Experiments and Calculations on Rate Coefficients for Pyrolysis of SO 2 and the Reaction O + SO at High Temperatures

Article abstract of DOI:10.1021/jp036025c

Rate coefficients for the pyrolysis of SO₂ in Ar in the temperature range 2188-4249 K were determined using a diaphragmless shock tube. The concentration of O atoms was monitored with resonance absorption. Rate coefficients determined in this work show Arrhenius behavior, with k _la(T) = (4.86 ± 1.31) × 10^-9 exp [-(50450 ± 730)/T] cm³ molecule^-1 s^-1; listed errors represent one standard deviation in fitting. These values are consistent with some previous measurements that show a preexponential factor and activation energy greater than other measurements. Theoretical calculations at the G2M(RCC2) level, using geometries optimized with the B3LYP/6-311+G(3df) method, yield energies of transition states and products relative to those of the reactants. Rate coefficients predicted with a microcannonical variational RRKM theory agree well with experimental observations; contributions from electronically excited states of SO₂ are significant. Rate coefficients for the recombination O + SO → SO₂ are predicted to decrease with temperature with k_10a(T) = (4.82 ± 0.05) × 10^-31(T/298)-^2.17±0.03 cm⁶ molecule^-2 s^-1 for the temperature range 298-3000 K. In some experiments, S atoms were monitored with resonance absorption. With detailed chemical modeling, we found that S atoms were mainly produced from the secondary reaction O + SO → S + O₂ rather than from direct pyrolysis of SO₂ or from further pyrolysis of the SO product. Rate coefficients for this secondary reaction, determined to be k_10b(T) = (3.0 ± 0.3) × 10^-11 exp [-(6980 ± 280)/T] cm ³ molecule^-1 s^-1, agree closely with the theoretically predicted value comprising three product-channels via one triplet and two singlet SOO intermediates.

Full text of DOI:10.1021/jp036025c

11020
J. Phys. Chem. A 2003, 107, 11020-11029
Experiments and Calculations on Rate Coefficients for Pyrolysis of SO2 and the Reaction
O + SO at High Temperatures
†
†
,†,‡
Chih-Wei Lu, Yu-Jong Wu, and Yuan-Pern Lee*
Department of Chemistry, National Tsing Hua UniVersity, 101, Sec. 2, Kuang Fu Road,
Hsinchu 30013, Taiwan, and Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan
R. S. Zhu and M. C. Lin*
Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322
ReceiVed: July 14, 2003; In Final Form: September 22, 2003
Rate coefficients for the pyrolysis of SO
using a diaphragmless shock tube. The concentration of O atoms was monitored with resonance absorption.
2
in Ar in the temperature range 2188-4249 K were determined
-
9
Rate coefficients determined in this work show Arrhenius behavior, with k1a(T) ) (4.86 ( 1.31) × 10 exp
3
-1 -1
[
-(50450 ( 730)/T] cm molecule s ; listed errors represent one standard deviation in fitting. These values
are consistent with some previous measurements that show a preexponential factor and activation energy
greater than other measurements. Theoretical calculations at the G2M(RCC2) level, using geometries optimized
with the B3LYP/6-311+G(3df) method, yield energies of transition states and products relative to those of
the reactants. Rate coefficients predicted with a microcannonical variational RRKM theory agree well with
2
experimental observations; contributions from electronically excited states of SO are significant. Rate
coefficients for the recombination O + SO f SO
2
are predicted to decrease with temperature with k10a(T) )
-
31
-2.17(0.03
6
-2 -1
(
4.82 ( 0.05) × 10 (T/298)
cm molecule
s
for the temperature range 298-3000 K. In some
experiments, S atoms were monitored with resonance absorption. With detailed chemical modeling, we found
that S atoms were mainly produced from the secondary reaction O + SO f S + O rather than from direct
pyrolysis of SO or from further pyrolysis of the SO product. Rate coefficients for this secondary reaction,
2
2
-
11
3
-1 -1
determined to be k10b(T) ) (3.0 ( 0.3) × 10 exp [-(6980 ( 280)/T] cm molecule s , agree closely
with the theoretically predicted value comprising three product-channels via one triplet and two singlet SOO
intermediates.
1
. Introduction
(UV) absorption or emission invariably yielded smaller rate
3-5
6
coefficients. Plach and Troe showed that these measurements
were in error because UV absorption spectra of SO and SO2
overlap extensively; observed results of smaller rate coefficients
are therefore attributed to interference from the absorption of
SO.
SO2 is a key species in oxidation reactions of sulfur
compounds that are important in atmospheric and combustion
chemistry. In experiments at high-temperatures, SO2 is com-
monly employed as a source of O atoms. The kinetics for the
thermal decomposition of SO2 has, however, a controversial
history. Previous rate measurements in the temperature range
of 2500-7500 K all employed shock-wave techniques, from
which reported rate coefficients fall into roughly three groups,
as listed in Table 1. Earlier experiments1,2 using SO2 at larger
concentrations yield rate coefficients k1a showing activation
Experiments using a laser schlieren technique,7 atomic
,8
9
resonance absorption of O atoms, infrared (IR) emission of
1
0
SO2, and UV absorption of SO2 at λ e 220 nm (ref 6) gave
reasonably consistent results with greater values of rate coef-
ficients. On close inspection, reported Ea/R values still vary by
∼
16%, and preexponential factors vary by nearly a factor of
0, from 5.55 × 10 to 4.82 × 10 cm molecule s . Other
reaction channels such as
-
1
energies, Ea ) R(28200-37700 K) ) 56.0-74.9 kcal mol ,
much smaller than the bond energy for O-SO
-9
-8
3
-1 -1
1
3
3
-
-1
3
3
-
-1
SO f O( P) + SO( Σ ) ∆H° ) 131.8 kcal mol (1a)
2
SO f S ( P) + O ( Σ ) ∆H° ) 137.3 kcal mol (1b)
2 2 g
-
1
Other reported rate coefficients all exhibit similar activation
energies in the range 100.3 < Ea/kcal mol < 116.4 (50500 K
SO f SOO ∆H° = 110 kcal mol
(2)
2
-
1
<
Ea/R < 58600 K), but with values differing by a factor as
have never been investigated. Hence, we sought to examine
carefully the pyrolysis reaction of SO2 and associated secondary
reactions in our newly constructed diaphragmless shock tube
by probing both O and S atoms with atomic resonance
absorption as part of extensive investigations concerning reac-
tions of SOx.
much as 50 at a specific temperature in the range 3000-5000
K. Experiments involving detection of SO2 through ultraviolet
*
To whom correspondence should be addressed. (Y.P.L.) E-mail:
yplee@mx.nthu.edu.tw. Fax: 886-3-572-2892. (M.C.L.) E-mail: chemmcl@
emory.edu. Fax: 1-404-727-6586.
