Reactivity and role of SO5?- radical in aqueous medium chain oxidation of sulfite to sulfate and atmospheric sulfuric acid generation

9142

J. Phys. Chem. A 2001, 105, 9142-9155

Reactivity and Role of SO5^•^-Radical in Aqueous Medium Chain Oxidation of Sulfite to

Sulfate and Atmospheric Sulfuric Acid Generation

Tomi Nath Das^†

Radiation Chemistry & Chemical Dynamics DiVision, Bhabha Atomic Research Centre,

Trombay, Mumbai 400 085, India

ReceiVed: April 4, 2001; In Final Form: July 12, 2001

-

•

•-

This study reevaluates the role of peroxymonosulfate anion radical ( O

3

SOO or SO

5

) intermediate during

-

2-

•-

radical-induced chain oxidation of HSO

band in the UV is weak: ꢀ ) 1065 ( 80 M cm at λmax (260-265 nm). The SO

two radical-radical and four radical-solute reactions, partially producing the other chain carrier, the SO

radical, in either case. In this study, employing the pulse-radiolysis technique but adopting a new approach,

3

/SO

3

-

in oxygenated aqueous solution. The SO

5

radical absorption

1

-1

•-

5

radical takes part in

•-

4

•

-

these two types of reactions of the SO

5

radical have been separately quantified (at room temperature). For

•

-

•-

example, over pH 3.5-12, the branching ratio of (SO

5

+ SO

is found to remain ∼1. The respective reaction rate constants for I f 0 are (2.2 ( 0.3) and

•-

5 4

) reactions giving rise to either the SO

2-

radical or S

2.1 ( 0.3) × 10 M s . The (SO

radical in one and regenerating the SO

2 8

O

8

-1 -1

•-

-

(

5

+ HSO

3

) reactions in acid pH follow two paths, forming the SO

radical in the other, with respective rates of ca. (6.0 ( 0.4) and (3.0

4

•

-

3

7

-1 -1

•-

2-

(

0.3) × 10 M s . In alkaline pH (for SO

5

+ SO

5.6 ( 0.6) and (1.0 ( 0.1) × 10 M s . From only these results, the earlier prediction of chain length

reaching a few thousands could be supported in simulation studies (Bigelow, S. L. Z. Phys. Chem. 1898, 28,

93. Young, S. W. J. Am. Chem. Soc. 1902, 24, 297. Titoff, A. Z. Phys. Chem. 1903, 45, 641. B a¨ ckstr o¨ m,

3

reactions), the rates for similar reactions are ca.

8

-1 -1

(

4

H. L. J. J. Am. Chem. Soc. 1927, 49, 1460. Alyea, H. N.; B a¨ ckstr o¨ m, H. L. J. J. Am. Chem. Soc. 1929, 51,

9

0). To explore the feasibility of controlling S(IV) chain oxidation to sulfuric acid in liquid hydrometeors,

•

-

the effect of radical scavenging on each SO

x

radical (x ) 3, 4, 5) was simulated. The results show that for

•

-

-1

the SO

However, in the case SO

5

radical a scavenger reactivity of ∼100 s may be enough to reduce the chain length by >98%.

•-

4

radical scavenging under similar conditions, only ∼75-80% reduction in acid

production was observed. These results suggest a fresh modeling of sulfuric acid generation in atmospheric

liquid hydrometeors.

Introduction

SCHEME 1

Oxygenated aqueous solution of HSO3 /SO3²^-is known to

-

undergo an autoxidation (chain) reaction to form sulfuric acid

-

2- 1

(

i.e., mainly HSO4 /SO4 ). The chain is initiated by free-

radical oxidants including metal ions, by UV light, or even as

a result of thermal oxidation.²

The simplified reaction Scheme 1 also represents the possible

radical-induced oxidative transformations of SO2 in atmospheric

radical either by H-atom or electron transfer, reaction 4, to

liquid hydrometeors.³In this scheme the SO3 radical is first

-6

•-

•

-

propagate the chain. The remaining SO5 radicals take part in

reaction 5, which may temporarily be considered as a chain-

exit reaction in Scheme 1. In the atmosphere, in addition to

-

2-

produced from HSO3 /SO3 by an H-atom or electron transfer

-

•

mechanism. The peroxymonosulfate anion radical ( O3SOO

or SO5 ) in reaction 1 is subsequently formed by O2 attachment

to SO3 radical. Postulated SO5 radical reactions are eqs

•-

•

-

these six primary reactions, SO5 radical scavenging by

dissolved impurities may open up additional reaction pathways

and influence the chain length.

•

-

•-

2

-5.²

The other related set of reactions include the SO4^•radical

reduction to form sulfate anion (i.e., sulfuric acid) following

mainly reaction 6 or dimerization following reaction 7.

-

^S^O3^•^-⁺^O^f^S^O5

2

•-

(1)

(2)

SO₅^•^-+ SO₅f 2SO₄^•^-+ O₂

•-

SO₄^•^-+ HSO /SO f SO₃^•^-+ SO₄(+H ) (6)

-

2-

+

SO₅^•^-+ HSO /SO f SO₄^•^-+ SO₄(+H O ) (3)

-

2-

+

3 3

3

SO₅^•^-+ HSO /SO f HSO /SO + SO₃

-

2-

-

2-

•-

(4)

(5)

SO₄^•^-+ SO₄f S O

•-

2-

(7)

3

5

2

8

^S^O5^•^-⁺^S^O5^•^-^f^S^O8

2

2-

⁺^O2

Sustenance of the oxidative chain is feasible as long as

reactions 3, 4, and 6 have higher propensities over reactions 5

and 7 or other radical-loss processes. Of course, under favorable

While one part generates SO4^•^-radical by radical dimeriza-

2

-

•-

tion-elimination in reaction 2 and O-atom transfer to excess

circumstances, S2O8 can regenerate the SO4 radical as a

S(IV) in reaction 3, another fraction regenerates the SO3^•^-

2-

•-

-

result of photolysis just as any S2O6 produced from SO3

radical dimerization can also decompose to regenerate the SO3^•

radical. However, these two reactions may not actively partici-

†

Fax: 91-22-5505151. E-mail: tndas@apsara.barc.ernet.in.

1

Published on Web 09/14/2001

Reactivity and Role of Aqueous SO5^•^-

J. Phys. Chem. A, Vol. 105, No. 40, 2001 9143

TABLE 1: Reported Reaction Kinetics of SO ^•^-

Radical

5

ref ) rate constant (M^-

1

s

-1 a

)

reactions

SO5^•^-+ SO5^•^-f 2SO4^•^-+ O2

16 ) 5.2 × 10 ; 15 ) 8.7 × 10 ; 13 < 1.0 × 10 ; 12 < 2.0 × 10 ; 17 ) 2.0 × 10 ; 10 ) 2.2 × 10 ; 6, 11,

6

7

8

6

1

4 ) 6.0 × 10 ; 5 ) 8.4 × 10

SO5^•^-+ SO5^•^-f S2O8²^-+ O2

15 ) 1.4 × 10 ; 10 ) 4.8 × 10 ; 13 < 1.0 × 10 ; 16 ) 1.2 × 10 ; 5, 6, 11, & 14 ) 1.4 × 10 ; 9 )

7

8

(

1.0-1.5) × 10

•

-

2-

-

2-

-

•-

2

4

5

SO5 + HSO3 f HSO4 + SO4

10 ) 3.6 × 10 ; 5 ) 2.5 × 10 ; 11 < 3.0 × 10

4

6

7

6

SO5 + SO3 f HSO4 + SO4

11 ) 7.5 × 10 ; 10 ) 5.5 × 10 ; 5 ) 9.0 × 10 ; 14 ≈ 1.0 × 10

3

4

5

SO5 + HSO3 f HSO5 + SO3

10 ) 8.6 × 10 ; 5 ) 7.5 × 10 ; 11 < 3.0 × 10

4 5 6

SO5 + SO3 f HSO5 + SO3

11 ) 2.5 × 10 ; 10 ) 2.1 × 10 ; 14 ) 3.0 × 10 ; 5 ) 3.8 × 10

a

As measured, reported, or used in previous studies.

pate in the time scale of the chain oxidation process. In Scheme

, the efficiency of O2 replenishment at the reaction zone is

tions), we can visualize the inherently unhelpful nature of the

-

2-

•-

1

HSO3 /SO3 matrix where all six or at least four major SO5

radical reactions are expected to take place at any instant. In

also expected to influence the chain length, especially at very

high S(IV) concentrations. Chain lengths of hundreds to

2

-

LFP with S2O6 , reaction 8

1

thousands in laboratory studies suggest that the atmosphere

SO₅^•^-+ S O f SO₄^•^-+ S O

2-

(8)

aqueous medium oxidation of SO2 may dominate over its gas

phase reactions to generate sulfuric acid and possibly introduce

2

6

2

7

2

-

2-

additional sulfur-oxygen species such as S2O6 , S2O8 , and

probably took place along with reactions 2 and 5.

Although reaction 8 has not yet been quantified, no better

explanation can be offered at this stage for the reported rapid

2-

HSO5 /SO5 into the atmosphere. In this scenario, a reduction

in the acid concentration may also become practicable by

arresting or slowing the chain with the help of suitable radical

scavengers. A scavenger, however, is expected to show mark-

edly different reactivity toward the two chain carriers (SO5

and SO4 ). The SO5 radical has a moderate oxidizing power

•

-

13

formation of SO4 radical following a first-order kinetics.

The acid dissociation constants of S(IV) species in water at

•

-

2

-7

•-

7

25 °C (1.26 × 10 and 5 × 10 M respectively for H2SO3

- 18

and HSO3 ) suggest that near neutral pH or in acidic pH all

four radical-solute reactions 3 and 4 are possible; therefore,

their differently mixed propensities may also have been a source

of mismatch between two results obtained at different pH values.

Additionally, the simultaneous presence of all three SOx^•

radicals (shown below in Figure 9) and their overlapping

but can also participate in O-atom and H-atom transfer reactions.

_O_n_t_h_e_o_t_h_e_r_h_a_n_d_,_S_O₄_•- radical is a strong oxidant and is also

8

capable of oxidizing chemicals by H-atom abstraction. There-

fore, to have a realistic control over any atmospheric scenario,

not only all the reaction kinetics pertaining to Scheme 1 but

also the appropriate radical-scavenging abilities of any potential

additive must be known precisely.

-

1

0

absorption characteristics are expected to produce complex

kinetic traces. Thus, reported first- or second-order rates were

actually oversimplification of these. In short, wide scatter in

•

-

A search for SOx radical (x ) 3, 4, 5) reactivity in the

9

solution kinetic database reveals that the magnitudes of the

•

-

the SO5 radical rate constant values originated or persisted

because (i) indirect methods overlooking unaccounted for radical

loss were repeatedly used to generate it, (ii) radical-radical

reactions could never be segregated or studied separately from

the radical-solute reactions, and (iii) as a consequence, during

kinetic fittings of experimental results, inappropriate or incom-

plete assumptions were made, sometimes disregarding the ionic

strength effect.

