Some complexities in the reaction of hydrogen atoms generated in H2 discharge with molecular chlorine

Article abstract of DOI:10.1021/jp014385z

The kinetics of the reaction H + Cl₂ → HCl + Cl was studied in the very low-pressure reactor system at 298 K using two different H atom generation sources. No traces of HCl(v) excited product side reaction could be found in the system due to th

Full text of DOI:10.1021/jp014385z

J. Phys. Chem. A 2002, 106, 4403-4410
4403
Some Complexities in the Reaction of Hydrogen Atoms Generated in H2 Discharge with
Molecular Chlorine
Otto Dobis and Sidney W. Benson*
Loker Hydrocarbon Research Institute, UniVersity of Southern California, UniVersity Park,
Los Angeles, California 90089-1661
ReceiVed: NoVember 30, 2001; In Final Form: February 18, 2002
1
The kinetics of the reaction H + Cl2 f HCl + Cl has been studied in the very low-pressure reactor (VLPR)
system at 298 K using two different H atom generation sources. The first one is the microwave decomposition
of HCl giving k1 ) (8.66 ( 0.18) × 10-12 cm3/(molecule-s). No traces of HCl(V) excited product side reaction
could be found in the system due to the much longer residence time in the reactor than the spontaneous decay
of excited HCl. The second H atom source is the microwave decomposition of H2. This technique produces
2
5% H2(V) which initiates the reaction Cl + H2(V) f HCl + H, hydrogen atom recovery and the quenching
tr
reaction, H + H2(V) f H2 + H. They are identified by differences in the HCl and Cl yields, as well as from
the extra H2 consumption. Rate constants k2 ) (2.88 ( 0.13) × 10-11 and ktr ) (2.95 ( 0.17) × 12-12
cm3/(molecule-s) are measured along with excellent mass balances between reactant consumption and product
formation. Consideration of the high value found for ktr leads to the conclusion that its mechanism is by atom
transfer rather than collisional deactivation. Both rate constants agree well with the corresponding A-factors
reported for thermal reactions indicating that the vibrational excitation energy of H2(V) provides the activation
energies of the thermal reactions.
Introduction
The fast, exothermic reaction
These complexities involving vibrationally excited species
make it impossible to set a reliable stoichiometry for the H atom
consumption kinetics. But they can be suppressed or isolated
in specially designed experimental runs in the very low-pressure
reactor (VLPR) system.
H + Cl2 9
a8 HCl(V) + Cl -45.2 kcal/mol
It was shown earlier4 that the HCl residence time in the reactor
cell of the VLPR system is at least 20 times longer than the
spontaneous radiation decay time of HCl(V ) 1). H atoms and
especially Cl atoms may also contribute to HCl(V) quenching.
Therefore, we could never observe any traces of HCl(V) reaction4
in our system. Now using the microwave partial decomposition
of HCl for H atom generation and reacting it with Cl2, the
investigation of the pure thermal reaction
represents a very complex kinetic system to establish a reliable
thermal rate constant for this apparently simple chemical step.
Due to its broad theoretical and practical interest, a large number
of experimental studies have been devoted to this kinetic
problem without reaching consensus. In a previous report,1 we
have compiled the related experimental results (Table 1 in ref
1) which shows that the reported rate constants vary by a factor
9 by ranging from 0.39 × 10-11 up to 3.5 × 10-11 cm3/
(molecule-s). Our analysis of those data pointed out two sources
of experimental difficulties in the kinetic investigation of this
reaction:
1. The formation of the highly reactive HCl(V) product. The
first vibrational excitation state (V ) 1) has 8.2 kcal/mol extra
energy which well exceeds the 3.4 kcal/mol activation energy2
requirement for the H + HCl reaction, thereby initiating a rapid
H atom consumption in competition with HCl(V) quenching on
the short contact time scale (1-15 ms) used in fast flow
experimental systems.
H + Cl2 9
18 HCl + Cl
is established for the measurement of k1. Knowing the thermal
rate constant k1, we can substitute the HCl/H atom source by
the microwave partial decomposition of H2 and explore the
kinetic perturbations arising from the presence of H2(V) in the
same system. These are the objectives of our present experi-
mental studies.
Experimental Section
2. All flow systems used for absolute rate constant measure-
ments use the partial microwave decomposition of H2 for H
atom generation. This technique also produces excited H2(V) in
an unknown ratio3 of the initial H2 flow. It will then react with
the Cl atom product of reaction (a) invoking the chain recovery
of H atom in a presumably fast process.
The VLPR system used for the present measurements is the
same three-stage, all-turbo-pumped equipment we have used
for previous studies.1 It has been described in detail earlier.5
For a short survey of its present application, a brief summary
of the system parameters, experimental sequence, and data
processing is given in the following.