†
‡
Pyrolysis of SO2 has never been studied theoretically. The
system is complicated because it involves atoms (S and O) in
National Tsing Hua University.
Academia Sinica.
1
0.1021/jp036025c CCC: $25.00 © 2003 American Chemical Society
Published on Web 11/20/2003

Pyrolysis of SO2 and the Reaction O + SO
J. Phys. Chem. A, Vol. 107, No. 50, 2003 11021
TABLE 1: Comparison of Reported Temperature Dependence of Rate Coefficients and Experimental Conditions for
Pyrolysis of SO
2
temp, K
pressure, 1017a
[SO2]/[M]
M
A
0
, 10-10 b
E
a
/R, K
detection method
ref
2
2
3
4
188-4249
000-4500
000-5000
000-6000
10.5-37.9
100-900 ppm
Ar
Ar
Ar
Ar
SO
Ar
48.6 ( 13.1
471
66.1
55.5
8.34
50450 ( 730
O absorption at 130.2 ( 1.4 nm
this work
55190
theory (Arrhenius fit for the listed T range) this work
6
800-6000 ppm
0.06-0.20
50510 ( 3970 SO
2
absorption, λ e 220 nm
PT
8
54150
33520
52800
54350
Laser Schlieren at 632.8 nm
RBR
1.00
2
5
4300-6200
2800-3880
2500-3400
4.52-13.8
48-205
20 & 100 ppm
0.0013-0.00527 Ar
20-200 ppm
5.89
SO
SO
2
2
emission at 392.5 nm
emission 7.26-7.47 µm
SYM
1
0
133 ( 33
GRS
5
62
72
9
Ar
Ar
482 ( 2
58590 ( 2270 O absorption at 130.5 nm
JR
SO absorption at 146.9 nm
6
.30
.59
AGT4
3
300-6500
30-403
100-2000 ppm
6.61 ( 3
53880 ( 2170 SO
2
absorption at 227 ( 0.2,
2
34 ( 0.2, and 238.5 ( 0.2 nm
SO absorption at 219.5 ( 0.13 nm
SO
SO emission at 275 ( 1 & 316.5 ( 0.5 nm
56360 ( 2010 laser schlieren at 632.8 nm
37740 ( 2010 SO emission at 436 ( 8 nm
35230 ( 3520 SO
55360 SO
2
emission at 7.25 ( 0.30 µm
7
2900-5200
2800-3400
3000-4000
4500-7500
3004-3978
4.52-60.2
2.56-12.0
60.2-482
0.03, 0.10, 0.30
0.01-0.40
0.0036-0.01
0.0005-0.01
0.04-0.32
Kr
Ar
SO
Ar
Ar
282
1.33 ( 0.27
16.6
Kiefer
LS
c
2
3
3
2
2
absorption 210-330 nm
absorption 210-330 nm
OTW
OTW
4.17
2
1
5.06-23.5
0.106 ( 0.012 28180 ( 3020 SO absorption 254.8, 258.1, 262.2 nm
GKP
a
In unit of molecule cm-3. b In unit of cm molecule s-1. c An intercept at [M] ) 0 was taken out.
3
-1
their triplet states and molecules (SO, SO2, and O2) in various
singlet and triplet states. The role of electronically excited SO2
in enhancing the rate of decomposition was previously pro-
We calibrated the concentration of O atoms in the shock tube
with N2O, assuming a 100% yield of O atoms from pyrolysis
of N2O. Similarly, the concentration of S atoms was calibrated
with OCS pyrolysis; the absorption cross section of S atoms
depends on pressure.
6
,9
posed.
We have performed a careful experimental work on the
decomposition of SO2 and extended rate measurements down
to 2188 K. The mechanism for production of S atoms has been
clarified to be due to the secondary reaction O + SO. We also
performed detailed theoretical calculations to predict rate
coefficients for both forward and reverse reactions and con-
firmed the important role of triplet SO2 in this reaction. The
theoretically predicted rate coefficient for O + SO f S + O2
also agrees well with experiments.
Ar (99.9995%, AGA Specialty Gases), N2O (99%, Scott
Specialty Gases), OCS (99.98%, Matheson), and SO2 (99.98%,
Matheson) were used without further purification. Mixtures of
SO2 in Ar (100-900 ppm), OCS in Ar (5.0-25.1 ppm), and
N2O in Ar (10.0-30.4 ppm) were used.
3
. Computational Methods
The geometries of the reactant, intermediates, transition states,
and products of the SO2 decomposition system were optimized
2. Experiments
at the B3LYP/6-311+G(3df) level of theory with Becke’s three-
Details of the diaphragmless shock tube apparatus have been
The shock tube (length 5.9 m and internal diameter
.6 cm) is coupled to a detection system using atomic resonance
1
6
reported.1
7
1,12
parameter nonlocal exchange functional and the nonlocal
17
correlation functional of Lee et al. Energies of all species were
18
calculated at the G2M(RCC2) level of theory using geometries
absorption. Three time-frequency counters were employed to
determine the speed of the shock wave based on signals detected
with sensors installed at 3, 20, 30, and 40 cm from the end of
the tube. A microwave discharge of a flowing gas mixture of
O2 ∼1.0% in He served as a lamp for atomic absorption of O
optimized with the B3LYP/6-311+G(3df) method. Intrinsic
1
9
reaction coordinate (IRC) calculations were performed to
connect each transition state with designated reactants and
20
products. All calculations were carried out with Gaussian 98
and MOLPRO 2002 programs.
2
1
atoms. Overlapped emission of the lamp at 130.22, 130.49, and
3
1
30.60 nm, corresponding to atomic transitions of O( S)-
The structures of the low lying electronically excited states
involved in the reaction were optimized at the RB3LYP/
3
O( P2,1,0), passes through the shock tube to a vacuum UV
monochromator (focal length 20 cm, reciprocal linear dispersion
6-311+G(3df) or UB3LYP/6-311+G(3df) level. As some
-
1
22-24
4
.0 nm mm , slit width 350 µm) before being detected with a
investigators
have shown, for systems with multireference
solar-blind photomultiplier tube. Variation of the signal from
the photomultiplier was monitored with a digital storage
oscilloscope and transferred to a computer for further processing.
In a few experiments, S atoms were monitored with absorption
at 180.73, 182.03, and 182.62 nm, corresponding to atomic
characters, density functional theory can predict molecular
properties reasonably. For the low-lying states of SO2, Katagiri
et al. showed that A A2, a B1, and b A2 states can be
dominantly constructed by the configuration of the electronic
2
5
1
3
3
1
2
ground state X A1 with the electronic configuration ...(2b1) -
3
3
2
2
2
transitions of S( S)-S( P2,1,0), from microwave discharge of a
mixture of SO2 ∼0.10% in He.