•-

concerned SO3 and SO4 radical rate constants from different

studies agree fairly well with each other. On the other hand, as

shown in Table 1, despite many laboratory studies in pristine

•-

aqueous matrix, the six SO5 reaction rates disagree consider-

ably with each other. Although these disagreements probably

reflect the differences in individual measurement procedures, a

resulting major concern is the repeated use of some of these

5

,6

values for modeling atmospheric sulfuric acid generation.

7

During our recent PR study on sulfur oxyanion radicals, we

found that the alternative method for obtaining the SO5 radical

from oxidation of HSO5 is simple, direct, and effective if

Without any satisfactory explanation or supporting evidence for

their specific choice of a set of rate values, the atmospheric

projections in these modeling studies still remain mainly

speculative, and therefore, their charted acid concentration, chain

length, or other related conclusions may be far removed from

reality.

•-

-

certain precautions are taken. The starting solute Oxone (from

DuPont as triple salt 2KHSO5‚KHSO4‚K2SO4) and its solutions

require some special handling, and from the expertise gathered

during the above study, we were successful in designing

appropriate matrixes to study the radical-radical reactions first.

After quantifying these two reactions, subsequently the other

sets of radical-solute reactions were studied. With careful

selection of experimental pH and control and correlation of ionic

strength (I) in these studies, a consistent set of six rate constants

was estimated that was able to provide satisfactory analysis of

all measurements.

To surmount this prevailing uncertainty in an otherwise

important aspect of atmospheric chemistry, in this study we first

present a new experimental approach to obtain fresh estimations

of these reaction rates. Subsequently, using our values, we

quantify the chain oxidation, and therein measure the potency

•

-

of any SO5 radical scavenger in controlling the chain length

and resulting sulfuric acid concentration. However, before we

present our study, it is advantageous to know the reasons behind

such a large spread in rate values in Table 1.

Experimental Section

The previous measurements were made employing either of

the following two complementary techniques. In the majority

Materials and Procedure. All solutions were prepared in

NanoPure water. The gases O2, N2, and N2O used for purging

solutions were obtained locally from British Oxygen Ltd. (purity

≈99.95%). Inorganic chemicals Na2SO3, Na2SO4, KHSO4,

KOH, KCl, KH2PO4, Na2HPO4, Na3PO4, and HClO4 were of

the highest purity available from Merck or Sigma. The Oxone

samples were obtained from two suppliers, Aldrich and Lan-

-

2-

of these experiments, oxygenated solutions of HSO3 /SO3

were used in pulse radiolytic (PR) measurements, while in laser

-

2-

flash photolytic (LFP) studies either oxygenated HSO3 /SO3

or S2O6²solution was used.

-

10-17

Keeping the nature and

complexity of reactions in Scheme 1 in perspective (i.e.,

occurrence of both radical-radical and radical-solute reac-

9144 J. Phys. Chem. A, Vol. 105, No. 40, 2001

Das

-

caster. The actual fractions of KHSO5 in these samples were

estimated separately from spectrophotometric estimation of

Dosimetry was performed with an aerated 10 mM SCN

•

-

solution, and Gꢀ and G(SCN)2 values were taken as 2.59 ×

-

-1

-4

2

-1

-7

-1

21

liberated I2 (as I3 at 352 nm; ꢀ ) 25 800 M cm at pH 7)

10 m J and 3.5 × 10 mol J , respectively, at 475 nm.

-

generated by HSO5 reaction with excess I . In the Aldrich

The parameters measured in pulse radiolysis experiments

generally have an uncertainty of (10-15%, which applies to

all subsequent results of this study.

-

sample, the HSO5 concentration was found to be ∼94-96%

of the above molecular formula, while in the Lancaster sample

the concentration was lower, ∼75-77%. The only other anion

Beyond the experiments, kinetic fitting of experimental data

was done with the help of the ACUCHEM Complex Reaction

-

2-

in both these samples was found to be sulfate (HSO4 /SO4 ).

These and other spectral measurements were made on a Hitachi

2

Modeling Package developed at NIST. To achieve this, the

rate constants of all reactions, the prevailing concentrations of

the reacting radicals or solutes, and their molar absorptivities

at the experimental wavelength are required. Most of the rate

constants were obtained from the literature; ones not available

were first measured and a few were accepted from comparison

of similar reactions reported in the literature (Appendix A). For

kinetic analysis, the concentrations of reacting species were

obtained from the amounts of solutes added in solution and from

the dose- and pulse-dependent yields of species radiolytically

generated from water (Appendix B). The aim was to overlay

the experimental traces with the ACUCHEM produced kinetics

in the best possible form. Only from such fittings could various

mixed processes be resolved satisfactorily and the detailed

picture of Scheme 1 emerge.

3

2

30 spectrophotometer. All measurements were made close to

5 °C.

The 7 MeV pulse radiolysis-kinetic spectrophotometric

detection setup used in this study has been described in detail

1

9,20

before.

Samples were irradiated in a 1 cm square Suprasil

cell. Optical detection of transients was performed within the

spectral range of 230-800 nm using a 450 W xenon lamp and

a Kratos monochromator blazed at 300 nm coupled to a

Hamamatsu R-955 photomultiplier tube. A spectral resolution

of ≈3 nm was routinely achieved, and the effect of scattered

light at 250 nm was <2%.

A solution of Oxone has a pH <3 mainly due to the presence

-

2-

18

of HSO4 /SO4 (pKa )1.92). In general, Oxone solution (i.e.,

-

the HSO5 fraction) is thermally unstable at high concentrations.

During the ACUCHEM analyses, if any reaction involving

two ionic species was referred to from the literature, the

concerned experimental ionic strength was also estimated from

the available matrix details. Then for the sake of convenience,

all such rate values were extrapolated and recorded for a

condition representing I f 0 using the Debye-H u¨ ckel relation.

Only if the necessary experimental details were not available

for any measurement was the reported value accepted without

any change. Similarly, all rates measured in this study were

also recorded for the I f 0 condition. This approach helped in

utilizing the results from one measurement into a subsequent

one. For each ACUCHEM analysis the concerned rates at I f

The extent of its decomposition or thermal instability was first

checked separately at different pH values. It was found that

while a few mM HSO5 was stable (at least 98% of starting

value) for a long time (1 h), at g100 mM concentration its

decomposition was ∼15% during the same time. In alkaline

pH close to 10 (in the presence of added KOH), the decomposi-

tion rate was high; a 3 mM starting concentration reduced to

-

∼

500 µM in 1 h. To minimize any uncertainty in a measurement

-

arising out of HSO5 decomposition, in most cases Oxone

solutions were used within 15 min. Additionally, for studies in

the alkaline pH, a matrix with the desired pH was generated

directly in the irradiation cell using a premixer assembly coupled

to the flow system (similar to the one discussed in our previous

0

were appropriately modified depending on the specific

7

experimental condition being analyzed.

study). In this case, Oxone solution (pH <3) flowing in one

channel was mixed with required amounts of alkali (or with

appropriate amounts of phosphate buffer) flowing in the other

channel at the same rate. Sample flow time from the mixing

zone to the irradiation cell was <2 s, and any thermal

decomposition during this period even in alkaline pH was found

negligible. The sample pH was also recorded at the exit of the

sample cell.

Results and Discussion

Radiolysis of dilute aqueous solution generates both oxidizing

(^•

OH, hydroxyl radical) and reducing radicals (H-atom and eaq )

-

2

3,24

from water.

At pH >3.5, if the solutions are saturated with

-

•

N2O, the eaq is converted into OH radical, doubling its yield

(first two reactions in Table 2). If an 1:1 mixture of N2O and

Similar sample premixing was found necessary for studies

•

•-

•

•-

O2 gas is used for purging, HO3 /O3 and HO2 /O2 radicals

-

2-

with HSO3 /SO3 when either O2 or Oxone was also needed

along with it. Details of these matrix designs are discussed below

at appropriate places in the text. For a study set, when variable

•

-

•

are also produced from O and eaq /H reactions shown in Table

. The rate constants for these radical reactions are taken from

2

9,23

the literature.

These rate constants have been used in all

-

2-

amounts of Oxone (or HSO3 /SO3 ) were used, it was found

desirable to add a balance amount of an equimolar mixture of

ACUCHEM kinetic analyses with any modification (due to ionic

strength) needed. In the range of pH 2.5-12 some solutes and

radicals undergo deprotonation. The concerned reactions are also

included in Table 2. It may be noted that some other reactions

that have negligible propensity have not been included, either

in Table 2 or below.

_S_O₅•- Radical Absorption Characteristics. In neutral and

-

2-

HSO4 /SO4 . The balance amount was equal to the difference

-

2-

of maximum Oxone (or HSO3 /SO3 ) concentration used in

the set and the working Oxone (or HSO3 /SO3 ) for each

measurement. Thus, the total amounts of HSOx /SOx (x ) 4

and 5 for Oxone or x ) 3 and 4 for HSO3 /SO3 ) remained

almost the same in any set of measurements. Although it

increased the ionic strength, it offered advantages such as (a)

-

2-

-

2-

-

2-

•

-

acidic pH, the rate constant of OH reaction with HSO5

-

(

O3SOOH) in reaction 9

ease in pH adjustment, especially in comparative studies, and

•

(

b) the same concentration of SO4²^-for Cl radical reactions,

•

OH + HSO₅f SO₅^•^-+ H O

-

(9)

2

and it prevented changes in experimental conditions in a series

of measurements. In both spectral and kinetic measurements

several oscilloscope traces at each wavelength were averaged

for improving the signal-to-noise ratio. For kinetic studies

requiring high ionic strength, Na2SO4 was used.

7

-1 -1 25

is reported to be low (1.7 × 10 M s ).

•

Therefore, a significant fraction of the OH radical is expected

to be lost in other reactions unless high concentration of Oxone

Reactivity and Role of Aqueous SO5^•^-

J. Phys. Chem. A, Vol. 105, No. 40, 2001 9145

TABLE 2: Rate Constants for Radiation-Induced

Homogeneous Radical-Radical and Some Radical-Solute

Reactions and Different Solute pK

a

Values^a

rate constant (M s^-¹

b

-1

)

reactions

-

•

-

9

eaq + N2O f O + N2

9.1 × 10 (ref 23)

•

-

•

-

7

O

+ H2O f OH + OH

9.4 × 10 (ref 48)

-

•

-

10

OH + OH f O + H2O

1.3 × 10 (ref 48)

•

9

OH + OH f H2O2

5.5 × 10 (ref 23)

•

7

OH + H2O2 f HO2 + H2O

2.7 × 10 (ref 23)

•

9

OH + H f H2O

7.0 × 10 (ref 49)

•-

-

10

OH + O2 f O2 + OH

1.1 × 10 (ref 50)

•

10

OH + HO2 f H2O + O2

1.0 × 10 (ref 51)

•

9

H + H f H2

5.0 × 10 (ref 23)

•

10

H + O2 f HO2

1.2 × 10 (ref 23)

•

10

H + HO2 f H2O2

2.0 × 10 (ref 52)

•

6

H + N2O f N2 + OH

2.1 × 10 (ref 53)

-

9

eaq + eaq f 2OH

5.5 × 10 (ref 23)

-

•-

10

eaq + O2 f O2

1.9 × 10 (ref 23)

-

•

-

10

eaq + OH f OH

3.3 × 10 (ref 54)

-

•

-

10

eaq + H f OH + H2

2.5 × 10 (ref 54)

-

•

10

eaq + H2O2 f OH + OH

1.3 × 10 (ref 54)

-

+

•

10

eaq + H3O f H + H2O

2.3 × 10 (ref 23

•

-

•

7

O2 + HO2 f H2O2 + O2

9.7 × 10 (ref 55)

•

-

•-

9

O

+ O2 f O3

2.0 × 10 (ref 23)

•

-

•

-

9

O3 + H2O f HO3 + OH

8.5 × 10 (ref 34)

•

-

Figure 1. SO

volume of N

saturated KOH; dose ) 104 Gy; G(SO

calculation of ꢀ. Transient spectrum corrected for SO

5

radical absorption spectrum at pH 11.5 (-b-). Equal

a

^•/O

•-

•

-

^•/

)

pK

a

: HO

2

) 4.8 (ref 55); OH/ O ) 11.9 (ref 48); HO

3

-

2

O saturated 5.0 mM HSO

5

•-

2

solution mixed with N O

•

-

2-

-

2-

O

7

2

3

) 8.2 (ref 34); HSO

5

/SO

) 1.92 (ref 18); H

3). In refs 23 and 55 values are selected/recommended.

