Kinetic Study of the Reaction of Hydrogen Atoms with Molecular Chlorine at MilliTorr Pressures

Article abstract of DOI:10.1021/jp9920601

The bimolecular reaction H + Cl₂ → HCl + Cl (1) is studied in the very low-pressure reactor (VLPR) system at room temperature. Excellent mass balances are found between the Cl₂ consumption and both HCl as well as Cl product formation. This indicates that only reaction 1 occurs in the system. Its rate constant is k₁ = (0.96 ± 0.04) × 10^-11 cm³/(molecule^?s) at 298 K. Two independent estimates of the A factor give a value log A₁(298 K) = -9.80 ± 0.15 (units of cm³(molecule^?s)). Together with the measured rate constant this yields an activation energy of 1.7 ± 0.2 kcal/mol. All experimental data support a bent transition state for reaction 1.

Full text of DOI:10.1021/jp9920601

J. Phys. Chem. A 2000, 104, 777-782
777
Kinetic Study of the Reaction of Hydrogen Atoms with Molecular Chlorine at MilliTorr
Pressures
Otto Dobis and Sidney W. Benson*
Loker Hydrocarbon Research Institute, UniVersity of Southern California, UniVersity Park,
Los Angeles, California 90089-1661
ReceiVed: June 21, 1999; In Final Form: NoVember 9, 1999
The bimolecular reaction H + Cl
2
f ΗCl + Cl (1) is studied in the very low-pressure reactor (VLPR)
consumption and both HCl
system at room temperature. Excellent mass balances are found between the Cl
2
as well as Cl product formation. This indicates that only reaction 1 occurs in the system. Its rate constant is
-
11
3
k
1
) (0.96 ( 0.04) × 10
cm /(molecule‚s) at 298 K. Two independent estimates of the A factor give a
3
value log A
1
(298 K) ) -9.80 ( 0.15 (units of cm /(molecule‚s)). Together with the measured rate constant
this yields an activation energy of 1.7 ( 0.2 kcal/mol. All experimental data support a bent transition state
for reaction 1.
Introduction
15 for the absolute rate calculation is that this work measures
the thermal rate of reaction 2 at high [HCl]0/[H]0 ratios using
SF6 as a vibrational quencher. It reproduces the equilibrium
The fast, exothermic reaction
constant for Cl + H2 T HCl + H in satisfactory agreement
H + Cl f HCl(V) + Cl + 45.2 kcal/mol
(1)
2
16,17
with thermochemistry
and gives the exact value of Keq )
1
8
0
.27 in combination with the forward reaction rate at 298 K.
has been intensively studied by a number of research workers.
1
9
The use of an evaluated kinetic expression for a thermal k2
gives the same k1 values at room temperature, but higher A1
values in compensation with a higher E1.
It is an integral part of the H2 + Cl2 chain reaction system and
1
is the pumping stage of the HCl chemical laser. Since the
reaction is highly exothermic, HCl can be produced with high
2
The different analytical methods used show no correlation
with the values of k1 reported. This suggests that the discrep-
ancies may arise from the fine details of experimental systems
and the extent of possible side processes.
vibrational (V e 6) excitation and an inverted vibrational
population. This nonequilibrium energy distribution has been a
spur to theoretical studies of the molecular dynamics of this
light-heavy-heavy type, exoergic exchange reaction. The fast
rate accompanied by this exoergicity presents quite difficult
experimental problems, especially in low-pressure, fast flow
systems, where the reaction
Pressure and flow rate variations investigated in the fast flow
2
3
tube moving inlet experimental test system have resulted in
about 25% higher k1 value with high-pressure turbulent flow
than with low-pressure (e10 Torr) laminar flow measurements
(rows 12 and 13 of Table 1). All other discharge flow (DF)
measurements shown in Table 1 were carried out at low pressure
(1-7 Torr) and at V ) 15-95 m/s linear flow conditions using
H + HCl(V) f H + Cl
(2)
2
enhances the H atom consumption rate and imposes difficult
constraints on the usual use of pseudo-unimolecular reaction
conditions ([H]0 , [Cl2]0). In the H2 + Cl2 chain system,
reaction 2 represents a very fast inhibition step. This and some
other side processes, like the quenching of HCl(V) and the wall
removal of free atoms, further complicate the experimental task.
This can be seen In Table 1, where the reported experimental
kinetic parameters for reaction 1 are summarized along with
some brief characteristics of the experimental systems: H atom
generation, input reactant conditions, and analytical method. In
spite of the large experimental effort, no easy conclusions can
be made from those data. The reported rate constants at room-
temperature spread over a factor of 9. The highest values are
obtained under [H]0 > [Cl2]0 conditions which may indicate
some interference by reaction 2. Low values are obtained from
relative measurements made in static systems where the
perturbation by side reactions is expected to be unimportant.
However, the choice of a standard reference, competitive
reaction is restricted by the speed of reaction 1. Although the
rate constant measurements of the reference reaction show
considerable variation, the reason for selecting the data of ref
1
2
3
[H] < 10 atoms/cm concentrations, where the resonance
fluorescence (RF) signal of H atoms is strongly linear with its
concentration. Since no details of experiments for the H +
Cl2 reaction are available, this observation remains a puzzle.
6
,7
2
3
In our earlier publication20 we have noted that our H3PO4-
coated microwave discharge tube produces a small H atom flow
which is independent of the applied microwave power. It
maintains a low, permanent background H atom concentration,
1
0
3
on the order of 10 atoms/cm , in the reaction cell which is
too small to measure with mass spectrometry at low voltages
due to the small ionization cross section of H atoms. It was
also shown that the HCl residence time in our reactor cell is
2
1
more than 20 times longer than the average spontaneous
radiative decay time of HCl(V)1). Since the mass spectrometric
measurements of Cl2, Cl, and HCl are well established in our
22
VLPR system, this “invisible” background H atom concentra-
tion can be explored by Cl2 titration under the thermalized
conditions of VLPR. As the Cl2 consumption as well as HCl
and Cl product formation rates are measured simultaneously in
our system, they can provide pure thermal kinetic information
1
0.1021/jp9920601 CCC: $19.00 © 2000 American Chemical Society
Published on Web 01/06/2000