(1a2) (5b2) (8a1) . Excited-state electronic configurations were
derived from the excitation of the electrons in the 8a1, 1a2, and
5b2 occupied orbitals to the 3b1 unoccupied orbital. The ground-
state structure obtained at the B3LYP/6-311+G(3df) level was
used as the initial input to construct the specific configurations.
Before each experiment, the shock tube was pumped below
-
7
5
(
.0 × 10 Torr. The temperature (T5), density (F5), and pressure
P5) in the reflected shock regime were calculated from the
1
1
measured velocity of the incident shock, the composition of the
test gas, the initial pressure, and the temperature according to
For SO2 ( A2), SOO ( A′′), and their triplet states, as well as
their related transition states, the unrestricted wave functions
were used. The constructed configurations and symmetry were
kept unchanged in the process of geometry optimization and
single energy calculations with the G2M method.
13
the ideal shock-wave theory; Mirels' boundary-layer correc-
tions were negligible under high temperature and with large
Mach number.1
4,15

11022 J. Phys. Chem. A, Vol. 107, No. 50, 2003
Lu et al.
Figure 2. Temporal profiles of [O] observed for pyrolysis of an Ar
1
8
sample containing SO
2
(200.1 ppm). T ) 2831 K and P ) 2.12 ×10
-
3
molecule cm . The solid line represents fitted results using the model
described in text.
O atoms is fitted with an equation
1
3
-3
2
3
[
O]/10 molecule cm ) 3.405A - 0.9188A + 1.442A
(
5)
for a total pressure (1.63-5.28) × 10 molecule cm-3.
18
Calibration of [S] was carried out similarly by the thermal
3
0,31
decomposition of OCS at high temperatures.
The concentra-
1
3
-3
tion of S atoms, (1.24-9.20) × 10 molecule cm , was fitted
with various quadratic equations depending on the total pressure
18
for concentrations in the range (2.48-3.62) × 10 molecule
Figure 1. (A) Calibration curve of [O] versus absorbance of O atoms;
B) Calibration curve of [S] versus absorbance of S atoms at total
-
3
(
cm , as shown in Figure 1B. At a total concentration of
1
8
-3
18
-3
pressures of 3.62 (O), 2.84 (0), and 2.48 (]) ×10 molecule cm
.
3.62 × 10 molecule cm , the concentration of S atoms is
Fitted equations are listed in the legends.
fitted with an equation
Rate coefficients for various reaction channels were calculated
with a microcannonical variational RRKM method using the
Variflex program. The component rates were evaluated at E,J-
resolved levels. The master equation was solved with inversion
13
-3
2
3
[
S]/10 molecule cm ) 1.747A + 0.4761A + 0.4745A
(
6)
26
4
.2. Rate Coefficient k1a of the Reaction SO2 f O + SO.
and eigenvalue-based approaches for association and dissociation
Figure 2 shows a typical temporal profile of [O] observed when
a gas mixture containing SO2 and Ar was heated with a shock
wave. The concentration of O atoms at reaction time t, [O]t, is
derived according to eqs 4 and 5, with the light intensity before
pyrolysis taken as I0 . If reaction 1a were the sole pyrolysis
channel and there were no interference reaction, a temporal
processes, respectively.2
7,28
For the barrierless transition state,
we used a Morse potential
-
â (R-Re) 2
E(R) ) D [1 - e
]
(3)
e
in which De is the dissociation energy (D0) plus zero-point
energy, Re is the equilibrium bond distance, and â is fitted from
calculated potential energies at discrete atomic separations R,
to represent the potential curve along the minimum energy path
of each individual reaction coordinate. For tight transition states,
the numbers of states were evaluated with a rigid-rotor
harmonic-oscillator approximation.
profile of [O] can be fitted to a first-order equation to yield a
t
pseudo-first-order rate coefficient kI
I
[
O] ) [SO ] [1 - exp(-k t)]
(7)
t
2 0
The apparent second-order rate coefficient, k′ , is thus derived
1a
from
4
. Results and Discussion
.1. Calibrations of [O] and [S]. Calibration of [O] using
I
k′ ) k /[Ar]
(8)
1
a
4
thermal decomposition of N2O is a standard procedure in the
shock-tube technique;29 it takes into account deviations from
the Beer-Lambert law. The calibration curve of [O] using
various concentrations of N2O is shown in Figure 1A. Absor-
bance A is calculated with the equation
At high temperatures, these secondary reactions involving O,
SO, and O must be considered
M
O + SO2
O + SO
9
8 SO
(9a)
(9b)
3
f SO + O2
A ) ln(I /I)
(4)
0
M
9
8 SO
(10a)
(10b)
2
in which the light intensity before and after production of O
atoms is denoted as I0 and I, respectively. The concentration of
f S + O2

Pyrolysis of SO2 and the Reaction O + SO
J. Phys. Chem. A, Vol. 107, No. 50, 2003 11023
M
TABLE 2: Experimental Conditions and Rate Coefficient
O + O 98 O2
(11)
(12)
a
k1a for Pyrolysis of SO to Form SO + O
2
P
1
/
P
4
/
T
K
5
/
[SO
10
2
]/ [Ar]/
k
1a
/
k
k
1a
/
SO + SO f S + SO2
14
18
cm molecule-1s-1
3
Torr Torr
M
s
10
1a
′
M
SO (100.0 ppm)
2
SO
9
8 S + O
(13)
(14)
-16
9
8
.08 2250 3.65 3116 2.20 2.20 (4.16 ( 0.08) × 10
1.010
1.030
0.996
0.997
0.998
0.990
0.990
0.993
0.987
0.993
0.981
0.972
-
16
.05 2250 3.72 3239 1.97 1.97 (7.55 ( 0.14) × 10
O + SO f O + SO
-15
3
2
2
7.52 2250 3.79 3361 1.86 1.86 (1.27 ( 0.02) × 10
-
-
-
-
-
15
15
15
15
14
7
