Gas-phase reaction of the OH-benzene adduct with O2: Reversibility and secondary formation of HO2

Article abstract of DOI:10.1039/a904887a

The reaction of OH radicals with benzene and consecutive reactions of benzene-OH adducts with O₂ were studied in the gas phase in N₂-O₂ mixtures at atmospheric pressure and room temperature. OH was produced by pulsed 248 n

Full text of DOI:10.1039/a904887a

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Gas-phase reaction of the OH–benzene adduct with O : reversibility
2
and secondary formation of HO
2
Birger Bohn and Cornelius Zetzsch*
Fraunhofer-Institut fur T oxikologie und Aerosolforschung, Nikolai-Fuchs-Strasse 1, D-30625
Hannover, Germany
Received 18th June 1999, Accepted 20th September 1999
The reaction of OH radicals with benzene and consecutive reactions of benzeneÈOH adducts with O were
2
studied in the gas phase in N ÈO mixtures at atmospheric pressure and room temperature. OH was produced
2
2
by pulsed 248 nm photolysis of H O . Time-resolved detection of both OH and benzeneÈOH adducts was
performed by continuous-wave (cw) UV-laser long-path absorption at around 308 nm. The reaction:
2
2
OH ] benzene ] products [reaction (1)] was not a†ected by the presence of O . Rate constants k \ (1.10
2
1
^ 0.07) ] 10~12 cm3 s~1 and (1.06 ^ 0.07) ] 10~12 cm3 s~1 were obtained in N and O , respectively. In N
2
2
2
addition of NO did not change k , from which an upper limit of 5% is derived for formation of H atoms in
2
1
reaction (1). An absorption cross-section of p(308 nm) \ (5.8 ^ 1.5) ] 10~18 cm2 and a self-reaction rate
constant of (3.4 ^ 1.7) ] 10~11 cm3 s~1 were determined for the benzeneÈOH adduct. Upper limits of
5 ] 10~15 cm3 s~1, 1 ] 10~14 cm3 s~1 and 5 ] 10~14 cm3 s~1 were obtained for reactions of the adduct with
benzene, H O and NO, respectively. The adduct kinetics in the presence of O is consistent with the
2
2
2
reversible formation of a peroxy radical: adduct ] O % adductÈO [reaction (2a/[2a)]. An equilibrium
2
2
constant of K \ (2.7 ^ 0.4) ] 10~19 cm3 was determined and a rate constant of k \ (2 ^ 1) ] 10~15 cm3
2a
2a
s~1 was roughly estimated. The e†ective adduct loss from the equilibrium can be explained by (i) an additional
irreversible reaction of the adduct with O with a rate constant of (2.1 ^ 0.2) ] 10~16 cm3 s~1, or (ii) a
2
unimolecular reaction of the peroxy radical, with a rate constant of (7.6 ^ 0.8) ] 102 s~1. For a reaction of the
peroxy radical with O an upper limit of 1 ] 10~17 cm3 s~1 is estimated. Addition of NO reveals formation of
2
HO in the presence of O by recovering OH via HO ] NO. Applying numerical methods, reaction models
2
2
2
were tested to describe the observed complex kinetics of OH. The data are consistent with rapid HO
2
formation following a peroxy radical ] NO reaction with a rate constant of (1.1 ^ 0.4) ] 10~11 cm3 s~1.
Extrapolation of HO formation rates to [NO] \ 0 points at a second source of HO not preceded by any
2
2
RO ] NO reaction.
2
with a yield of 25% was reported,4 which has very recently
been conÐrmed in a Ñow-tube study where a phenol yield of
23% was found.5 Product studies on the OH-initiated benzene
degradation in air report similar yields of phenol3 but phenol
is usually considered a secondary product of reactions of the
Introduction
Aromatic compounds contribute signiÐcantly to anthropo-
genic emissions of organic compounds and have a major
impact on the photochemical production of ozone.1 Neverthe-
less, the details of the tropospheric oxidation mechanisms of
aromatics are still uncertain. The degradation is mainly initi-
ated by reaction with OH radicals, where addition of OH to
the aromatic ring is dominant at low temperatures. These
reactions have been studied for a large number of aromatic
compounds and reviews of experimental work are given by
Atkinson.2,3 In the case of the OH ] benzene reaction, the
addition,
benzeneÈOH adduct with O (ref. 3).
2
However, the fate of the adduct under tropospheric condi-
tions is still uncertain. The reaction adduct ] O was studied
2
before using UV absorption detection of the adduct6,7 and by
observing the inÑuence of O on the kinetics of OH in equi-
2
librium with the adduct.6,8 The data, obtained at O pressures
2
of up to 4 kPa, are consistent with a slow, irreversible reaction
with a rate constant of about 2 ] 10~16 cm3 s~1.
On the other hand, theoretical work9 predicts a fast, but
reversible, formation of a hydroxycyclohexadienylÈperoxy
radical,
OH ] C H ] C H ÈOH
(1a)
6
6
6 6
forming
hydroxycyclohexadienyl
radicals,
C H ÈOH,
6
6
accounts for more than 95% of the reaction,2 while H-atom
abstraction,
C H ÈOH ] O H HOÈC H ÈO
(2a/[2a)
6
6
2
6
6
2
with the equilibrium strongly shifted towards the peroxy
OH ] C H ] C H ] H O
(1b)
6
6
6
5
2
radical, HOÈC H ÈO , at atmospheric levels of O (ref. 9).
6
6
2
2
The reversibility of the possible reaction (2a) was discussed
earlier10 but experimental evidence for the existence of the
peroxy radical in the gas phase has not yet been presented
except in one study, where a strong transient absorption at
280 nm was assigned to this species.4 Theoretically9 it was
is a minor process at room temperature.2
On the other hand, in a recent study direct formation of
phenol via
OH ] C H ] C H ÈOH ] H
(1c)
6
6
6 5
Phys. Chem. Chem. Phys., 1999, 1, 5097È5107
This journal is ( The Owner Societies 1999
5097

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found that reactions (2a) and ([2a) compete with irreversible
known Ñow of N or O . From the ratio of the gas Ñows, the
2
2
reactions of the adduct with O ,
total pressure and the vapour pressure of benzene (5.11 kPa),13
2
concentrations were calculated. NO (99.5%) and NO (98%)
2
were used in premixed form: 500 ppm diluted in N and 1000
2
C H ÈOH ] O ] other products
(2b)
(3)
6
6
2
ppm diluted in synthetic air, respectively (Messer Griesheim).
and unimolecular reactions of the peroxy radical,
Before entering the cell the mixture containing NO was fed
HOÈC H ÈO ] other products
through
a glass tube Ðlled with solid iron(II) sulfate
6
6
2
(FeSO É 5H O) to remove NO traces.
respectively. Both reactions (2b) and (3) are predicted to lead
4
2
2
OH was monitored by time-resolved continuous-wave (cw)
mainly to either a bicyclic peroxy radical or phenol ] HO
2
UV-laser long-path absorption on the Q (2) rotational line of
(refs. 9, 10). However, the respective rate constants9 predicted
1
the OH(A 2&` ^ X 2%) transition at 307.995 nm (air) with a
are too small to account for the experimentally observed
folded path-length of 100 m (100 reÑections, typical laser
power: 200 lW). This technique and the experimental set-up
have been described elsewhere.12,14,15 The line-width of the
laser is about 500 kHz, much narrower than that of the
pressure-broadened rovibronic line. Thus, the laser can be
tuned to the maximum of the rotational line and the BeerÈ
Lambert law can be applied to derive absolute OH concentra-
tions if needed. Literature data on the absorption
cross-section at the centre of the line as a function of pressure,
temperature and gas composition are available.16,17 The OHÈ
benzene adduct was detected in the same spectral range
adduct loss in the presence of O (refs. 6È8). On the other
hand, if reaction (2a) were reversible, also a reaction of the
2
peroxy radical with O ,
2
HOÈC H ÈO ] O ] products
(4)
6
6
2
2
could contribute to the e†ective adduct loss rate.
The present work addresses the fate of the benzeneÈOH
adducts at higher concentrations of O . The UV absorption
2
technique allows us to perform direct kinetic studies on both
OH and the adduct at O pressures of up to 100 kPa (1 bar)
2
and indeed we Ðnd evidence for a reversible reaction (2a).
[usually [0.045 nm o† the OH Q (2) line]; however, the
Moreover in the presence of NO we investigated the second-
1
sensitivity was less owing to a smaller absorption cross-
ary formation of HO by recovering OH via HO ] NO.
2
2
section4,7 (more details are given in the “ResultsÏ section). OH
decay curves were recorded by averaging over 3È10 single
measurements. Due to the lower absorption signal of the
The question with respect to HO formation is whether
2
HO is formed directly in the adduct ] O reaction (“prompt
HO Ï) or as a result of a reaction sequence involving RO
2
2
2
2
adduct, especially at high O concentrations, adduct decay
] NO reactions (“delayed HO Ï). For example, in a recently
2
2
curves were averaged over 10È200 single measurements. In
proposed new mechanism11 the adduct ] O reaction (2b) is
2
any case, after 10 laser pulses (repetition rate: 0.2 s~1) 5È10
min were allowed to elapse to prevent accumulation of pho-
tolysis and/or reaction products.
assumed to lead to high yields of benzene oxide/oxepin and
HO , while previously3 “promptÏ HO was associated with
2
2
abstraction of an H atom from the aromatic ring forming
phenol with a yield of only about 25%. Thus, the yield and
Results
Rate constant of OH + benzene
formation kinetics of HO is a key to distinguish between cur-
2
rently discussed mechanisms of the tropospheric degradation
of benzene and other aromatic compounds.