5

) 9.4 (ref 56); HSO

3

/SO

3

-1

5

) taken ) 0.57 µmol J for

-

2-

-

2

.2 (ref 18); HSO

4

/SO

4

O

2 2

/HO

) 11.7 (ref

2-

5

bleaching

b

(

-O-) from its absorption (s). Inset: Transient absorption spectrum

obtained 6 µs after the end of pulse.

can be used. However, restricted then by HSO5^-thermal

instability, the alternative choice of reaction 10

In Figure 1 (inset), the transient absorption spectrum above

3

00 nm obtained 6 µs after the end of pulse is shown. This

•

-

spectral profile matches well with the SO4 radical absorption

^•^O^H⁺^S^O5²^-^f^S^O5^•^-+ OH^-

(10)

10,27

spectrum

and is expected to form following only reaction

2

. From experimental ∆Amax values at 440-450 nm and the

9

-1 -1 25

•-

in alkaline pH (k ) 2.1 × 10 M s ) was appropriate for

absorbed dose, the maximum yield of the SO4 radical is found

•-

a quantitative generation of the SO5 radical. Employing a dose

of 104 Gy to an N2O saturated 2.5 mM Oxone (Aldrich) solution

to be ∼20% of the SO5 radical yield in the experimental

•

-

matrix. The remaining SO5 radicals are expected to react

following only reaction 5. As shown in Table 1, the branching

ratio of reactions 2 and 5 in previous studies reveal a wide

•

-

•-

at pH 11.5, the SO5 radical was produced with G(SO5 ) ∼

-

1

0

.57 µmol J . The flow mixer assembly was used with N2O

9-17

saturated Oxone solution in one channel and N2O saturated

solution of appropriate amount of KOH in the other channel.

scatter, with values ranging from ∼0.04 to 0.9.

In our

measurement, it is to be noted that, unlike the inactive product

•

-

2-

•-

The resulting after-pulse SO5 radical absorption spectrum is

shown in Figure 1. The parent SO5²absorption spectrum is

included in Figure 1 to account for its bleaching. A molar

S2O8 formed by reaction 5, the SO4 radical from reaction 2

is reactive toward matrix components such as SO5 and OH .

Thus, the SO4 radical absorbance maximum cannot be a true

measure of its maximum yield. In this case, even the concentra-

tion of S2O8

branching of reaction 5, cannot be correlated with the initial

radical yield as S2O8

Therefore, a true picture of the branching ratio cannot be

obtained from mere experimental measure of ∆A445 nm or final

-

2-

-

•

-

1

-1

•-

absorptivity value of 1065 M cm for the SO5 radical is

2

-

obtained at the 260-265 nm peak after taking into account the

loss of parent SO5 absorption. Although most of the previous

studies on the SO5 radical absorption spectrum generally

agreed on the spectral profile and its λpeak value at 260-265

nm, there was considerable disagreement on the reported ꢀ value

as an end product, and consequently the

2-

•

-

2-

also forms following reaction 7.

-

1

-1 10,13,16,26

2-

(

ranging from ∼700 to 1030 M cm ).

In those

S2O8 concentration. Instead, only detailed kinetic analyses of

•

-

•-

studies, the SO5 radical was generated via the SO3 radical.

Under those conditions loss (small but unaccounted fraction)

experimental traces are expected to provide the ratio k2/k5.

Details of such ACUCHEM analyses are presented below.

However, some other related and constitutive measurements for

use in such studies are first presented in the next section.

•

-

of the parent SO3 radical due to its dimerization reaction and

•

-

loss of SO5 radical following radical-solute reactions (large

fraction) are expected. At present, if rates from Table 1 are used,

the loss due to the latter reactions might seem negligible;

however, as shown later in this study, these are significant. Thus,

the actual yield of the SO5 radical was always less than the

assumed value and this difference was reflected in the lower

measure of ꢀ value reported in all cases. The only study using

-

HSO5 Reaction with H-atom. In N2 saturated solutions

below pH 4, with increasing acidity, it was observed that the

after-pulse yield of the SO4 radical increased rapidly. The rate

constant for H-atom reaction with H2SO5 generating the SO4

•-

•

-

•-

8

-1 -1 28

radical is reported to be ca. 1.3 × 10 M s . However, in

-

+

acidic pH the two reported eaq scavenging reactions by H3O

12

•-

-

impure Caro’s acid reported direct generation of SO5 radical

and HSO5 also need to be taken into account with the latter

producing 80% OH radical and 20% SO4 radical. Experi-

-

1

-1

•

•-

26

and an ꢀ value of ∼1000 M cm at ∼260 nm. In our

experiment, the clean matrix also ensured that such impurity

effects or unaccounted for radical loss remained minimal,

resulting in the best possible representation of the SO5 radical

absorption characteristics.

mentally, in pH ∼2.5 Oxone solution (Lancaster sample, 1.5

-

mM) where only ∼ 2% of HSO5 remains as H2SO5 (first pKa

•-

of Caro’s acid ∼1), the observed after-pulse yield of SO4

-

radical could not be explained only on the basis of H2SO5/eaq

9146 J. Phys. Chem. A, Vol. 105, No. 40, 2001

Das

The transient spectrum obtained for 92 Gy dose in the

-

presence of 1.2 M H2PO4 , 50 mM tert-butyl alcohol, and 14

mM Oxone is also included in Figure 2 for comparison. In this

•

-

-1

•

matrix the total G(SO4 ) is seen to be ∼0.12 µmol J {)g(H )

[g(eaq )]f (where f ) fraction of eaq reacting with H3O ) +

-

+

•

-

G(SO4 ) from 20% of remaining eaq + HSO5 reaction}. In

these measurements, made at a pH more than 3 units away from

the first pKa of H2SO5, any interference from it is expected to

•

be negligible. Additionally, interference from H2PO4 radical

•

-

produced in the OH + H2PO4 reaction is also expected to be

negligible in the microsecond time scale of measurement.³¹In

these measurements, however, in the presence of such a high

concentration of salt, the SO4 radical decay reactions become

faster and the resulting k11 values have a larger uncertainty than

our previous estimate at pH 2.5. The above sets of results have

no direct relation to the main aim of our study, but since at pH

•-

•

-1 23

g4 G(H ) remains ∼65 nmol J , they nevertheless allowed

us quantification of H-atom reactions in the presence of Oxone.

Thus, the general practice of ignoring the same in oxidative

PR studies was avoided.

Reaction Kinetics of the SO4^•^-Radical with HSO5 /SO5²^-.

-

During the course of our main study, we frequently encountered

•

-

situations where the SO4 radical formed in the presence of

Figure 2. Time-resolved transient spectra in pH 2.5, N

2

saturated 20

-

2-

-

2-

-

5

solutes HSO5 /SO5 . Then oxidation of HSO5 /SO5 respec-

tively by H-atom or electron transfer reactions 12 and 13 is

expected.

mM HSO

solution with 0.2 M tert-butyl alcohol; dose ) 35 Gy;

•-

-1

G(SO

of 1.2 M H

also included for comparison; dose ) 92 Gy; G(SO

4

) ∼ 0.21 µmol J . Transient spectrum at pH 4.7 in the presence

- -

2 4 5

PO , 20 mM HSO , and 0.05 M tert-butyl alcohol is

•

-

4

) ∼ 0.12 µmol

-

1

J

.

SO₄^•^-+ HSO₅f SO₅^•^-+ HSO₄

-

(12)

(13)

reactions. Therefore, to check if an additional reaction

SO₄^•^-+ SO₅f SO₅^•^-+ SO₄

2-

•

-

•-

H + HSO₅f H O + SO₄

(11)

2

Only one limiting estimate of reaction 12 kinetics is available

was responsible for the observed SO4^•^-radical generation, first

a spectral measurement was made employing a dose of 35 Gy

with N2 saturated 14 mM Oxone solution at pH ∼2.5 containing

from the literature (k12 < 1.0 × 10 M s ), but no estimate

is available for k13. The magnitude of k12 was first verified

employing a matrix consisting of N2 saturated acidic solution

5

-1 -1 25

•

0

.2 M tert-butyl alcohol.

of Oxone. To minimize reaction complexity, no OH scavenger

The time-resolved transient spectra shown in Figure 2

was used. Low propensity of reaction 9 then allowed only partial

•

-

-1

•-

•

indicates that the SO4 radical yield is ∼0.21 µmol J . The

generation of SO5 radical and a large fraction of OH decayed

•

-

•-

value is close to G(H ) {)g(H ) + [g(eaq )]f (where f ) fraction

following other reactions of Tables 2 and 3. The SO4 radical

-

+

•-

of eaq reacting with H3O ) + G(SO4 ) from 20% of the

formed by reaction 11 or otherwise from reaction 2 decayed

mainly following radical dimerization reaction 7, following

reaction 12, and following its radical-radical reaction with the

-

remaining eaq + HSO5 reaction}, suggesting the existence

of reaction 11. The increase in transient absorption below 300

nm in Figure 2 is due to the â-hydroxy radical produced from

•

32

remaining OH. (Its minor reactions include reactions with the

•

29

•

reaction of OH with tert-butyl alcohol. Employing 50 ns

remaining H-atom, HO2 radical, H2O2, and H2O.) The decay

pulses delivering 14 Gy dose to N2 saturated solutions containing

trace at 450 nm shown in Figure 3 was obtained employing a

dose of 34 Gy in a N2 saturated solution at pH 2.8 containing

5 mM Oxone (Aldrich), 10 mM each K2SO4 and KHSO4 at I

ca. 80 mM. The value of k7 in this matrix was taken ca. 1.0 ×

0

.1 M tert-butyl alcohol and 0.5-3.0 mM Oxone (Lancaster)

-

2-

at pH 2.5 (with balance HSO4 /SO4 ), the reaction 11 kinetics

was measured. The kinetic traces (not shown here) at 450 nm

in this case showed a two-step formation of the SO4 radical.

•

-

9

-1 -1

•-

10 M s . The presence of some SO5 radical necessitated

use of accurate k2 and k5 values in ACUCHEM analysis, and

these were obtained from results discussed in the next section

(see Appendix C). The best ACUCHEM overlay was obtained

-

In the first step it was rapidly generated from the eaq + HSO5

reaction (with ∼20% branching as before), and in the slower

step it was obtained from reaction 11. An overall rate value ca.

