Reaction dynamics of Cl+H2S: Rotational and vibrational distribution of HCl probed with time-resolved Fourier-transform spectroscopy

Article abstract of DOI:10.1063/1.1592508

Using time-resolved Fourier-transform spectroscopy (TR-FTS), the nascent rotational and vibrational distribution of HCl produced from the bimolecular reaction Cl+H₂S→HCl(v,J)+HS(v,J) were determined. A rotational energy of HCl much greater than reported previously, but consistent with other similar reactions, was observed.

Full text of DOI:10.1063/1.1592508

Reaction dynamics of Cl + H 2 S : Rotational and vibrational distribution of HCl probed
with time-resolved Fourier-transform spectroscopy
Kan-Sen Chen, Shin-Shin Cheng, and Yuan-Pern Lee
Citation: The Journal of Chemical Physics 119, 4229 (2003); doi: 10.1063/1.1592508
View online: http://dx.doi.org/10.1063/1.1592508
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 119, NUMBER 8
22 AUGUST 2003
Reaction dynamics of Cl¿H2S: Rotational and vibrational distribution
of HCl probed with time-resolved Fourier-transform spectroscopy
Kan-Sen Chen, Shin-Shin Cheng, and Yuan-Pern Leea)
Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan
͑Received 6 May 2003; accepted 27 May 2003͒
Following laser irradiation of a flowing mixture of S2Cl2 and H2S at 308 nm to initiate the reaction
of ClϩH S, vibration–rotation resolved emission spectra of HCl( ϭ1,2) in the spectral region
v
2
2436–3310 cmϪ1 are detected with a step-scan time-resolved Fourier-transform spectrometer. The
Boltzmann-type rotational distributions of HCl( ϭ1) and HCl( ϭ2) yield rotational temperatures
v
v
that decrease with reaction time; extrapolation to time zero based on data in the range 0.5–4.0 ␮s
yields nascent rotational temperatures of 1250Ϯ70 K and 1270Ϯ120 K, respectively; an average
rotational energy of 8.3Ϯ1.5 kJ molϪ1 is determined for HCl( ϭ1,2), much greater than a previous
v
report. Observed temporal profiles of the vibrational population of HCl( ϭ1,2) are fitted with a
v
kinetic model that includes formation and quenching of HCl( ϭ1,2) to yield a branching ratio of
v
0.14Ϯ0.01 for formation of HCl( ϭ2)/HCl( ϭ1) and a thermal rate coefficient of k ϭ(3.7
v
v
1
Ϯ1.5)ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1. Combining an estimate of the vibrational population of
HCl( ϭ0) based on a surprisal analysis of previous investigations on the reaction ClϩD S, we
v
2
report a ratio of vibrational distributions of HCl( ϭ0):( ϭ1):( ϭ2)ϭ0.41:0.52:0.07, which
v
v
v
gives an average vibrational energy of 23Ϯ4 kJ molϪ1 for HCl. Internal energies, especially
rotational energy, of HCl derived with this method is more reliable than with previous techniques;
the fractions of available energy going into rotation and vibration of HCl are frϭ0.12Ϯ0.02 and
fvϭ0.33Ϯ0.06, respectively. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1592508͔
I. INTRODUCTION
to derive an average rotational energy is to assume a Boltz-
mann distribution and to transform an observed population
distribution, which contains substantial low-J components
due to quenching, back to the high-J envelope.7 Because of
such a limitation, reported distributions of rotational energies
of HX typically have large uncertainties.
Step-scan time-resolved Fourier-transform spectroscopy
͑TR–FTS͒ is capable of quantitative measurements of IR
chemiluminescence within microsecond range;8–12 the tem-
poral evolution of populations of vibrational–rotational lev-
els of each species detected with this technique provides
much information on rates of formation and quenching. Our
previous applications of this technique to photodissociation
of halogen-containing compounds have been successful; ob-
served internal state distributions of HX provide direct evi-
dence of photoelimination of HX via three-center and four-
center transition states.8–11 We report here an application of
this technique to dynamics of a bimolecular reaction
The energy disposal of HX (XϭF, Cl, Br) from hydro-
gen abstraction reactions by halogen atoms X has generated
continued interest partly because these reactions generate vi-
brationally inverted HX products that are excellent media for
chemical lasers,1 and partly because the heavy–light–heavy
mass relationship in these reactions is a prototype in chemi-
cal dynamics.2 In these reactions, the newly formed H–X
bond carries most vibrational excitation, leaving the counter-
part vibrationally cold. The fraction of available energy
transforming into vibrational energy of HX, fv , is typically
0.4–0.5 for various reactions of type XϩHY, whereas that
into rotational energy of HX, fr , ranges from 0.1 to 0.2.3
For this type of reactions, infrared ͑IR͒ chemilumines-
cence of HX is generally detected to yield its vibrational and
rotational state distributions.4 Earlier experiments were car-
ried out either with a fast-flow reactor5 or with a cold-wall
flow reactor using the arrested-relaxation technique;6 a con-
ventional Fourier-transform infrared ͑FTIR͒ spectrometer
was later coupled to the reactor to provide improved detec-
tivity and spectral resolution. In these experiments for a bi-
molecular reaction, effects of vibrational quenching on a na-
scent vibrational distribution are small, but rotational
quenching is non-negligible so that direct detection of na-
scent rotational distribution of products is difficult. A method
typically employed to correct for the quenching effects and
ClϩH S→HCl ,J͒ϩHS ,J͒.