A new, thin Teflon-coated, cylindrical, thermostated flow cell
* Corresponding author.
reactor of volume Vr ) 216.5 cm3 is sealed at its bottom to the
10.1021/jp014385z CCC: $22.00 © 2002 American Chemical Society
Published on Web 04/04/2002

4404 J. Phys. Chem. A, Vol. 106, No. 17, 2002
Dobis and Benson
TABLE 1: HCl Decomposition and Recombination of Cl
Atoms Using Φ2 Orifice and an Initial Flow of [HCl]ikeHCl
5.43 × 1012 molecules/(cm3-s)
constants appearing in kinetic equations later on were calculated
according to the above formula. The stepwise switch-over of
orifices changes the values of the first-order escape rate constants
of gases which allows the variation of the reactor residence time
by a factor of 4.7.
The well-controlled gas inlet and outlet dynamics establishes
the strictly defined steady-state flow condition in the reactor
that operates in the Knudsen flow regime. The uncertainty in
flow is less than 1% and is incorporated in the overall scatter
of measured data.
The gas mixture of products and unreacted reagents leaves
the reactor cell in the form of an effusive molecular beam
through one of the selected exit orifices. This beam is chopped
by a tuning fork and further collimated by two successive
pinholes in the differentially pumped vacuum system to reduce
the background mass signal. The beam is sampled with the off-
axis mass analyzer of the quadrupole mass spectrometer and
the mass signals are fed to a phase sensitive lock-in amplifier
tuned to the chopping frequency. This chopping modulated
phase sensitive detection ensures that we are sampling species
which have not made collisions after leaving the reactor. The
measured mass ranges are repeatedly scanned, usually 20-30
times, to give a good statistical average and the mass intensities
are recorded for data acquisition. Each mass signal is corrected
for any small background value recorded prior to start-up of
mass flow.
Mass spectral calibration for a given molecular gas component
of mass M is carried out by measuring the mass signal intensity
IM as a function of the specific flux F(M) according to the
relationship IM ) RMF(M), where RM is the mass spectral
efficiency for mass M and F(M) ) flux/Vr in units of molecules/
(cm3-s). This relationship is strictly linear in the mass flow range
of our experiments. The steady-state concentration of the gas
component M in the reactor cell can then be calculated from
)
microwave
power,
W
2[Cl2]k
/
eCl2
I35/(I35 + I36) × 102,
[HCl]ikeHCl × 102,
%
[Cl2]keCl × 10-10
%
20
30
40
50
55
60
65
70
56.16 ( 0.34
56.46 ( 0.58
58.69 ( 0.29
60.12 ( 0.42
59.52 ( 0.38
60.15 ( 0.45
59.12 ( 0.10
59.85 ( 0.21
1.86
1.43
1.05
0.94
1.14
1.00
0.99
1.04
0.68
0.53
0.38
0.35
0.42
0.37
0.36
0.38
TABLE 2: Initial and Final Steady-State Concentrationsa of
Cl2 Reactant and of Cl and HCl Products in Reaction 1b
no./Φx [Cl2]0 [Cl2] [Cl] [HCl]
initial conditions
1/Φ2
2/Φ2
3/Φ2
4/Φ2
5/Φ2
6/Φ2
2.18 0.27 5.21 4.07 nos. 1-7/Φ2:
3.01 0.43 5.66 4.53
3.76 0.58 6.06 5.05
4.58 0.93 6.43 5.32
5.64 1.32 6.92 5.73
9.82 4.42 7.64 6.46
[HCl]i ) 6.61
102 I35/(I35 + I36) ) 59.12 ( 0.10%
[Cl]0 ) 3.86
[HCl]0 ) 2.70
[H]Cl )0.65c
7/Φ2 12.88 7.27 7.81 6.77
8/Φ3
9/Φ3
0.70 0.18 2.51 1.63 nos. 8-15/Φ3:
1.13 0.32 2.72 1.88 [HCl]i ) 3.44
10/Φ3 1.57 0.47 2.96 2.09
11/Φ3 2.06 0.71 3.08 2.22
12/Φ3 2.93 1.06 3.42 2.59
13/Φ3 5.72 2.98 4.03 3.20
14/Φ3 8.45 5.04 4.23 3.41
15/Φ3 11.58 8.45 4.40 3.55
102 I35/(I35 + I36) ) 63.27 ( 0.27%
[Cl]0 ) 2.14
[HCl]0 ) 1.26
[H]Cl ) 0.36c
16/Φ5 0.21 0.12 1.04 0.50 nos. 16-22/Φ5:
17/Φ5 0.37 0.22 1.08 0.54 [HCl]i ) 1.42
18/Φ5 0.57 0.35 1.14 0.60 102I35/(I35+I36) ) 69.56 ( 0.23%
19/Φ5 0.85 0.53 1.24 0.66 [Cl]0 ) 0.97
20/Φ5 1.21 0.77 1.30 0.76 [HCl]0 ) 0.43
21/Φ5 2.35 1.62 1.54 0.98 [H]Cl ) 0.16c
22/Φ5 4.10 3.05 1.74 1.19
a All concentrations are in units of 1012 particles/cm3. b H atom source
is the microwave decomposition of HCl. c [H]Cl is the initial concentra-
tion of H atoms generated by HCl decomposition calculated as [H]Cl
the relation [M] ) F(M)/keM
.