7

-1 -1

•-

6

-1 -1

(

8.5 ( 0.7) × 10 M

s

was obtained for SO4 radical

for k12 ) (1.6 ( 0.2) × 10 M s . To change experimental

formation rate in the slower step. Taking into account the rate

constant of H-atom reaction with H2SO5 and its contribution at

pH 2.5, k11 was estimated to be ca. (8.0 ( 0.7) × 10 M s .

Similar spectral and kinetic measurements at pH ∼4.7 also

supported these results. These studies were possible in the

conditions, the dose (between 20 and 40 Gy using 520 ns pulse),

-

2-

the Oxone concentration (2-8 mM with balance HSO4 /SO4 ),

and the working pH (between 2 and 3.5) were varied separately.

From ACUCHEM analysis of these results an average k12 )

7

-1 -1

6

-1 -1

(1.0 ( 0.1) × 10 M

s

was obtained for I f 0. Figure 3

-

presence of ∼1.0 M H2PO4 following the method proposed

also compares the ACUCHEM analysis if the previously

by Ye et al.³⁰In this set of measurements with N2 saturated

reported literature value of ∼1.0 × 10 M

5

-1 -1

s

or some other

solutions of 50 mM tert-butyl alcohol and 0.5-2.5 mM Oxone,

k12 value (at I f 0) is used. From the nature of these kinetic

overlays, we conclude that our rate value satisfying a wider

range of experimental conditions and incorporating analyses of

all major and minor reactions provides the best description for

7

-1 -1

-

k11 was estimated tobe ca. (8.7 ( 1.2) × 10 M s . The eaq

was again partially converted to H-atom as a result of its reaction

-

with H2PO4 .

Reactivity and Role of Aqueous SO5^•^-

J. Phys. Chem. A, Vol. 105, No. 40, 2001 9147

•

-

2-

TABLE 3: Generation and Reactions of SO

4

Radical in N

2

balance HSO4 /SO4 was used while the other channel carried

2

-

2-

Saturated Solution of HSO

5

or S

2

O

8

and Formation and

2-

mM N2 saturated S2O8 solution with appropriate amounts

of KOH. The final matrix pH in these experiments was

maintained within (0.1 unit of the target value 10 by using a

calculated amount of KOH proportional to the prevailing HSO4

and HSO5 concentrations in solution. The pH was also checked

at the cell exit before radiolysis. Unlike in acidic pH, OH was

efficiently scavenged by the SO5 anion. As a consequence,

in addition to the direct formation of SO4 radical following

the first reaction of Table 3, it was also continuously regenerated

by reaction 2. Taking into consideration appropriate reactions

from Table 3 for alkaline pH, and following a similar approach

as described for acidic solutions, the best-fit value of k13 at the

•

-

Reactions of SO

3

Radical

rate constant (M^-s^-¹

1

)

reactions

eaq + S2O8²^-f SO4 + SO4

-

•-

2-

1.2 × 10 (ref 23)^a

10

-

•

2-

9

-

eaq + HSO5 f OH + SO4

8.4 × 10 (ref 26)

-

•-

9

eaq + HSO5 f OH + SO4

2.1 × 10 (ref 26)

•

2-

-

•-

7

H + S2O8 f HSO4 + SO4

1.4 × 10 (ref 28)

2

-

•

•-

+

8

H + H2SO5 f SO4 + H3O

1.3 × 10 (ref 28)

•

-

•

-

•-

7

H + HSO5 f SO4 + H2O

8.0 × 10 (this study)

•

2-

•-

-

7

OH + S2O8 f S2O8 + OH

1.2 × 10 (ref 57)

-

•-

6

OH + HSO5 f SO5 + H2O

5.0 × 10 (this study)

2-

•-

-

9

OH + SO5 f SO5 -⁺^O^H

2.1 × 10 (ref 25)

•-

10

OH + SO4 f HSO5

1.0 × 10 (ref 32)

•

-

•

-

7

SO5 + HO2 f HSO5 + O2

5.0 × 10 (ref 58)

•

-

•-

2-

8

-1 -1

SO5 + SO5 f S2O8 + O2

2.2 × 10 (this study)

experimental I ∼ 30 mM was (2.0 ( 0.3) × 10 M s . The

•

-

•-

8

SO5 + SO5 f 2SO4 + O2

2.1 × 10 (this study)

8

-1 -1

k13 value reduces to ca. (1.0 ( 0.2) × 10 M

s

at I f 0.

•

-

•-

2-

8

SO4 + SO4 f S2O8

7.0 × 10 (see Appendix A)

•

-

•-

•

-

•-

6

SO5 Radical Decay Kinetics and Yield of the SO4

Radical. The radical-radical reactions 2 and 5 could not be

isolated in past studies. Therefore, our evaluation of reactions

in Scheme 1 started with these reactions so that accurate

evaluation of the radical-solute reactions was subsequently

SO4 + HSO5 f HSO4 + SO5

1.0 × 10 (this study)

•

-

2-

•-

8

SO4 + SO5 f SO4 + SO5

1.0 × 10 (this study)

•

-

2-

•-

5

SO4 + S2O8 f SO4 + S2O8

6.3 × 10 (ref 16)

•

-

2-

•

7

SO4 + OH f SO4 + OH

2.0 × 10 (ref 9; for I f 0)

•

-

•

SO4 + H2O f HSO4 + OH

9.3 (ref 16)

•

-

•

-

9

SO4 + HO2 f HSO4 + O2

3.5 × 10 (ref 59)

•

-

•-

2-

9

•-

SO4 + O2 f SO4 + O2

6.0 × 10 (assumed)

possible. The most convenient way to measure SO5 radical

decay was by following the simultaneous formation of reaction

product, i.e., the SO4 radical. The working solution pH was

restricted between 3.5 and 11 since SO4 radical kinetics above

pH 12 was severely affected due to its rapid reaction with OH

(Table 3). For the sake of convenience, initially measurements

were made at fixed solution pH 4, 7.9, and 10.4. Taking a cue

from our earlier SO5 radical spectral results, a high dose of

15 Gy (2.2 µs fwhm pulse) was used to overcome a low yield

of SO4 radical. To keep the reaction complexities to a

minimum, buffer was avoided in these measurements. An N2O

saturated 1.4 mM Oxone solution (Lancaster sample) was used

in all cases. At the three selected solution pH values, prevailing

SO4 + H2O2 f HO2 + SO4 + H3O⁺1.2 × 10 (ref 31)

•

-

•

2-

7

•

-

•-

9

OH + HSO3 f SO3 + H2O

4.5 × 10 (ref 11)

•-

2

2-

•-

-

9

OH + SO3 f SO3 + OH

5.4 × 10 (ref 11)

•-

•

-

•-

2-

8

SO3 + SO3 f S2O6

2.4 × 10 (ref 9; for I f 0)

-

•

-

•-

2-

8

SO3 + SO3 f SO3 + SO3

3.2 × 10 (ref 9; for I f 0)

•

-

•-

9

SO3 + O2 f SO5

1.1 × 10 (see Appendix A)

a

In ref 23 values are selected/recommended.

•

-

1

•

-

starting concentrations of the solutes (mM) H2SO5/HSO5 /

2

-

2-

-5

SO5 /HSO4 /SO4 were: 0.002/2.158/77 × 10 /0.027/3.2

respectively at pH 4, ∼0/2.094/0.066/∼0/3.23 at pH 7.9, and

•

-

∼

0/0.196/1.96/∼0/3.23 at pH 10.4. The SO4 radical kinetic

traces were recorded at 450 nm while the decay traces

•

-

originating mainly from parent SO5 radical were recorded at

60 nm. Next, ACUCHEM analysis of each trace was per-

formed. At 260 nm, apart from the SO5 radical, other species

2

•

-

•-

that show appreciable/significant absorbance are SO4 radical

-

1

-1

•

2-

•-

(

ꢀ ) 400 M cm ), OH (475), H2O2 (12), S2O8 (14), O2

•

27

radical (1680), and HO2 radical (520). To account for the

-

2-

loss of parent (HSO5 /SO5 ) absorption at different pH values,

the apparent ꢀ for the SO5 radical in these analyses was taken

as follows: 875 M cm at pH 10.4, 980 at pH 7.9, and 1025

at pH 4. At 450 nm, the SO4 radical is the only species that

•-

-1

•

-

showed significant absorption and its ꢀ450 nm value was taken

-

1

-1 10

•-

as 1630 M cm . For kinetic analysis, apart from the SO5

radical-radical decay reactions 2 and 5, other pertinent reactions

from Tables 2 and 3 including reactions of different species

arising out of water radiolysis, SO5 radical generation by OH

Figure 3. Decay trace at 450 nm obtained employing dose of 34 Gy

•-

•

-

in a N

mM each of K

2

saturated solution at pH 2.8 containing 10 mM HSO

SO and KHSO

5

and 10

•

-

reaction (also see the last paragraph of this section), SO4

2

4

(I ca. 0.08 M). Lines (s and ---)

•

-

radical generation by the H-atom, and SO4 radical reactions

with OH, H2O, OH , HSO5 /SO5 , etc. were taken into

consideration.

represent ACUCHEM kinetic analysis with different k12 values for I

f 0. See text for explanation. See Appendix B for an explanation of

shaded area shown in this and other figures.

•

-

2-

•

-

Figure 4 shows the 260 nm SO5 radical decay (mixed with

some SO4 radical formation/decay, especially at later stages)

and 450 nm (only) SO4 radical formation/decay traces.

Appropriate ACUCHEM analyses are also shown superimposed

on the respective experimental traces. These kinetic overlays

at the experimental I ) 12-16 mM were possible with a

•

-

reaction 12 kinetics. In the previous study a similar detailed

analysis is not reported.

To measure k13, experiments were carried out in mildly

alkaline pH. In a typical experiment, a dose of 15 Gy was used.

In the flow mixer assembly, in one channel N2 saturated Oxone

solution (amounts varied from 0.25 to 2.0 mM) along with

•

-

8

uniform pair of values of (2.9 ( 0.4) × 10 and (2.8 ( 0.4) ×

9148 J. Phys. Chem. A, Vol. 105, No. 40, 2001

Das

(9.4, Table 2) because of relative values of k9 and k10.

ACUCHEM analysis of kinetic traces gave satisfactory overlays

with k2 and k5 values of similar magnitude as obtained above.

Therefore, as shown in Figure 5 (inset), the branching ratio (k2/

k5) over the pH range remained ∼1. Even when some of these

measurements were repeated at high ionic strength in the

presence of Na2SO4 (∼0.4 M), no significant deviations were

noticed in the results if all concerned ionic reaction rates were

first modified accordingly. These results indicate that reactions

2

and 5 probably take place independent of each other.