.07 2250 3.85 3449 1.76 1.76 (3.35 ( 0.05) × 10
for which rate coefficients have the reported dependence on
temperature
5.86 2250 3.90 3541 1.47 1.47 (5.56 ( 0.09) × 10
5
5
.61 2250 3.97 3664 1.42 1.42 (4.57 ( 0.11) × 10
.55 2250 4.00 3718 1.41 1.41 (9.93 ( 0.20) × 10
k (T) ) 1.21 × 10 exp (3163/T) cm molecule s-1
-
33
6
-2
5.53 2500 4.09 3890 1.42 1.42 (1.29 ( 0.03) × 10
9
a
-14
5
.02 2500 4.13 3960 1.29 1.29 (2.43 ( 0.04) × 10
-
-
-
14
14
14
(
ref 32) (15)
4.42 2500 4.20 4084 1.15 1.15 (1.74 ( 0.03) × 10
.34 2500 4.23 4138 1.13 1.13 (2.17 ( 0.05) × 10
4.02 2500 4.29 4249 1.05 1.05 (3.83 ( 0.09) × 10
4
k (T) ) 8.3 × 10 exp (-9800/T) cm molecule s-1
-12
3
-1
9b
SO (200.1 ppm)
2
(
ref 33) (16)
-17
1
3.05 2000 3.24 2494 5.90 2.95 (1.10 ( 0.03) × 10
1.039
1.042
1.039
1.027
1.018
1.022
1.016
1.015
1.005
1.005
0.999
-
17
1
2.51 2000 3.29 2559 5.71 2.85 (1.57 ( 0.04) × 10
k10a(T) ) 3.3 × 10 T-1.84 cm molecule s-1
-26
6
-2
-17
11.51 2000 3.40 2665 5.32 2.66 (3.40 ( 0.06) × 10
-
17
1
0.51 2000 3.39 2709 4.89 2.44 (3.50 ( 0.09) × 10
(
ref 10) (17)
-16
9
9
.54 2000 3.46 2831 4.49 2.13 (1.71 ( 0.05) × 10
.19 2000 3.53 2924 4.37 2.19 (2.28 ( 0.13) × 10
-
16
k10b(T) ) 3.63 × 10 exp (-7700/T) cm molecule s-1
-
11
3
-1
-16
7.80 2000 3.61 3061 3.76 1.88 (4.12 ( 0.11) × 10
-
-
-
-
16
16
16
15
7
6
5
.54 2000 3.64 3103 3.65 1.82 (3.49 ( 0.08) × 10
.04 2000 3.74 3269 2.97 1.48 (9.27 ( 0.27) × 10
.51 2000 3.76 3307 2.72 1.36 (8.49 ( 0.28) × 10
(18)
k (T) ) 5.21 × 10 exp (900/T) cm molecule s-1
-
35
6
-2
5.10 2000 3.83 3425 2.54 1.27 (1.37 ( 0.08) × 10
11
(
ref 34) (19)
SO
5.03 2000 3.14 2340 16.6 3.32 (2.65 ( 0.08) × 10
13.08 2000 3.22 2465 14.7 2.94 (8.59 ( 0.16) × 10
2
(499.8 ppm)
-
-
18
18
1
1.086
1.079
1.072
1.081
1.078
1.107
1.092
1.086
1.046
1.024
1.015
1.011
k (T) ) 4.73 × 10 exp (-880/T) cm molecule s-1
-
13
3
-1
12
-17
1
2.53 2000 3.27 2539 14.2 2.85 (1.37 ( 0.03) × 10
-
-
-
17
17
17
(
ref 35) (20)
12.15 2000 3.33 2622 14.0 2.79 (2.12 ( 0.05) × 10
0.82 2000 3.39 2709 12.6 2.51 (3.03 ( 0.06) × 10
11.08 2125 3.44 2784 13.0 2.60 (3.61 ( 0.05) × 10
1
k (T) ) 6.61 × 10 exp (-53890/T) cm molecule s-1
-
10
3
-1
13
-16
9
.06 2000 3.48 2856 10.7 2.14 (1.18 ( 0.04) × 10
-
-
-
16
16
16
(
ref 6) (21)
8.44 2000 3.54 2943 10.1 2.02 (1.88 ( 0.08) × 10
.53 2000 3.59 3028 9.05 1.81 (2.99 ( 0.07) × 10
7.35 2000 3.68 3166 8.94 1.79 (3.53 ( 0.13) × 10
7
k (T) ) 2.19 × 10 exp (-3070/T) cm molecule s-1
-
12
3
-1
14
-16
5
.92 2000 3.73 3254 7.26 1.45 (5.86 ( 0.50) × 10
-16
(
ref 32) (22)
5.53 2000 3.77 3322 6.81 1.36 (8.18 ( 0.68) × 10
SO (698.1 ppm)
2
in which k10b was estimated from reported rate coefficients of
-19
-18
1
7.52 2000 3.07 2263 26.4 3.79 (7.48 ( 0.33) × 10
1.148
1.071
1.136
1.117
1.088
3
6
the reverse reaction (2732-3463 K) and the equilibrium
15.12 2000 3.14 2358 23.3 3.33 (2.65 ( 0.11) × 10
14.13 2000 3.20 2441 22.0 3.16 (4.62 ( 0.08) × 10
-
-
-
18
18
17
constant derived from literature values of ∆G(T) for corre-
sponding species.37 Values of k12 might have large errors
16.58 2250 3.26 2519
1
26.0 3.74 (7.50 ( 0.16) × 10
2.50 2000 3.33 2628 20.0 2.86 (1.49 ( 0.02) × 10
because there is only one study at high temperature (1000 K),
SO (900.2 ppm)
2
and we estimate the activation energy based on reported values
-
-
19
19
at 1000 and 298 K.35 We modeled observed temporal profiles
17.06 2000 3.03 2188
33.1 3.67 (4.87 ( 0.48) × 10
1.170
1.201
1.184
1.162
1.168
1.206
1.103
1.061
1
1
1
6.53 2000 3.06 2237 32.3 3.59 (8.95 ( 0.48) × 10
5.03 2000 3.13 2335 29.9 3.32 (2.28 ( 0.08) × 10
3.52 2000 3.21 2441 27.3 3.03 (6.16 ( 0.18) × 10
of [O] with reactions 1a and 9-14 using a commercial kinetic
-18
-18
modeling program FACSIMILE;3 rate coefficients listed in eqs
8
-
-
-
-
17
17
17
17
1
5-22 were held constant, and the second-order rate coefficient
12.51 2000 3.26 2524 25.6 2.84 (1.18 ( 0.04) × 10
of the title reaction, k1a, was varied to yield the best fit.
Experimental conditions and values of k1a for 48 measurements
involving SO2 at five initial concentrations (in a range 100-
12.11 2000 3.33 2617 24.9 2.78 (1.79 ( 0.03) × 10
1
1.80 2000 3.39 2715 24.6 2.74 (2.82 ( 0.08) × 10
9
.05 2000 3.48 2856 19.1 2.14 (7.96 ( 0.37) × 10
a
9
00 ppm in Ar) within the temperature range 2188-4249 K
are summarized in Table 2; we also list k /k′ for comparison.
Values of k′ obtained with eq 8 based on pseudo-first-order
P
1
, pressure of reactant gas mixture; P
, temperature of reaction. Concentrations are in
molecule cm ; k1a are fitted with kinetic modeling, and k1′a are
4
, pressure of driver gas;
M
s
, Mach number; T
5
1
a
1a
-
3
1
a
derived from pseudo-first-order kinetics.
kinetics deviate from k1a by less than 20% (<4% for mixtures
with [SO2] e 200 ppm), indicating that secondary reactions play
only a minor role under our experimental conditions. Detailed
modeling shows that secondary reactions are negligible at high
temperatures because reaction 1a increases much more rapidly
than possible interfering reactions, whereas at low temperatures
and greater [SO2], reaction 9b is the only interfering reaction
accounting for more than 3% of correction, with a maximal
contribution ∼14 % to k1a under our experimental conditions.