Determination of the rate constant of OH ] benzene was not
a primary aim of this work. However, the applied experimen-
tal technique allows us to measure this constant at atmo-
spheric pressures of N or O . If there were a regeneration of
Experimental
Measurements were made in slowly Ñowing (about 3 L min~1,
STP) gas mixtures in a cylindrical 20 L glass cell at atmo-
spheric pressure (99 ^ 2 kPa) and room temperature (297 ^ 2
K). N ÈO mixtures with varying amounts of O were pre-
2
2
OH in a reaction of benzeneÈOH adducts with O , which for
2
example has been observed in the case of acetyleneÈOH
adducts,12,18 di†erences in the kinetic behaviour of OH would
be expected. Moreover, the rate constant is needed as a
parameter in model-Ðtting procedures described below.
2
2
2
pared using calibrated mass-Ñow controllers (FC 260, Tylan)
and high purity samples of N (99.999%) and O (99.995%)
2
2
(Messer Griesheim). The total pressure was measured with
capacitance manometers (Baratron, MKS).
Adduct absorption can be neglected in O at atmospheric
2
pressure (see subsection on “Adduct kinetics in the presence of
H O served as a photolytic OH precursor by pulsed 248
nm KrF excimer laser photolysis (typical Ñuence: 1.5 mJ
O Ï) and OH absorption signals were found to decay mono-
exponentially. Two sets of Ðtted decay rates as a function of
2
2
2
cm~2). H O was prepared and introduced as described else-
benzene concentration gave similar rate constants k of
2
2
1
where,12 concentrations ranging between 1 and 14 Pa. The
purity of the benzene sample (Rathburn, glass distilled grade)
was checked by gas chromatographic (GC) analysis
([99.99%). Benzene was introduced by purging the liquid in a
thermostated gas saturator at T \ (279.9 ^ 0.1) K with a
(1.06 ^ 0.07) ] 10~12 cm3 s~1 and (1.05 ^ 0.04) ] 10~12 cm3
s~1. Experimental conditions are listed in Table 1.
OH decay curves in N are a†ected by an underlying
2
absorption of the adduct. Fig. 1 shows two experimental
curves obtained with the dye laser tuned (a) on and (b) [0.045
Table 1 Rate constants of reaction (1) at di†erent experimental conditions [T \ (297 ^ 2) K]. Error bars are 2p (statistical)
[H O ]/
1014 cm~3
[NO ]/
2
[C H ]b/
1015 cm~3
k /
2
2
6
6
1
p
/kPa
tot
Bu†er gas
Na
1014 cm~3
10~12 cm3 s~1
100
N
2
7
5
5
6
8
8
5
5
6.5
7.2
5.0
2.5
4.6
4.6
2.2
2.2
È
4.3
3.7
4.7
2.1
1.8
1.8
1.8
1.8
1.10 ^ 0.07
1.11 ^ 0.06
1.06 ^ 0.07
1.05 ^ 0.04
1.10 ^ 0.03
1.06 ^ 0.06
0.99 ^ 0.04
1.04 ^ 0.04
99.4
97.3
98.0
25.7
25.7
10.1
10.1
N
2
È
O
O
N
2
È
2
È
2
È
N
N
N
c
d
1.3
È
2
2
2
1.3
a Number of data points. b Maximum benzene concentration. c 0.4% of O . d 1.0% of O .
2
2
5098
Phys. Chem. Chem. Phys., 1999, 1, 5097È5107

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Fig. 1 Time dependences of absorption signals in N . (a) Probe laser
Fig. 2 Adduct decay curves in N and Ðts of eqn. (II) (dotted lines).
2
tuned on the OH Q (2) absorption line (OH ] adduct absorption). (b)
1
2
[H O ] \ 5 ] 1014 cm~3; (a) [C H ] \ 3.4 ] 1015 cm~3; (b)
2
2
6 6
Probe laser tuned [ 0.045 nm o† the OH line (adduct absorption). (c)
[C H ] \ 1.2 ] 1015 cm~3. Note the strong increase of initial adduct
6
6
Di†erence of (a) and (b) (OH signal). Experimental conditions:
concentration caused by the higher benzene concentration (see text).
[H O ] \ 7.0 ] 1014 cm~3, [C H ] \ 3.6 ] 1015 cm~3.
2
2
6 6
obviously not Ðrst-order, which can be explained by the inÑu-
ence of a self-reaction of the adduct:
nm o† the OH line. The third curve (c) is the di†erence, which
represents the OH signal alone (assuming the same absorption
cross-section for the adduct at both wavelengths). The di†er-
ence indeed decays monoexponentially, which is expected
since the rate constant of adduct dissociation back to the reac-
tants can be neglected under the conditions employed (about
3 s~1 at 297 K).6,19
C H ÈOH ] C H ÈOH ] products
(5)
6
6
6 6
To determine the respective rate constant, absolute concentra-
tions of the adduct are needed, i.e. the absorption cross-
section.
The absorption cross-section was calculated from experi-
mental ratios of adduct and OH absorption signals and a lit-
To determine OH decay rates in N , biexponential Ðts (sum
2
of two exponentials ] background) to the signal obtained on
erature value of p \ 1.57 ] 10~16 cm2 at the centre of the
the absorption line [curve (a) in Fig. 1] were made. This is
justiÐed since the underlying adduct absorption [curve (b)]
rises with a rate similar to the decay rate of OH while it
decays monoexponentially in good approximation on the time
scale of the OH decay. Thus, a biexponential time behaviour
results for the sum where the smaller time constant corre-
sponds to the reciprocal OH decay rate. Two sets of Ðtted
decay rates as a function of benzene concentration gave rate
OH
Q (2) absorption line at 300 K and atmospheric pressure of
1
N .16,17 The falling parts of the decay curves of OH and the
adduct were extrapolated to t \ 0 and corrected with respect
2
to their formation kinetics where in the case of OH
“formationÏ is caused by the rise-time of the experimental set-
up22 (Fig. 1). The correction addresses the question of which
absorption signals are representative for the OH concentra-
tion present at t \ 0 and the respective adduct concentration
formed by the reaction with benzene. In case of a rise-and-fall
type biexponential decay, the Ðtted amplitude is multipied by
the di†erence of rising and falling rates divided by the rising
rate. The fraction f of OH converted to the adduct was calcu-
constants
k
of (1.10 ^ 0.07) ] 10~12 cm3 s~1 and
1
(1.11 ^ 0.06) ] 10~12 cm3 s~1, i.e. within the error limits the
rate constants obtained in O and N are similar. Experimen-
tal conditions are listed in Table 1.
2
2
By addition of NO a possible formation of H atoms via
2
lated from the loss rate constant of OH, 1k
(Ðrst-order and
reaction (1c) was investigated. NO rapidly reacts with H
l, OH
2
pseudo-Ðrst-order rate constants will be denoted by an upper
atoms to form OH.20,21 Under the conditions employed,
index 1 in the following), k and the benzene concentrations,
[NO ] \ 1.3 ] 1014 cm~3, the regeneration of OH would be
l
2
i.e. f \ k [C H ]/1k
, where a yield of one is assumed for
fast enough to cause an e†ective rate constant of reaction (1),
l
6
6
l, OH
adduct formation in reaction (1).
k
\ k [ k . Since the NO sample was diluted in syn-
1, eff
1
1c
2
The absorption signal ratios derived under various condi-
tions are listed in Table 2. The average corresponds to an
thetic air, the pressure was reduced to diminish the competing
H ] O reaction. Two sets of measurements were made each
2
absorption cross-section p (308 nm) \ (5.8 ^ 1.5) ] 10~18
with and without added NO at total pressures of 10 and 25
add
2
cm2. The 25% error limit is estimated from the reproducibility
kPa of N . In the presence of NO the adduct absorption
signal virtually vanished, which is in accord with a rapid
2
2
of the signal ratios and possible errors in the determination of
signal heights and concentrations.
adduct ] NO reaction (k \ 2.8 ] 10~11 cm3 s~1).6,8 Taking
2
No change of the absorbance by the adduct was observed in
measurements at 307.8 nm and 308.1 nm (the usual detection
wavelength was 307.95 nm), i.e. there appears to be no Ðne
structure in this range of the spectrum. Since the equipment is
optimised for detection of OH, the dye laser can be tuned in
this narrow range only.
into account literature data20,21 on the rate constants of H
] NO and H ] O , 83% and 67% of possibly formed H
2
2
atoms should be converted to OH at 10 and 25 kPa total
pressure, respectively. However, the obtained rate constants
(Table 1) are not inÑuenced by the presence of NO while the
2
intercepts were increased by 750 s~1 (25 kPa) and 390 s~1 (10
It should be noted that the benzene concentration had an
unexpected inÑuence on the OH starting concentration. With
the available excimer laser Ñuence an H O concentration of
kPa), owing to the pressure dependent OH ] NO reaction.
