The Dimethylhydroxysulfuranyl Radical

Article abstract of DOI:10.1021/jp953613k

By use of pulse radiolysis the one-electron reduction potentials, E⁰(DMS(.+)/DMS) and E⁰(DMS(.+)/DMS) and E⁰((DMS)2(.+)/2DMS) (dimethyl sulfide, DMS) were determined to be 1.66 +/- 0.03 and 1.40 +/- 0.02 V vs NHE, respectively.DMS(.+) was found to be in equilibrium with DMSOH(.) with a pK_a = 10.2.The conditional equilibrium constant for the reaction DMSOH(.) + DMS ->/<- (DMS)2(.+) + OH(1-) was found strongly dependent on both ionic strength and DMS concentration.In the thermodynamic limit this equilibrium constant is ca. 1.3.The dimerization reaction DMS(.+) + DMS ->/<- (DMS)2(.+) was shown to have its equilibrium constant between 1E4 and 5E4 M^-1.DMSOH(.) reacts with O2 with a rate constant of 2E8 M^-1 s^-1, independent of pH (11-14).From this and other observations, we estimate the pK_a for deprotonation of DMSOH(.) to exceed 17.From spectral and kinetic data, the maximum lifetime of the radical (DMS)2OH(.) was predicted to be 10 ns.The stability of DMS-X(.) (X = OH, I, Br, Cl) in aqueous solution was shown to correlate with the one-electron reduction potential of X(.).Comparison of gaseous and aqueous behavior of DMS-OH(.) reveals that aqueous solvation strongly stabilizes the S-O bond against dissociation into DMS and OH(.).The Gibbs free energy of solvation of DMSOH(.) was calculated to be -12 +/- 3 kcal/mol, an unusually large value for a neutral species.

Full text of DOI:10.1021/jp953613k

J. Phys. Chem. 1996, 100, 8875-8881
8875
The Dimethylhydroxysulfuranyl Radical
Ga´bor Mere´nyi* and Johan Lind
Nuclear Chemistry Laboratory, Department of Chemistry, Royal Institute of Technology, Stockholm, Sweden
Lars Engman
Department of Organic Chemistry, Institute of Chemistry, UniVersity of Uppsala, Uppsala, Sweden
ReceiVed: December 6, 1995; In Final Form: February 15, 1996X
By use of pulse radiolysis the one-electron reduction potentials, E0(DMS•+/DMS) and E0((DMS)2•+/2DMS)
(dimethyl sulfide, DMS) were determined to be 1.66 ( 0.03 and 1.40 ( 0.02 V vs NHE, respectively. DMS•+
was found to be in equilibrium with DMSOH• with a pKa ) 10.2. The conditional equilibrium constant for
the reaction DMSOH• + DMS h (DMS)2•+ + OH- was found strongly dependent on both ionic strength and
DMS concentration. In the thermodynamic limit this equilibrium constant is ≈1.3. The dimerization reaction
DMS•+ + DMS h (DMS)2 was shown to have its equilibrium constant between 104 and 5 × 104 M-1.
•+
DMSOH• reacts with O2 with a rate constant of 2 × 108 M-1 s-1, independent of pH (11-14). From this and
other observations, we estimate the pKa for deprotonation of DMSOH• to exceed 17. From spectral and
kinetic data, the maximum lifetime of the radical (DMS)2OH• was predicted to be 10 ns. The stability of
DMS-X• (X ) OH, I, Br, Cl) in aqueous solution was shown to correlate with the one-electron reduction
potential of X•. Comparison of gaseous and aqueous behavior of DMS-OH• reveals that aqueous solvation
strongly stabilizes the S-O bond against dissociation into DMS and OH•. The Gibbs free energy of solvation
of DMSOH• was calculated to be -12 ( 3 kcal/mol, an unusually large value for a neutral species.
Introduction
the S-O bond in DMSOH• appeared to be a relatively nonpolar
two-center three-electron bond. In contrast to the elusive nature
Dimethyl sulfide (DMS) is an important molecule, being the
principal organosulfur compound to be released into the
atmosphere. Its destruction there is mainly effected by OH•
of DMSOH• in the gas phase, the occurrence of this species is
well documented in water during OH•-induced oxidation of
DMS. By means of optical,5-7 conductivity,5,8 and ESR9
monitoring, a whole spectrum of transient species has been
detected. In the course of kinetic investigations, mostly by
means of pulse radiolysis, reactions 3-11 have been identified.
In particular, the properties of the two-center three-electron bond
radicals and to a lesser extent by Cl• and NO3 . In the gas phase
•
the reactivity of OH• toward DMS has been the subject of a
number of investigations.1 In these studies the disappearance
of the OH• radical was measured and thus the occurrence and
properties of other intermediates could only indirectly be
assessed. By monitoring the time course of OH• radicals in
the absence and presence of O2 and by varying the amount of
DMS, the following reaction scheme was arrived at, where M
denotes the third body.