Our k2 and k5 values differ significantly from the previous

suggestions shown in Table 1, in respect to both their magni-

tudes and their branching ratio. A comparison is strictly not

possible due to entirely different approaches taken earlier. For

example, referring to some values in Table 1, the frequently

1

referred sets in the literature were reported by Huie and Neta

8

-1 -1

(

k2 ) 6.0 × 10 and k5 ) 1.4 × 10 M s ) and were later

used for modeling by Deister and Warneck, Rudich et al.,⁵

14

6

van den Berg et al., and others. Other values were suggested

1

0

8

7

-1 -1

by Buxton et al. (k2/k5 ca. 2.2 × 10 /4.8 × 10 M s ,

1

6

8

respectively), Herrman et al. (k2/k5 ca. 5.2 × 10 /1.2 × 10

-

1

-1

15

M

1

s , respectively), and Yermakov et al. (k2/k5 ca. 8.7 ×

7 -1 -1

7

0 /1.4 × 10 M s , respectively). The actual effects of

radical-solute reactions on these indirect results are presented

•-

in the next section, where the effects of S(IV) on SO5 radical

decay is revealed. With [S(IV)] > [SO5^•^-], these reactions

Figure 4. Kinetic traces for SO ^•^-

15 Gy in 2.2 mM N O saturated HSO

radical-radical reactions. Dose )

5

-

1

2

solution. Lines (s) represent

and k values reported in the text

•

-

always modified the product SO4 radical yield and formation

kinetics. However, in analysis of radical kinetics, these con-

cerned reactions were not granted due importance, and as a result

these estimations were severely affected.

ACUCHEM kinetic analysis with k

for I f 0.

2

5

In the above studies, when kinetic traces obtained in acidic

and near neutral pH were subjected to ACUCHEM analysis,

2

5

use of the k9 value reported by Maruthamuthu and Neta

produced higher yields and faster formation kinetics for SO5^•

-

radical as compared to the corresponding experimental traces.

Even in the presence of a few tens of mM Oxone concentration,

•

-

the measured experimental yields of the SO5 radical and its

formation rates remained less than half of the calculated values

based on the above rate. To arrive at a consensus k9 value, a

•

-

fresh estimation of G(SO5 ) was made using a reactivity

3

formula similar to the proposal of Schuler et al. The

•

-

experimental SO5 radical concentrations obtained at high

Oxone concentrations were compared with their projected

values, and the two sets matched closely only if the previous

7

-1 -1

k9 value ()1.7 × 10 M s ) was reduced by ∼70% to ca.

6

-1 -1

(

5.0 ( 0.3) × 10 M s . The results obtained are shown in

Table 4. For such high concentrations of Oxone, any thermal

loss of HSO5 during the time interval of each measurement

-

(

∼4-8%) was measured separately and the correction factor

taken into consideration. To measure the kinetics, a dose of 15

Gy was used. To calculate SO5 radical concentration from

•-

5

Figure 5. After-pulse ∆Amax at 260 nm (parent bleach corrected, SO

•

-

•

-

radical) and 450 nm (SO

4

radical) obtained at different solution pH

/k ) obtained from ACUCHEM

the 260 nm trace, contributions of reaction 11 and ꢀ260 nm of

values. Inset: Branching ratio (k

2

5

•

-

-1

analysis of kinetic traces covering the experimental pH range.

the SO4 radical (400 M cm ) as well as absorption from

•

-

OH and HO2 radicals and the bleaching of the parent HSO5

absorption (ꢀ ) 40 M cm , making effective ꢀ(SO5 )260 nm

) 1025 M cm ) were also taken into account. In this context,

if a comparison is made for H-atom abstraction reactions from

H2O2 and HO2 radical by OH/SO4 radicals, it is observed

that the respective oxidation rates are within 1 order of

magnitude from each other. The rate constants of H-atom

abstraction from HSO5 having a similar -OOH group are also

expected to remain close to each other, and our lower k9 and

higher k12 values are further supported by this trend. Thus, this

1

0⁸M^-¹s , respectively, for k2 and k5. At I f 0 the respective

-1

•-

8

-1

values reduce to ca. (2.2 ( 0.3) × 10 and (2.1 ( 0.3) × 10

s , indicating almost equal propensity of reactions 2 and

. These measurements were subsequently made at other pH

-1 -1

M

5

•

•-

values covering the working range, and the results are shown

in Figure 5. The observed maximum after-pulse absorbances at

9

•

-

•-

-

2

60 nm (mainly due to the SO5 radical) and 450 nm (SO4

•

-

radical) are plotted against the pH value. The yields of SO5

•

-

(

and consequently the SO4 radical) followed the HSO5 pKa

Reactivity and Role of Aqueous SO5^•^-

TABLE 4: Yield of SO ^•^-

Radical in N

J. Phys. Chem. A, Vol. 105, No. 40, 2001 9149

-

5

2

O Saturated Solution at pH ≈ 5 in the Presence of High Concentration of HSO

5

•

- c

•

-

[SO5 ] (µM)

[

SO5 ] (µM)

-

I^a(M)

•- b

k ) 5.0 × 10 M s^-¹

6

-1

k ) 1.7 × 10 M s^-¹

7

-1

[

HSO5 ] (M)

∆A260 nm(max)

[SO4 ] (µM)

obsd

0

.05

0.2

0.4

0.8

1.2

0.008 27 ( 0.000 28

0.008 36 ( 0.000 22

0.008 41 ( 0.000 25

0.008 50 ( 0.000 19

1.53

1.64

1.68

1.71

7.41

7.47

7.54

7.62

7.43

7.50

7.55

7.64

7.57

7.64

7.72

7.80

.1

.2

.3

a

-

^-) wrt the total (eaq + HSO

-

O). ^bG(SO

•-

) ) g(H ) + g(eaq^-){0.2[fraction of (eaq

•

-

I decides the fraction of (eaq + HSO

5

) + (eaq + N

2

4

2

+

-

c

•-

•

-

HSO

5

)]}. G(SO

5

) ) g( OH) + g(eaq ){0.8[fraction of (eaq + HSO

5

) + fraction of (eaq + N

O)]}.

increased, as shown in Figure 6 (inset), the resulting SO4^•^-

radical concentration first showed an increase (up to a few 100

2-

µM SO3 concentration) and thereafter decreased steadily with

2

-

further increase in SO3 concentration (from 0.4 to 20 mM).

•

-

Although the SO3 radical yield increased continuously as a

•-

result of increase in reactivity in its generation (the SO5 radical

•

-

yield is expected to follow the SO3 radical in the presence of

O2), the observed faster rate of increase in concentration of

•

-

•-

SO4 radical as compared to the SO3 radical (for first few

00 µM SO3²concentration) suggests that, in addition to

reaction 2, the SO4 radical also formed following reaction 3

at higher solute concentration. On the other hand, the observed

-

1

•

-

•-

2-

reduction in SO4 radical yield in the case of SO3 concentra-

tion >0.4 mM resulted from its enhanced scavenging by SO3²

-

.

These qualitative observations predict comparative or close

magnitudes of k2, k4, and possibly k3; i.e., the latter values are

7

-1 -1

expected to be >10 M s . Table 1 reveals only a few k3

and k4 values meeting this order while most of the others are

significantly low. To arrive at consensus k3 and k4 values, a

reevaluation of reactions 3 and 4 was made as follows.

The PR study by Buxton et al.¹⁰with a few mM SO3

2-

•

-

concentration reports ∼7% yield of SO4 radical with respect

to the initial yield of the oxidizing radical. A similar conclusion

is drawn from the plot in Figure 6 (inset). In other words, a

high dose producing an initial high concentration of the

2

-

Figure 6. Time-resolved transient spectra obtained in 75 µM SO

3

2-

and 5 mM HPO

with N O and O

4

pH 9 solution with 110 Gy dose. Solution saturated

2

in 1:1 ratio. Inset: Effect of progressive increase in

2

-

•-

3

SO

3

concentration on various parameters: (-0-) [SO

]; (-b-)

•

-

•-

4

].

oxidizing radical ( OH in this case) is necessary for obtaining

ionic strength; (-O-) [SO

3

]/[SO

4

]; (-4-) [SO

•

-

even moderate SO4 radical absorption signals. The HSO3

-

pKa of 7.2 and HSO5 pKa of 9.4 also necessitated two separate

working pH ranges of 4-4.5 and 9.5-11.5.

In alkaline pH, the SO5 radical could be generated following

lower k9 value was used in all the ACUCHEM analyses

mentioned earlier and also later in the text.

•-

•

-

2-

SO5 Reactions with HSO3 /SO3 . A comparison of the

either of the following two methods. In the first method, it was

obtained from oxidation of N2O saturated solution of Oxone.

In this case, N2O saturated few mM Oxone solutions (Aldrich

sample, balanced with Na2SO4) were mixed in equal proportions

with N2O saturated solution containing an appropriate amount

of S(IV). The required amount of alkali or buffer for achieving

the desired experimental pH was used in the S(IV) channel.

•

-

•-

one-electron reduction potentials of SO5 and SO3 radicals

∆E ) 0.08 V ) suggest that in the case of equilibrium reaction

4 in alkaline pH, the equilibrium constant K (i.e., kf/kb) value

would be low, ∼23.

SO₅^•^-+ SO₃T SO₅²^-+ SO₃

7

(

1

8

2-

•-

(14)

2-

The ratio of [SO5 ]/[SO3 ] (the latter in the 0.1-0.4 mM range

and balanced with Na2SO4) was maintained g25 so that mainly

Since the O-atom transfer reaction 3 is expected to compete

with equilibrium 14, experimental measurement of either kf or

kb may not be possible directly. Indeed, separate attempts to

measure these rate constants (keeping [solute]/[radical] ratio >

5 in either case) failed, and only SO4 radical formation could

be confirmed, suggesting a higher propensity of reaction 3 as

compared to reaction 4.

•

-

•

the SO5 radical was generated from OH. In the second

method, N2O saturated S(IV) solution was mixed in 1:1 volume

•

-

ratio with O saturated alkali/buffer solution producing 12.5 mM

2

N2O and 0.64 mM O2 concentrations in the irradiation cell. In

2

-

this case SO3 concentration could be varied over the 0.1-5

•

-

mM range (balanced with Na2SO4) and the yield of SO3

As an example, the time-resolved spectra obtained in a

•

-

2-

radical and subsequently the SO

radical were taken to be

solution of 75 µM SO3 under irradiation with 110 Gy dose is

5

shown in Figure 6. The N2O saturated SO3²^-solutions at pH 9

-1 10

∼0.52 µmol J . In either case, for a few selected solute

concentrations, subsequently the dose was also increased from

∼50 to 120 Gy to increase the influence of reactions 2 and 5.

For ACUCHEM analysis of the resulting kinetic traces, ap-

propriate reactions from Tables 2 and 3 were considered (after

taking into account the solution I in each case) and only the

(

with 5 mM buffer) flowing in one channel was mixed with

equal proportion to O2 saturated buffer solution at pH 9 in the

2-

other channel. For such a low SO3 concentration, the majority

•

-

of SO4 radical was presumably formed by reaction 2. The

•

-

observed Amax (450 nm) value indicates ∼10% SO4 radical

•

-

•-

2-

yield compared to the after-pulse SO3 radical concentration.

However, when the SO3²concentration was progressively

rates k3 and k4 (representing SO5 + SO3 reactions) were

-

6

9

-1 -1

systematically varied, covering the range of 10 -10 M s .