Mass spectral calibration for HCl was carried out in the flow
range of (0.49-9.58) × 1012 molecules/(cm3-s) giving RM
)
(3.783 ( 0.075) × 10-11 with a negligibly small Cl/HCl
fragmentation ratio of 0.30 ( 0.11% using 20 eV electron
energy. It is almost four times more sensitive with 40 eV
spectrometry giving RM ) (1.424 ( 0.026) × 10-10, but the
fragmentation ratio is 7.59 ( 0.36% for which the measured
ICl signal intensities are corrected before converting them into
[Cl] concentrations. The Cl atom flow measurement is based
on the total balance of Cl and HCl signal intensities studied in
detail earlier using absolute mass signal intensity measurements6
which sets RCl ) RHCl within a (2% scatter.
) [Cl]0keCl/keH
.
top of the main vacuum chamber. Gas inlets are affixed on the
top of the reactor preceded by resistive capillary flow subsystems
calibrated for regulating the inlet fluxes of initial gas components
with the use of Validyne transducers. Two gas inlets are used
in the present series of measurements. One of the inlets is
connected through a detachable phosphoric acid coated quartz
discharge tube centered in the Opthos microwave generator
cavity of a McCarrol antenna before joining at the tapered
capillary inlet of the reactor cell. This feed-through is used for
a 3.8% HCl/He gas mixture inlet flow in the first series of
experiments and then for a 4.7% H2/He gas composition
controlled flow in the second series of runs. The other separate
supply line serves for a 10% Cl2/He gas mixture inlet flow that
provides the variable Cl2 reactant concentration for reaction 1
in the reactor cell.
The reactor base is seated on a Teflon-coated, rapidly
adjustable slide5 having three interchangeable escape orifices
with diameters of 0.193, 0.277, and 0.485 cm. Their use in
different runs is indicated as Φ2, Φ3, and Φ5, respectively, in
Table 2 and marked with different symbols in Figures. With
the above reactor volume Vr, the first-order escape rate constant
for any gas component of mass M is given by keM ) aφ (T/
M)1/2 s-1, where T is the absolute temperature and aφ ) 0.285
for Φ2, 0.549 for Φ3, and 1.334 for Φ5 orifices. All escape rate
The Cl2 mass spectrometry in our system is reported earlier.1
Its Cl atom fragmentation ratio of 0.67% with 20 eV and 3.56%
with 40 eV electron energy involves a second correction to the
Cl mass signal produced in reaction 1.
Mass spectral sensitivity for low masses, like those of H and
H2 is very poor. Even with 40 eV spectrometry the H atom
signal at mass 1 appears as inconclusive small traces, almost
indistinguishable from the background signal. Therefore, the
initial [H]0 concentration is derived from the HCl decomposition
as will be shown. H2 is measurable at mass 2 with low efficiency
and with relatively high scatter. Its flow calibration gives aH
2
) (6.60 ( 0.29) × 10-13 with 40 eV ionization energy.
Results
The microwave decomposition of HCl is a new method of
free atom generation in our VLPR system. Therefore, this
decomposition was studied first using Φ2 exit orifice and a

Reaction of H Atoms Generated in H2 Discharge with Cl2
J. Phys. Chem. A, Vol. 106, No. 17, 2002 4405
stepwise increase of the microwave power. The reason for using
Φ2 orifice is that wall recombination products, if any, would
likely appear at the longest residence time.
HCl initial flow of 5.431 × 1012 molecules/(cm3-s) was started
up and mass range of 35-38 repeatedly scanned recording the
signal intensities of Cl and HCl as well as their isotopes with
20 and 40 eV spectrometry. It is a regular procedure with the
start of every run to check the constancy of mass spectral
sensitivity using the known HCl flow as standard. Then the
microwave generator is turned on and its power regulated in
steps between 20 and 70 W. Mass ranges of 35-38 and 70-
74, the only new small signals of Cl2 in the spectrum, are
scanned with each power setting. The results, summarized in
Table 1, show that an almost uniform HCl decomposition of
59.6 ( 0.3% can be achieved in the microwave power range
40-70 W. In this range, only a very small part of the initial
HCl, 0.38 ( 0.02%, is converted into Cl2 product. Since the
Cl2 product ratio is somewhat higher at low microwave power,
it indicates that the Cl atom recombination occurs in the
discharge tube rather than in the reactor cell. Also, the Cl atom
recombination increases slightly with the aging of the discharge
tube. It reaches about 1% after running the microwave discharge
for 50 h. Therefore, the discharge tube is regularly recoated
with H3PO4 after 40 h service.
Figure 1. Mass flow balance between Cl atom and HCl product
formations plotted according to eq 1. Symbols of orifices for data pairs
are: O, Φ2; ∆, Φ3; 0, Φ5.
It is assumed that the HCl decomposition provides an equal
amount of H atom per Cl atom formed or HCl decomposed.
This can be tested experimentally by measuring the flow balance
of Cl2 consumption against HCl and Cl product formations in
reaction 1.
After recording the initial conditions set by the initial flow
and the microwave decomposition of HCl (see the last column
of Table 2), gradually increased flow of the 10% Cl2/He gas
composition is introduced through the second inlet which
corresponds to the [Cl2]0 initial concentrations given in the
second column of Table 2. Then the actual concentrations of
Cl2, Cl, and HCl were measured in each step using both 20 and
40 eV mass spectrometry. Their values averaged for both
electron energy measurements are given in Table 2.