͑v ͑v
͑1͒
2
Coombe et al. reported intense laser emission of HCl(
v
ϭ1) that was produced from reaction ͑1͒ by irradiating a
mixture of H2S:Cl2 :He ͑1:10:40 at 40 Torr͒ with flash
lamps.13 Dill and Heydtmann employed the arrested relax-
ation method to observed IR chemiluminescence of HCl
from reaction ͑1͒ with an FTIR;14 they reported emission
only from HCl( ϭ1) with a rotational distribution peaked
v
near J ϭ4 and an average rotational energy of 4.5 kJ molϪ1
.
Ј
a͒
Author to whom correspondence should be addressed. Jointly appointed by
Braithwaite and Leone detected IR chemiluminescence of
HCl to determine rates of formation and the internal state
the Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei,
Taiwan. Electronic mail: yplee@mx.nthu.edu.tw
0021-9606/2003/119(8)/4229/8/$20.00
4229
© 2003 American Institute of Physics
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4230
J. Chem. Phys., Vol. 119, No. 8, 22 August 2003
Chen, Cheng, and Lee
0.043 Torr for H2S, 0.11–0.22 STP cm3 sϪ1 and 0.045–0.090
Torr for S2Cl2 , and 0.94–2.60 STP cm3 sϪ1 and 0.40–1.11
Torr for Ar; STP indicates standard temperature at 273 K and
pressure at 1 atm. Ar ͑Scott Specialty Gases, 99.999%͒ and
H2S ͑AGA Specialty Gases, 99.95%͒ were used without pu-
rification. S2Cl2 ͑Hayashi Co., 99%͒ was degassed at 180 K
before use.
distribution of HCl produced from reaction ͑1͒ that was ini-
tiated with laser irradiation.15 By comparison of the signal
filtered with a gas cell filled with HCl with that through
an interference filter passing emissions of HCl( ϭ1,2), they
v
estimated HCl( ϭ2) / HCl( ϭ1) ϭ0.067. They also
͓
v
͔ ͓
v
͔
determined
a
rate coefficient of (6.0Ϯ1.2)ϫ10Ϫ11
cm3 moleculeϪ1 sϪ1 for reaction ͑1͒. Later, Nesbitt and
Leone used a similar method and reported a revised branch-
ing ratio of HCl( ϭ2) / HCl( ϭ1) р0.02 and a rate co-
͔ ͓
͓
v
v
͔
III. RESULTS AND DISCUSSION
16
efficient (7.3Ϯ0.9)ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1
.
More re-
Following previous reports,15 we employed S2Cl2 rather
than Cl2 as a source of Cl atoms because HS reacts with Cl2
readily and propagates chain reactions; reaction of HS with
Cl2 produces HSCl that further reacts with Cl or Cl2 to form
HCl in its highly vibrationally excited states, consequently
interfering with measurements.15 Photodissociation of S2Cl2
in a molecular beam at 308 nm has been extensively inves-
tigated with fragmentation translational spectroscopy.23 At
this wavelength, S2Cl2 undergoes a simple S–Cl bond sciss-
ion with fragments carrying translational energy averaged at
88 kJ molϪ1. The average translational energy of Cl atoms
immediately after photolysis is thus 64 kJ molϪ1, yielding an
average collisional energy of 33.6 kJ molϪ1 between Cl and
H2S. At a pressure of 0.6 Torr, there are more than ten col-
lisions within 1 ␮s; hence most Cl atoms are thermalized
within 1 ␮s. At 0 K, reaction ͑1͒ has an enthalpy of reaction
of ⌬HoϭϪ57.7 kJ molϪ1, derived from enthalpies of for-
mation ͑in unit of kJ molϪ1͒ of Cl ͑119.62͒, H2S ͑Ϫ17.58͒,
HS ͑136.49͒, and HCl ͑Ϫ92.13͒.24 Hence the available en-
ergy for reaction ͑1͒ at 298 K is ϳ69 kJ molϪ1, after taking
into account of translational and rotational energies of Cl and
H2S, but without adding a calculated barrier height of ϳ5
kJ molϪ1 ͑Ref. 25͒ that is smaller than thermal energy. Avail-
able energy used for reaction ͑1͒ in previous work was 64
cent measurements on the rate coefficient of reaction ͑1͒
range from 4.0 to 10.5ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1 17–21 HS
.
was found to be vibrationally cold.15
Agrawalla and Setser3 detected infrared chemilumines-
cence of DCl and laser-induced fluorescence of DS to study
the reaction of Cl with D2S in a fast-flow reactor,
ClϩD S→DCl ,J͒ϩDS ,J͒.
͑v ͑v
͑2͒
2
They determined DCl( ϭ2) / DCl( ϭ1) Х3/7 and
͓
v
͔ ͓
v
͔
DS( ϭ1) / DS( ϭ0) ϭ0.08Ϯ0.04. Hossenlopp et al.