•+
in (DMS)2 and similar species have been extensively
covered.10-12
DMS + OH• h DMSOH•
(3)
(4)
DMS + OH• f •CH2SCH3 + H2O
DMS + OH• + M f DMSOH• + M
(1)
(2)
DMS + OH• f •CH2SCH3 + H2O
DMSOH• h DMS•+ + OH-
(5)
(6)
At all temperatures studied the main reaction mode was
hydrogen abstraction by OH• to form the (methylthio)methyl
radical (•CH2SCH3). However, the lower the temperature, the
more important the second channel was found to become,
namely, formation of the dimethylhydroxysulfuranyl radical
(DMSOH•) in equilibrium with DMS + OH•. While Hynes et
al.2 estimate the S-O bond strength in DMSOH• at ca 13 kcal/
mol, Gu and Turecek3 believe that DMSOH• does not exist at
all except as a transition state. More recently, a high-level ab
initio quantum chemical calculation4 has substantiated the
existence of DMSOH•, but it also revealed that the S-O bond
is somewhat elusive and rather different from the S-X bonds
in DMS-halogen atom (X) adducts. The existence of the latter
species was readily predicted even at a relatively simple
computational level and they were found to be well described
in terms of soft acid-soft base complexes. On the other hand,
DMS•+ + H2O h DMSOH• + H+
DMSOH• + DMS h (DMS)2•+ + OH-
(7)
DMS+ + H2O(B-) f •CH2SCH3 + H3O+(BH) (8, 8′)
•+
DMS•+ + DMS h (DMS)2
(9)
DMSOH• h DMSO•- + H+
DMSO + eaq- f DMSO•-
(10)
(11)
While the qualitative picture of DMS degradation by OH• is clear,
not all parameters appear sufficiently well established to allow for
a consistent description of the system over the whole concentration
and pH range. In particular, some ambiguities persist regarding
X Abstract published in AdVance ACS Abstracts, May 1, 1996.
S0022-3654(95)03613-6 CCC: $12.00 © 1996 American Chemical Society

8876 J. Phys. Chem., Vol. 100, No. 21, 1996
Mere´nyi et al.
the acid-base equilibria and reactivity of the DMSOH• species. In
their pioneering work, Meissner et al.13 observed an acid-base
equilibrium of some transient formed subsequent to both reactions
3 and 11. The above authors ascribed this equilibrium, character-
ized by a pKa ) 10.2 ( 0.3, to eq 10, the deprotonation of
DMSOH•, a suggestion adopted and retained ever since. Recently,14
however, this claim was challenged on the following grounds. In
ref 7 k5 was measured to be (1.3 ( 0.2) × 106 s-1
. On the
reasonable assumption that k-5 is probably close to the diffusion-
controlled limit, i.e., ca. 1010 M-1 s-1, and certainly cannot exceed
this value, the observed pKa ) 10.2 was ascribed to eq 6. As a
result, pKa(10) was deduced to be larger than 10 and probably even
larger than 14. Clearly, if pKa(6) and pKa(10) were close to each
other, one would observe a steeper change with pH of the transient
signal around pH 10 than was reported in ref 13. In addition, the
yield of (DMS)2•+ should decrease with increasing pH at a constant
ratio of [OH-]/[DMS]. In fact, we shall, in what follows, show
that this is not the case. In the present work we shall firmly
establish the acid-base properties of DMSOH• and discuss the
differences between its properties in water and the gas phase.
Figure 1. Spectra of intermediates. The full lines are splined fits to
the data. Gꢀ is given in units of 100 eV-1 M-1 cm-1. (a) (DMS)2
•+
from irradiation of N2O-saturated unbuffered solutions: (9) 0.01 M
DMS; (0) 5 × 10-4 M DMS and the points are scaled by a factor of
1.16 (see text). (b) DMSOH•: ([) N2O-saturated 10-3 M DMS solution
containing 1 M NaOH; (×, ‚‚‚) scaled data (see text) which refer to
argon-purged 2.6 M DMSO solutions containing 10-3 and 1 M NaOH,
respectively. (c) The dotted line is a calculated composite spectrum
compounding 21% a with 79% b. (b) Experimental points measured
in N2O-saturated 10-2 M DMS solutions containing 1 M NaOH.
Experimental Section
Pulse radiolysis was performed at room temperature utilizing
doses of 2-15 Gy/pulse corresponding to 1.2 × 10-6-9 × 10-6
M radicals. The 4.6-MeV linear accelerator is characterized
by a fwhm of 8 ns and a beam current of 1.8 A. The
computerized optical detection system15 has been described
elsewhere. In all experiments a monochromator bandwith of
2.5 nm was used. When recording spectra each point represents
5-10 superimposed traces. During titration as many as 30
superpositions were utilized for each point. The relative dose/
pulse was monitored by a secondary emission chamber, the latter
having been calibrated against an aerated 10-2 M KSCN solution
taking16 Gꢀ ) 2.23 × 104 100 eV-1 M-1 cm-1 at 500 nm. The
solutions were made up in Millipore-deionized water and purged
for 10 min by the appropriate gas. DMS was added, pure or
from stock solutions, after purging. In order to keep the O2
concentration well below 5 × 10-6 M, the added volume was
always <1% of that of the purged solution.
Chemicals. Dimethyl sulfide (99+%), dimethyl sulfoxide
(99.9%), di-tert-butyl sulfide (98%), diphenyl sulfide (98%),
NaOH (99.99% semiconductor grade or 97+%), KSCN (99+%),
NaN3 (99%), [10-(2-dimethylaminopropyl)phenothiazine] hy-
drochloride (promethazine, 98%), 1,1′-dimethyl-4,4′-bipyri-
dinium dichloride (methyl viologen, MV2+, 98%) all Aldrich,
bis(4-hydroxyphenyl) sulfide (Crown Zellerbach Corp.), 2-meth-
yl-2-propanol, KH2PO4, and K2HPO4 (Merck p.a.), Ar (AGA),
N2O (AGA), and O2 (AGA) were used as received.
purged solutions on the other. Furthermore, in Ar-purged
neutral solutions containing 2 M DMSO and 10-3 M DMS only
-
60% of eaq was found to produce (DMS)2•+. We therefore
employ 0.6 as the efficiency factor of eaq- to reduce DMSO to
the intermediate in Figure 1b. The scaled DMSO-derived
spectra (at pH 11 and 14) are seen to be congruous onto that of
the OH• adduct to DMS. We note the good agreement between
our spectrum and the one observed in neutral solution.7 This
similarity suggests that between pH 7 and 14 DMSOH• does
not change its protonation state.