We also used the theoretically predicted value of k10a (to be
discussed in section 4.5) and the experimental value of k10b (to
be discussed in section 4.3) to replace values listed in eqs 17
and 18 in the model and derived nearly identical values of k1a.
Values of k1a determined with various concentrations of SO2
at various temperatures are plotted in Figure 3; comparison of
results of previous reports is shown in Figure 4 with lines of
various types drawn only for their respective investigated range
of temperature. Our data support previous reports of greater rate
coefficients; they agree well with those of Plach and Troe6
(designated PT in Figures 3 and 4) in the overlapping range of
7
temperature 3000-4249 K. Results of Kiefer are also within

11024 J. Phys. Chem. A, Vol. 107, No. 50, 2003
Lu et al.
fit. Comparing with previous reports listed in Table 1, we found
that both the preexponential factor A0 and the activation energy
Ea determined in our work agree with those reported by Plach
6
and Troe, who monitored UV absorption of SO2 free from
7
interference of SO. Rate coefficients reported by Kiefer are
also within experimental uncertainties of ours, but their Ea and
A0 values are greater than ours. The activation energy Ea/R )
9
5
8600 ( 2300 K reported by Just and Rimple, who employed
a method similar to ours, is about 14% greater than ours; it is
unclear why the errors are greater than expected experimental
uncertainties. Previous reports of smaller rate coefficients,3
although having a similar Ea, are clearly in error; the possibility
that the absorption of SO interferes with that of SO2 has been
-5
6
discussed previously.
4
.3. Formation of S Atoms and Kinetics of SO + O f
S + O2. Figure 5 shows a temporal profile of S atoms during
pyrolysis of SO2 at 3369 K; about 12% of S atoms are produced
in ∼300 µs under such experimental conditions. The concentra-
tion of S atoms decreases as temperature decreases and becomes
nearly undetectable ∼2258 K, as shown in trace B of Figure 6.
Production of S atoms might result from pyrolysis of SO2
through a direct channel
SO f S + O
2
(1b)
Figure 3. Arrhenius plots of k1a for the reaction SO
2
f O + SO. Our
2
fitted equation is shown as a solid line, and previous results are shown
6
7
as dotted (Plach and Troe), dashed (Kiefer) and dot-dashed (Levitt
or through further pyrolysis of the product SO
2
and Sheen) lines.
M
experimental uncertainties of ours. At temperatures below 3000
K, rate coefficients reported by Levitt and Sheen (designated
SO
98 S + O
(13)
2
LS) are slightly greater than ours. Results of Just and Rimpel
or through possible secondary reactions
9
10
(
JR) and Grillo et al. (GRS) are smaller than our data by a
O + SO f S + O2
(10b)
(12)
factor of 1.3-4.2. We extended the temperature range of
investigation down to 2188 K.
Fitting our results yields the expression
SO + SO f S + SO2
k (T) ) (4.86 ( 1.31) ×
According to literature values of rate coefficients listed in the
previous section, reactions 12 and 13 contribute little to the
formation of S atoms. Some experiments were carried out with
a mixture of N2O, SO2, and Ar, for which O atoms were also
1a
-9
exp [-(50450 ( 730)/T] cm molecule s-1 (23)
3
-1
10
in which listed errors represent one standard deviation of the
Figure 4. Comparison of reported values of k1a for the reaction SO
see Table 1 for references. Lines are drawn for the temperature range of study.
2
f O + SO. Each character represents the first letter of the author’s last name;

Pyrolysis of SO2 and the Reaction O + SO
J. Phys. Chem. A, Vol. 107, No. 50, 2003 11025
TABLE 3: Experimental Conditions and Rate Coefficient
a
k
10b for the Reaction O + SO f S + O
2
k
10b/10-
12
P
1
/
P
4
/
T
K
5
/
[SO
10
2
]/ [Ar]/ [N
2
O]/
1
4
18
14
cm molecule s-1
3
-1
Torr Torr
M
s
10
10
SO
2
(350.0 ppm)
1
1
1
1
9
9
0.01 2000 3.48 2843 8.26 2.36 0.00
0.03 2250 3.57 2988 8.40 2.40 0.00
0.01 2350 3.64 3109 8.40 2.42 0.00
0.10 2550 3.77 3314 8.71 2.49 0.00
.53 2500 3.80 3369 8.26 2.36 0.00
.52 2500 3.81 3385 8.26 2.36 0.00
2.47 ( 0.04
2.58 ( 0.05
3.03 ( 0.06
4.04 ( 0.06
3.73 ( 0.07
3.44 ( 0.06
2
SO (499.3 ppm)
1
1
1
9
9
0.05 2250 3.54 2943 12.0
0.04 2250 3.55 2962 11.9
0.10 2500 3.69 3195 12.3
2.40 0.00
2.39 0.00
2.46 0.00
2.34 0.00
2.35 0.00
3.21 ( 0.04
2.71 ( 0.06
3.23 ( 0.06
3.75 ( 0.06
3.82 ( 0.06
.51 2500 3.39 3314 11.7
.54 2500 3.46 3330 11.8
Figure 5. Representative temporal profile of [S] observed for pyrolysis
2 2
SO (100.2 ppm) and N O (247.7 ppm)
of a sample containing SO (350 ppm) and Ar. T ) 3369 K and P )
2
1
1
1
1
1
1
1
1
1
1
1
1
7.03 2000 3.04 2212 3.69 3.68 9.12
7.00 2000 3.05 2224 3.69 3.68 9.13
7.04 2000 3.10 2296 3.75 3.74 9.26
6.52 2250 3.17 2394 3.69 3.68 9.11
6.53 2250 3.21 2441 3.71 3.71 9.18
6.51 2250 3.23 2470 3.73 3.72 9.21
6.04 2250 3.28 2544 3.66 3.65 9.06
6.02 2250 3.29 2564 3.66 3.65 9.05
5.56 2250 3.32 2601 3.57 3.57 8.84
5.53 2500 3.39 2709 3.62 3.61 8.94
0.09 2250 3.58 3008 2.43 2.42 5.99
0.02 2500 3.66 3138 2.44 2.43 6.03
1.23 ( 0.02
1.25 ( 0.02
1.67 ( 0.02
1.95 ( 0.04
1.75 ( 0.02
1.90 ( 0.04
2.04 ( 0.03
2.19 ( 0.04
1.90 ( 0.03
2.19 ( 0.03
3.05 ( 0.04
3.53 ( 0.04
4.39 ( 0.05
3.01 ( 0.04
3.78 ( 0.06
18
-3
2
.36 × 10 molecule cm . The solid line represents fitted results using
the model described in text.