͓
v
͔ ͓
v
͔
used time-resolved infrared diode laser absorption spectros-
copy to probe DCl that was produced from reaction ͑2͒ and
determined
a vibrational distribution of DCl( ϭ0)
͓ v ͔
: DCl( ϭ1) : DCl( ϭ2) ϭ33Ϯ7:56Ϯ7:11Ϯ3; they also
͓
v
͔ ͓
a
v
͔
determined
rate coefficient of (3.2Ϯ0.3)ϫ10Ϫ11
cm3 moleculeϪ1 sϪ1 for reaction ͑2͒.22
Using TR–FTS, we determined the nascent rotational
and vibrational distribution of HCl produced from reaction
͑1͒. Our results show a rotational energy of HCl much
greater than that reported previously, but consistent with
other similar reactions.
II. EXPERIMENTS
The apparatus employed to obtain step-scan time-
resolved Fourier-transform spectra has been described
previously;8,10 only a brief summary is given here. A tele-
scope mildly focused the photolysis beam from a XeCl laser
͑308 nm͒ to ϳ20 mm2 at the reaction center with a fluence
ϳ100 mJ cmϪ2. A filter passing 2436–3310 cmϪ1 was em-
ployed for detection of HCl. The transient signal of an InSb
detector with a rise time of 0.22 ␮s was amplified with an
effective bandwidth of 1 MHz before being digitized with
either an internal digitizer ͑16-bit, 5-␮s resolution͒ or an ex-
ternal data-acquisition board ͑PAD1232, 12-bit ADC, 25 ns
resolution͒. Data were typically averaged over 60 laser
pulses at each scan step; 4188 scan steps were performed to
yield an interferogram resulting in a spectrum of resolution
0.5 cmϪ1. For analysis of nascent rotational distributions,
typically 20 consecutive time-resolved spectra at 25 ns inter-
vals were summed to yield a satisfactory spectrum represent-
ing emission averaged over a period of 0.5 ␮s. For analysis
of the vibrational distribution and quenching, 150 spectra
were typically recorded at 5 ␮s intervals with the internal
ADC.
kJ molϪ1,3 or 50 kJ molϪ1 14
.
Although the branching between spin–orbit states of Cl
produced from photolysis of S2Cl2 at 235 nm has been de-
termined to be Cl(2P ) : Cl(2P ) ϭ35:65 by the three-
͓
͔ ͓
͔
3/2
1/2
dimensional ͑3D͒ imaging technique,26 there is no such in-
formation for photolysis of S2Cl2 at 308 nm. We assume that
most Cl(2P1/2), if produced, is quenched under out experi-
mental conditions.
To observe directly a nascent rotational distribution of
products from a bimolecular reaction in a flow system is
difficult because one is unlikely to find a condition for the
reaction to proceed to produce products in detectable amount
while maintaining a nearly collisionless condition to avoid
rotational quenching. By decreasing the pressure of the re-
agent as much as possible while maintaining a satisfactory
signal to noise ratio, we recorded emission of HCl with a fast
external digitizer at 25 ns resolution, followed by averaging
every 20 consecutive time-resolved spectra to yield spectra
with resolution of 0.5 ␮s; a nascent rotational population of
HCl was subsequently derived by short extrapolation to
tϭ0 based on observed population. To determine the vibra-
tional distribution of HCl, we added about 1.1 Torr of Ar to
thermalize the rotational excitation and used an internal 16-
bit digitizer at 5 ␮s resolution to obtain temporal profiles of
Flow rates of H2S and Ar were measured with mass flow
meters, and that of S2Cl2 was determined with a dP/dt
method that measures the pressure increase in a calibrated
volume over a specific period of time. Typical flow rates and
partial pressures are 0.04–0.10 STP cm3 sϪ1 and 0.017–
HCl( ) up to 750 ␮s after initiation of reaction. We looked
v
carefully but found no evidence of emission of HS ( ).
v
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4231
J. Chem. Phys., Vol. 119, No. 8, 22 August 2003
Reaction dynamics of ClϩH2S
FIG. 1. Infrared emission spectra of HCl in spectral region 2500–3100 cmϪ1 recorded after irradiation of a flowing mixture of S2Cl2 ͑0.090 Torr͒, H2S ͑0.087
Torr͒, and Ar ͑0.403 Torr͒ with a XeCl excimer laser at 308 nm. Spectral resolution is 0.5 cmϪ1; 60 laser pulses were averaged at each scan step. ͑A͒ 1.0–1.5
␮s, ͑B͒ 1.5–2.0 ␮s, and ͑C͒ 2.0–2.5 ␮s after laser irradiation. Assignments are shown as stick diagrams; J values are listed in parentheses.
Љ
A. Nascent rotational distribution of HCl„v…
ments with pressures 0.580 and 0.830 Torr, respectively; an
average value of T0ϭ1250Ϯ70 K is thus derived. Similarly,
Figure 1 shows partial emission spectra of HCl recorded
values of T0ϭ1290Ϯ120 and 1250Ϯ80 K were derived for
1.0–1.5, 1.5–2.0, and 2.0–2.5 ␮s after photolysis of a flow-
HCl( ϭ2) in experiments with pressures 0.580 and 0.830
v
ing mixture containing S2Cl2 ͑0.090 Torr͒, H2S ͑0.087 Torr͒,
Torr; an average value of T0ϭ1270Ϯ120 K is thus derived.
and Ar ͑0.403 Torr͒ at a spectral resolution of 0.5 cmϪ1
.