One-Electron Reduction Potential of (DMS)2•+. In ref 17
the below equilibria were measured
Br2•- + DMS h DMS-Br + Br-
K12 ) 1.1 × 104 (12)
K13 ) 1.64 (13)
DMS-Br + DMS h (DMS)2•+ + Br-
From these values and E0(Br2•-/2Br-) ) 1.62 V,18,19 we obtain
E0((DMS)2•+/2DMS) ) 1.37 V vs NHE. In the present work
we attempted to determine this potential more directly by having
the (DMS)2•+/2DMS couple equilibrate with N3 /N3
.
•
-
•
(DMS)2•+ + N3- h 2DMS + N3
(14)
Diphenyl sulfoxide (Aldrich 97%) was recrystallized from
CH2Cl2/hexanes before use.
In order to achieve rapid equilibration the concentration of DMS
was varied from 3 × 10-2 to 0.11 M. Within this limited
concentration interval we could observe an equilibration. By
monitoring the absorbance of (DMS)2•+ at 465 nm, which was
found to conform to the expression OD-1 ) OD0-1(1 + K14-
[N3-]/[DMS]2), we obtained K14 ) 16.4. The rate of equilibra-
Results and Discussion
Spectra of Intermediates. Figure 1a is the spectrum of
(DMS)2•+ with a maximum at 485 nm. The closed squares and
the curve pertain to a DMS concentration of 0.01 M recorded
in an unbuffered solution. The open squares were taken from
measurements on a 5 × 10-4 M DMS solution and scaled by a
factor of 1.16 to account for losses due to reaction 8, etc. It is
evident that the spectral shape is invariant with [DMS].
Spectrum b, peaking at 358 nm, was recorded in 1 M NaOH
containing 10-3 M DMS. It is assigned to the adduct of OH•
to DMS. The spectra obtained upon reduction of DMSO by
eaq had the same shape, albeit a smaller size. A factor of 2
follows from the different yield of OH• in N2O-saturated
solutions on the one hand as compared with that of eaq- in Ar-
tion was calculated from the kinetic traces assuming kobs
)
k14[N3-] + k-14[DMS]2. Within this model the values of k14
and k-14 come out as (2 ( 1) × 108 M-1 s-1 and (1.6 ( 0.6)
× 107 M-2 s-1, respectively. Utilizing E0(N3 /N3-) ) 1.33 V19
•
we calculate from K14 ) 16.4 E0((DMS)2•+/2DMS) ) 1.40 V.
The agreement between this value and 1.37 V, derived above
from eqs 12 and 13, is satisfactory. We believe, however, 1.40
V to be somewhat more accurate, its determination being based
on a single equilibrium.

Dimethylhydroxysulfuranyl Radical
J. Phys. Chem., Vol. 100, No. 21, 1996 8877
360 nm, due to DMSOH•. We could confirm a pKa ) 10.2,
identical with the one reported in ref 13. As was mentioned
above, we ascribe this pKa to eq 6. The simple sigmoidal curve
observed argues against the pKa of deprotonation of DMSOH•
to yield DMSO•- (eq 10) being close to 10. In addition to
studying the variation of the size of the 360 nm absorbance,
we also measured its decay rate as a function of the pH. Well
below pH 10 the rate was ca. 1.2 × 106 s-1, i.e., identical to k5
determined in ref 7. Above ca. pH 9.5 this rate was followed
by a slower decay. The amplitude of the fast decay decreased
with increasing pH at the expense of that of the slow decay.
The rate of the latter diminished with increasing pH to attain a
lower limit23 of ca. 5 × 104 s-1 at pH > 11. We note that
above pH 11 identical dynamics were observed, independently
of whether DMSOH• was produced in reaction 3 or subsequent
to reaction 11. In the presence of DMS, the same dynamics
were seen at 360 and 465 nm, an observation attesting to
equilibria 5 and 9 being maintained throughout. From the pH
behavior of the slow decay rate we obtained the same pK(6) )
10.2 as from the absorbance measurements. We interpret the
fast process to be the attainment of eq 6. The pH behavior of
the slow component is then given by kobs ) (k8[H+] + klimK6)/
([H+] + K6).
The pH-independent rate constant, klim, for the disappearance
of DMSOH• is interpreted as follows. The main reaction of
DMS•+ with OH- is addition to form DMSOH• in reation -5.
A minor side reaction is proton transfer between them to yield
•CH2SCH3 in reaction 8′. From K5 ) 1.6 × 10-4 M-1 and k5
) 1.3 × 106 s-1, k-5 ) 8 × 109 M-1 s-1 is calculated. Hence
the formal rate constant, k′8, with OH- as the base B-, would
come out as ca. 3 × 108 M-1 s-1. Thus klim ) k5k′8[OH-]/
(k-5[OH-] + k′8[OH-]). More likely, however, is the following
scenario. DMS•+ and OH- diffuse together with a rate constant
of ca. 8 × 109 M-1 s-1. Then in the encounter complex ca.
4% of the OH- ions deprotonate a methyl group while the rest
adds to sulfur. Evidently, these two cases are mathematically
indistinguishable.