Reaction 1 provides four steady-state flow equations, two for
the reactants consumed and two for the products formed:
([H]0 - [H])keH ) -∆[Cl]keCl ) -∆[HCl]keHCl
)
∆[Cl2]keCl ) k1[H][Cl2] (1)
2
Note that both Cl and HCl products increase with the progress
of reaction 1, so their changes are negative according to the
convention ∆[Cl] ) [Cl]0 - [Cl] and ∆[HCl] ) [HCl]0 - [HCl].
The mass balance between Cl and HCl products is presented in
Figure 1. The good equality found suggests that the average of
product formation as (∆[Cl]keCl + ∆[HCl]keHCl)/2 can be used
further on. It takes account for the overall scatter of product
formation. The balance between Cl2 reactant consumption and
product formation is shown in Figure 2. These Figures represent
an excellent mass balance based exclusively on reaction 1.
Expressing the H atom concentration from the last equality
Figure 2. Mass flow balance between Cl2 consumption and Cl + HCl
product formations in reaction 1 plotted according to eq 1. Symbols of
orifices are the same as in Figure 1.
initial H atom concentration. Note that both the Cl atom and
HCl concentrations are increasing with the progress of reaction
1. Therefore, their changes are negative by the convention [X]0
- [X] ) ∆[X], where X is either Cl or HCl. The plot of
measured data according to eq 2 is presented in Figure 3.While
the evaluation of k1 shows good agreement within the scatters
for all three orifices, the obtained [H]0 concentrations are
somewhat higher than calculated from the initial [Cl]0 concen-
trations given in the last column of Table 2. The [H]0 - [H]Cl
differences are: 7.22 × 1010 for Φ2, 7.37 × 1010 for Φ3, and
7.03 × 1010 atoms/cm3 for Φ5 orifices. It indicates that our
experimental system has a small, permanent, background H atom
concentration calculated as [H]b ) [H]0 - [H]Cl ) (7.2 ( 0.2)
× 1010 atoms/cm3 which is independent of the exit orifice size
in eq 1 as [H] ) ∆[Cl2]keCl /k1[Cl2] and substituting it into the
2
first equality of H atom consumption, a steady-state kinetic
equation for the relative Cl2 consumption in the function of
product formation is obtained as
∆[Cl2]
k1 ∆[Cl]keCl + ∆[HCl]keHCl
keCl ) k1[H]0 +
(2)
(
)
2
keH
2
[Cl2]
where the slope is proportional to k1 and the intercept to the

4406 J. Phys. Chem. A, Vol. 106, No. 17, 2002
Dobis and Benson
Figure 3. Relative Cl2 consumption vs the average of Cl and HCl
product formation plotted according to eq 2. Symbols of orifices are
the same as in Figure 1. The slopes and intercepts are proportional to
k1 cm3/(molecule-s) and [H]0 atoms/cm3, respectively. Evaluation give
k1 ) (8.64 ( 0.38) × 10-12 and [H]0 ) (7.24 ( 0.33) × 1011 for Φ2,
k1 ) (8.71 ( 0.89) × 10-12 and [H]0 ) (4.36 ( 0.19) × 1011 for Φ3,
and k1 ) (8.81 ( 0.54) × 10-12 and [H]0 ) (2.34 ( 0.15) × 1011 for
Φ5 measurements.
Figure 4. Relative Cl2 consumption vs the H atom concentration
plotted according to eq 2a. The slope gives k1 directly. Symbols of
orifices are the same as in Figure 1.
TABLE 3: Initial and Final Steady-State Concentrationsa of
Reactants and Products in Reactions 1-3; H Atom Source Is
b
the Microwave Decomposition of H2
and is present only when the microwave discharge is on. This
background H atom concentration originates from the decom-
position of the H3PO4 coat of the discharge tube.1 Depending
on the orifice size used, it constitutes 10-30% of the initial H
atom concentration.
With the knowledge of the above corrected initial H atom
concentrations, the rate constant k1 can now be recovered from
the relationship of the relative Cl2 consumption with the actual
H atom concentration:
(IiH - I0H )/
(IiH - IH )/
2
2
no. [Cl2]0 [Cl2] [HCl] [Cl] [H2]0
2 Ii
[H2]
2 Ii
H2
H2
1
2
3
4
5
6
7
8
9
0.98 0.31 0.85 0.50 1.23
1.13 0.35 0.94 0.63 1.10
1.57 0.53 1.20 0.87 1.05
2.06 0.75 1.49 1.13 1.05
2.61 1.03 2.00 1.69 0.98
2.93 1.14 2.05 1.69 1.10
5.72 2.81 3.92 3.54 1.05
8.82 5.72 5.99 5.51 0.98
11.58 10.61 7.92 7.28 1.23
0.420
0.477
0.505
0.505
0.534
0.477
0.505
0.534
0.420
0.477
0.534
1.18
1.08
1.02
0.99
0.93
1.07
1.02
0.95
1.16
1.02
0.92
0.440
0.490
0.517
0.529
0.561
0.495
0.519
0.549
0.449
0.515
0.566
∆[Cl2]
∆[Cl]keCl + ∆[HCl]keHCl
2keH
10 15.09 19.88 10.23 9.50 1.10
11 17.95 32.82 11.62 10.77 0.98
keCl ) k1 [H]0 +
(2a)
(
)
2
[Cl2]
a [Cl2] final state concentration is in unit of 1011 molecules/cm3. All
other concentrations are in units of 1012 particles/cm3. b Initial H2 flow
(without running the microwave discharge) corresponds to [H2]i ) 2.11
The plot of experimental data according to eq 2a is presented
in Figure 4. Measurements made with all three exit orifices lead
to a good uniform straight line whose slope gives
× 1012 molecules/cm3, its mass signal intensity is IiH
.