2
From these data no formation of
H
atoms in the
OH ] benzene reaction is evident. An upper limit of 5% is
estimated for the respective yield from the di†erence of the
rate constants which remains possible within the statistical
error limits of the measurements at 10 kPa total pressure.
2
2
2 ] 1014 cm~3 gave an OH starting concentration of about
5 ] 1010 cm~3. However, the amount of OH was found to
increase strongly with benzene concentration. The increase
was linear up to a factor of 6 at about 3 ] 1015 cm~3 of
benzene and then levelled o† at higher concentrations. The
levelling o† is probably due to absorption of 248 nm light
within the cell since the light passes a distance of about 50 cm
before it reaches the actually probed volume. Absorption of
UV absorption and self-reaction of the adduct
In the absence of O the adduct absorption decays rather
2
slowly. Fig. 2 shows two examples. The time dependence is
Phys. Chem. Chem. Phys., 1999, 1, 5097È5107
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Table 2 Ratios of OH [centre of Q (2) line] and adduct absorption signals at 308 nm (\p /p ) at p \ (99 ^ 2) kPa and T \ (297 ^ 2) K.
1
add OH
tot
First-order loss (1k0 ) and second-order self-reaction rate constants (k ) obtained from Ðts of eqn. (II)
add
5
[C H ]/
1015 cm~3
[H O ]a/
1014 cm~3
[NO]/
1014 cm~3
[HO ] /
[add]
0
I
/( f bI
)
1k0 /
add
k c/
6
6
2
2
2 0
0, add
0, OH
5
(\p /p )/10~2
s~1
10~11 cm3 s~1
add OH
1.18
1.51
2.23
2.28
3.30
3.36
3.36
3.65
3.65
3.65
3.65
4.34
5
7
7
5
7
14
5
7
7
7
È
0.69
0.75
0.51
0.36
0.34
0.68
0.24
0.31
0.31
0.31
0.31
0.26
3.7
3.1
3.7
3.0
3.5
È
3.6
3.4
4.0
4.4
4.2
3.4
10
16
3.7
3.5
5.0
3.9
3.7
4.6
3.5
3.9
3.7
4.3
2.9
3.3
È
È
4.3
2.0
9.4
0.0
5.6
8.1
10
0.0
17
12
È
È
È
È
È
0.84
1.64
2.41
È
7
7
Averaged
3.7 ^ 0.7
8 ^ 8
3.8 ^ 1.1
a Approx. values ^ 0.5 ] 1014 cm~3. b Conversion factor OH ] adduct (see text). c Calculated taking p \ 5.8 ] 10~18 cm2. d Error limits
add
include largest deviations within the sets.
248 nm radiation by benzene leads to an electronically and
both radicals strongly absorb in the 308 nm region.4,24 On the
other hand, no evidence for reactions (6) or (6a) was reported
in studies where OH was observed in equilibrium with the
adduct.6,8
vibrationally excited singlet state S (1B ) followed by e†ec-
1
2u
tive intersystem crossing into the lowest lying triplet state T
1
(3B ).23 The increase of OH concentration is therefore tenta-
tively attributed to a benzene sensitised decomposition of
1u
In an experiment with roughly doubled H O concentra-
2
2
H O :
tion, 1.4 ] 1015 cm~3, 1k0 was not increased. Thus, for the
2
2
add
rate constant of the reaction
C H (T ) ] H O ] C H ] 2OH
6
6
1
2
2
6 6
C H ÈOH ] H O ] products
(7)
This idea is supported by the observation that addition of the
6
6
2 2
lowest concentration of O used (0.3 kPa) completely sup-
an upper limit k O 1 ] 10~14 cm3 s~1 is estimated. Addition
2
7
pressed the increase in initial OH in accordance with rapid
of up to 2.4 ] 1014 cm~3 of NO also did not increase 1k0
add
quenching of benzene (T ) by O . The ratio of adduct and
from which an upper limit k O 5 ] 10~14 cm3 s~1 is esti-
1
2
8
OH absorption signals did not increase, i.e. there is no signiÐ-
mated for the reaction
cant formation of the adduct in a reaction of benzene (T )
1
C H ÈOH ] NO ] products
(8)
with H O .
6
6
2
2
The adduct decays can be explained in terms of the follow-
ing di†erential equation combining Ðrst- and second-order
kinetics:
in accordance with an earlier reported6,8 upper limit k O 3
8
] 10~14 cm3 s~1.
On the other hand, the reaction
d[add]
C H ÈOH ] HO ] products
(9)
\ [2k [add]2 [ 1k0 [add]
add
(I)
6
6
2
5
dt
may inÑuence the observed kinetics although in most experi-
ments a marked excess of the adduct was present. Simulations
show that if k is of the order of k , an increase of the Ðtted k
The Ðrst-order rate constant 1k0 allows for an additional
loss of the adduct for example by di†usion, decomposition or
reaction. Eqn. (I) can be solved to satisfy an initial value
add
9
5
5
based on eqn. (II) is expected with the initial ratio of HO and
2
[add] \ [add] at t \ 0:
adduct concentrations ([HO ] /[add] , also listed in Table 2).
0
2 0
0
Indeed a slight increase is found. In order to eliminate any
[add] 1k0 exp([1k0 t)
inÑuence of HO , a linear extrapolation to [HO ] /[add] \
0
add
add
[add] \
(II)
2
2 0
5
0
1k0 ] 2[add] k M1 [ exp([1k0 t)N
0 was made, which gave a rate constant of k \ (3.4 ^ 1.0)
add 0 5 add
] 10~11 cm3 s~1 (2p error limits), slightly smaller than the
After conversion of the absorption signals to absolute concen-
trations, eqn. (II) was Ðtted to the adduct decay curves (also
considering experimental background and omitting the Ðrst
few data points where the signal rises with the decay rate of
OH).
average stated above but similar within the error limits. No
attempt was made to determine k on the basis of the data in
9
Table 2. Taking into account the uncertainty of the absorp-
tion cross-section, a relative error of 50% is Ðnally estimated
for the rate constant of the adduct self-reaction, i.e. k \ (3.4
From a set of 12 measurements averaged rate constants
k \ (3.8 ^ 1.1) ] 10~11 cm3 s~1 and 1k0 \ (8 ^ 8) s~1 were
5
^ 1.7) ] 10~11 cm3 s~1. Note the direct dependence of k on
5
5
add
the absorption cross-section used. As a consequence, the
Ðtted. The error limits reÑect the largest deviations within the
data set listed in Table 2. A strong mutual dependence of the
rate constants k and 1k0 can be recognised, but no depen-
kinetic result can also be expressed in terms of the ratio
k /p \ (5.9 ^ 1.7) ] 106 cm s~1.
5
add
5
add
dence on benzene concentration in the range (1È4) ] 1015
cm~3. Thus, for the reaction:
Adduct kinetics in the presence of O
2
A total of 24 measurements were made at O concentrations
C H ÈOH ] C H ] products
(6)
2
6
6
6 6
ranging from 7 ] 1016 to 2.5 ] 1019 cm~3. Fig. 3 shows three
a rate constant k O 5 ] 10~15 cm3 s~1 was estimated.
examples of adduct decay curves at relatively high O levels.
6
2
However, the reaction
After a rapid rise the signals decay monoexponentially within
experimental scatter. Decay rates were determined by apply-
ing monoexponential (omitting the rising parts of the curves)
or biexponential Ðts (di†erence of two exponentials) including
C H ÈOH ] C H ] C H OH ] C H ÈH
(6a)
6
6
6
6
6
6
6 6
forming phenol and cyclohexadienyl radicals, cannot be
excluded from the absorption measurements of this work since
experimental background. For the two lowest O concentra-
2
5100
Phys. Chem. Chem. Phys., 1999, 1, 5097È5107

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Fig. 3 Adduct decay curves in the presence of di†erent O concen-
Fig. 4 E†ective adduct decay rates as a function of O concentra-
2
trations. [H O ] \ 1.2 ] 1015 cm~3; [C H ] \ 3.2 ] 1015 cm~3;
2
tion. (a) Fit to eqn. (III) with k held Ðxed at the estimated upper limit
2
2
6 6
[O ]/1018 cm~3 \ (a) 2.2, (b) 6.0, (c) 16.2. (d) Possible time depen-
4
of 1 ] 10~17 cm3 s~1. (b) Fit to eqn. (III) with k \ 0. (c) Limiting
2
dence of the background signal as a product of adduct reactions.
4
slope at low O concentrations corresponding to a rate constant of
2
2.1 ] 10~16 cm3 s~1. … Measurement at 20.5 kPa total pressure
(otherwise 99 kPa).
tions eqn. (II) was used to determine the decay rate but the
inÑuence of the self-reaction was found to be almost negligible
since the adduct starting concentrations decreased in the pres-
possibly (4), one of the time constants decreases strongly and
biexponential decays e†ectively result with rising and falling
rates corresponding to OH decay rates and e†ective adduct
loss rates, respectively. However, experimentally a deviation
from biexponential behaviour was observed with Ðtted rising
rates consistently larger than the OH decay rates. This e†ect
will be discussed later.
ence of O .