Average rotational energies E ( ) for HCl( ϭ1) and
v
v
r
Assignments based on spectral parameters reported by
HCl( ϭ2) were derived by summing a product of level en-
v
Arunan et al.27 and Coxon and Roychowdhury28 are shown
ergy and normalized population Pv(J) for all rotational level
in each vibrational state; for overlapped lines, the popula-
tions were estimated with interpolation based on Fig. 2. Only
as stick diagrams; notations P(J ) and R(J ) are used. The
Љ
Љ
spectrum shows emission of HCl( ϭ1) with rotational lev-
v
els J up to 12 and weak emission of HCl( ϭ2) with J up
v
Ј
Ј
to 9. Each vibration–rotation line in the P branch was nor-
malized with the instrument response function, integrated,
and divided by its respective Einstein coefficient27 to yield a
relative population P (J ). Semilogarithmic plots of
Ј
v
P (J )/(2J ϩ1) vs J (J ϩ1) for HCl( ϭ1) at a few rep-
v
Ј
Ј
Ј
Ј
v
resentative intervals after reaction are shown in Fig. 2. Data
of overlapped lines, J ϭ2 and 9 of ϭ1, are not shown.
v
Ј
Ј
Fitted Boltzmann-type rotational distributions yield rota-
tional temperatures of 1090Ϯ140 K ͑1.0–1.5 ␮s͒, 1030
Ϯ100 K ͑1.5–2.0 ␮s͒, and 920Ϯ40 K ͑2.0–2.5 ␮s͒ for
HCl( ϭ1); the uncertainties represent one standard devia-
v
tion in fitting. Also shown in Fig. 2 are the rotational distri-
bution of HCl( ϭ1) reported by Dill and Heydtmann;14
v
their results correspond to a temperature smaller than ours, as
expected. Emission lines associated with HCl( ϭ2) are
v
treated similarly to derive associated rotational temperature;
results are summarized in Table I.
The decrease in rotational temperature of HCl( ϭ1) af-
v
ter initiation of reaction is shown in Fig. 3 for two total
pressures ͑0.580 and 0.830 Torr͒; rotational temperature is
smaller at a greater pressure or a greater reaction period be-
cause quenching is more effective. We fitted all data to an
exponential decay
FIG. 2. Semilogarithmic plots of relative rotational populations of HCl(
v
Tϭ298ϩ T Ϫ298͒exp Ϫkt͒
͑3͒
͑
͑
0
ϭ1) after irradiation of a flowing mixture of S2Cl2 ͑0.090 Torr͒, H2S ͑0.087
Torr͒, and Ar ͑0.403 Torr͒ at 308 nm. ͑A͒ 1.0–1.5 ␮s, ͑B͒ 1.5–2.0 ␮s, and
͑C͒ 2.0–2.5 ␮s after laser irradiation; ͑D͒ data reported by Dill and Heydt-
man ͑Ref. 14; symbol ᭞͒. Solid lines represent least-squares fits. For ͑B͒–
͑D͒ the y axes are displaced vertically for clarity.
in which T0 is the nascent rotational temperature and k is a
decay coefficient that varies linearly with pressure. Values of
T0ϭ1270Ϯ40 and 1230Ϯ50 K were derived for experi-
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4232
J. Chem. Phys., Vol. 119, No. 8, 22 August 2003
Chen, Cheng, and Lee
TABLE I. Rotational temperature (T ), rotational energy (E ), and nascent rotational energy (E0) of HCl( ϭ1,2) produced from ClϩH S in various reaction
v
r
r
2
r
periods.