2
HCl is formed and/or a small part of Cl product is converted to
HCl.
k1 ) (8.66 ( 0.18) × 10-12 cm3/(molecule-s)
Neglecting the above deviation and employing eq 2 for the
kinetic presentation of data given in Table 3, a curved
relationship shown with broken line in Figure 7 is obtained. It
clearly indicates that the kinetics cannot be described by a single-
step reaction mechanism attributed to eq 2. At the same time,
Figure 7 illustrates some sources of variances in k1 values found
in the literature. The slope determined by the first six points,
where conditions [H]0 g [Cl2]0 prevails, gives k1 ) (2.9 ( 0.5)
× 10-11 cm3/(molecule-s). This value is in agreement3 with k1
) (3.5 ( 1.2) × 10-11 and (3.0 ( 1.6) × 10-11 cm3/(molecule-
s)7 measured under the conditions of high H/Cl2 ratios. On the
other hand, the slope determined by the last three data points,
where the initial conditions are [Cl2]0 > [H]0, gives k1 ) (1.0
( 0.1) × 10-11 cm3/(molecule-s) approaching the low k1 value
derived from the former experimental technique.
In the second series of experiments, the H atom generation
is replaced for the microwave decomposition of H2 using a 4.7%
H2/He gas composition flowing through the discharge tube.
These experimental runs are carried out with a permanent initial
flow of H2 which corresponds to [H2]I ) 2.111 × 1012
molecules/cm3 in the reactor cell using Φ3 orifice. The
microwave decomposition of H2 is less effective than that of
HCl. It is 42.0-53.4% in the microwave power range of 50-
70 W. The measured concentrations of reactants and products
are summarized in Table 3, where Cl2, Cl, and HCl concentra-
tions are the averages of 20 and 40 eV mass spectrometry, while
H2 concentrations are measured with 40 eV only.
Analysis of mass flow balances indicates that the Cl2
consumption is in good accordance with Cl and HCl product
formation presented in Figure 5. Nevertheless, the HCl and Cl
products shown in Figure 6, exhibit some deviation from
equalty. Due to hitherto unknown side reactions, some extra
The results shown in Figures 6 and 7 require a multistep
reaction mechanism which takes account of the Cl < HCl
product formation and the extra H2 consumption with the

Reaction of H Atoms Generated in H2 Discharge with Cl2
J. Phys. Chem. A, Vol. 106, No. 17, 2002 4407
Figure 5. Mass flow balance between Cl2 consumption and Cl + HCl
product formation using H2 decomposition for H atom source.
Figure 7. Relative Cl2 consumption vs the average of Cl and HCl
formation plotted according to eq 2.
is k3 ) 1.6 × 10-14 cm3/(molecule-s), while that for the
backward reaction9 is k-3 ) 4.1 × 10-14 cm3/(molecule-s). The
equilibrium constant: K-3 ) 2.5 is very well-known. Excited
H*2 products with high vibrational levels, V > 1, are produced
in a very small ratio10 in the microwave discharge and rapidly
relaxed to V ) 1. H2(V)1) is a long-lived excited state. Its
quenching is slow with molecular colliders. Even with HCl, it
has a rate coefficient11 of 4 × 10-14 cm3/(molecule-s) and about
3 orders of magnitude less12 with H2. But H atom is found to
be an effective collision partner13 through H atom exchange
reaction with a rate constant of (5.2 ( 0.2) × 10-12 cm3/
(molecule-s).
The above extended mechanism provides the following
steady-state equations for reactant consumption and product
formations. For HCl formation:
[HCl]keHCl ) (k1[Cl2] - k-3[HCl])[H] +
(k2[H*2] + k3[H2])[Cl] (3)
Figure 6. Mass flow balance between HCl and Cl product formations
using H2 decomposition for H atom source.