Figure 2. Experimental pseudo-first-order rate constant for the decay
of the absorbance of (C6H5)2S•+ observed at 750 nm as a function of
DMS concentration: (b) Experimental points. The full line is
calculated from the expression kobs ) 3.4 × 104 + 3.0 × 107[DMS] +
1.5 × 1010[DMS]2. Inset: an expanded portion of the lower left part
of the figure, where the linear component is prominent. The broken
line is the best fit to the whole data set with the first-order component
of the above expression neglected.
Determination of E0((DMS•+/DMS). If the equilibrium
constant K9 is known, it is an easy matter to calculate
E0((DMS•+/DMS) from E0((DMS)2•+/2DMS). Unfortunately,
there are two conflicting values for K9 in the literature. From
data in ref 13 it transpires (see below) that K9 is approximately
104 M-1. On the other hand, the value derived for K9 in ref 20
is as high as 2 × 105 M-1. Consequently, we attempted to
directly determine E0((DMS•+/DMS) by measuring the forward
and reverse rates of reaction 15. The rate of the forward
(C6H5)2S•+ + DMS h (C6H5)2S + DMS•+
(15)
reaction, k15, was readily measured by bringing (C6H5)2S•+,
produced14 in the reaction of eaq- with (C6H5)2SO, to react with
varying amounts of DMS. This reaction was found to be first
order in DMS, when [DMS] was below ca. 1 × 10-3 M, but
tended more and more toward second order at higher DMS
concentrations (see Figure 2). The data was fitted to a
polynomial, second order in [DMS]. From the first-order
component k15 ) (3.0 ( 0.3) × 107 M-1 s-1 was calculated.21
The reverse reaction rate, k-15, was more difficult to determine
due to the poor solubility of (C6H5)2S. The rate constant could
be estimated from the rates of buildup and the size of the
absorbance of (C6H5)2S+ at 750 nm14 in a system where only
DMS•+ was generated initially. DMS•+ was produced by
bringing DMSO to react with eaq- in reaction 11 in the presence
of 1.9 × 10-5 or 3.8 × 10-5 M (C6H5)2S. Due to the slowness13
of reaction 11, 2 M DMSO had to be employed. The maximum
size of the absorbance observed at 750 nm was only ca. 35%
(at 1.9 × 10-5 M), and 50% (3.8 × 10-5 M) of the signal that
would have been obtained had no loss of DMS•+ occurred
through deprotonation (reaction 8). In combination with k8,
which in the present system is 1.7 × 105 s-1 (vide infra), these
absorbances yield k-15 ) 4.6 × 109 M-1 s-1. If we utilize the
increase of the observed rate with [(C6H5)2S], a rate constant
k-15 ) 4.4 × 109 M-1 s-1 is calculated. From k15 and k-15 we
The combination of equilibria 5 and 9 leads to eq 7.
Clearly K7 ) K5K9. K7 can be measured directly by, e.g.,
•+
monitoring the 465 nm absorbance due to (DMS)2 as a
function of [OH-] at constant [DMS]. Consequently, we
performed a number of such titrations, presented in Figure 3.
Several features emerge from the figure. The main observation
is that all experiments are described by equilibria, which are
first order in [OH-]. Therefore, invoking the arguments in the
Introduction, we can safely exclude eq 10; i.e., DMSOH• does
not deprotonate below pH 13.
As expected, the equilibrium constant K7 is dependent on
ionic strength (I), varying by a factor of 2 when I goes from 0
to 0.2 M (compare the curve pertaining to 5 × 10-4 M DMS at
I ) 0.2 M with that at I ) 0 M and [DMS] ) 1.1 × 10-3 M).
However, even though we have not elaborated it in detail, K7
also seems to increase with increasing DMS concentration.
Thus, when I is made up of added NaOH in the presence of 1.1
× 10-2 M DMS, the (DMS)2•+ signal is halved at [OH-] ) 0.1
M, which corresponds to a formal K7 ) 9. On the other hand,
K7 is merely ca. 3 at I ) 0.2 M and [DMS] < 1.5 × 10-3 M.
Formally, this implies a decrease in the activity coefficient of
(DMS)2•+ with increasing [DMS]. On the molecular level, this
could be taken to imply complexation between DMS and
(DMS)2•+. However, no spectral indication (see Figure 1a),
whatsoever, could be had for such a process. The value of K7
at [DMS] ) 1.1 × 10-3 M and negligible ionic strength is
calculted to be 1.4. This is almost the same as 1.3, extracted
from the data in ref 13 pertaining to zero ionic strength and
finally obtain K15 ) 7 × 10-3
.
Utilizing E0((C6H5)2S•+/
(C6H5)2S) ) 1.53 V22 we calculate E0((DMS•+/DMS) ) 1.66
V. From this value and E0((DMS)2•+/2DMS) ) 1.40 V we
obtain K9 ) 2.5 × 104 M-1
.
Assessment of Equilibria 6 and 7. First, we repeated the
-
titration in ref 13 by reducing DMSO with eaq in reaction 11
in the absence of DMS and by measuring the absorbance at

8878 J. Phys. Chem., Vol. 100, No. 21, 1996
Mere´nyi et al.
SCHEME 1
of (DMS)2OH•. We agree, in the main, with the mechanism of
the authors, except that we suggest their proposed intermediate
to be the transition state depicted in Scheme 1. By the logic of
microscopic reversibility k-7 has also to involve a H2O molecule.
The necessity for H2O can be rationalized by assuming a H2O
molecule to be strongly complexed to (DMS)2•+. We note that
in ref 25 a tight complex between DMS•+ and H2O was
predicted and this possibility is substantiated by our finding14
that DMS•+ is hydrated much more strongly (by ca. 14 kcal/
mol) than (C6H5)2S•+. In view of these points, the suggestion
of a relatively tight (DMS)2•+-H2O complex would not appear
too audacious.