2
With increasing O concentration two main features were
2
observed which are inconsistent with a simple, irreversible
adduct ] O reaction. Firstly, the decay rates increased non-
2
linearly with O concentration, and secondly, the absorption
2
signal decreased accordingly. The data are listed in Table 3
and plotted in Fig. 4 and 5. The explanation for these obser-
vations is the reaction model shown in Fig. 6. The adduct
The assumption of a fast equilibrium (2a/[2a) leads to the
following approximate expression for the e†ective adduct loss
reacts reversibly with O under fast establishment of an equi-
2
librium with a peroxy radical (2a/[2a). Loss reactions of the
adduct (2b) and/or peroxy radical (3) are responsible for the
nonlinear dependence of the adduct decay rates on O con-
2
centration (Fig. 4), while a lower absorption cross-section of
the peroxy radical at 308 nm explains the decrease of the
absorption signal (Fig. 5).
In general the reaction scheme as shown in Fig. 6 results in
triexponential adduct decay curves. However, if reactions (2a/
[2a) are fast compared to the loss reactions (2b), (3) and
Table 3 E†ective adduct decay rates (1keff ) and ratios of OH and
add
adduct absorption signals at 308 nm at di†erent O concentrations
2
[p \ (99 ^ 2) kPa and T \ (297 ^ 2) K]
tot
[O ]/
1018 cm~3
[C H ]/
1015 cm~3
[H O ]/
1015 cm~3
1keff /
add
I
/ f aI
2
6
6
2
2
0, add 0, OH
s~1
/10~2
Fig. 5 Ratio of adduct and OH absorption signals as a function of
0.071
0.17
0.95
0.95
0.97
0.98
2.2
2.2
2.3
2.8
3.6
4.6
4.6
4.6
4.8
4.9
5.0b
6.0
6.0
7.2
1.5
1.5
1.7
2.2
2.2
3.4
3.2
3.2
3.4
1.7
3.4
1.2
2.2
2.2
3.4
2.5
1.8
3.2
3.2
2.2
1.7
2.2
3.2
3.2
0.8
0.8
0.6
1.2
1.2
1.4
1.2
1.2
1.4
0.6
1.4
0.6
0.9
1.2
1.4
0.5
0.5
1.2
1.2
1.2
0.5
1.2
1.2
1.2
28
40
3.73
3.16
3.41
3.01
3.47
3.38
2.42
2.56
2.90
2.71
2.23
1.98
2.01
1.96
1.38
È
O
concentration. The line was calculated taking the equilibrium con-
2
stant of K \ 2.7 ] 10~19 cm3 and assuming no absorption by the
2a
158
160
159
164
266
287
296
291
400
429
445
418
449
382
444
511
434
532
572
556
616
640
peroxy radical (see text).
È
1.51
1.46
1.37
1.18
1.09
0.730
0.481
9.4
9.5
16.2
24.6
Fig. 6 Reaction model explaining the results shown in Figs. 4 and 5.
The presence of H O , leading to an additional loss of OH, is not
2
2
shown. Only one of two possible isomers of the peroxy radical (O in
a Conversion factor OH ] adduct. b 20.5 kPa total pressure.
2
ortho or para position) is shown.
Phys. Chem. Chem. Phys., 1999, 1, 5097È5107
5101

View Article Online
rate as a function of O concentration (see Appendix):
radical reactions, the absorption would rise with a rate similar
to the decay of the adduct (except for a short delay of the
order of the OH lifetime). This possible time behaviour of the
background is indicated in Fig. 3 [curve (d)]. As a conse-
quence, a Ðt to the total signal assuming a constant back-
ground still gives the correct rate constant. On the other hand,
the background must then be added to the absorption signal
of the adduct extrapolated to t \ 0 which would lift the data
points in Fig. 5 by about 0.003. This leaves room for a small
fraction of the signal caused by absorption of the peroxy
2
[O ](K 1k ] k ) ] [O ]2K
k
2
2a
3 2b
1 ] K [O ]
2a
2
2a 4
1keff \
(III)
(IV)
add
2
where K is the equilibrium constant:
2a
k
2a
K
\
2a
1k
~2a
If the magnitude of k , i.e. reaction of the peroxy radical with
4
O , were considerable, the O dependence of the loss rate
radical at 308 nm [p
(308 nm) \ 2 ] 10~19 cm2].
2
2
peroxy
would become linear at higher O levels, but no such behav-
iour is observed. A Ðt of eqn. (III) to the data in Fig. 4 even
The magnitudes of the rate constants k and 1k
have
2
2a
~2a
also been estimated. As mentioned above, the rising rates of
adduct absorptions obtained in biexponential Ðts were larger
than the OH decay rates. Due to the lower signal the preci-
sion of the Ðtted adduct rising rates is much poorer than that
of the OH decay rates and there is considerable scatter in the
data. Moreover, the Ðrst few data points at very short times
are not reliable because of an inÑuence of laser stray light and
the rise time of the detection system. Nevertheless, the devi-
ation was signiÐcant and became more pronounced at higher
gave a slightly negative value k \ ([4 ^ 5) ] 10~18 cm3 s~1
4
(2p error limits). Thus, reaction (4) appears to be of no impor-
tance. Nevertheless, considering a relative error of 25% for the
decay rates at the highest O concentrations (see below), an
2
upper limit k O 1 ] 10~17 cm3 s~1 is estimated. Curve (a) in
4
Fig. 4 shows a Ðt to the data with k held Ðxed at this value.
4
With k set to zero, an equilibrium constant K \ (2.7
4
2a
^ 0.4) ] 10~19 cm3 and a value of (2.1 ^ 0.2) ] 10~16 cm3
s~1 for the sum (K 1k ] k ) were obtained (2p error
O concentrations. It was checked that the e†ect is not caused
2a
3
2b
2
limits). Curve (b) in Fig. 4 shows the corresponding Ðt. The
cause of the adduct loss cannot be assigned to either reaction
(2b) or (3) since only the sum of the respective rate constants is
by the decrease of the signal or by photolysis of reaction pro-
ducts by the excimer laser.
Fig. 7 shows a comparison of an experimental decay curve
(corrected for excimer laser stray light) and numerical simula-
tions (FACSIMILE)26 based on the reaction model in Fig. 6
where the equilibrium constant was held Ðxed while the rate
constants of reactions (2a) and ([2a) were changed. The rise-
time of the detection system and the presence of H O have
available. With the assumption 1k \ 0 the result would be
3
similar to that of earlier studies6h8 where the adduct loss was
attributed to reaction (2b) alone. A reversible formation of a
peroxy radical has not been considered in these studies since
at low O concentrations the dependence of the e†ective loss
2
2 2
rate on O is linear in good approximation, as indicated by
also been considered in the simulations which were scaled
with the experimentally determined OH concentration. The
observed deviation is reproduced in an intermediate range
between tri- and biexponential behaviour. A distinct tri-
2
curve (c) in Fig. 4. On the other hand, the data are equally
well described by reaction (3) alone. If k \ 0 is assumed,
2b
1k \ (760 ^ 80) s~1 would be obtained for the rate constant
3
of a possible unimolecular reaction of the peroxy radical. This
exponential curve is obtained if k is equal to or less than
2a
rate constant corresponds to the maximum value of 1keff
1 ] 10~15 cm3 s~1 while biexponential curves with rising
add
approached at high O concentrations. Of course, any inter-
2
rates similar to the OH decay rate are obtained if k is equal
2a
mediate case is possible, i.e. part of the loss may be attributed
to or larger than 3 ] 10~15 cm3 s~1. Experimentally no indi-
to reaction (2b) and part to reaction (3).
In a further experiment the adduct decay rate was measured
cation of a triexponential behaviour was observed while the
rising rates were clearly enhanced in comparison with the OH
at a total pressure of 20.5 kPa in O . A similar rate was
obtained as in synthetic air at atmospheric pressure, i.e. in this
range the total pressure does not inÑuence the kinetics.
decay rates. Thus, for the rate constant k \ (2 ^ 1) ] 10~15
2
2a
cm3 s~1 is roughly estimated. For the rate constant of peroxy
radical decomposition back to adduct ] O this leads to
2
The dependence of the absorption signals on O concentra-
1k
\ (8 ^ 4) ] 103 s~1.
2
~2a
tion is in accordance with the equilibrium constant derived
In the simulations of Fig. 7 only reaction (3) was considered
above. Assuming that the peroxy radical does not signiÐcantly
absorb at 308 nm, which is true for most peroxy-type radicals
investigated so far,25 the expected decrease of the adduct
with the limiting rate constant derived above. If reaction (2b)
is used instead, a qualitatively similar picture is obtained as in
Fig. 7. However, the triexponential behaviour is slightly more
absorption signal with O concentration was calculated. This
pronounced at k O 1 ] 10~15 cm3 s~1 and the signal heights
2
2a
includes the slight change of p caused by di†erent pressure
OH
broadening in N and O .16,17 In Fig. 5 the result is com-
2
2
pared with the experimental data. Although, compared with
Fig. 4, the scatter of these data is higher, the agreement is
satisfactory.