For Cl consumption:
[Cl]keCl )(k1[Cl2] + k-3[HCl])[H] -
(k2[H*2] + k3[H2])[Cl] (4)
progress of reaction 1 shown in columns 8 and 9 of Table 3. In
principle, both deviations could be described by the Cl atom
reaction with undecomposed H2, but, with ground state thermal
H2, this reaction is slow and makes only a small part of
corrections to the kinetics. Vibrationally excited H*2 formed in
the microwave discharge has a long life span12 and enhanced
reactivity with Cl. The following reactions are thus added to
eq 1:
For Cl2 consumption:
∆[Cl2]keCl ) k1[H][Cl2]
(5)
(6)
2
For H*2 consumption:
∆[H*2]keH ) (k2[Cl] + ktr[H])[H*2]
H*2 + Cl 9
28 HCl + H
2
3
H2 + Cl T HCl + H
For H2 consumption:
tr8 H2 + H
∆[H2]keH ) (k2[H*2] + k3[H2])[Cl] - k3K-3[H][HCl] (7)
H*2 + H
9
2
The rate of reaction 2 is unknown. Equilibrium 3 is a well-
established process. The rate constant for the forward reaction8
where ∆[H2] ) [H2]0 - [H2], the difference of data of columns
6 and 8 in Table 3.

4408 J. Phys. Chem. A, Vol. 106, No. 17, 2002
Dobis and Benson
Figure 9. Kinetics of H2(V ) 1) + Cl reaction derived from the total
mechanism of reactions 1-3 and the energy transfer process. Data
are plotted according to eq 11a using the optimalized ratio of k1/ktr )
0.34. The slope is directly proportional to -1/k2 and the intercept is
2[H2](V ) 1)]0keH
.
2
For practical computational treatment, this complex equation
can be written in the short form:
Figure 8. H2 consumption in reactions 2 and 3 plotted according to
eq 10.
1
k2
The steady-state concentrations, which are not measurable
directly, like H*2, can be derived from eqs 3 and 4:
A ) 2[H2*]0keH
-
B × A/[Cl]
(11a)
2
where A and B are the obvious sets of constants and variables
given in eq 11. Its linear form would permit the calculation of
k2 as the inverse of the slope and of the initial [H*2]0
concentration from the intercept.
For numerical calculations of A and B, the data of Table 3,
k1 measured in the first series of experiment (shown in Figure
4), as well as k3 and K-3 values8,9 are used. Since the ratio of
ktr/k1 is a significant factor of linearity and the referred13 ktr
value does not fit precisely to that requirement, eq 11 was
subjected to linear regression by varying ktr/k1 between 0.2 and
0.6. The best fit is obtained with
[HCl]keHCl - [Cl]k
2k2[Cl]
[HCl]
[Cl]
[H2*] )
eCl + K-3[H]
- [H2] (8)
(
)
and H from the rearrangement of eq 5:
∆[Cl2]keCl
2
[H] )
(9)
k1[Cl2]
Substituting eqs 8 and 9 into eq 7 a flow balance equation
[HCl]keHCl - [Cl]keCl
∆[H2]keH
)
(10)
ktr/k1 ) 0.34 ( 0.02
2
2
which yields the rate constant of the vibrational energy transfer
process to
is obtained. The corresponding data of Table 3 are plotted
according to this equation in Figure 8.
Due to small changes (the order of 1011) in flow rate
differences and the low efficiency of H2 mass spectrometry,
the relatively large scatter ((16%) is anticipated. The slope is
consistent with the H2 consumption and the extra HCl formation.
Note that the origin is a valid point on this line.
Multiplying eq 6 by two and substituting H*2 and H
concentrations from eqs 8 and 9, a general steady-state kinetic
equation can be derived in the form:
ktr ) (2.95 ( 0.17) × 10-12 cm3/(molecule-s)
Using the above ratio for the calculation of B and plotting
the data according to eq 11, the linear relationship presented in
Figure 9 is obtained. The intercept corresponds to
[H*2]0 ) (1.06 ( 0.02) × 1011 molecules/cm3
which is 5% of the [H2]i initial concentration. The slope gives
k2 ) (2.88 ( 0.13) × 10-11 cm3/(molecule-s)
[HCl]keHCl - [Cl]keCl
∆[Cl2]keCl
+
2k3 K-3
2[HCl] - [H2][Cl] ) 2[H2*]0keH
-
(
)
2
k1[Cl2]
which indicates that reaction 2 is 1800 times faster than reaction
3 at room temperature.
∆[Cl2]keCl
ktr
[HCl]keHCl - [Cl]keCl
1
×
2 + keH
+
(
){
2
k2 k1
[Cl2]
[Cl]
Discussion
∆[Cl2]keCl
k1[Cl2]
[HCl]
[Cl]
2
The microwave decomposition of HCl proved to be the most
appropriate H atom source to investigate the kinetics of reaction
2k3 K-3
×
- [H2] (11)
(
)}

Reaction of H Atoms Generated in H2 Discharge with Cl2
J. Phys. Chem. A, Vol. 106, No. 17, 2002 4409
1 in our VLPR system. The equal distribution of Cl and HCl
products shown in Figure 1 excludes any involvement of excited
HCl(V) side reaction. This is in accordance with rapid and
complete relaxation of HCl(V) in our reaction system due to its
relatively long reactor residence time: 0.26-1.22 s. The H atom
concentration is too low to measure directly, but its change can
be calculated from the flow balance eq 1 as shown in Figure 2.
Its initial concentration [H]0 be calculated from eq 2 as shown
in Figure 3.
by eq 2 in that wide range of initial conditions as shown in
Figure 7. However, the point-by-point differentiation of this
curve reproduces the entire range of k1 values reported from
investigation employing the same H2 decomposition technique
(see Table 1 of ref 1).