9150 J. Phys. Chem. A, Vol. 105, No. 40, 2001

Das

Figure 7. Kinetic traces and ACUCHEM overlay for measurements

in alkaline pH range 10-10.6. pH adjusted with KOH; dose ) 102

Figure 8. Kinetic traces and ACUCHEM overlay for measurements

in acidic pH range 3.8-4.5. pH adjusted with HClO ; dose ) 102 Gy

4

2

-

Gy with 2.2 µs pulse. Traces for N

2

O/O

2

saturated SO

3

solutions:

with 2.2 µs pulse. Traces for N O/O saturated HSO solutions: (1)

2

3

(

4

4) 100 µM; (3) 300 µM; (1) 400 µM; (2) 750 µM; (5) 1.95 mM; (6)

135 µM; (2) 650 µM; (4) 1.95 mM; (5) 4.8 mM. Trace 3 with 6 mM

-

.8 mM. Inset: Experimental trace and ACUCHEM overlay for N

2

O

H PO₄(no HClO ) for 650 µM HSO₃.

2

4

2

-

2-

3

saturated pH 10.5 solution of 2.5 mM SO

)

5

and 100 µM SO

; dose

•

-1

48 Gy with 520 ns pulse.

HO3 radical pKa ()8.2 and ꢀ450 nm < 10 M cm ) ensures

•

-

34

complete protonation of any O3 radical formed. Thus, no

contribution from O3 radical is expected in these cases.

The k2 and k5 values from the previous section were used to

•-

•

-

account for the SO5 radical-radical reactions. At 450 nm,

Employing the previously estimated k2 and k5 values (and also

•

-

•-

apart from the SO3 and SO4 radicals, only the O3 radical

2-

k3 and k4 values to account for any SO3 present even in acidic

-

1

-1 27,34

has significant absorption (ꢀ450 nm ) 1700 M cm ).

best kinetic analyses of the traces and correlation of the SO4

The

pH), satisfactory analyses of experimental traces representing

•

-

the HSO3 reactions were possible with the following set of

radical yields obtained by the first method (at I ) 60-100 mM)

rate values. In the case of I ∼ 0.4 mM, the k3 and k4 values

9

-1 -1

were possible with k3 values within (1.3-1.8) × 10 M

s

7

-1 -1

ranged over (5.9-6.7) × 10 and (2.8-3.4) × 10 M s ,

respectively. At I ∼ 11 mM representing higher concentration

of solutes, the respective k3 and k4 values marginally increased

8

-1 -1

and k4 values within (2.4-3.3) × 10 M s . In the second

method (at I ) 10-30 mM) the respective k3 and k4 values

8

-1 -1

remained within (9.2-12.0) × 10 M

s

and (1.6-2.2) ×

7

-1 -1

to (7.0-8.0) × 10 and (3.4-4.1) × 10 M s . Taking into

8

-1 -1

1

0 M s . Taking into account results from all other related

account the ionic strengths in different cases, at I f 0, the k3

measurements, at I f 0 the k3 and k4 values reduce to ca. (5.6

-

7

and k4 values (for HSO3 ) reduce to ca. (6.0 ( 0.4) × 10 and

8

-1 -1

(

0.6) × 10 and (1.0 ( 0.1) × 10 M s .

7

-1 -1

(

3.0 ( 0.3) × 10 M s , respectively.

Some experimental traces with ACUCHEM analyzed overlays

A few experimental traces and their respective ACUCHEM

are shown in Figure 7. The relative magnitudes of k3 and k4

analyses are shown in Figure 8. A comparison of these traces

reveals that, at low solute concentration, the after-pulse maxi-

mum absorbance first decreased and then increased before its

final slower decay (to the baseline value). In alkaline pH with

•

-

2-

values indicate that only ∼15% of the SO5 + SO3 reaction

follow the electron transfer path and a majority (∼85%) lead

•-

to the formation of SO4 radical by O-atom transfer. The higher

propensity of the O-atom transfer reaction explains our earlier

unsuccessful attempt to follow the equilibrium (14) kinetics.

In acidic pH, the rate of reaction 9 is almost 3 orders of

2-

only SO3 , the effect, however, was less pronounced (Figure

7

). The time-resolved absorption spectra shown in Figure 6

clearly reveal that the first after-pulse maximum is mainly due

9

-1 -1

magnitude less than the corresponding rate (4.5 × 10 M s )

•-

to the SO3 radical, as expected from reactions 9 and 15, and

•

-

11

of OH + HSO3 reaction 15.

•-

that the second maximum is due to the SO4 radical. The

•-

intervening SO5 radical, however, does not absorb at 450 nm.

When the solutions were saturated only with N2O, the second

maximum vanished completely. In that case, formation of neither

HSO ^-+ OH f SO₃+ H O

•

•-

(15)

3

2

Therefore, unlike in alkaline pH, to preferentially generate SO5^•^-

radical from HSO5^-following the first method would necessitate

use of very high concentrations (>100 mM) of Oxone. Due to

SO5 nor SO4 radical took place, supporting our after-pulse

peak assignment even in the presence of O2.

•-

10

Buxton et al. have claimed that, in the presence of dissolved

O2, the after-pulse (i.e., first) maximum arises mainly from the

-

thermal instability of such a high concentration of HSO5 in

•

-

•

-

solution and also due to its reported thermal reaction with

O3 radical produced from O2 addition to O radical formed

-

35

-

HSO3 , only the second method could be used. Similar to

as a result of eaq scavenging by N2O (see reactions in Table

-

the alkaline pH measurements, in this case HSO3 solution with

2). In our analysis it was observed that even in alkaline pH in

2

-

(

1:1) N2O and O2 saturation was used. In acidic pH, at 450 nm

the presence of SO3 , as in their experiments, the prevailing

•

-

•-

only the SO3 and SO4 radicals show absorption while the

concentration of O3 radical accounts for only a part of the

Reactivity and Role of Aqueous SO5^•^-

J. Phys. Chem. A, Vol. 105, No. 40, 2001 9151

TABLE 5: Reaction Scheme in the Presence of Cl^-

rate constant (M^-s^-¹

1

)

reactions

•

-

•

2-

8

SO4 + Cl f Cl + SO4

3.0 × 10 (ref 9; for I f 0)

•

2-

-

•-

8

Cl + SO4 f Cl + SO4

2.5 × 10 (ref 37)

-

•

•-

9

Cl + OH f ClOH

4.3 × 10 (ref 36)

•

-

•

9

ClOH f Cl + OH

6.1 × 10 (ref 36)

•

-

•-

8

10

Cl + OH f ClOH

1. × 10 (ref 38)

•

-

+

•

10

ClOH + H3O f Cl + H2O

2.1 × 10 (assumed)

•

•-

+

3

Cl + H2O f ClOH + H3O

4.5 × 10 (ref 60)

•

-

•-

-

4

ClOH + Cl f Cl2 + OH

1.0 × 10 (ref 61; for I f 0)

•

-

•-

-

9

Cl + Cl f Cl2

8.0 × 10 (ref 62)

•

-

•

5

Cl2 f Cl + Cl

1.1 × 10 (ref 36)

•

8

Cl + Cl f Cl2

1.0 × 10 (ref 39)

•

-

•-

-

9

Cl2 + O2 f 2Cl + O2

1.0 × 10 (ref 9; for I f 0)

•

-

•

-

+

9

Cl2 + HO2 f 2Cl + O2 + H3O

1.0 × 10 (ref 63)

•

-

•-

-

9

Cl2 + Cl2 f Cl + Cl3

1.3 × 10 (ref 64)

•

-

•-

-

7

Cl2 + OH f ClOH + Cl

2.0 × 10 (ref 61; for I f 0)

Cl + HSO3 f Cl + SO3 + H3O⁺1.0 × 10 (assumed,

•

-

•-

9

comparing with related Cl^•

reactions)

Cl2^•^-+ HSO3 f 2Cl^-+ SO3^•^-

-

+

1.8 × 10 (ref 9; for I f 0)

8

+

H3O

Cl2^•+ SO3²^-f 2Cl^-+ SO3^•^-

-

5.0 × 10 (assumed,

8

comparing with other Cl2^•

reactions)

-

Cl2^•^-+ HSO5 f 2Cl^-+ SO5^•^-

-

+

<1.0 × 10 (assumed,

5

+

•-

H3O

comparing with SO4

+

-

HSO5₈reaction)

Cl2^•^-+ SO5²^-f 2Cl^-+ SO5^•^-

1.0 × 10 (assumed,

comparing with SO4

SO5²reaction)

•-

Figure 9. ACUCHEM analysis of two representative traces from

-

•-

x

Figures 7 and 8 showing simultaneous presence of all three SO

-

2-

radicals. Acid pH [HSO

3

] ) 650 µM; Alkaline pH [SO

3

] ) 750

moderate concentration of SO4^•^-radical and consequently

modest absorption signals. To boost the signal strength, two

approaches were possible: (i) use of a higher absorbed dose

and (ii) suitable modification of the reaction scheme to generate

a radical with high molar absorptivity. In our experimental setup

the first possibility could not be adopted because of the upper

limitation on available dose of ∼125 Gy from the accelerator.

(Even otherwise, beyond a limiting high dose, to offset the

resulting increases in radical-radical reactions, high solute

concentrations would be necessary. At high solute and O2

concentrations, associated thermal changes are expected to

increase the level of uncertainty in results. Limited solubility

of O2 in water may also prevent ideal matrix design beyond a

few 100 Gy dose.) The second approach was instead practicable

µM.

observed after-pulse transient absorbance. For example, in the

presence of 100 µM SO3²^-at pH 10.5, the ACUCHEM

•

-

•

projected after-pulse concentration of O3 + HO3 radicals is

∼

-6

10 M and has only ∼60% contribution toward the transient

absorption. However, in acidic pH these values are almost

•-

negligible. In addition, the O3 radical shows a broad absorption

profile with λmax close to 430 nm while the HO3^•radical

-

1

absorption is less intense (λmax ) 350, ꢀ350 nm ) 300 M

-1 34

cm ). Both are quite different from the after-pulse absorption

profile with λmax at 260 nm shown in Figure 6. Additionally, at

the experimental pH 9 in their study, the reaction scheme dealing

•

-

with reported protonation of O3 radical is not supported by

the pKa value of 8.2 for HO3 /O3 reported by B u¨ ehler et al.

•

•-

34

-

with the use of Cl and with a moderate dose of 36 Gy from a

•

-

Therefore, the set of reactions used in data analysis in the paper

by Buxton et al.¹⁰seems to be incomplete. Similar omissions

or overlook of many prevalent (but maybe unknown then)

reactions in other studies explains the wide scatter in Table 1

rate values. The final support of our mechanism comes from

the quality of ACUCHEM analysis of the experimental traces

500 ns pulse. In presence of SO4 radical, Cl quantitatively

•-

produces Cl2 radical that shows more intense absorption

-

1

-1 27

•-

(ꢀ345 nm ) 8800 M cm ) than the SO4 radical. To further

examine the degree of consistency in our rate measurements, a

few studies were repeated in N2O/O2 saturated acidic (buffered)

matrix with HSO3 and Cl . For kinetic analysis of these traces,

along with reactions from Tables 2 and 3, additional reactions

-

10

shown in Figures 7 and 8. Earlier, Buxton et al. failed to

achieve a complete fitting of any experimental trace with their

•

-

from Table 5 were required to account for the Cl2 radical

•

-

•

9,36-41

scheme stressing O3 /HO3 reactions.

generation and reactions.