Deprotonation of DMS•+ by H2O. When in neutral
solutions DMSO (2 M) was reduced by eaq- in the presence of
(4-OH-C6H4)2S or promethazine, the latter compounds were
oxidized to their radicals. At low concentrations of the
reductant, [Red], the rate of growth of the radical absorbance
was proportional to [Red]. However, when the observed rate,
kobs, approached ca. 106 s-1, kobs vs [Red] deflected from
straight-line behavior. This was analyzed in terms of a limiting
rate corresponding7 to k5 ) 1.3 × 106 s-1. Now in reaction 11
DMSO•- is formed primarily. As DMSO•- is extremely
unlikely to expel O2- to produce DMS•-, one has to assume
that reaction 5 is preceded by protonation of DMSO•- by water
with a rate >1.3 × 106 s-1. Deprotonation of DMSOH• by
OH- cannot exceed ca. 1010 M-1 s-1. Consequently, pKa(10)
is larger than 10, a conclusion deduced in ref 14 in an alternative
way.
As a spin-off of these titrations by (4-OH-C6H4)2S or
promethazine, the rate of DMS•+ disappearance, k8, was obtained
with a value of 1.7 × 105 s-1. The rates were extracted from
the intercepts of the observed rate constants vs (4-OH-C6H4)2S
or promethazine concentration.26 The competition kinetic plots
representing the inverse of the size of the Red-radical signal vs
[Red]-1 yielded rate ratios which tallied with the directly
determined rates. In agreement with ref 20, k8 was found to
increase upon addition of phosphate. In another set of experi-
ments in neutral solutions we measured the entire dynamics of
the 465 nm absorbance while varying the DMS concentration
from 5 × 10-5 to 3 × 10-4 M during its oxidation by OH•
radicals. The observed curves were compared with simulated
ones, where the values for k-9 and k8 were varied and k9 ) 3
× 109 M-1 s-1 was taken from ref 6. Fits were obtained for
k-9 ) 2 × 105 s-1, k8 ) 6 × 104 s-1 or k8 ) 2 × 105 s-1, k-9
) 5 × 104 s-1. The second set of data is in agreement with k8
measured in 2 M DMSO solutions. It is conceivable though
that k8 may be more rapid in the presence of DMSO than in
pure water. In support of this we have observed that even
(C6H5)2S•+, which cannot undergo deprotonation, decayed more
rapidly in the presence of 2 M DMSO than in its absence. All
in all, determination of K9 in neutral solution is not straight-
forwardsonly an interval 1.5 × 104 M-1 < K9 < 6 × 104 M-1
can be obtained. Even though the true value of k8 and hence
of K9 is left somewhat in limbo in the simulations, we believe
k8 ) 6 × 104 s-1 to be the more reliable rate constant, it leading
to a K9 in better agreement with the independnet measurements
described above.
Figure 3. 3 pH titration of the yield of (DMS)2•+ measured at 465 nm
in N2O-saturated solutions at various ionic strengths (I) made up of
NaClO4 and NaOH. The yields are normalized to the values observed
in neutral solutions at the pertinent DMS concentrations. (×) 1.1 ×
10-3 M DMS, I ) 0 M; (b) 5 × 10-4 M DMS, I ) 0.2 M; ([) 1.5 ×
10-3 M DMS, I ) 0.2 M; (9) 4.5 × 10-3 M DMS, I ) 0.2 M; (O) 1.1
× 10-2 M DMS, I ) [NaOH] M; (1) 1.1 × 10-2 M DMS, I ) 1 +
[NaOH] M (Lines) The lines are calculated using the expression (K7-
[DMS] + 0.1[OH-])/(K7[DMS] + [OH-]), where K7[DMS] (M) is set
to (a) 1.6 × 10-3, (b) 5.6 × 10-3, (c) 3.2 × 10-2, (d) 0.1.
[DMS] ) 4 × 10-4 M. We thus set K7 ) 1.3 as the true
thermodynamic equilibrium constant. From this value and K5
) 1.6 × 10-4 M, we obtain K9 ) 0.8 × 104 M-1, in fair
agreement with 2.5 × 104 M-1, the value calculated above from
redox potentials.
Does (DMS)2OH• Exist? In the literature the possible role
of a species, surmised to be an adduct of DMS to DMSOH•,
or, what is equivalent, an OH- adduct to (DMS)2•+, has
sometimes been invoked.7,24 We therefore thought it of interest
to inquire into the nature of this species. Consider spectrum c,
recorded in Figure 1 at pH 14 in the presence of 10-2 M DMS.
It is readily seen that the experimental points can be fitted to a
composite spectrum consisting of 79 ( 2% DMSOH• and 21
( 2% (DMS)2•+. On the reasonable assumption that (DMS)2-
OH•, were it to exist, would not absorb (or would absorb
considerably weaker than (DMS)2•+) above ca. 500 nm, and
granting the error margin to bear on the maximum amount of
(DMS)2OH• present in eq 16, we deduce K16 > 10 M.
(DMS)2OH• h (DMS)2•+ + OH-
(16)
Extrapolated to zero ionic strength and low [DMS] (see above)
K16 > 1 M is obtained. As K7 ) K16K17 ) 1.3 it follows that
K17 < 1 M-1
.