.60 2500 3.69 3180 3.34 2.34 5.79
.52 2500 3.77 3322 2.35 2.35 5.81
a
P
1
, pressure of reactant gas mixture; P
, temperature of reaction. Concentrations are in
molecule cm ; k10b are fitted with kinetic modeling.
4
, pressure of driver gas;
s 5
M , Mach number; T
-
3
k (T) ) 2.83 × 10 exp (11300/T) cm molecule s-1
-
35
6
-2
2
6
Figure 6. Temporal profiles of [S] observed for a sample, containing
(refs 32 and 39) (29)
SO
P ) 3.72 × 10 molecule cm . (A) with N
O.
2
(300 ppm) and Ar, heated by the shock wave to T ) 2258 K and
18
-3
2
O (248 ppm); (B) without
and found satisfactory agreement between the observed ones
with the predicted profiles. Rate coefficients k25 and k26 were
derived by reported rate coefficients of their reverse reactions
and equilibrium constants. The temporal profile of S atoms fit
poorly with a model in which reaction 1b replaces reaction 10b.
S atoms produced during pyrolysis of SO2 clearly arise mainly
from reaction 10b; the contribution of direct pyrolysis (reaction
N
2
produced through thermal decomposition of N2O. Under such
conditions, [O] was much greater than when only SO2 was
present. Figure 6 compares temporal profiles of S atoms for a
mixture containing SO2 (300 ppm) with no N2O and one
containing SO2 (300 ppm) and N2O (248 ppm), both heated to
1
b) is likely much smaller than reaction 10b. With modeling,
∼
2258 K. Without N2O scarcely any S atom was detectable at
we estimated that k1a/k1b > 100 for T > 3300 K.
this temperature, whereas with N2O producing [O], production
of S was enhanced, indicating the importance of reaction 10b.
We modeled observed temporal profiles of [S] with reactions
We modeled observed temporal profiles of [S] with reactions
3
8
1a, 9-14, and 24-26 with FACSIMILE; rate coefficients
except for reaction 10b were held constant, and the second-
order rate coefficient of the title reaction, k10b, was varied to
yield the best fit. Experimental conditions and values of k10b
for 26 measurements at various initial concentrations ([SO2] )
1a and 9-14 and reactions
S + O f SO + O
(24)
2
M
1
00-499 ppm and [N2O] ) 0 or 248 ppm in Ar) in the
S + O
9
8 SO
(25)
(26)
temperature range 2212-3385 K are summarized in Table 3.
Values of k10b at various temperatures are plotted in Figure 7.
To our knowledge, there is no previous report on the rate
coefficient of this reaction. Values of k10b were also estimated
from rate coefficients of the reverse reaction, reaction 24,
M
S + S 98 S2
with literature values of rate coefficients
k (T) ) 1.32 × 10 exp (-5075/T) cm molecule s-1
-
10
3
-1
36
reported by Woiki and Roth, and the equilibrium constant
24
derived from literature values of ∆G(T) for corresponding
(ref 36) (27)
3
7
species. Derived rate coefficient
k (T) ) 3.55 ×
25
-
37 0.7231
exp (9658/T) cm molecule s-1
6
-2
k10b(T) ) 3.63 ×
10
T
10 exp [-(7700/T)] cm molecule s-1 (18)
-
11
3
-1
(
ref 6) (28)

11026 J. Phys. Chem. A, Vol. 107, No. 50, 2003
Lu et al.
TABLE 4: Vibrational Wave Numbers and Rotational
Parameters Calculated at the B3LYP/6-311+G(3df) Level
vibrational wavenumbers/cm-
1
species
B/GHz
3
-
1156.7 (1136.7)a
519.1 (517.7), 1178.1 (1151.4),
SO ( Σ )
21.4
59.8, 10.3, 8.8
1
SO
2
(X A
1
)
b
1
376.9 (1361.8)
1
SO
SO
2
(A A
(a B
2
)
)
28.8, 12.5, 8.7
67.8, 8.9, 7.8
414.7, 453.8, 1031.5
3
2
1
373.9 (362), 946.3 (904),
9
55.3 (967)c
3
SO
2
(b A
SOO-1 ( A′)
2
)
28.7, 12.5, 8.7
95.3, 6.9, 6.4
414.9, 586.7, 1027.8
492.9, 800.9 (739.9),
1
d
1
142.1 (1006.1)
1
SOO-2 ( A")
SOO-3 ( A")
SOO ( A")
60.2, 7.1, 6.4
47.3, 8.5, 7.2
52.2, 8.0, 6.9
59.7, 6.2, 5.6
48.6, 6.8, 6.0
93.9, 6.4, 6.0
27.2, 11.4, 8.0
43.6
209.2, 551.7, 1130.6
353.7, 650.8, 921.8
280.6, 590.4, 1050.2
685.4i, 322.2, 972.5
687.1i, 218.4, 970.4
328.8i, 678.5, 801.9
845.7i, 320.9, 1065.2
1645.3
1
3
TS1
TS2
TS3
TS4
3
-
O
2
( Σ )
g
Figure 7. Arrhenius plots of k10b for the reaction O + SO f S + O
2
.
SO (b
3
A2)
43.0, 10.8, 8.1
e
(780, 700, 300)
c
2
Our fitted equation is shown as a solid line, and the dashed line
represents values derived from experimental rates of the reverse reaction
a
b
Values in parentheses are experimental values from ref 42. Values
c
in parentheses are experimental values from ref 41. Values in
S + O f SO + O and equilibrium constant; see text. Lines are drawn
2
d
parentheses are experimental values from ref 43. Values in parentheses
for the temperature range of study.
are experimental values from ref 45. e Rotational parameters are
experimental values from ref 44.
9
. Reaction paths involving transition states with energies greater
-
1
than 15 kcal mol relative to O + SO are not shown; a
complete description of the theoretical study on the SOO system
will be published separately. Predicted vibrational wavenum-
bers and rotational constants as well as available experimental
data
40
4
1-45
for the species involved are summarized in Table 4.
The results indicate that the predicted vibrational wavenumbers
are underestimated by 0.2-2.3% from experimental values.
1
A. Ground-State SO2 (X A1). The most stable conformation
1
of SO2 has C2V symmetry; its ground electronic state ( A1) has
4
1,46
been extensively investigated experimentally
cally
and theoreti-
4
5,47
with various methods. At the B3LYP/6-311+G(3df)
level, the optimized S-O bond length is 1.437 Å, which can
be compared with 1.448, 1.462, 1.471, and 1.450 Å, obtained
47
47
from calculations at the CCSD(T)/TZ2P(f,d), CCSD(T)/DZP,
BP86/cc-pVTZ, and B3LYP/cc-pVTZ levels, respectively,
and the experimental value of 1.431 Å. A calculated OSO
bond angle of 119.2° agrees well with the experimental value
of 119.3°. The enthalpy of formation for SO2 is predicted to be
4
5
45
4
6
Figure 8. Optimized geometries of four transition states and reactants
2
and products of the SO system, with bond lengths in Å and bond angles
in degree.