In earlier sections we have hinted that oxygenated S(IV)

matrix used in some previous studies was an inappropriate

selection for estimating k2 and k5. Figure 9 clearly shows that,

in the presence of O2 and even a few 100 µM S(IV), all three

Figure 10 shows some experimental kinetic traces and their

ACUCHEM analysis. In this case, the volume ratio N O:O was

2

maintained ca. 3:2, producing 15 mM N O and 0.5 mM O in

2

the sample. Satisfactory overlay of experimental traces employ-

•

-

SOx radicals coexist after initiation of oxidation and proves

ing our set of k -k values once again confirms their correct

2

5

•

-

the following. (i) Interference due to SO4 radical absorption

magnitude. These results also indicate that any missing reaction

or reaction deliberately not included in these fitting exercises

•

-

•-

is significant even during the estimation of SO3 + O2 f SO5

1

0,11

-

reaction kinetics

(also see Appendix A). (ii) Unless [SO5

has negligible contribution. In the presence of Cl with only

•

-

radical] . [S(IV)], all radical-solute reactions 3 and 4

N O saturation, reactions of O /O , etc. were absent, but other

2

•

-

•

•-

contribute significantly and alter the desired effects of reactions

reactions such as those of ClOH , Cl , and Cl radicals were

2

•

-

•-

2

and 5, apparently increasing SO4 radical generation. Thus,

existent. Thus, only a direct after-pulse formation of Cl₂radical

these two types of reactions needed to be separately quantified,

and it has been accomplished only in this study.

Reactions in the Presence of Cl . In the above experiments,

took place at pH 4.3. In the presence of O , when 20 mM

phosphate (as NaH2PO4) was used at the same pH 4.3, the 345

nm trace showed a slightly faster kinetics mainly because of

overall increase in the ionic reaction rates.

2

-

even a high initial radical concentration produced only a

9152 J. Phys. Chem. A, Vol. 105, No. 40, 2001

Das

Figure 10. Kinetic traces and ACUCHEM overlay for measurements

-

in acidic pH in the presence of 12 mM Cl . Dose ) 38 Gy with 520

-

ns pulse. Traces for 3:2 N

2

O/O

2

saturated 450 µM HSO

4

3

solutions:

(

1) pH 3:9 adjusted with HClO

; (2) pH 4.3 adjusted with 20 mM

-

H

2

PO

4

; (3) N O saturated pH 4.3 solution with 20 mM H PO .

2

4

Figure 11. Simulation studies for chain oxidation of S(IV) in acidic

If any set of the lower estimate of k3 and k4 values from

solutions projecting concentrations of oxidized species under different

conditions. Starting fixed concentration of S(IV) ) 10 µM; O ) 240

2

previous studies (Table 1) were reasonable, then even in the

presence of high S(IV) concentrations (10-100 mM) the

propensities of reactions 2 and 5 would not be expected to be

significantly influenced. Consequently, chain lengths would fall

•

µM. Conditions varied: pH from 3 to 6; initiating [ OH] from 1 nM to

0 µM. Final concentrations also include thermal reaction between

1

-

3

and HSO .

HSO

5

1

•

much short of the projected value of 1000. Employing our rate

reached a value <10 for a few µM OH radical concentration,

-

values instead, all such projections could be explained satis-

factorily and these studies are presented below.

the productions of other sulfur-oxygen species such as HSO

5

2

-

and S O

2

8

increased steadily from ∼pM level to ∼µM level.

Chain Oxidation of S(IV) Revisited. First, taking into

account reactions 1-7, chain oxidation was simulated in

This trend of continuous reduction of chain length mainly

resulted from the increasing propensities of radical-radical

reactions that competed favorably with the radical-solute

reactions even in the beginning stages. (As mentioned above,

similar reduction in chain length was also observed even at low

initiating radical concentration if any of the previous lower

estimates of k and k from Table 1 were used.)

-

oxygenated HSO3 solutions, and next, possibilities of reducing

-

2-

sulfuric acid (mainly as HSO4 /SO4 ) production vis- a` -vis

atmospheric S(IV) oxidation were explored. In these simulation

-

studies the second pKa of HSO3 , HSO4 , and HSO5 , etc.

Table 2) were taken into account to correlate the resulting

(

3

4

•

changes in matrix pH. The starting solute concentrations were

taken as follows: O2 ) 240 µM (as present in an aerated

For a given value of the starting OH radical concentration,

the final sulfuric acid yield is greater in lower pH. Since we

have already observed that the SO₅radical dimerization rate

-

2-

•-

solution) and total HSO3 /SO3 ) 10 µM (as expected in

42

•

polluted atmosphere). For the sake of convenience, OH radical

was taken as the chain initiator and its concentration was varied

in different sets from 1 nM to 10 µM. The starting solution pH

was separately changed from 3 to 6 in unit steps, reflecting

different atmospheric scenarios.⁴³After the chain oxidation, the

constants are invariant over this selected pH range, this behavior

may seem to contradict our other rate estimations wherein we

found that all (chain) favoring radical-solute reactions involving

-

the S(IV) species have lower propensity for HSO as compared

3

2-

to SO₃. However, this slower change took place not because

of the SO₅radical reactions but only because of the strongly

-

•-

possibility of thermal reaction between HSO5 formed and any

remaining HSO3 was also included in these studies.

-

35

pH dependent thermal reaction 16.

The final results from these simulations are shown in Figure

1. Since, during the chain oxidation, the O2 concentration

remained . radical concentration, almost complete conversion

HSO₅^-+ HSO₃f 2HSO₄^-

-

(16)

1

•

-

•-

of SO3 to SO5 radical took place. This is supported by an

With decreasing pH, its rapidly increasing rate value (k ) 1.04

2-

+

7

-1 -1

almost negligible final concentration of S2O6 anion obtained

in all cases (not shown in Figure 11). Even for the highest

+ [H3O ] × 10 M s ) ensured a simultaneous scavenging

-

of any HSO5 formed and a corresponding increase in sulfuric

•

starting OH radical concentration used, the maximum product

acid concentration. This explanation was supported by a similar

reaction scheme wherein reaction 16 was omitted. In this case

the yield of sulfuric acid increased marginally from 4.6 to 4.7

2

-

•

[

S2O6 ] was ∼1 nM. At low starting OH radical concentration,

•

the ratio [total sulfuric acid]/[ OH] was found to be as high as

4

•

1

0

and the concentration of other sulfur-oxygen species

µM going from pH 3 to pH 6 for 1 nM starting OH radical

-10

•

produced remained <10 M. With increase in starting radical

concentration. At 10 µM starting OH radical concentration, the

concentration, as the chain length decreased progressively and

corresponding values were 4.0-4.3 µM for pH 3 and pH 6,

Reactivity and Role of Aqueous SO5^•^-

J. Phys. Chem. A, Vol. 105, No. 40, 2001 9153

concentrations were close to 4.8-5.5 µM for pH 3 and pH 6,

respectively, in the absence of scavenger, and it decreases to

3

.6-4.4 µM for pH 3 and pH 6, respectively, in the presence

of the scavenger. About 30% and 20% S(IV) remains nonoxi-

dized in the presence of scavenger at pH 3 and pH 6,

respectively.

•-

In the case of SO4 radical scavenging, effect of scavenging

-

was stronger. For example, both sulfuric acid and HSO5

concentrations remained ∼1 µM over pH 3-6. Thus, the

efficiency of oxidative change decreased to ∼20-25% as

compared to the absence of scavenger and ∼80% of S(IV)

remains nonoxidized. If reaction 16 was taken into account, as

-

expected, an additional 10% S(IV) (equivalent of the HSO5

yield) was thermally oxidized to give a final sulfuric acid

concentration ca. 3 µM. However, when scavenging was

•

-

considered for the SO5 radical, the effects were found to be

substantial. Over the pH range of interest, only ∼1% of S(IV)

was oxidized and even with contribution from reaction 16 the

value increased marginally to ∼2%. These results clearly

indicate that, to break the chain oxidation and minimize sulfuric

acid production, it is sufficient to utilize a suitable SO5^•radical

scavenger with its reactivity ()concentration × scavenging rate)

-

1

of ∼100 s .

Figure 12. Scavenging of SO ^•^-

final concentration of sulfuric acid, inclusive of reaction 16. As-

radicals (x ) 3, 4, 5) and related

x

9

In the NIST database, only a few aqueous medium reactions

•

-

of the SO5 radical are yet reported, and a majority of these

involve electron transfer from a reducing species. However,

since O-atom and H-atom transfer reactions are also possible,

unless comprehensive kinetic results are available, possibilities

8

-1 -1

•

sumed: [scavenger] ) 1 µM; k(scavenging) ) 10 M

s ; [ OH] )

1

0 nM; [S(IV)] ) 10 µM; [O ] ) 240 µM.

2

respectively. In may be noted that in this set of studies we have

•

-

_i_g_n_o_r_e_d_t_h_e_p_o_s_s_i_b_i_l_i_t_y_o_f_p_h_o_t_o_l_y_s_i_s_o_f_S₂_O₈₂_-_t_o_t_h_e_S_O₄•-

of SO₅radical scavenging by chemicals of atmospheric

abundance will remain mainly speculative. However, even from

radical, feasible in the presence of sunlight. If the photolysis

rate competes with the rates of reaction 5 and 7, then the yield

of sulfuric acid will increase further; however other trends would

remain similar to the above results.

•

these limited references we find that aromatic amines and HO2

•

-

radical show sufficient reactivity toward the SO5 radical and

presumably can act as scavengers under favorable conditions.

In B a¨ ckstr o¨ m’s studies, it was reported that diphenylamine

1

Continuing with the simulation studies, our next aim was to

_s_e_p_a_r_a_t_e_l_y_c_h_e_c_k_t_h_e_e_f_f_e_c_t_s_o_f_s_c_a_v_e_n_g_i_n_g_t_h_e_t_h_r_e_e_S_O_x_•-

inhibited the chain oxidation. The rate constant of reaction 18

7

-1 -1 44

is reported to be ca. 5 × 10 M s ,

and its ability to

radicals, with the intent to reduce sulfuric acid concentrations.

Radical scavenging is possible at every stage of the reactions,

influence the chain is explained from our above results.

•

including the scavenging of the starting OH radicals. However,

^S^O5^•^-+ (C H ) NH f HSO + (C H ) N

-

•

(18)

the latter reactions are not considered here and only scavenging

6

5 2

5

6

5 2

•

-

•

of the SOx radicals are discussed. At starting OH radical

concentration of 10 nM, total S(IV) concentration of 10 µM,

and dissolved O2 concentration of 240 µM, the extent of radical

1

On the other hand, reference to alcohols as chain retardants

45

or production of phenol in the presence of added benzene can

be explained by the reactions of SO4 radical (and intermediate

OH radical from SO4 ), the other chain carrier. Thus, satisfac-

•-

_s_c_a_v_e_n_g_i_n_g_w_a_s_s_e_p_a_r_a_t_e_l_y_c_o_n_s_i_d_e_r_e_d_f_o_r_e_a_c_h_S_O_x•- radical.