Kinetic perturbation by side reactions has long been recog-
nized and several attempts were made to find the exact
stoichiometry of that complex mechanism. Mass balance equa-
tion ∆[H] + ∆[H2] ) ∆[Cl2] found3 can also be derived for
our system in the form ∆[H]keH + ∆[H2]keH ) ∆[Cl2]keCl by
To obtain measurable signal intensities at m/e ) 1, high H
atom concentrations, the order of 1014-1016 atoms/cm3 would
be needed,14 which is outside the Knudsen flow limit of our
system. Therefore, [H]0 e 7.24 × 1011 atoms/cm3sincluding
the small background H atom concentrationswas used.
The initial reactant concentration ratios [Cl2]0/[H]0 were varied
from 0.9 up to 26.7. In this wide range, the H atom consumption
varies between 0.5 × 1011 and 5 × 1011 atoms/cm3. These
changes well describe the kinetics of reaction 1 according to
eq 2a as displayed in Figure 4. All measured data points fit one
line regardless of the exit orifice size. The measured rate
constant k1 is 10% lower than we had reported1 earlier, where
the H atom reactant was supplied by the background H atom
concentration alone. That permitted us to make measurements
only in narrow ranges of both the H atom and Cl2 concentrations.
The k1 value represents a relatively slow rate for reaction 1.
Combining it with our estimated1 A1 ) (1.6 ( 0.6) × 10-10
cm3/(molecule-s), it gives 1.8 kcal/mol for the activation energy.
The microwave decomposition of HCl also has a prospective
advantage for the kinetic investigation of radical cracking
reactions. This method generates both H and Cl atoms.
Substituting Cl2 flow for C2H6, C2H5 radicals are formed in the
reaction Cl + C2H6 f HCl + C2H5 which then further react
with H atoms establishing the H + C2H5 f 2CH3 cracking
reaction. The H + C2H6 f H2 + C2H5 side reaction is
insignificant at 298 K. Preliminary experimental results show
significant CH3 radical formation at m/e ) 15. Introducing Cl2
as a third component flow into the reactor, CH3 radicals are
partially converted into CH3Cl recorded at m/e ) 50 and 52
MS. Although the initial H and Cl concentrations cannot be
varied independently, this is the only method known so far
which permits the kinetic investigation of the ethyl radical
cracking reaction at room temperature.
2
2
combining eqs 5 and 7 with the steady-state flow equation of
H atoms. But it is actually equivalent to the overall flow balance
presented in Figure 5. It is not an explicit indicator of the side
reactions. Rather the difference between HCl and Cl product
distributions shown in Figure 6 and its direct connection to H2
consumption according to eq 10 are the direct consequences of
an extended mechanism. The work of Ambidge et al.17 takes
into account the H + HCl(V) side reaction only. Since the
residence time of their system is short (<8 ms) and [Cl2]0/[H]0
ratios are low, reaction 4 is probably the most significant side
reaction. They report17 k1 ) (7.7 ( 2.2) × 10-12 cm3/(molecule-
s) at room temperature. Within this large scatter, it agrees with
our present k1 value.
No rate measurement for reaction 2 is reported in the
literature. Our measured rate constant shows that this reaction
is 1800 times faster than the thermal reaction 3. Also, our k2
value is within the range of reported9,10,18 A3-factors range from
2.4 × 10-11 to 3.7 × 10-11 cm3/(molecule-s). This indicates
that the 12.6 kcal/mol (4400 cm-1) excitation energy of H2(V
) 1) provides the 4.4-4.6 kcal/mol activation energy of the
thermal reaction 3.
The initial concentration of H2(V ) 1) is small. It represents
only 5% of [H2]i. This ratio is close to the ∼4% value10
estimated from the shift in the Lyman absorption bands of H2.
Reaction 2 is a considerable source of H atom recovery and of
extra HCl product formation.
Rate constant derived for the H + H2(V ) 1) energy transfer
reaction is lower by 40% than that reported13 in the literature.
But our rate constant ktr ) (2.95 ( 0.17) × 10-12 cm3/(molecule-
s) is derived independently from the thermal rate of the above
H atom exchange reaction, while the earlier data13 is bound to
one of the reported19 kH ) 5.6 × 10-10 exp[(-8300 ( 400)/
RT] values for the H + H2 thermal reaction. Despite numerous
experimental and theoretical efforts, there is no consensus on
the rate parameters of this thermal H atom exchange reaction.
Theoretical calculation according to the variational transition
theory combined with quantum dynamic coupling for accurate
Earlier applications of HCl decomposition for H atom source
have used 60Co γ-radiolysis15 of gaseous HCl and the photolysis
of HCl using 184.9 nm wavelength of a low-pressure Hg lamp.16
Both made measurements of k1 relative to the H + HCl f H2
+ Cl reaction. The reported k1/k-3 values are 115 and 93,
respectively. Taking the value9 of k-3 for the absolute rate
calculation, k1 ) 4.7 × 10-12 and 3.8 × 10-12 cm3/(molecule-
s) are obtained. They are the lowest values reported for k1.