HCl( ϭ1)
HCl( ϭ2)
v
v
Time
/␮s
Tr
/K
E ( )
E0( )b
Tr
/K
E ( )
E0( )b
v
v
v
v
r
r
r
r
⌺JPv(J)a
/kJ molϪ1
/kJ molϪ1
⌺JPv(J)a
/kJ molϪ1
/kJ molϪ1
(T0r ϭ1270Ϯ40 K)
1090Ϯ140
1030Ϯ100
920Ϯ40
(T0r ϭ1290Ϯ120 K)
1190Ϯ540
1070Ϯ260
1020Ϯ350
890Ϯ240
0.580 Torr
1.0–1.5
1.5–2.0
2.0–2.5
2.5–3.0
3.0–3.5
3.5–4.0
0.830 Torr
0.5–1.0
1.0–1.5
1.5–2.0
2.0–2.5
2.5–3.0
3.0–3.5
3.5–4.0
2435
2991
3353
4091
4216
4672
7.00Ϯ0.39
6.76Ϯ0.29
6.56Ϯ0.15
6.34Ϯ0.42
5.97Ϯ0.20
5.74Ϯ0.15
8.1
8.3
9.1
9.1
8.7
8.9
560
530
500
684
616
686
4.83Ϯ0.61
4.62Ϯ0.34
4.30Ϯ0.55
4.42Ϯ0.49
4.50Ϯ0.15
3.98Ϯ0.32
5.2
5.6
5.4
6.4
5.6
5.6
890Ϯ60
870Ϯ50
820Ϯ40
1040Ϯ90
920Ϯ160
(T0r ϭ1230Ϯ50 K)
1010Ϯ70
850Ϯ30
(T0r ϭ1250Ϯ80 K)
1190Ϯ370
990Ϯ300
3470
4498
5816
6829
7761
8512
9543
6.53Ϯ0.22
5.91Ϯ0.12
5.85Ϯ0.18
5.78Ϯ0.10
5.58Ϯ0.09
5.63Ϯ0.17
5.44Ϯ0.15
7.9
8.5
8.5
8.6
8.7
8.8
9.2
544
558
679
865
896
897
1083
4.40Ϯ0.45
4.46Ϯ0.51
4.11Ϯ0.34
4.26Ϯ0.25
3.95Ϯ0.34
4.16Ϯ0.23
4.04Ϯ0.26
4.6
5.6
5.9
5.8
5.9
6.8
5.7
840Ϯ40
820Ϯ20
780Ϯ20
780Ϯ40
870Ϯ150
910Ϯ120
830Ϯ140
760Ϯ80
720Ϯ30
800Ϯ100
Ave. E0( ϭ1)ϭ8.6Ϯ0.7
Ave. E0( ϭ2)ϭ5.7Ϯ1.4
v
r
v
r
aPv(J)ϭ(relative intergrated emittance)/͓͑instrumental response factor͒͑Einstein coefficient͔͒; arbitrary unit.
bE0r ϭErϫ(Tr0/Tr).
limits represent one standard deviation in fitting. An aver-
aged nascent rotational energy E0r ϭ8.3Ϯ1.5 kJ molϪ1 for
HCl( ϭ1,2) was derived on multiplying E0( ) by its corre-
observed levels HCl( ϭ1,Jр12) and HCl( ϭ2,Jр9) are
v
v
summed, hence averaged rotational energies of HCl( ϭ1)
v
v
v
and HCl( ϭ2) are different, even though their rotational
v
r
sponding vibrational population. The only previously re-
ported value14 of Erϭ4.5 kJ molϪ1 is about 54% of our
value.
temperatures are nearly identical. Nascent rotational energies
E0( ) were derived on multiplying experimental rotational
v
r
energies E ( ) at each intervals by a correction factor T /T,
v
r
0
The largest rotational level (J ϭ9) observed for
Ј
as listed in Table I. As Table I shows, such correction yields
consistent nascent average rotational energies, even when the
rotational distribution is substantially quenched near 4 ␮s
after initiation of the reaction. We averaged values listed in
HCl( ϭ2) lies at 6549 cmϪ1 above the ground state. With
v
the same energy, J ϭ18 level of HCl( ϭ1) should be popu-
v
Ј
lated. We observed rotational levels of HCl( ϭ1) only up to
v
Table
I
and obtained E0( )ϭ8.6Ϯ0.7 and 5.7
v
r
J ϭ12; the absence of higher levels might be due to limited
Ј
Ϯ1.4 kJ molϪ1 for ϭ1 and ϭ2, respectively; the error
detectivity. We assume a Boltzman distribution and associate
v
v
an extrapolated population with unobserved lines for J
Ј
ϭ13–18 of ϭ1. Average nascent rotational energies for
v
HCl( ϭ1), E0( ϭ1)ϭ10.6Ϯ0.8 and 10.1Ϯ0.6 kJ molϪ1
v
v
r
in experiments under pressures of 0.580 and 0.830 Torr, re-
spectively, are determined by including these fitted popula-
tions; the average value of E0( ϭ1)ϭ10.3Ϯ1.0 kJ molϪ1
v
r
and the average rotational energy of HCl( ϭ1,2), E0ϭ9.7
v
r
Ϯ1.7 kJ molϪ1, should be taken as upper limits.
B. Vibrational distribution and rate coefficient
Experiments were carried out with flowing gaseous mix-
tures containing S2Cl2 ͑ϳ0.045 Torr͒, H2S ͑0.017–0.043
Torr͒, and Ar ͑ϳ1.09 Torr͒; HCl emission was recorded at 5
␮s intervals. Figure 4 shows partial emission spectra of HCl
recorded at 41.5 and 161.5 ␮s after photolysis of a flowing
mixture containing S2Cl2 ͑0.045 Torr͒, H2S ͑0.043 Torr͒, and
Ar ͑1.09 Torr͒ at a spectral resolution of 1.0 cmϪ1. The ratios
of signal to noise for these spectra are better than those re-
corded for rotational studies because a 16-bit ADC was used
and because more HCl was produced at a later reaction pe-
riod. The rotational temperature is determined as previously
described; it reaches ϳ350Ϯ50 K at 5 ␮s, indicating a
nearly thermal distribution for rotation under these experi-
FIG. 3. Variation of rotational temperatures as a function of period after
irradiation; solid lines represent least-squares fits of Eq. ͑3͒; see text.