However, as is evident from Fig. 3, there is a residual
absorption which remains more or less constant at the di†er-
ent levels of O and does not change on the time scale of the
2
experiment. Since the adduct absorption signal decreases, the
relative importance of this background increases. Unfor-
tunately, the time behaviour of the background is unknown.
In the Ðts it has simply been treated as constant. This is
correct at least in part because it has also been observed in the
absence of H O , i.e. in the absence of any OH-initiated reac-
2
2
tions, where the signal appeared virtually instantaneously
after the laser pulse. Addition of H O increased the residue
2
2
Fig. 7 Experimental adduct decay curve (open circles, background
subtracted) and simulations with varying rate constants k and 1k
but its time dependence after the laser pulse is hidden behind
the absorption of OH or the adduct. If the absorbing species
were formed in an OH reaction, the absorption would rise
quickly and not inÑuence the adduct decay. On the other
hand, if it were formed as a product of adduct or peroxy
2a
~2a
at a Ðxed equilibrium constant K \ 2.7 ] 10~19 cm3. Full lines
2a
from top to bottom (k /10~15 cm3 s~1): 0.5, 1.0, 2.0, 3.0 and limiting
2a
biexponential behaviour for large k (see text). Experimental param-
2a
eters as in Fig. 3; [O ] \ 1.6 ] 1019 cm~3.
2
5102
Phys. Chem. Chem. Phys., 1999, 1, 5097È5107

View Article Online
of the simulations are lower (except for the limiting biexponen-
tial behaviour). However, this should not be taken as an indi-
cation that reaction (3) dominates since the simulated signal
heights depend on experimental uncertainties (OH concentra-
tion, equilibrium constant) and underlying assumptions
(background signal, absorption cross-section).
representative for tropospheric conditions (see below). Never-
theless, information relevant to the troposphere may be
obtained by an extrapolation of kinetic parameters towards
lower NO concentrations.
Eight sets of data were recorded at di†erent NO and O
2
concentrations each consisting of OH decay curves at 5È10
Nevertheless, although k is only about one order of mag-
di†erent benzene concentrations. Experimental parameters are
listed in Table 4. In the absence of benzene, i.e. in the presence
of H O and NO alone, OH decay curves are biexponen-
tial.18,22 From an analysis of these decays pseudo-Ðrst-order
rate constants of the following reactions were obtained for
each set of decay curves under the conditions employed:
2a
nitude faster than the maximum value of k , the assumptions
2b
of deriving eqn. (III) are still reasonable. The simulations in
2
2
Fig. 7 show that the Ðnal slope of the adduct decays is hardly
inÑuenced by a limited magnitude of k and 1k
. Combin-
2a
~2a
ing the uncertainties of the background signal and the sta-
tistical errors from the Ðts, a relative error of 25% is Ðnally
estimated for the measured e†ective adduct decay rates.
OH ] H O ] HO ] H O
(10)
(11)
(12)
2
2
2
2
HO ] NO ] OH ] NO
2
2
OH kinetics in the presence of O and NO
2
OH ] NO ] HONO
Adduct decay curves in the presence of O and NO were inÑu-
2
The evaluation procedure of the biexponential decays has
enced by NO formation. Despite a relatively low absorption
2
been described in detail previously.18,22 In addition the 1k
cross-section of NO at 308 nm (1.8 ] 10~19 cm2),20,21 the
signal was strong enough to cover the later parts of adduct
10
2
were measured independently in the absence of benzene and
NO. The di†erent 1k and 1k are listed in Table 4. The
decay curves which are not expected to decay mono-
exponentially. On the other hand, OH decay curves were
11
12
corresponding rate constants k \ (9.4 ^ 0.4) ] 10~12 cm3
11
s~1 and k \ (7.1 ^ 0.4) ] 10~12 cm3 s~1 at 98 kPa (2p
12
hardly a†ected by NO or adduct absorption, especially at
2
error limits) agree well with our previous results obtained by
high O concentrations. Fig. 8 shows examples of OH decay
2
the same method.18,22
curves obtained at atmospheric pressure of O at di†erent
benzene concentrations in the presence of NO. Regeneration
2
The rate constants of reactions (1), (2a/[2a) and (10)È(12)
were then used as Ðxed parameters in numerical model Ðts
(FACSIMILE)26 to OH decay curves recorded in the presence
of benzene. However, compared to the estimates derived in the
previous section, the rate constants of reactions (2a) and
of OH, i.e. secondary formation of HO , is clearly recognis-
2
able.
To obtain OH decay curves which can be properly
analysed, fairly high NO concentrations of the order 1 ] 1014
cm~3 had to be used to increase the levels of regenerated OH
and to limit the length of the reaction chain by OH ] NO. As
a consequence, a reaction of the peroxy radical with NO,
([2a) were increased by a factor of 103, i.e. k \ 2 ] 10~12
2a
cm3 s~1 and 1k
\ 7.4 ] 106 s~1 for the model Ðts. Thus, a
~2a
fast equilibrium is presumed to make reactions (2b) and (3)
indistinguishable in the reaction model. The underlying
adduct absorption was also considered in the Ðts but its inÑu-
which is expected to lead to HO formation in secondary
2
reactions, is inevitable although this reaction is probably not
ence was found to be negligible except at the lowest O con-
2
centration (5 ] 1018 cm~3).
The simplest model that was able to describe the obser-
vations successfully had three adjustable parameters: the
initial OH concentration and the rate constants of the follow-
ing two hypothetical Ðrst-order reactions:
HOÈC H ÈO ] HO
(M1)
(M2)
6
6
2
2
HOÈC H ÈO ] other products
6
6
2
Examples of Ðts are shown in Fig. 8. No apparent dependence
of the rate constants 1k and 1k on the benzene concentra-
M1
M2
tions was found within the data which were therefore aver-
aged for each set and listed in Table 4. As expected, the rate
constants exhibit a strong dependence on NO concentration
which is illustrated in Fig. 9. Error bars indicate uncertainties
of 150 and 90 s~1 for 1k and 1k , respectively (averaged
Fig. 8 OH decay curves obtained in 100 kPa of O in the presence
2
of 9.3 ] 1013 cm~3 of NO and varying concentrations of benzene.
M1
M2
maximum deviations within the sets). The dependence of both
rate constants on NO concentration is linear in good approx-
[C H ]/1015 cm~3 \ (a) 0.33, (b) 0.83, (c) 1.32. The dotted lines show
6
6
the (averaged) result of numerical Ðts to a simpliÐed reaction model
(see text).
imation. Linear regressions gave rate constants k \ (8.7
M1
Table 4 Results of Ðts to OH decay curves in the presence of O and NO. First-order rate constants of reactions (11) and (12) (from biexponen-
2
tial Ðts in the absence of benzene) and of model reactions (M1) and (M2) (from numerical Ðts in the presence of benzene) (see text)
[NO]/
1014 cm~3
[O ]/
1018 cm~3
[C H ]b/
1015 cm~3
[H O ]/
1014 cm~3
1k
103 s~1
/
1k
103 s~1
/
1k
103 s~1
/
1k /
103 s~1
2
6
6
2
2
11
12
M1
M2
Na
0.59
0.85
1.67
0.92
0.93
0.93
0.94
1.59
4.9
4.9
4.9
12
12
24
5
6
6
10
12
9
2.1
2.5
2.5
3.2
2.1
2.1
1.8
2.1
5.2
7.7
5.1
6.1
3.1
5.4
2.6
2.6
0.57
0.80
1.59
0.86
0.86
0.86
0.91
1.48
0.44
0.60
1.19
0.63
0.65
0.63
0.64
1.12
0.78
1.03
1.69
1.18
1.38
1.20
1.46
1.90
0.11
0.26
0.42
0.29
0.21
0.27
0.26
0.42
24
24
8
9
a Number of data points. b Maximum benzene concentration.
Phys. Chem. Chem. Phys., 1999, 1, 5097È5107
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However, no distinction is possible as to whether reaction (2b)
or (3) is more likely to contribute to the intercept in Fig. 9 and
thus only the more general result based on a fast equilibrium
is considered.
Discussion
Rate constant of OH + benzene
The rate constants of the OH ] benzene reaction listed in
Table 1 are in good agreement with literature data. The room-
temperature rate constant recommended by Atkinson,2,3
covering
a
large number of experimental studies, is
1.23 ] 10~12 cm3 s~1 with an uncertainty of 30%. The cor-
rectness of the rate constants reported here depends on the
knowledge of the vapour pressure of benzene and thus on the
respective literature data13 and the temperature measurement
in the saturator. The latter should be reliable since the tem-
perature chosen was just above the melting point of benzene,
which is close to 0 ¡C where a calibration was made using a
waterÈice mixture. Knispel et al.6 used the same method of
introducing benzene and obtained a very similar rate constant
at a total pressure of 13.3 kPa of Ar. This indicates that both
studies were made at (or very close to) the high-pressure limit
of the addition reaction.