DMSOH• + DMS h (DMS)2OH•
(17)
In conditions, where the reverse rate in eq 7 was negligible,
the forward rate constant of eq 7 was measured7 to be 1.5 ×
108 M-1 s-1. Within the above tentative model, this rate should
be k7 ) k17k16/(k16 + k-17). If k16 . k-17, then k7 ) k17, and
since K17 < 1 M-1, it follows that k-17 > 108 s-1 and hence, a
fortiori, k16 > 108 s-1. If, on the other hand, k16 , k-17, then
k7 ) k16K17, whence both k16 and k-17 come out larger than 108
s-1. In conclusion, either way, the lifetime of (DMS)2OH• can
be 10 ns at most. This is a tenuous basis for postulating such
an intermediate and we rather propose reaction 7 to be a one-
step bimolecular homolytic substitution, a SH2 process, albeit
catalyzed by the water solvent. In ref 7 the large solvent kinetic
deuterium isotope effect on k7 was given a plausible interpreta-
tion, namely that water transfers a proton to the oxygen atom
At this point it may be worthwhile to digress for a brief
comment on the acidity of DMS•+. In ref 27 the C-H bond
strength in DMS was reported to be ca. 95 kcal/mol. On the

Dimethylhydroxysulfuranyl Radical
J. Phys. Chem., Vol. 100, No. 21, 1996 8879
In order to check the reducing properties of DMSOH•
(DMSO•-?) we produced it at pH 14 by O•- oxidation of 5 ×
10-3 M DMS in N2O-saturated solutions in the presence of
methyl viologen, MV2+. The concentration of MV2+ was varied
from 5 × 10-5 to 3 × 10-4 M. We could not observe any
buildup of the characteristic absorbance of MV•+.31 This is
telling evidence for DMSOH• to be a poor reductant, and by
implication, of pKa(10) being above 14. Indeed, as will be
demonstrated, DMSOH• rather acts as an oxidant. When
produced of pH 14 in the presence of (4-O--C6H4)2S, DMSOH•
oxidized the latter compound to its radical with a rather high
rate (≈109 M-1 s-1). Formally, this reaction is somewhat
similar to reaction 7, except that no sulfide dimer is formed.
Even more to the point, DMSOH•, produced at pH 14 in the
presence of 10-2-1 M N3-, oxidized the latter rapidly (>108
•
M-1 s-1) to N3 . While we have not explored the mechanism
Figure 4. Spectra obtained upon pulsed irradiation of N2O-saturated
solutions containing 5 × 10-4 M tert-butyl sulfide: (b) pH 5, ([) pH
12. Inset: pH titration of the absorbance at 425 nm. The drawn line
is calculated for pKa ) 10.4.
of this reaction, the overall process is in keeping with known
redox properties. Thus, from E0(DMS•+/DMS) and K5 we
•
calculate E0(20) to be 1.43 V, well above E0(N3 /N3-) ) 1.33
V.
reasonable assumption that S0(•CH2SCH3) - S0(DMS) ≈
S0(•CH2OH) - S0(CH3OH) ) 1.4 eu28 and the free energies of
solvation of DMS and •CH2SCH3 are equal we calculate
E0(•CH2SCH3,H+/DMS) ) 1.64 V. Then by means of E0-
(DMS•+/DMS) ) 1.66 V we obtain pKa(DMS•+) ≈ 0. Thus
DMS•+ would seem to be an extremely strong acid and its
relatively slow deprotonation by water should be ascribed to
kinetic stabilization of carbon acids.
One-Electron Reduction Potential and Pseudobase For-
mation of the tert-Butyl Sulfide Radical Cation, (t-Bu)2S•+.
In view of the complications present with DMS we undertook
measurements on (t-Bu)2S as well. The one-electron oxidized
radical of this compound, (t-Bu)2S•+, undergoes neither depro-
tonation nor dimerization (reactions 8 and 9). Figure 4 shows
the spectra taken at pH 7 and 12, respectively, upon oxidation
of (t-Bu)2S by the OH• radical. The inset presents a titration
curve, which discloses a pKa ) 10.4. This value is very close
to pKa(6) and is surely the corresponding pseudobase equilibrium
constant of (t-Bu)2S•+. We have also determined the below
equilibrium by bringing (t-Bu)2S to react with the anisole couple.
DMSOH• + e- h DMS + OH-
(20)
As a final confirmation of the protonation state of DMSOH•
we investigated its reactivity toward molecular oxygen. We
produced DMSOH• in two ways: by reducing DMSO (2-4 M
solutions) with eaq- in the presence of (1.3-6.5) × 10-4 M O2
or by having OH• react with DMS using N2O/O2 mixtures as
purging gas. From the decay of the 360 nm absorbance we
obtained the rate constant k21 to be (2.0 ( 0.5) × 108 M-1 s-1
.
The relatively low value of k21 is compatible with the almost
quantitative formation of (DMS)2•+, observed in ref 24 at pH
values well below pKa(6), in the presence of 10-3 M DMS and
up to 5 × 10-4 M O2. It should be mentioned that we found
(t-Bu)2SOH• to react with O2 immeasurably slowly, i.e., with a
rate constant below ca. 107 M-1 s-1. This is ascribed to steric
hindrance and is in keeping with the known reluctance12 of e.g.
(t-Bu)2S•+ to form three-electron bonded complexes.