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4233
J. Chem. Phys., Vol. 119, No. 8, 22 August 2003
Reaction dynamics of ClϩH2S
FIG. 4. Infrared emission spectra of HCl in spectral region 2500–3100 cmϪ1 recorded at 41.5 ͑A͒ and 161.5 ␮s ͑B͒ after photolysis of a flowing mixture of
S2Cl2 ͑0.045 Torr͒, H2S ͑0.043 Torr͒, and Ar ͑1.09 Torr͒ with a XeCl excimer laser at 308 nm. Spectral resolution is 1.0 cmϪ1; 60 laser pulses were averaged
at each scan step. Assignments are shown as stick diagrams.
mental conditions. We averaged values of ⌺ P (J ) associ-
ated with each vibrational state to yield relative vibrational
populations.
Ј
HCl ϭ1͒→HCl ϭ0͒, rateϭkql HCl ϭ1͒ ,
͑5͒
in which kI ϭk ϫ H S is the pseudo-first-order rate coef-
͑v ͑v ͑v
͓
͔
J
v
͓
͔
2
1
1
Figure 5 shows representative temporal profiles of
ficient and kq1 and kq2 are rate coefficients of vibrational
quenching. Typically we fit the later portion of temporal pro-
files with a single exponential decay to derive estimates of
kq1 and kq2 , followed by fitting both temporal profiles col-
lectively with the above model by keeping both kq1 and kq2
invariant to derive estimates of Cl ͑relative value͒, kI1 and
␥2 /␥1 . Finally these five parameters were further optimized
to provide the best fit. Values of kI1 , ␥2 /␥1 , kq1 , and kq2
thus derived under various experimental conditions are listed
in Table II; we report an average value of ␥2 /␥1ϭ0.143
HCl( ϭ1) and HCl( ϭ2) obtained upon photolysis of a
v
v
flowing mixture containing S2Cl2 ͑0.045 Torr͒, H2S ͑0.043
Torr͒, and Ar ͑1.09 Torr͒. We fit both temporal profiles col-
lectively with a commercial kinetic modeling program
FACSIMILE29 according to a model containing the follow-
ing reactions:
͓
͔
0
ClϩH S→HCl ϭ1͒ϩHS, rateϭkI1 Cl ,branching ␥ ,
͑v
͓
͔
2
1
͑1a͒
ClϩH S→HCl ϭ2͒ϩHS, rateϭkI1 Cl ,branching ␥ ,
͑v
͓
͔
Ϯ0.009, corresponding to a product ratio HCl( ϭ2) /
͓
v
͔
2
2
͑1b͒
HCl( ϭ1) . Our observed value is greater than a value
͓
v
͔
␥2 /␥1ϭ0.07 reported by Braithwaite and Leone who used
filters to distinguish populations of separate vibrational
states.15
HCl ϭ2͒→HCl ϭ1͒, rateϭkq2 HCl ϭ2͒ ,
͑v ͑v ͑v
͑4͒
͓
͔
Previous work3,14 used a ratio HCl( ϭ0) / HCl(
͓
v
͔ ͓
v
ϭ1) ϭ0.6, estimated by a surprisal analysis based on an
͔
experimentally observed value of HCl( ϭ2) / HCl(
͓
v
͔ ͓
v
ϭ1) ϭ0.40 for the reaction30,31
͔
ClϩHBr→HCl ϭ1,2͒ϩBr,
͑v
͑6͒
because reaction ͑6͒ has an exothermicity and a ratio of
atomic masses involved similar to those of reaction ͑1͒. If
this value is used, the vibrational distribution of HCl in re-
action ͑1͒ becomes 34:58:8; consequently the average vibra-
tional energy is 25.4 kJ molϪ1. Because the ratio HCl(
͓
v
ϭ2) / HCl( ϭ1) ϭ0.14 observed for reaction ͑1͒ is much
͔ ͓
v
͔
smaller than the value of 0.40 observed for reaction ͑6͒, we
are uncertain about such an estimate of HCl( ϭ0) .
͓
v
͔
The population of ϭ0 is typically estimated with sur-
v
prisal analysis based on an observed vibrational distribution
for у1. However, in this work, such an analysis has large
v
errors because only two data points are available. Hossen-
lopp et al.22 used time-resolved infrared diode laser absorp-
tion spectroscopy to probe DCl product from reaction ͑2͒ and
FIG. 5. Temporal profiles of HCl ( ) recorded after photolysis of a flowing
mixture of S2Cl2 ͑0.045 Torr͒, H2S ͑0.043 Torr͒, and Ar ͑1.09 Torr͒ with a
v
determined a vibrational distribution of ͓DCl͑ ϭ0͔͒:͓DCl͑
v
v
XeCl excimer laser at 308 nm. ͑A͒ HCl( ϭ1), ͑B͒ HCl( ϭ2).
ϭ1͔͒:͓DCl͑vϭ2͔͒ϭ33Ϯ7:56Ϯ7:11Ϯ3. They carried out a
v
v
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4234
J. Chem. Phys., Vol. 119, No. 8, 22 August 2003
Chen, Cheng, and Lee
TABLE II. Experimental conditions and fitted rate coefficients and branching ratios for the reaction ClϩH2S
→HCl( ,J)ϩHS.
v
Expt. No.