-
1
-
69.2 kcal mol at the G2M(RCC2) level at 0 K, which is in
good agreement with the experimental value, -70.3 ( 0.3 kcal
is shown in Figure 7 as a dashed line drawn only for their
temperature range of investigation, 2732-3463 K, for com-
parison. Fitting our results to an Arrhenius equation yields
-
1 37
mol . The calculated dissociation energy D0(O-SO), 129.4
-
1
kcal mol , for the ground-state SO2 agrees with the experi-
3
7
-1 48
mental value of 130.5 ( 0.4 and 130.7 kcal mol .
B. Low-Lying States A A2, a B1, and b A2 of SO2. Figures
1
3
3
k10b(T) ) (3.0 ( 0.3) ×
-11
exp [-(6980 ( 280)/T] cm molecule s-1 (30)
3
-1
8 and 9 also present the structures and energies of three low-
lying states, A A2, a B1, and b A2, of SO2 which are bound
states with no barriers for their dissociation to the lowest
10
1
3
3
in which listed errors represent one standard deviation of the
fit. Estimated errors for k10b are (25% because rate coefficients
were derived from secondary reactions. When our experimental
results are compared with eq 18, the agreement is satisfactory.
3
-
3
1
asymptotes of SO( Σ ) + O( P). The A A2 state is predicted
-
1
1
to lie 73.4 kcal mol above the ground X A1 state, which is
smaller than the experimental value, 79.8 kcal mol . The a
B1 state is predicted to lie 75.5 kcal mol above the ground
X A1 state, which agrees with the value 75.2 kcal mol
obtained by Katagiri et al. at the MRCI/cc-pVDZ level; they
are slightly greater than the experimental data, 73.6 kcal
For the b A2 state, the calculated result lies above
the X A1 state by 76.8 kcal mol , which is close to the
-
1 49
3
-1
4
.4. Potential-Energy Surfaces and Reaction Mechanism.
40
1
-1
Our preliminary calculations show that there are many triplet
and singlet intermediates and transition states involved in the
2
5
3
-
3
3
3
-
reaction of SO(X Σ ) + O( P) to produce S( P) + O2(X Σg ).
In this paper, only relevant low-lying energy channels are
presented and discussed. The optimized geometries of the
reactants, intermediates, transition states, and products are shown
in Figure 8. The energy diagram calculated with the G2M-
-
1 43,50
3
mol .
1
-1
-
1 43,44
experimental value, 77.3 kcal mol .
C. S + O2 Formation. Figure 9 shows that S( P) + O2(X
Σg ) can be formed via singlet and triplet SOO intermediates.
3
3
3
3
-
(RCC2)//B3LYP/6-311+G(3df) method is presented in Figure

Pyrolysis of SO2 and the Reaction O + SO
J. Phys. Chem. A, Vol. 107, No. 50, 2003 11027
Figure 9. Potential-energy diagram for reactions 1a and 1b based on energies calculated with G2M(RCC2)//B3LYP/6-311+G(3df). Energies are
-
1
-1
listed in kcal mol . Reaction paths with transition state energies greater than 15 kcal mol above O + SO are not shown; a complete diagram is
shown in ref 40.
1
1
The singlet channels proceed via two surfaces, A′ and A′′.
1
1
The entrance barriers for A′ and A′′ from SO + O are 5.0
-1
1
(
TS1) and 9.6 kcal mol (TS2), respectively; the A′ intermedi-
1
ate (SOO-1) is more stable than those of A′′ (SOO-2 and SOO-
). The predicted energy of SOO-1, 113.6 kcal mol above
SO2 (X A1), is similar to a value of 117 kcal mol predicted
-
1
3
1
-1
47
by Kellogg and Schaefer but greater than a value of 105 kcal
mol predicted by Dunning and Raffenetti,51 who employed a
-1
two-reference CI method with generalized valence-bond (GVB)
natural orbitals. The triplet channel proceeds through the SO2
3
(
b A2) intermediate followed by dissociation via TS4 to produce
-
1
S + O2. The predicted heat of reaction, 4.8 kcal mol , for
reaction 10b is close to the value obtained from JANAF, 5.5
-
1 37
kcal mol .
4
.5 Calculations of Rate Coefficients. Calculations based
on variational transition-state and RRKM theories were carried
out with the Variflex code26 for the following reactions:
3
3 -
SO f O( P) + SO( Σ )
(1a)
2
M
3
3 -
Figure 10. Comparison of predicted rate coefficient k1a (solid line)
for SO f O + SO with experimental data (O, this work; 2, Plach
and Troe ). Contributions from decomposition via various electronic
states of SO are shown with broken lines as indicated in the legend.
O( P) + SO( Σ )
9
8 SO2
(10a)
(10b)
2
6
3
3
-
3
3
-
g
O( P) + SO( Σ ) f S( P) + O ( Σ )
2
2
-
1
3
respectively; the value of 1.634 Å predicted for the a B1 state
The energies used in the calculation are shown in Figure 9;
vibrational wavenumbers and rotational parameters are listed
in Table 4.
3
was also used for the b A2 state in the calculation. States A
A2, a B1, and b A2 lie below the dissociation limit of SO2 by
1
3
3
-
1
3
more than 52 kcal mol ; contributions of these states to the
total rate coefficient for dissociation are calculated by multiply-
ing rate coefficients of decomposition by relative populations
of each state assuming that these electronic states are strongly
mixed.
The Lennard-Jones (LJ) parameters required for the RRKM
calculations, ꢀ/ k ) 328.5 and 113.5 K, and σ ) 4.102 and
3.465 Å, for SO2 X A1 and Ar, respectively, are taken from
A. SO2 f SO + O. The decomposition of SO2 to form O( P)
3
-
and SO( Σ ) proceeds without a well-defined transition state
due to the absence of an intrinsic reaction barrier. To predict
the dissociation rate reliably, we implemented a flexible
variational transition-state approach, originally developed by
Marcus and co-workers,5
2,53
into the Variflex code. The
26
dissociation energy for reaction 1a was calculated by increasing
1
the S-O bond distance from its equilibrium value, 1.437 Å, to
1
3
3
4
.0 Å at intervals 0.1 Å. Energies of A A2, a B1, and b A2
ref 54. The LJ parameters for other states of SO2 were assumed
1
states were calculated similarly. Calculated energies were fitted
to a Morse equation (eq 3) scaled to match the dissociation
to be the same as those of the X A1 state.