Fig. 9 NO concentration dependences of Ðrst-order rate constants of
model reactions (M1) and (M2) (see text).
^ 3.3) ] 10~12 cm3 s~1 and k \ (2.6 ^ 0.7) ] 10~12 cm3
M2
s~1 (2p error limits). While 1k goes through the origin at
M2
[NO] \ 0 [Ðtted intercept: (8 ^ 80) s~1], this is not the case
for 1k [Ðtted intercept: (420 ^ 360) s~1]. Note that mea-
M1
surements at quite di†erent O concentrations (20, 50, 100
2
kPa) give consistent results in terms of this model.
Reactions (M1) and (M2) can be rationalised in terms of
actual processes. Certainly, the peroxy radical will react with
NO:
The similarity of k obtained in N and O at 100 kPa
1
2
2
shows that there is no fast regeneration of OH in the adduct
] O reaction which would lead to a lower e†ective rate con-
HOÈC H ÈO ] NO ] HOÈC H ÈO ] NO
(13a)
2
stant for OH ] benzene. A slow regeneration cannot be
6
6
2
6
6
2
The resulting oxy radical can (possibly after ring
excluded because the level of regenerated OH would remain
low at the high benzene concentrations used in this work.
fragmentation)10,11 react with O to give HO . If this process
2
2
is fast, the NO reaction is rate-limiting which leads to the
However, any regeneration of OH in the adduct ] O reac-
2
observed linear dependence of 1k on NO. Accordingly, the
tion would have been noticed in studies where OH was
M1
chain-terminating reaction (M2) can be associated with the
observed in equilibrium with the adduct in the presence of O
(refs. 6, 8).
2
nitrate-forming channel of the peroxy radical ] NO reaction:
The unchanged rate constant k obtained in the presence of
HOÈC H ÈO ] NO ] HOÈC H ÈOÈNO
(13b)
1
6
6
2
6
6
2
NO (Table 1) shows that there is no signiÐcant formation of
2
Thus, the increase of the sum (1k ] 1k ) with NO concen-
H atoms in reaction (1) except if the regeneration of OH via
M1
M2
tration is suggested to correspond to the rate constant of the
H ] NO were compensated by an unknown opposing e†ect.
2
peroxy radical ] NO reaction k \ (1.1 ^ 0.4) ] 10~11 cm3
A similar result was reported earlier in a di†erent range of
13
s~1 with a nitrate yield 1k /(1k ] 1k ) of (23 ^ 12)%,
benzene and NO
concentrations using resonance-
M2
M1
M2
2
comparable to other peroxy radical ] NO reactions.25
Ñuorescence detection of OH.27 However, studies by Bjerg-
bakke et al.4 and Berndt et al.5 conclusively report formation
of phenol in reaction (1) with H atoms being the obvious, but
not detected, co-product. The study of Bjergbakke et al.4 was
discussed controversially by Koch28 and Pagsberg29 since for-
mation of H ] phenol with the reported yield of about 25%4,5
is also in contradiction with studies where OH decay curves
were recorded in equilibrium with the adduct. In these studies
reaction (1c) is indistinguishable from reaction (1b). At slightly
increased temperatures (T O 360 K), where signiÐcant OH
concentrations are present under equilibrium conditions, an
upper limit of the rate constant of reaction (1b) [and hence
also for (1c)] below 3 ] 10~14 cm3 s~1 was derived.8 Thus,
the rate constant of reaction (1c) would have to increase
strongly with decreasing temperature to account for a 25%
yield of phenol at room-temperature conditions. In view of
calculations by Lay et al.9 which predict a positive activation
energy for reaction (1c) this would be a surprising e†ect. To
clarify this point a selective, time-resolved detection of phenol
and/or H atoms (for example by laser-induced Ñuorescence,
LIF) following pulsed production of OH in the presence of
benzene would be helpful.
However, the positive intercept of 1k at [NO] \ 0 hints
M1
towards a second source of HO not preceded by any NO
2
reaction. For example, if a rearranged bicyclic peroxy radical
O R were formed quantitatively in reaction (3) [or (2b)] fol-
2
lowed by addition of O (leading to O RÈO ), reaction with
2
2
2
NO and (fast) formation of HO , no intercept would be
2
expected unless the rate constant of the O RÈO ] NO reac-
tion were signiÐcantly larger than k . If the intercept is com-
2
2
13
pared with the maximum rate constant 1k (760 s~1, assuming
3
k
\ 0), a fraction of 55% of “promptÏ HO is calculated.
2b
2
This fraction is about a factor of 2 higher than typical phenol
yields and hints towards other HO -forming channels associ-
2
ated with reactions (3) or (2b), possibly followed by fast, not
rate-limiting, reactions with O . Unfortunately this result is
2
limited by the large error of the Ðtted intercept.
It should be noted that reaction (3) as well as (2b) may con-
tribute to the intercept of 1k since these reactions cannot be
M1
distinguished if the equilibrium (2a/[2a) is fast. A second
model was tested where reactions (M1) and (M2) were substi-
tuted by the reactions:
C H ÈOH ] O ] HO
(M3)
(M4)
6
6
2
2
Absorption cross-section and self-reaction of the adduct
C H ÈOH ] O ] other products
6
6
2
The Ðtted rate constants were identical to those of reactions
(M1) and (M2) multiplied by the equilibrium constant K
There are two previous determinations of the adduct absorp-
tion cross section in the gas phase around 308 nm. Fritz et al.7
report a value of (9.2 ^ 2.0) ] 10~18 cm2 at 308.3 nm basi-
cally applying a similar method as used here but utilising a
di†erent OH absorption line at a smaller total pressure. Bjerg-
bakke et al.4 for the Ðrst time recorded a gas-phase spectrum
.
2a
This e†ect is caused by the increased rate constants of reac-
tions (2a) and ([2a) in the model Ðts. If the rate constants
estimated in the previous section were used, rather similar, but
not identical, results were obtained applying the two models.
5104
Phys. Chem. Chem. Phys., 1999, 1, 5097È5107

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in the range 250È350 nm with a narrow local maximum of
3.4 ] 10~18 cm2 at about 310 nm. The value obtained in this
work, (5.8 ^ 1.5) ] 10~18 cm2, lies between those of the other
studies. The reason for the discrepancies is unknown. Bjerg-
bakke et al.4 who were limited to a spectral resolution of
about 0.8 nm suggested that a Ðne structure may lead to
strong di†erences in a narrow wavelength range but this is not
supported by the present study where at three wavelength
positions in a 0.3 nm range around 308 nm no signiÐcant
change of the absorption signal was observed.
the value of Lay et al.9 were correct, K would change by a
2a
factor of almost 10 in a 40 K range around room temperature,
while with the result of Ghigo and Tonachini31 hardly any
change is expected in the range of tropospheric temperatures.
To Ðnd out which prediction is more realistic, the equilibrium
constant determined in this work was used to calculate the
reaction entropy *S on the basis of the predicted enthalpy
2a
changes:
A
pÖ N
RT
B
*H
2a
*S
R
A
2a
ln K
\ [
]
(V)
2a
RT
The self-reaction (5) of the adduct was, to our knowledge,
not studied before. Recently, a very similar rate constant,
(3.1 ^ 1.0) ] 10~11 cm3 s~1, was measured by Berho et al.24
for the self-reaction of the benzeneÈH adduct, C H . Among
The factor pÖN /RT [pÖ \ standard pressure (105 Pa), N \
Avogadro constant, R \ gas constant, T \ temperature] con-
A
A
verts the concentration-based K into a dimensionless equi-
librium constant.
6
7
2a
the products possibly formed in reaction (5) are phenol and
hydroxy-2,4(or 5)-cyclohexadiene, benzene and 1,4(or 2)-
dihydroxy-2(or 3),5-cyclohexadiene, 1,2(or 4)-dihydroxyben-
zene and 1,3(or 4)-cyclohexadiene, and a variety of dimers.
With the enthalpy data of Lay et al.9 and Ghigo and
Tonachini31 *S
\ [145 J mol~1 K~1 and ]0.2 J
2a, 298 K
mol~1 K~1 were obtained, respectively. A reaction entropy
close to zero is unrealistic, while an entropy change of [136 J
mol~1 K~1 was predicted by Lay et al.9 in reasonable agree-
ment with the value above. Thus, a strong temperature depen-
dence of the equilibrium constant is expected.
Adduct kinetics in the presence of O
2
In aqueous phase the existence of the equilibrium (2a/[2a) is
well established. Pan and von Sonntag30 determined an equi-
In the theoretical work by Lay et al.9 also detailed calcu-
lations were made with respect to rate constants and product
yields of possible reactions summarised here as (2b) and (3).
