for the reduction potential of the
•
-
•
3-
(S2O3)2
radical is close to the reported reduction potential
value of 1.12 V for the phenoxyl radical derived from 4-cy-
•
dimer is closer to that of monomeric RS radicals and thus is in
3
8
anophenol. This prompted us to utilize this couple to verify
line with a structure in which the radical is localized on one
sulfur, as suggested.
-
the results relative to the N3‚/N3 couple. As shown in Table 4
-
1
and Figure 7 at I ) 0.28 mol L , a value of K ) 2.2 was
obtained following similar arguments as in the case of azide
above, and thus E ) 1.082 V at zero ionic strength. The finding
that in both experiments good linear plots are obtained when
the equilibrium is assumed to involve the dimeric species
suggests that the species absorbing at 375 nm has the dimeric
structure. Combining the results of the two studies, we obtain
Acknowledgment. We thank Dr. David Stanbury for helpful
comments on this manuscript.
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,
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3, 444.
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