DMSOH• + O2 f products
(21)
k
21 was independent of the pH (10-14) and of DMS concentra-
tion (0-10-2 M), as long as eq 7 was sufficiently shifted to the
left. These findings suggest that, up to at least pH 14, DMSOH•
is the only species present. Had DMSO•- formed, it would
have been expected to react with O2 by way of a simple outer-
sphere electron transfer, just like CO2•-, with a diffusion-
•+
(t-Bu)2S•+ + CH3O-C6H5 h (t-Bu)2S + CH3O-C6H5
(18)
The equilibrium constant K18 was found to be 1.5. From this
value and E0(CH3OC6H5•+/CH3OC6H5) ) 1.62 V29 we obtain
E0((t-Bu)2S•+/(t-Bu)2S) ) 1.63 V. Within experimental error
this is the same as E0(DMS•+/DMS), and thus our confidence
in the latter value increases.
controlled rate, i.e., ca 3 × 109 M-1 s-1
.
The fact that the measured value of k21 at pH 14 is, within
experimental accuracy (10%), equal to those at lower pH then
suggests that pKa(10) is probably 16 or higher. A similar
estimate is arrived at upon considering the absence of any
significant buildup at pH 14 of the MV•+ absorbance, as
described above. As this implies a second-order rate constant
<107 M-1 s-1, and on the assumption of DMSO•- reacting with
The Properties of DMSOH•. In the above sections it has
been shown that the pKa for deprotonation of DMSOH•, pKa-
(10), is significantly higher than 10 and in ref 14 its value was
surmised to exceed even 14. We shall now provide additional
evidence for this conjecture. First of all, DMSO•- is expected
to be a powerful one-electron reductant, similar to CO2•-. This
can be deduced from known thermochemistry as follows: From
MV2+ about as rapidly as CO2 (ca. 1010 M-1 s-1), pKa(10)
•-
comes out as 17 or higher. We thus arrive at E0(DMSO/
DMSO•-) e -2.1 V.
2
E0(DMS•+/DMS) ) 1.66 V, pKa(6) ) 10.2, and E0(DMSO,-
The very high value of pKa(10) suggests a strongly polarized
S-O bond with substantial negative charge on O. On the other
hand, the S-O bond in the gas phase appears to be relatively
unpolar, judging by the results of an an initio calculation.4 These
findings suggest a major role for water in polarizing the S-O
bond, presumably by way of specific solvation.
Stability of DMSOH and Other DMS Adducts in Water.
The equilibrium constant of heterolysis Khet of DMSOH• is K5
) 1.6 × 10-4 M. Consequently ∆G0het ) 5.2 ( 0.3 kcal/mol.
2H+/DMS,H2O) ) 0.574 V,30 we calculate E0(19) to be -1.11
V.
DMSO + e- + H+ h DMSOH•
(19)
Were pKa(10) no higher than 10, E0(DMSO/DMSO•-) would
still be as negative as -1.7 V and would become progressively
more negative with increasing pKa(10).

8880 J. Phys. Chem., Vol. 100, No. 21, 1996
Mere´nyi et al.
obtain between redox potentials and free energies of DMS-X
bond dissociation in water. Our finding seems to indicate that
the aqueous solvation free energies of DMSX• parallel those of
X-. This, in turn, implies a substantial stabilization of the three-
electron bonded species by solvation, a possibility earlier
suggested in ref 36.
The following relationships with error margins and correlation
coefficients are obtained:
log(Khet) ) (-20.6 ( 0.8) + (0.49 ( 0.06)(E0/0.059)
r ) 0.984
log(Khom) ) (7.5 ( 0.8) - (0.51 ( 0.06)(E0/0.059)
r ) 0.984
Figure 5. Dependence on E0 (X•/X-) of the equilibrium constants for
DMS-X T DMS•+ + X- and DMS-X T DMS + X•, respectively.
The numbers refer to X: (1) I, (2) OH, (3) Br, (4) Cl.
Although the linearity in Figure 5 is impressive, E0(X•/X-) is
apparently not the sole determinant of adduct equilibria. For
instance, we were unable to identify a DMS-N3 adduct under
any conditions, which we should have were N3 to follow
quantitatively the above relationships. We suspect, however,
oxygen-centered radicals such as HO2• and alkylperoxyl radicals,
ROO•, to conform, like OH•, to the linear relationship in Figure
5. If so, this would imply a very low stability for a DMS-
OOR• adduct, E0(ROO•/ROO-) merely being ca. 0.77 V.37
By way of concluding remark we observe that, in view of
the dramatic difference in stability of the DMSOH• adduct in
water and the gas phase, the mechanism and rate of the
atmospheric destruction of DMS may vary considerably,
depending on whether or not water droplets are present.
In a similar fashion one can define a homolysis reaction of
DMSOH• according to
DMSOH• h DMS + OH• Khom
Then log(Khom) ) log(Khet) + (E0(DMS•+/DMS) - E0(OH•/
OH-))/0.059 ) -3.8 + (1.66 - 1.90)/0.059 ) -7.9. Hence
Khom ) 1.3 × 10-8 M and ∆G0hom ) 10.8 ( 1.2 kcal/mol. It is
readily seen that DMSOH• is fairly stable against homolysis.
Thus, the rate constant for the expulsion of OH•, k-3, is predicted
to be as low as ca. 250 s-1. This is, of course, a fictitious value
and merely implies that homolysis in water will never occur in
practice. In stark constrast, the stability of DMSOH• against
homolysis in the gas phase is much less, while, of course,
heterolysis is completely suppressed. From the data of Hynes
et al.2 and ref 1b one can calculate that the rate of addition of
OH• to DMS, k2, at room temperature and atmospheric pressure
is 6 × 109 M-1 s-1, while the rate of homolysis is ca. 6 × 107
s-1. Thus, the equilibrium constant Khom is as high as 10-2 M,
whence the free energy of homolysis (where the standard states
Acknowledgment. This work owes much to stimulating
discussions with Professor K.-D. Asmus and Dr. C. Scho¨neich.