The microwave decomposition of H2 generates a complicated
reaction system. In our case it involves reactions 1, 2, equilib-
rium 3, and the energy transfer reaction H*2 + H. In fast flow
systems, where the contact time is around 2-15 ms, reaction
account for tunneling in the 200-300 K range20 gives kH
)
(3.61 ( 1.24) × 10-12 exp[(-4940 ( 160)/RT] cm3/(molecule-
s). Comparison of our ktr rate constant with that theoretical kH
value shows that the H exchange reaction is 3300 times faster
with H2(V ) 1) than with thermal H2 at room temperature. The
value of the AH-factor is in good agreement with our ktr which
indicates that the H2(V ) 1) excitation energy provides the entire
activation energy requirement for the H + H2 exchange process.
H + HCl(V) 9
48 H2 + Cl
Both reaction 2 and the energy transfer process occur with
the participation of the excited H2(V ) 1). There are no other
product formation channels, that is no branching that would be
affected by the excitation. The rate constants are in good
agreement with the A-factors of the corresponding thermal
processes. It indicates that Evib is effective in providing the
activation energy, Ea, determined for the thermal reactions; Ea
- REvib ) 0. With the reasonable assumption that Av ) A,
the vibrational efficiency factor can be calculated21 as R )
has to be included. The number of rate constants involved, as
well as unknown concentrations of H*2 and HCl(V) reactants
create immense technical difficulties for a precise kinetic
investigation.
In our experiments, the initial concentration ratios of reactants
[Cl2]0/[H]0, where [H]0 ) 2([H2]I - [H2]0)keH /keH + [H]b, are
2
varied from 0.74 up to 10.78. The kinetics cannot be described

4410 J. Phys. Chem. A, Vol. 106, No. 17, 2002
Dobis and Benson
RT ln(kv/k)/Evib which gives R2 ) 0.36 and Rtr ) 0.38. Since
R2 ≈ Rtr, it indicates that the energy transfer reaction occurs
rather via H atom exchange than collisional deactivation.
Acknowledgment. Acknowledgment is made to the donors
of the Petroleum Research Fund administered by the American
Chemical Society, for the support of this research. We are also
indebted to Professor Irving S. Reed of the Electrical Engineer-
ing Department at USC for a gift in support of the present work.
Conclusions
Microwave decomposition of HCl is the most convenient
method of H atom generation for the kinetic investigation of
reaction 1 in the VLPR system. The relatively long residence
time ensures the complete relaxation of excited HCl(V) product
reducing thereby the reaction mechanism to the single-step
thermal process of H + Cl2. Wide range changes in reactant
concentrations as well as residence time alterations provide an
accurate rate constant measurement for k1 ) (8.66 ( 0.18) ×
10-12 cm3/(molecule-s) at 298 K, in good agreement with total
mass balance changes. Investigation performed under real
second-order kinetics also permits the exact determination of
the small background concentration of H atoms, [H]b ) (7.2 (
0.2) × 1010 atoms/cm3, arising from the operation of the H3PO4
coated microwave discharge tube.
Due to the dual H and Cl atom generation, this method has
a prospective kinetic application for the investigation of ethyl
radical cracking by initiating both the Cl + C2H6 f HCl +
C2H5 and H + C2H5 f 2CH3 reactions in our system.
H atom generation by the microwave decomposition of H2
introduces a number of complexities. 5% of the initial H2
concentration is converted into H2(V ) 1) starting up therewith
the reaction 2 in competition with the energy transfer quenching
reaction H + H2(V ) 1). Neglecting these side reactions, the
kinetics of reaction 1 cannot be described by a single-step
mechanism. But, as shown in Figure 7, such simplification
reproduces the entire range of reported k1 values derived from
measurements with the use of the same H atom generation
technique.
References and Notes
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(3) Stedman, D. H.; Steffenson, D.; Niki, H. Chem. Phys. Lett. 1970,
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(4) Dobis, O.; Benson, S. W. J. Phys. Chem. 1995, 99, 4986.
(5) Dobis, O.; Benson, S. W. Int. J. Chem. Kinet. 1987, 19, 691.
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Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R.; Colbe, C. E.; Molina,
M. J. Chemical Kinetics and Photochemical Data for Use in Stratospheric
Modeling. Evaluation Number 12. JPL Publication 97-4, 1977. Atkinson,
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Troe, J. J. Phys. Chem. Ref. Data 1997, 26, 521.
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V. P.; Dodonov, A. F.; Lavrovskaya, G. K.; Tal’roze, V. L. Kinet. Catal.
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Using our present k1 value, the kinetics for reactions of Cl
and H atoms with excited H2(V ) 1) reactant can be resolved.
The derived rate constants are k2 ) (2.88 ( 0.13) × 10-11 and
ktr ) (2.95 ( 0.17) × 10-12 cm3/(molecule-s). Both rate
constants agree well with corresponding A-factors reported for
the thermal reactions.
(19) Gordon, E. B.; Ivanov, B. I.; Perminov, A. P.; Medvedev, E. S.;
Ponomarev, A. N.; Tal’roze, V. L. Chem. Phys. 1975, 8, 147.
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