Predicted rate coefficients of decomposition of SO2 and partial
contributions from the four electronic states of SO2 are compared
with experimental results in Figure 10. To reproduce experi-
mental data satisfactorily, a larger 〈∆Edown〉 has to be used for
1
8
energy predicted at the G2M(RCC2) level of theory. Values
of â in the Morse potential were determined to be 2.779, 1.891,
and 1.634 Å for the X 1A1, A 1A2, and a 3B1 states,
-
1

11028 J. Phys. Chem. A, Vol. 107, No. 50, 2003
Lu et al.
Figure 12. Comparison of the predicted rate coefficient k10b for the
Figure 11. Comparison of predicted rate coefficient k10a (solid line)
for O + SO f SO with experimental data (O, Miyazaki and
Takahashi; 3, Cobos et al.; 4, Singleton and Cvetanovic ). An
estimate of temperature dependence of k10b by Grillo et al.10 is shown
with broken lines.
reaction SO + O f S + O
2
. Contributions from different channels are
shown as broken lines, as indicated in the legend.
2
5
5
56
33
3
3
-31
cm6
for M ) Ar by Singleton and Cvetanovic, 5.1 × 10
-
2
-1
molecule s , but deviates from values of (2.07 ( 0.23) ×
-
31
6
-2 -1
55
this system; the values are temperature dependent and can be
approximated by
10
cm molecule
s
by Miyazaki and Takahashi and
-
31
6
-2 -1
56
7.69 × 10
cm molecule
s
(M ) N ) by Cobos et al.
2
The temperature dependence of the rate coefficient may be
expressed as
0.43
〈
∆Edown〉 ) 560 (T/298) cm-1
(31)
The best predicted total rate coefficients (thick line in Figure
k
10a(T) ) (4.82 ( 0.05) ×
10) can be expressed in an Arrhenius form
-31
-2.17(0.03
cm molecule s-1 (33)
6
-2
1
0
(T/298)
k (T) ) 4.71 × 10 exp [-(55190/T)] cm molecule s-1
-
8
3
-1
1a
for the temperature range 298-3000 K, in satisfactory agree-
-31
-1.84
6
-2
(
32)
ment with the expression 9.3 × 10 (T/298)
reported by Grillo et al. based on an equilibrium constant
derived from Gibb’s free energies, the previously reported values
cm molecule
-
1
10
s
Predicted activation energy of Ea/R ) 55190 K is ∼9% greater
than our experimental value, but within experimental uncertain-
ties.
It should be pointed out that SO2 cannot effectively dissociate
to give S + O2; this product channel proceeds via tight
-centered TSs producing SOO intermediates with relatively
high barriers. The lowest isomerization barrier, SO2 ( A2) f
SOO ( A′′) is 9.2 kcal mol above O + SO (Figure 9). For
other possible isomerization processes, the barriers are even
9,10
of k1a
and an erroneous value of k10a at 298 K.
C. O + SO f S + O2. As described in the previous section,
3
3
-
1
1
3
S( P) + O2(X Σg ) can be formed via A′, A′′, and A′′ PES
see Figure 9). The predicted individual and total rate constants
(
3
are presented in Figure 12 for comparison with experimental
values determined in this work. It is readily seen that combina-
tion of three reaction channels can well reproduce experimental
data. The predicted total rate constant in the temperature range
of 2000-5000 K can be expressed as
3
3
3
3
-1
1
1
1
higher; for example, the barriers for SO2 ( A2) f SOO ( A′′)
1
1
1
-1
and SO2 ( A1) f SOO ( A′) are 15.2 and 19.5 kcal mol above
O + SO, respectively (not shown in Figure 9). Therefore, the
reaction channel (1b) for pyrolysis of SO2 to form S and O2 is
negligible. Our experimental observation of temporal profiles
for production of S atoms is consistent with the dominant
secondary reaction
k10b(T) ) 3.92 ×
-17 1.51
3
-1 -1
1
0
T
exp [-(2537/T)] cm molecule s (34)
or
-
11
3
-1 -1
k10b(T) ) 3.4 × 10 exp [-(7122/T)] cm molecule s
35)
O + SO f S + O2
(10b)
(
rather than with direct formation via reaction 1b, agreeing with
theoretical prediction.
in close agreement with the experimental value
B. O + SO f SO2. Figure 11 compares predicted and
experimental rate coefficients for the association reaction 10a;
k10b(T) ) (3.0 ( 0.3) ×
-
11
exp [-(6980 ( 280)/T] cm molecule s-1 (30)
3
-1
∆Edown〉 ) 400 cm-1 was employed for collisional stabilization.
10
〈
1
3
3
Formation of SO2 in its X A1, a B1, and b A2 states contributes
42, 31, and 27% to the total rate coefficients at 298 K and
5
. Conclusion
∼
changes to ∼37, 37, and 26%, respectively, at 1000 K. The
results show that the total rate coefficient decreases with
increasing temperature, as expected for an association reaction.
Rate coefficients for pyrolysis of SO2 to form O and SO in
the temperature range 2188-4249 K were determined using a
diaphragmless shock tube with atomic resonance absorption
detection of O and S atoms. Our results are consistent with
measurements by Plach and Troe but show a slightly smaller
-
31
6
The predicted rate coefficient at 298 K, 4.8 × 10
cm
-
2 -1
molecule s , agrees satisfactory with a recommended value

Pyrolysis of SO2 and the Reaction O + SO
J. Phys. Chem. A, Vol. 107, No. 50, 2003 11029
preexponential factor. Rate coefficients may be expressed with
(20) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.;
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H.-J.; Knowles, P. J. with contributions from Alml o¨ f, J.; Amos, R. D.;
Berning, A.; Cooper, D. L.; Deegan, M. J. O.; Dobbyn, A. J.; Eckert, F.;
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-
9
the equation k1a(T) ) (4.86 ( 1.31) × 10 exp [-(50450 (
3
-1 -1
7
30)/T] cm molecule s , in which listed errors represent
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3
3
a
B1 and b A2 contributes significantly; the total rate
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-
31
-2.17(0.03
6
-2 -1
1
0
(T/298)
cm molecule
s
for the temperature
range 298-3000 K. Experimental observation of S atoms fits
satisfactorily with a model involving a secondary reaction O +
SO f S + O2; the rate coefficient k10b(T) ) (3.0 ( 0.3) ×
-
11
3
-1 -1
1
0
exp[-(6980 ( 280)/T] cm molecule
s
was deter-
(
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the MOE Program for Promoting Academic Excellence of
Universities (Grant No. 89-FA04-AA) for support. R.S.Z. and
M.C.L. thank the Office of Naval Research, U.S. Navy (Contract
No. N00014-89-J1949) for support. M.C.L. also acknowledges
the support from the National Science Council of Taiwan for a
distinguished visiting professorship at the Center for Interdis-
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