PH S /mTorr
1
2
3
4
Average
17
46
1110
88
3.4
9.8Ϯ0.7
7.5Ϯ0.8
23.0Ϯ1.9
4.2Ϯ0.4
25
45
1090
88
3.4
10.5Ϯ0.6
9.5Ϯ0.7
28.6Ϯ2.0
3.5Ϯ0.3
33
44
1070
79
3.1
10.7Ϯ0.6
10.9Ϯ1.0
36.1Ϯ2.8
3.4Ϯ0.3
43
45
1090
88
3.4
10.3Ϯ0.5
10.5Ϯ1.0
49.1Ϯ3.5
3.5Ϯ0.3
2
PS
P
/mTorr
Cl
2
A2r /mTorr
laser fluence /mJ cmϪ2
% S2Cl2 photolyzed
k
q1/103 sϪ1
kq2/103 sϪ1
kI1/103 sϪ1
k1/10Ϫ11 cm3
moleculeϪ1 sϪ1
␥2 /␥1
3.7Ϯ0.4
0.148
0.152
0.135
0.135
0.143
Ϯ0.013
Ϯ0.010
Ϯ0.011
Ϯ0.010
Ϯ0.009
surprisal analysis for two models. For a model assuming that
available energy does not distribute into vibration of DS
͑cold-DS model͒ with a prior function
and Setser,3 but slightly greater than the value of 0.28 when
the same ratio, HCl( ϭ0) / HCl( ϭ1) ϭ0.8, is em-
͓
v
͗ ͘
͔ ͓
f ϭ0.12 is much greater than the
r
v
͔
ployed. Our value of
value 0.065 reported previously ͑using a revised available
P0 f ͒ϭ 1Ϫf ͒3/⌺ 1Ϫf ͒3,
͑7͒
͑
͑
͑
energy͒,14 but is consistent with other similar reactions in-
v
v
v
volving Cl or F atoms, with f in the range 0.13–0.19.3
in which fv is the ratio of the DCl vibrational energy to the
total available energy,
͗ ͘
r
We performed calculations to locate structures of transi-
tion state for the reaction ClϩH2S with the B3LYP/aug-cc-
pVTZ density functional theory32,33 using the Gaussian 98
program.34 Geometries of transition state and displacement
vectors corresponding to imaginary vibrational wave num-
bers predicted with the B3LYP method are shown in Fig. 6.
This transition structure has a H–Cl bond length of 1.619 Å,
smaller than a value of 1.65 Å previously report by Wilson
ln P f ͒/P0 f ͒ ϭϪ0.83ϩ4.6f
͓ ͑
v
͑8͒
͑
͔
v
v
was derived. The surprisal plot for a model with an assump-
tion that vibrational energies of both DCl and DS are statis-
tically distributed ͑warm-DS model͒ with a prior function
5/2
P0 fЈ͒ϭ 1ϪfЈ͒5/2/⌺ 1ϪfЈ͒
,
͑9͒
͑
͑
͑
v
v
v
and Hirst,25 who employed the MP2(full)/6-311G method
in which fЈ is defined as the sum of vibrational energies of
**
v
DCl and DS divided by the total available energy, does not fit
as well as the cold-DS model; this is consistent with experi-
mental observation of little vibrational excitation of DS.22
We assume that the surprisal plot is the same for reac-
tions ͑1͒ and ͑2͒ and estimated the vibrational distribution of
to predict the transition structure; molecular parameters re-
ported by them are listed parenthetically in Fig. 6 for com-
parison. Predicted vibrational wave numbers for the transi-
tion state are 98, 214, 407, 1206, 2679, and 953.7i cmϪ1
.
The dynamics for H abstraction by Cl atoms are ex-
pected to be dominated by consequences of the heavy–light–
heavy mass combination.2 The kinematic effect of the Cl–
H–S mass combination is more important than details of the
potential surface in determining the internal energies of HCl.
The small internal energy of the radical fragment HS is con-
sistent with rapid motion of the reacting H atom, which
leaves without interacting with the remainder of the radical
fragment.
HCl( ) for ϭ0–2 from corresponding values of f . The
v
v
v
normalized vibrational distribution of HCl for ϭ0–2 is
v
approximately 40:50:10 based on the cold-HS model. Using
the estimated ratio of HCl( ϭ0) / HCl( ϭ1) ϭ0.8, we
͔ ͓
͓
v
v
͔
derive a vibrational distribution of 41:52:7, which yields an
average vibrational energy of 22.7 kJ molϪ1 for HCl. Con-
sidering possible errors associated with experimental mea-
surements and estimate of the population of HCl( ϭ0), we
v
report an average vibrational energy of 23Ϯ4 kJ molϪ1 for
HCl. This value is within experimental uncertainties of a
previously reported value of 22 kJ molϪ1 that used HCl(
If the modified impulse model is valid, rotational ener-
gies can be predicted according to the equation
͓
v
E ϭ m m / m ϩm ͒ m ϩm ͒ Eavail sin2 ␣
͑10͒
ϭ0) / HCl( ϭ1) ϭ0.6;3 an average vibrational energy of
͓
͑
͑
͔
S
r
Cl
S
H
Cl
H
͔ ͓
v
͔
19 kJ molϪ1 is derived if HCl( ϭ0) / HCl( ϭ1) ϭ0.8 is
͓
v
͔ ͓
v
͔
in which Eavail is the available energy and ␣ is the torque
angle between the direction of motion of H and that of the
H–Cl bond in the reaction coordinate of the transition
structure.9,10 If we use the small value of ␣ϭ1.5° calculated
for the vector of reaction coordinate based on the vibrational
motion corresponding to the imaginary frequency, little rota-
tional energy is expected for HCl from reaction ͑1͒, in con-
trast to the experimental observation. The impulse model us-
ing displacement vectors of imaginary frequencies is hence
unfit for prediction of rotational distributions of HCl pro-
duced from reaction of ClϩH2S. In contrast, if we consider
used.