However, while the typical phenol yield of product studies is
correctly predicted by the relative magnitudes of the com-
peting reactions, their absolute values are too small to explain
the experimentally observed kinetics. For example, the loss
term deÐned in this work by eqn. (III), (K 1k ] k ), is an
librium constant K
the gas-phase result of this work, K \ 2.7 ] 10~19 cm3, the
peroxy radical is much more favoured. Surprisingly it was
\ 4.3 ] 10~17 cm3. Compared with
2a, aq
2a
found that the peroxy radical with O bound in para position
2
with respect to OH dominates in the aqueous phase30 while in
the gas phase the radical with O in ortho position (altogether
2
four stereoisomers), which allows the remaining double bonds
2a
3
2b
to conjugate, is expected to be favoured.10 This is also pre-
sumed in the theoretical study by Lay et al.9 who did exten-
sive calculations on primary and secondary steps of the
OH-initiated benzene oxidation. The equilibrium constant
order of magnitude smaller, i.e. 2 ] 10~17 cm3 s~1 at 298 K.
Formation of HO
2
predicted by these authors,9 K \ 2 ] 10~18 cm3, is lower
The reaction model used to describe secondary HO forma-
tion, i.e. reactions (M1) and (M2), is rather simple. However,
2a
2
than that measured in aqueous phase but still larger than that
determined in this work. Moreover, the rate constants k and
the main question concerning HO formation is the fraction
2a
2
1k
predicted by Lay et al.9 (assuming that the peroxy
of “promptÏ HO which is reasonably addressed by the model.
~2a
2
radical formation proceeds with no activation energy) are
roughly three orders of magnitude larger than the estimates
obtained here on the basis of the deviation from biexponential
behaviour. This result hints towards a barrier for the forma-
tion (and dissociation) of the peroxy radical. This is in accord-
ance with a theoretical study by Ghigo and Tonachini31,
where an activation energy of 18 kJ mol~1 is predicted. Even
higher barriers of about 40 kJ mol~1 were determined theo-
retically by Andino et al.32 for the formation of peroxy rad-
icals from OH adducts of di†erent methylated aromatic
compounds.
Moreover, the fact that there is no marked dependence of the
Ðtted parameters on benzene, O and H O concentrations
2
2 2
justiÐes the simpliÐcations. The deÐciency is mainly due to the
experimental limitation to comparatively high NO concentra-
tions where HO formation appears to be dominated by con-
2
secutive reactions succeeding the peroxy radical ] NO
reaction. The oxy radical formed in (13a) is expected to react
with O to give HO and 2-hydroxy-3,5-cyclohexadienone, or
2
2
to undergo ring fragmentation followed by reaction with O
2
to give HO ] 2,4-hexadienedials.10 Although the rate con-
stants are unknown, at the
2
O
concentrations used
2
In the study by Bjergbakke et al.4 a rapidly emerging extra
(P5 ] 1018 cm~3), the consecutive reactions are probably not
absorption at 280 nm in the presence of O was assigned to
rate-limiting which leads to the increase of HO formation
2
2
rates (1k in Fig. 9). However, even if the NO reaction is
M1
the peroxy radical. From the formation kinetics of this signal
a rate constant similar to that in aqueous phase was deter-
rate-limiting, a strictly linear increase of the parameters in Fig.
mined,4 k \ (5 ^ 1) ] 10~13 cm3 s~1. However, it is ques-
9 is only expected if either the fraction of “prompt HO Ï is one
2a
2
tionable whether the strong increase of the absorption signal
(which is apparently not the case) or if the rate constants k
13a
is due to the peroxy radical. Firstly, taking the equilibrium
constant determined here, only about 11% of the adduct is
and k
of all other, secondarily formed peroxy radicals are
13b
similar (again assuming that a consecutive O addition, for
2
expected to be converted to the peroxy radical at the O con-
example to a bicyclic intermediate, would not be rate-limiting).
2
centration used in the other study (2 kPa).4 Secondly, the
The latter is a reasonable assumption justifying the linear
extrapolation to determine the intercept and this way the frac-
absorption wavelength chosen (280 nm)4 is in a region where,
at least in aqueous phase, no change of the absorption signal
tion of “promptÏ HO .
2
was observed upon increasing the O concentration.30 More-
The magnitude of the intercept shows that the fraction of
2
over, the experiment of Bjergbakke et al.4 was carried out at a
“promptÏ HO is higher than 25% (the expected yield of
2
2
2
temperature of 320 K where the equilibrium constant is prob-
ably even lower than at room temperature.
phenol ] HO ) indicating the existence of additional reactions
forming HO with no preceding NO reaction. There are a
The temperature dependence of the equilibrium constant is
determined by the reaction enthalpy of the peroxy radical for-
mation which has not yet been determined experimentally.
number of possibilities for what these processes could be.
Klotz et al.11 proposed formation of benzene oxide/oxepin
] HO in reaction (2b/3). However, in a recent study by
2
Recent theoretical studies predict *H \ [47.6 kJ mol~1
Berndt et al.5 strong evidence against this possibility was
2a
(Lay et al.9) and [4.6 kJ mol~1 (Ghigo and Tonachini31). If
reported. Bartolotti and Edney33 suggested formation of
Phys. Chem. Chem. Phys., 1999, 1, 5097È5107
5105

View Article Online
epoxide alkoxy radicals in reaction (2b) followed by reaction
with O to give HO and cyclic or open-ring epoxides. On the
While / is dependent on O concentration, / is not.
Also the possible competition of reactions (2b) and (3) is not
14
2
13
2
2
other hand, Berndt et al.5 observed formation of smaller ring-
cleavage products, namely formic acid, CO and carbonyl com-
pounds also in the absence of NO. Thus it can be speculated
whether a decomposition of secondarily formed peroxy rad-
icals may lead to these products. For example, the proposed
bicyclic intermediate9,10 is converted to a peroxy radical
(denoted as O RÈO in the previous section) which could
inÑuenced by the O concentration:
2
/
k
2b
3
2b
1k
\
(VIII)
/
K
2a
3
On the other hand, the relative importance of reactions (2b)
and (3) could be strongly temperature dependent as a result of
the temperature dependences of both the equilibrium constant
and the individual processes (2b) and (3). If di†erent products,
or di†erent distributions of similar products, were formed in
these processes, a signiÐcant shift of the product distribution is
expected in the range of tropospheric temperatures. Other
aromatic compounds may behave similarly. A temperature-
dependent product study of key products, for example phenol
in the case of benzene, would be helpful to assess this possi-
bility.
2
2
decompose to formic acid, butenedial and HCO (i.e. CO
] HO in the presence of O ). A second cyclisation step of the
2
2
O RÈO , followed by addition of a further O , would lead to
2
2
2
a peroxy radical which could decompose to formic acid,
glyoxal and HCO (CO ] HO ).
2
Unfortunately the accuracy of the fraction of “promptÏ HO
2
is restricted by the large statistical error of the Ðtted intercept
(85%). However, similar experiments with toluene could be
more conclusive. In the case of toluene the rate constant mea-
sured for the adduct ] O reaction at low O concentrations
Acknowledgements
2
2
is about a factor of 3 larger.6,8 Thus, provided the equilibrium
Support of this study by the Bundesminister fur Wissenschaft,
Bildung, Forschung und Technologie (BMBF), grant
07TFS30/D3, is gratefully acknowledged. The authors thank
T. Berndt, O. Boge and H. Herrmann for making their unpub-
lished results available (ref. 5).
constant is similar, also the loss rate of the peroxy radical is
higher and any “promptÏ HO is expected to result in a higher
2
intercept than in case of benzene.
Implications for atmospheric degradation of aromatic
compounds
Appendix
As can be seen in Fig. 4 the existence of the fast equilibrium
(2a/[2a) causes the e†ective lifetimes of both the adduct and
the peroxy radical to be similar and limits them to about 2.5
The reaction model in Fig. 6 is described by the following
system of di†erential equations:
ms at tropospheric levels of O . The lifetime and equilibrium
2
d[OH]
concentration of the peroxy radical determine the competition
\ [1k
[OH]
l, OH
(IX)
dt
between reaction of the peroxy radical with NO and reactions
(2b) or (3). The rate constant of the peroxy radical ] NO reac-
tion determined in this work [(1.1 ^ 0.4) ] 10~11 cm3 s~1] is
about the maximum rate constant one would expect for any
d[add]
\ k [OH][C H ] [ 1k
[add] ] 1k [per] (X)
1
6
6
l, add
~2a
dt
RO ] NO reaction.25 Nevertheless, considering typical levels
d[per]
2
of NO in the troposphere, the fraction / of adducts which
\ k [add][O ] [ 1k
2a
[per]
l, per
(XI)
13
2
dt
react with NO is almost negligible and can be calculated using
the following equation:
[OH], [add] and [per] are the time-dependent concentrations
of OH, the adduct and the peroxy radical, respectively. The
K
k
[NO]
2a 13
three loss rate coefficients, 1k (i \ OH, add, per) are deÐned
/
\
(VI)
l, i
13
k
] K 1k ] K
k
[NO]
as follows:
2b
2a
3
2a 13
For example, even at a 50 ppb level of NO, / is below 2%.
1k
1k
\ k [C H ] ] k [H O ]
(XII)
13
However, in chamber experiments performed at elevated NO
x
l, OH
1
6
6
10
2 2
\ (k ] k )[O ]
(XIII)
(XIV)
levels reaction (13) may play an important role and observed
l, add
2a 2b
2
product distributions may not be transferable to tropospheric
conditions. A similar problem may arise for secondarily
formed peroxy radicals if these were in fact subject to com-
peting decomposition reactions.