•

•-

To simplify the scheme, the starting scavenger concentration

8

-1 -1

tory explanation of all the previous experimental results is

available from our analysis of Scheme 1 reactions.

was taken as 1 µM and k17 was taken as 1 × 10 M s .

•

-

In Table 6 the six rate constants obtained in this study are

presented for easy reference. It may be noted that the uncertainty

in the rate value for SO5 + HSO3 f HSO4 + SO4

reaction is slightly lower than the generally accepted value of

scavenger + SO_x(x ) 3, 4, or 5) f

scavenger]_o_x_i_d_i_z_e_d+ SO_x(17)

2

-

•

-

•-

[

Figure 12 shows the effect of scavengers on the final sulfuric

acid concentration including the effect of reaction 16. As above,

reaction 16 once again played an important role in limiting the

sulfuric acid concentration. The apparent higher value for acid

concentration in the case of SO3 radical scavenger as compared

to the case when no scavenger was considered is due to reaction

(10-15% in PR measurements. On the other hand, the

•

-

2-

corresponding uncertainty for the reaction SO4 + SO5

f

•

-

2-

SO5 + SO4 is higher than the generally accepted value. As

indicated before, the uncertainty in each rate value originates

from the complete range (or spread) of rate constant values that

permitted satisfactory ACUCHEM analysis of each set of

experimental measurements. These uncertainties, following the

Debye-H u¨ ckel relation, appropriately reduce in magnitude for

the I f 0 condition but continue to represent the real

experimental uncertainties in each case. Thus, in each case these

rate values with their associated actual experimentally derived

uncertainties have been retained over the average value. Possible

reasons may be (a) incorporation of H-atom reactions instead

of following the general practice of ignoring these (in oxidative

studies), especially in acidic pH, and (b) higher accuracy (and

•-

1

6. On the other hand, when reaction 16 was not considered

for a realistic evaluation of the role of scavengers in chain

oxidation, the following results were obtained.

•

-

In the case of SO3 radical scavenging, the high propensity

of its reaction with O2 was found to mask the effect of scavenger

to a large extent and [sulfuric acid]final over the pH 3-6 reduced

marginally from ∼4.4 µM in the absence of scavenger to 3.6-

3

.4 µM in the presence of scavenger. In this case, peroxymono-

-

sulfate anion (HSO5 ) was the other major product. Its final

9

154 J. Phys. Chem. A, Vol. 105, No. 40, 2001

Das

(2) Reactions between the SO4 radical and the solutes

•

-

TABLE 6: Results from This Study and Selected Rates for

Other Reactions of Scheme 1^a

-

2-

HSO3 /SO3 . A survey of the database reveals rate values

rate constant (M s^-¹

b

-1

)

8

-1 -1

reactions

ranging between 4 × 10 and 20 × 10 M s . The selected

46

_S_O₃_•- ₊_O₂_f_S_O₅•-

9

values in our study were taken from the works of Wine et al.

and Neta and Huie. However, an opposite trend of rate constant

values proposed by Hayon et al. could not be confirmed in

1.1 × 10 (recommended;

47

see Appendix A)

•

-

•-

-

2-

-

2-

-

•-

2-

-

8

SO5 + SO5 f 2SO4 + O2

(2.2 ( 0.3) × 10

12

8

SO5 + SO5 f S2O8 + O2

(2.1 ( 0.3) × 10

•-

3•-

•-

7

our study and was not considered further.

SO5 + HSO3 f HSO4 + SO4

(6.0 ( 0.4) × 10

8

•-

SO5 + SO3 f HSO4 + SO4

(5.6 ( 0.6) × 10

(3) Radical dimerization reaction of the SO4 radical. The

-

7

SO5 + HSO3 f HSO5 + SO

(3.0 ( 0.3) × 10

2-

8

reaction plays an important role in our study, and its value of

SO5 + SO3 f SO5 + SO3

(1.0 ( 0.1) × 10

-

•-

4

8

-1 -1

SO3 + HSO5 f HSO3 + SO5

(1.3 ( 0.1) × 10 (calcd from ∆E

in ref 7 and kf above)

(7.0 ( 0.6) × 10 M s for I f 0 was arrived at by

9

extrapolating the literature decay rates (NIST database ) at the

SO3 + SO5 f SO5^•^-+ SO3

•

-

2-

-

2-

(4.3 ( 0.4) × 10 (as above)

6

•-

-

6

reported ionic strengths and by using the latest ꢀ values from

SO4 + HSO5 f SO5 + HSO4

(1.0 ( 0.10 × 10 (previous result

1

0

•-

modified)

Buxton et al. for the SO4 radical absorptions at the

wavelengths reported in these measurements. Similarly, for the

SO4 + SO5 f SO5 + SO4²^-

•

-

2-

•-

(1.0 ( 0.2) × 10

8

•

-

•-

7

H + HSO5 f SO4 + H2O

(8.0 ( 0.7) × 10

•

-

•

-

•-

6

reaction of H2O with the SO4 radical the more recent value

OH + HSO5 f SO5 + H2O

(5.0 ( 0.3) × 10 (previous result

-

1

-1

modified)

of ∼9.3 M

s

from the database was used.

SO5 + S2O6 f SO4 + S2O7²^-∼10 (see Appendix A for details)

•

-

2-

•-

7

•

-

•-

2-

8

SO4 + SO4 f S2O8

(7.0 ( 0.6) × 10 (calcd from ref 9

details)

Appendix B

values; see Appendix A for

Although the yields of radiolytically produced radicals, ions

SO4^•^-+ HSO3^-f SO3^•^-+ HSO4^-(7.0 ( 0.6) × 10 (best from

SO4^•^-+ SO3²^-f SO3^•^-+ SO4²^-

8

-7

and molecular species in aqueous solutions at 10 s are well

previous estimates)

9

established, the after-pulse concentrations of these and other

23

(1.1 ( 0.1) × 10 (as above)

radical absorption: λmax ) 260-265 nm; ꢀ(260-265 nm) )

species arising out of solute reactions change in some cases.

These changes are expected when the electron-beam pulse

a

•-

SO

5

-

1

-1 b

1

065 ( 80 M cm . For I f 0.

-7

widths are greater than 10 s. For example, in our experiments,

ease) of matrix preparations in acid pH. In Table 6, additionally

other rate constants that have been modified, calculated, or

selected (Appendix A) from other studies are also included for

the sake of completion. For future modeling or simulation of

atmospheric S(IV) chain oxidation, these values are recom-

mended. However, at this stage, it is to be noted that these results

at 25 °C may not always present a complete picture of chemistry

in atmospheric liquid hydrometeors. Since wide fluctuations in

ambient temperatures are common phenomena, representative

modeling of atmospheric sulfuric acid generation in liquid

hydrometeors would be closer to reality only after the variations

of ambient temperature are suitably incorporated in the models.

to get a dose of more than 16 Gy, the 520 ns and 2.2 µs pulses

(beam fwhm) were needed. Various rate constant values in

different tables suggest that partial radical-solute and radical-

radical reactions are possible even within the pulse duration.

Therefore, the prevailing after-pulse concentrations of dif-

ferent species were first obtained from ACUCHEM analyses

of their generations (proportional to individual G values and

the dose rate) and reactions for the duration of the pulse. The

actual pulse profile (duration) was divided into sections of

-7

narrower widths (e10 s), and a similar approach was adopted

for each section separately and sequentially. For example, the

dose rate for each section was equal to the fraction of the total

dose {)(total dose × area of pulse profile in this section/total

pulse profile area)/section time width in s}. Concentrations of

various species at the end of the first section were used as the

starting concentrations for the next section. We found that,

instead of assuming a square pulse shape for the electron beam,

use of the actual pulse shape for these calculations produced

better results. This happened because the beginning, some

middle, and also the end sections of the pulse had irregular

curved profiles. A few examples are as follows.

Acknowledgment. I thank Dr. Pedatsur Neta and Dr. Robert

E. Huie for valuable comments and helpful suggestions during

the course of this study and Dr. Tulsi Mukherjee for a preview

of the manuscript. I sincerely appreciate the magnanimous

comments offered by the reviewers.

Appendix A

A few examples of selected rate constants are as follows.

•

-

(

1) Addition of O2 to SO3 radical. More recent data of

(1) For a 48 Gy 520 ns pulse in N O saturated pH 10.5

2

10

9

-1 -1

2-

Buxton et al. provides a value of 2.5 × 10 M

s

from PR

solution of 2.5 mM SO₅and 100 µM SO , the concentra-

tions of various species (in µM) are SO

0.034, SO ) 0.18, OH ) 9.3, H O ) 3.6, H ) 2.9, HO

) 0.1, O₂) 0.023, remaining SO₃) 99.7, and SO₅

3

•-

2-

•-

measurement in the presence of SO3 and O2. As discussed

later in the text, the inherent complexity of reactions in this

matrix and incorrect projections of their reaction scheme for

kinetic analysis lend incomplete support for this value. Instead,

) 15.7, SO₃

)

2

5

•

-

•

4

2

2-

•

-

2-

)

1980.

9

-1 -1

37

the rate constant 1.1 × 10 M

s

proposed by Huie et al.

(2) For a 102 Gy 2.2 µs pulse in N O (12.5 mM) and O

2

2-

-

was obtained from LFP of S2O6 in the presence of O2

following a simple reaction scheme without any significant

interference from any solute or radical in the matrix. Although

we have not been able to arrive at a final estimate of the reaction

(0.64 mM) bubbled 0.65 mM HSO₃solution at pH 4.0, the

•

-

concentrations of various species (in µM) are SO

4

) 0.37,

•-

•

•-

•

SO₃) 21, OH ) 17.6, SO ) 9.2, H O ) 9.2, H ) 0.065,

HO₂) 8.3, O₂) 1.17, O₃+ HO₃) 0.4, and remaining

5

2

•

•-

•

7

-1 -1

-

8

rate, a limiting value of ∼10 M

s

was obtained from

HSO₃) 630.

•

-

preliminary experiments with the SO5 radical in the presence

In the figures representing cases where such steps were

followed, the time window covering the pulse width is shaded.

of S2O6². Therefore, interference of reaction 8 in LFP

-

•-

experiments is expected to be low in the time scale of the SO3

O2 reaction. In this context, a possible explanation for the

first-order kinetics at 450 nm observed by Huie et al. is that

it probably originated as a result of oversimplification of an

actual complex kinetics of simultaneous formation and decay

Appendix C

+

3

7

In the first analysis of SO5^•^-radical decay in acid pH

described above, the literature value for reaction 12 was used.

The resulting k2 and k5 were used next in the analysis of reaction

12 here, and the resulting redefined k12 was again used for

•

-

of the SO4 radical.

Reactivity and Role of Aqueous SO5^•^-

J. Phys. Chem. A, Vol. 105, No. 40, 2001 9155

analysis of SO5^•^-radical decay in the next section. This cycle

was repeated until further change in results in either analysis

became negligible. Thus, the k2 and k5 values described and

used in this analysis represent the final set from the next section.

Effect of solution ionic strength was appropriately followed in

every step. During analysis of other related rates, a similar

approach was essential.

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Article Doi

Reactivity and role of SO5?- radical in aqueous medium chain oxidation of sulfite to sulfate and atmospheric sulfuric acid generation

DOI: 10.1021/jp011255h

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