C. Reaction dynamics and the transition state
of Cl¿H2S
With an available energy of 69 kJ molϪ1, the fraction of
energy that leads to vibrational excitation of HCl is
f
͗
͘
v
ϭ0.33Ϯ0.06 and the fraction of energy that leads to rota-
tional energy, f , is 0.12Ϯ0.02. The value of f is similar
͗ ͘
r
v
to that ͑0.32, using an available energy of 69 kJ molϪ1 in-
stead of 64 kJ molϪ1 that they used͒ reported by Agrawalla
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4235
J. Chem. Phys., Vol. 119, No. 8, 22 August 2003
Reaction dynamics of ClϩH2S
that these experiments were not specifically designed for ac-
curate kinetic measurements and that only a small range of
H S was employed, we report a rate coefficient k ϭ(3.7
͓
͔
2
1
Ϯ1.5)ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1 for reaction ͑1͒, with
listed uncertainties representing estimated errors.
This value is close to the small value, (4.0Ϯ0.2)
ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1, reported previously by Clyne
and Ono,17 but slightly smaller than more recent val-
ues of (7.4Ϯ1.1)ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1, reported by
Nicovich et al.21
IV. CONCLUSION
Rotationally resolved infrared emission of HCl ( ϭ1
v
and 2͒ is observed with a step-scan Fourier-transform spec-
trometer after irradiation of a flowing mixture of S2Cl2 ,
H2S, and Ar with an excimer laser at 308 nm to initiate the
reaction ClϩH2S. Average rotational energy and its fraction
of partition derived with this technique, Erϭ8.3
FIG. 6. Geometry ͑A͒ and vector displacements ͑B͒ of transition state for
the reaction ClϩH2S predicted with the B3LYP/aug-cc-pVTZ method. Dis-
placement vectors corresponding to imaginary wave numbers are shown in
solid arrows in the lower part. Bond lengths have unit of Å. Results from
Wilson and Hirst ͑Ref. 25͒ are shown in parentheses.
Ϯ1.5 kJ molϪ1 and f ϭ0.12Ϯ0.02, are much greater than
͗ ͘
r
previous reports, but consistent with those determined for
similar reactions involving Cl or F atoms. Observed vibra-
tional excitation of HCl( ϭ2) / HCl( ϭ1) ϭ0.14Ϯ0.01
͔ ͓
͓
v
v
͔
indicates slightly more excitation of HCl( ϭ2) than previ-
ously reported, with estimated fraction of energy partition
v
the geometry of the transition state and assume that breaking
the H–S bond provides the impulse, the torque angle of ␣
ϭ42.1° for HCl production yields a rotational energy ϳ30
kJ molϪ1 according to Eq. ͑10͒; this value is much greater
than our experimental value. The impulse model is sensitive
to the torque angle which is subject to large errors associated
with calculations using various methods.
into vibration, f ϭ0.33Ϯ0.06 within experimental uncer-
͗
͘
v
tainties of that reported previously. Improved temporal reso-
lution and detection sensitivity of time-resolved Fourier-
transform spectroscopy proves useful in determining
internal-state distributions of products from bimolecular re-
actions, especially in measuring nascent rotational distribu-
tions which could not be determined directly previously. We
hope that such information obtained with this technique will
stimulate more theoretical calculations and provide further
understanding on reaction dynamics of more complex sys-
tems.
Wilson and Hirst25 performed calculations on the ab-
straction path of reaction ͑1͒ and predicted a rate coefficient
of 2.8ϫ10Ϫ12 cm3 moleculeϪ1 sϪ1, much smaller than re-
ported experimental values in the range (4.0–10.5)
15–21
ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1
.
They also located an ad-
duct H2S•Cl, with Cl attaching to the S-end of H2S, for the
reaction of Cl and H2S; the bond distance of S–Cl is pre-
dicted to be 2.71 Å and there is no barrier for this path. They
proposed that the adduct H2S•Cl might play a critical role in
the reaction, and the small negative temperature dependence
is consistent with such a model. If the H2S•Cl adduct is
formed rapidly, rearrangement of the adduct to form HS and
HCl might serve as the rate-determining step. The involve-
ment of the adduct H2S•Cl would lead to greater rotational
excitation of HCl. Further theoretical studies on the potential
energy surfaces and associated reaction dynamics are needed
in order to provide more detailed information on this reaction
and to compare with experimental results.
ACKNOWLEDGMENTS
We thank the National Science Council of Taiwan ͑Grant
No. NSC91-2119-M-007-003͒ and MOE Program for Pro-
moting Academic Excellence of Universities ͑Grant No. 89-
FA04-AA͒ for support.
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