The competition of adduct ] O and adduct ] NO reac-
tions, determined by Knispel et al.6 and discussed in detail by
Atkinson3 with regard to product studies, is not inÑuenced by
the equilibrium character of the O reaction. The NO reac-
1k
\ 1k ] 1k ] k [O ]
l, per
~2a
3
4
2
The initial conditions at t \ 0 are: [OH] \ [OH] and
0
[add] \ [per] \ 0. Since decomposition of the adduct back
0
0
into OH and benzene can be neglected, OH decays mono-
exponentially:
2
2
[OH] \ [OH] exp([t/q )
(XV)
0
1
2
2
tion,
with the time constant q ~1 \ 1k
.
1
l, OH
The general solutions for adduct and peroxy radical con-
centrations are triexponential,
C H ÈOH ] NO ] products
(14)
6
6
2
is fast (k \ 2.8 ] 10~11 cm3 s~1)6,8 but nevertheless only of
[add] \ C exp([t/q ) ] C exp([t/q ) ] C exp([t/q )
14
1
1
2
2
3
3
importance at high NO concentrations (P100 ppb).
2
(XVI)
Although, due to the equilibrium, the e†ective lifetime of the
adduct at atmospheric conditions is longer than previously
thought (by a factor of about 2.5), the fraction of the adducts
which react with NO , / , remains similar (in the absence of
[per] \ C exp([t/q ) ] C exp([t/q ) ] C exp([t/q )
4
1
5
2
6
3
(XVII)
2
14
NO):
with the additional time constants:
k
[NO ]
1k
] 1k
2
14
3
2
/
\
(VII)
l, add
l, per
q
~1 \
14
(k ] K 1k )[O ] ] k [NO ]
2, 3
2b
2a
2
14
2
Accordingly, the importance of a reaction of the peroxy
radical with NO can be estimated as demonstrated by
S
(1k
[ 1k
)2
l, per
(XVIII)
l, add
^
] k [O ]1k
2a
2
2
~2a
4
eqn. (VI).
5106
Phys. Chem. Chem. Phys., 1999, 1, 5097È5107

View Article Online
5
6
T. Berndt, O. Boge and H. Herrmann, private communication.
q ~1 \ q ~1 was deÐned arbitrarily. Coefficients C ÈC
3
2
1
6
R. Knispel, R. Koch, M. Siese and C. Zetzsch, Ber. Bunsen-Ges.
satisfying the initial conditions [add] \ [per] \ 0 can be
0
0
Phys. Chem., 1990, 94, 1375.
determined by di†erentiation of eqns. (XVI) and (XVII) and
inserting the results in eqns. (X) and (XI). For example, for the
adduct the following expression results:
7
8
B. Fritz, V. Handwerk, M. Preidel and R. Zellner, Ber. Bunsen-
Ges. Phys. Chem., 1985, 89, 343.
C. Zetzsch, R. Koch, B. Bohn, R. Knispel, M. Siese and F. Witte,
in Chemical Processes in Atmospheric Oxidation, ed. G. Le Bras,
Springer, Berlin, 1997, p. 247.
[OH] k [C H ]
0 1
6 6
[add] \
9
T. H. Lay, J. W. Bozzelli and J. H. Seinfeld, J. Phys. Chem., 1996,
100, 6543.
(1k
[ q ~1)(1k
[ q ~1) [ k [O ]1k
l, add
1
l, per
1
2a
2
~2a
10 R. Atkinson and A. C. Lloyd, J. Phys. Chem. Ref. Data, 1984, 13,
315.
11 B. Klotz, I. Barnes, K. H. Becker and B. T. Golding, J. Chem.
G
A
t
B
] (1k
[ q ~1) exp [
l, per
1
q
1
Soc., Faraday T rans., 1997, 93, 1507.
C
k [O ]1k (q~1 [ q~1)
D
2a
~2a
2
~2a 1
3
12 B. Bohn, M. Siese and C. Zetzsch, J. Chem. Soc., Faraday T rans.,
1996, 92, 1459.
13 R. M Stephenson and S. Malanowski, in Handbook of the T her-
modynamics of Organic Compounds, Elsevier Science, New York,
1987, and references therein.
14 A. Wahner, PhD Thesis, University of Bochum, 1984.
15 A. Wahner and C. Zetzsch, Ber. Bunsen-Ges. Phys. Chem., 1985,
89, 323.
16 C. Leonard, PhD Thesis, University of Hannover, 1990.
17 H.-P. Dorn, R. Neuroth and A. Hofzumahaus, J. Geophys. Res.,
1995, 100, D4, 7397.
18 B. Bohn and C. Zetzsch, J. Chem. Soc., Faraday T rans., 1998, 94,
1203.
]
k [O ]1k
2a
[ (1k
[ q ~1)(1k
[ q ~1)
2
l, per
3
l, add
2
A
[tB C
] exp
] q ~1 [ 1k
3
l, per
q
2
(q ~1 [ q ~1)(1k
[ q ~1)(1k
[ q ~1)
[ q ~1)
D
1
3
~2a
BH
l, per
[ (1k
3
l, add
l, add
2
[
k [O ]1k
[ q ~1)(1k
2a
2
l, per
3
2
A
t
] exp [
(XIX)
q
3
Since q ~1 and q ~1 are roots of a quadratic equation they
are connected by VietaÏs root theorem:
19 S.-C. Lin, T.-C. Kuo and Y.-P. Lee, J. Chem. Phys., 1994, 101,
2
3
2098.
20 W. B. DeMore, S. P. Sander, D. M. Golden, R. F. Hampson, M.
J. Kurylo, C. J. Howard, A. R. Ravishankara, C. E. Kolb and M.
J. Molina, in Chemical Kinetics and Photochemical Data for Use
in Stratospheric Modeling, Evaluation Number 12, JPL Pub-
lication 97-4, Jet Propulsion Laboratory, Pasadena, 1997.
21 R. Atkinson, D. L. Baulch, R. A. Cox, R. F. Hampson Jr, J. A.
Kerr, M. J. Rossi and J. Troe, J. Phys. Chem. Ref. Data, 1997, 26,
577, 580, 617.
22 B. Bohn and C. Zetzsch, J. Phys. Chem. A, 1997, 101, 1488.
23 W. A. Noyes Jr and K. E. Al-Ani, Chem. Rev., 1974, 74, 29.
24 F. Berho, M.-T. Rayez and R. Lesclaux, J. Phys. Chem. A, 1999,
103, 5501.
25 P. D. Lightfoot, R. A. Cox, J. N. Crowley, M. Destriau, G. D.
Hayman, M. E. Jenkin, G. K. Moortgat and F. Zabel, Atmos.
Environ., 1992, 26A, 1805.
26 FACSIMILE, by AEA Technology, Harwell, Didcot, UK, 1993.
27 R. Koch, private communication.
28 R. Koch, J. Phys. Chem. B, 1997, 101, 293.
29 P. Pagsberg, J. Phys. Chem. B, 1997, 101, 294.
30 X.-M. Pan and C. von Sonntag, Z. Naturforsch., 1990, 45B, 1337.
31 G. Ghigo and G. Tonachini, J. Am. Chem. Soc., 1998, 120, 6753.
32 J. M. Andino, J. N. Smith, R. C. Flagan, W. A. Goddard III and
J. H. Seinfeld, J. Phys. Chem., 1996, 100, 10967.
33 L. J. Bartolotti and E. O. Edney, Chem. Phys. L ett., 1995, 245,
119.
q ~1 ] q ~1 \ 1k
] 1k
1k
(XX)
2
3
l, add
l, per
[ k [O ]1k
q ~1q ~1 \ 1k
(XXI)
2
3
l, add l, per
2a
2
~2a
which is used to derive an approximate expression for q ~1 if
3
q ~1 A q ~1:
2
3
q ~1q ~1
1k
1k
[ k [O ]1k
2
3
l, add l, per
2a
2
l, per
~2a
q ~1 B
\
3
q ~1 ] q ~1
1k
] 1k
2
3
l, add
[O ](k 1k ] k 1k
] k k [O ])
2
2a 2a ~2a
3
2a 4
2
B
(XXII)
k [O ] ] 1k
2a
2
~2a
The second approximation means that (after multiplication)
sum terms are neglected which do not contain the (large) rate
constants k or 1k
. The Ðnal expression corresponds to
2a
~2a
eqn. (III).
References
1
R. G. Derwent, M. E. Jenkin and S. M. Saunders, Atmos.
Environ., 1996, 30, 181.
R. Atkinson, J. Phys. Chem. Ref. Data, 1989, Monograph 1, 204.
R. Atkinson, J. Phys. Chem. Ref. Data, 1994, Monograph 2, 147.
E. Bjergbakke, A. Sillesen and P. Pagsberg, J. Phys. Chem., 1996,
100, 5729.
2
3
4
Paper 9/04887A
Phys. Chem. Chem. Phys., 1999, 1, 5097È5107
5107