We are grateful to the Swedish Natural Science Research
Council for its financial support.
References and Notes
(1) (a) For critical reviews see: Atkinson, R. J. Phys. Chem. Ref. Data
Monograph 1989, 1, 1. (b) Atkinson, R.; Baulch, D. L.; Cox, R. A.;
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21, 1341-1342.
(2) Hynes, A. J.; Wine, P. H.; Semmes, D. H. J. Phys. Chem. 1986,
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Soc. 1984, 106, 5988.
of all species refer to 1 atm pressure) is calculated as ∆G0
hom
) 1 ( 2 kcal/mol. Apart from influencing the rate of homolysis,
the water solvent is also found to affect the selectivity of OH•
in its reaction with DMS. Thus, while in the gas phase k1/k2 is
0.44, k4/k3 in water is lower than 0.1, as can be judged by the
•+
fact that in the presence of >10-3 M DMS the yield of (DMS)2
is equal to that of OH• within experimental error.
As the free energies of hydration, ∆G0g-aq, of DMS31 and
OH•32,33 are 0.4 and -2.6 kcal/mol, respectively, it follows that
(7) Scho¨neich, C.; Bobrowski, K. J. Am. Chem. Soc. 1993, 115, 6538.
(8) Janata, E.; Veltwisch, D.; Asmus, K.-D. Radiat. Phys. Chem. 1980,
16, 43.
the corresponding ∆G0
for DMSOH• is as negative as -12
g-aq
( 3 kcal/mol. Figure 5 presents the equilibria Khet and Khom as
a function of the redox potentials of the X•/X- couples.34 There
is a linearity observed for both Khet and Khom. The fully drawn
line represents the stability of the DMS-X species irrespective
of the mode of its dissociation. As expected, the crossing point
of the two lines corresponds to E0 ) 1.66 V, the reduction
potential of DMS•+. It then follows that the DMS-X adduct
is at its most stable, when E0(X•/X-) ) E0(DMS•+/DMS).
Now, other things being similar, it is reasonable to expect
that the S-X bond in a DMSX• adduct in the gas phase will be
the stronger the closer the ionization potentials, i.e., the smaller
∆Ip, of X- and DMS. Unfortunately, no values on gaseous
DMSX• other than DMSOH• exist. Nevertheless, quantum
chemical calculations in ref 35 predict a relationship between
∆Ip and the dissociation energies of three-electron bonded
species. However, even if such a relationship exists in the gas
phase, it is far from obvious why a linear relationship should
(9) Gilbert, B. C.; Hodgeman, D. K. C.; Norman, R. O. C. J. Chem.
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(10) Asmus, K.-D. Acc. Chem. Res. 1979, 12, 436.
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(12) Asmus, K.-D. In Sulfur-Centered ReactiVe Intermediates in Chem-
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Study Institutes Series A; Plenum: New York, 1990; Vol. 197, pp 155-
172.
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by Electron Pulse Radiolysis; Baxendale, J. H., Busi, F., Eds.; Nato
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Dimethylhydroxysulfuranyl Radical
J. Phys. Chem., Vol. 100, No. 21, 1996 8881
(19) Stanbury, D. M. In AdVances in Inorganic Chemistry; Sykes, A.
D., Ed.; Academic Press: San Diego, CA, 1989; Vol. 33, pp 81-83.
(20) Mo¨nig, J.; Goslich, R.; Asmus, K.-D. Ber. Bunsenges, Phys. Chem.
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(30) Wood, P. M. FEBS Lett. 1981, 124, 11.
(21) From the second-order component the third-order rate constant, i.e.,
(31) A referee suggested that methyl viologen may be unstable at pH
k{(C6H5)S+ + 2DMS} was estimated to be ≈1.5 × 1010 M-2 s-1
.
•-
14 and therefore may not be reduced even by CO2
. However, in the
(22) Recalculated from the value in ref 14 by use of E0(Br2•-/2Br-) )
presence of formate at pH 14 we could confirm the rapid reduction of MV2+
by CO2•- to form MV•+. The only effect of the high pH was the diminished
lifetime of MV•+ as compared with low pH.
1.62 V.
(23) Above pH 12.5 use of low grade (97+%) NaOH caused the rate to
increase.
(32) Hine, J.; Mookerjee, P. K. J. Org. Chem. 1975, 40, 292.
(33) Schwarz, H. A.; Dodson, R. W. J. Phys. Chem. 1984, 88, 3643.
(34) Kla¨ning, U. K.; Sehested, K.; Holcman J. J. Phys. Chem. 1985,
89, 760.
(35) The necessary data for the DMS-halogen adducts were taken from
ref 17.
(36) Clark, T. J. Am. Chem. Soc. 1988, 110, 1672.
(37) Mere´nyi, G.; Lind, J.; Engman, L. J. Chem. Soc., Perkin Trans. 2.
1994, 2551.
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115, 11376.
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and Biology; Chatgilialoglu, C., Asmus, K.-D., Eds.; Nato Advanced Study
Institutes Series A; Plenum: New York, 1990; Vol. 197, pp 13-18.
(26) From the slopes of the lines the following rate constants were
obtained: k{DMS+ + (4-OH-C6H4)2S} ) 4.2 × 109 M-1 s-1 and k{DMS•+
+ promethazine} ) 1.2 × 109 M-1 s-1
.
(27) Stickel, R. E.; Nicovich, J. M.; Wang, S.; Zhao, Z.; Wine, P. H. J.
Phys. Chem. 1992, 96, 9875.
JP953613K