778 J. Phys. Chem. A, Vol. 104, No. 4, 2000
Dobis and Benson
TABLE 1: Experimental and Theoretical Kinetic Parameters for the Reaction H + Cl
2
f HCl + Cl
anal method
T, K
Aa
5.43
9.23)
3.10
5.16)
7.6 ( 2.1
14.4 ( 2.8
14.1 ( 1.2
62 ( 6
E
a
, cal/mol
k
298
a
system, conditions
ref
3
2
1
73-335
1570
(1880)
1120
(1430)
1420 ( 200
1190 ( 144
1150 ( 129
1800 ( 300
0.39
static,
[H(T)Cl/[Cl2] ∼ 0.5
rel to
H + HCl
rel to
b
(
(0.39)
0.46
(0.46)
0.70
1.94
2.04
3.00
1.83
1.70
2.13
1.60
3.50
96-296c
static,
4
b
(
[HCl]/[Cl
2
] ) 10-60
H + HCl
d
2
2
3
2
2
2
2
2
2
2
2
3
92-434
52-458
00-750
94-557
98
98
98
98
98
98
98
DF, [Cl
2
2
2
] > [H]
] . [H]
] . [H]
MS of Cl
2
, HCl; ESR of H
5
6
7
8
d
e
DF, [Cl
RF of H
d
e
DF, [Cl
RF of H
d
DF, [H] > [Cl
2
]
MS of H, Cl
esr of H, Cl
RF of H
2
d
DF, [Cl
2
2
2
2
] > [H]
9
d
e
DF, [Cl
] . [H]
] . [H]
] > [H]
10
11
12
13
23
23
14
d
DF, [Cl
UV absorbance of H
d
e
DF, [Cl
RF of H
d
DF, [H] > [Cl
2
]
MS of Cl
2
f
d
e
2.0
1.5
DF, [Cl
2
] . [H]
] . [H]
RF of H
g
d
e
DF [Cl
static,
2
RF of H
00
0.39
rel to
(
0.39)
[HCl]/[Cl
2
] ) 20-120
] > [H]
H + HClb
2
50-730
7.2 ( 0.7
(16.0)cal
1200 ( 100
(1680)cal
0.96h
34
this work
2
98
0.96 ( 0.04
VLPR, [Cl
2
MS of Cl
2
, Cl, HCl
a
A and k are in units of 10-11 cm /(molecule‚s). Absolute values of A, E, and k are calculated using kref ) (7.8 ( 1.8) × 10 exp(-3110 (
3
b
-12
-
11
d
1
67)/RT of ref 15 and kref ) 1.32 × 10 exp(-3420/RT) of ref 10 (in parentheses). c Data are limited to three steps of T. DF ) discharge flow.
e
f
g
RF ) resonance fluorescence. Measured with high pressure (60-160 Torr) turbulent flow conditions. Measured with low pressure (2-10 Torr)
h
plug flow conditions. Obtained by ab initio potential energy surface (PES) calculations.
on reaction 1 independently of any possible perturbation from
reaction 2 or other side reactions.
signals are fed to a phase sensitive lock-in amplifier tuned to
the chopping frequency. The measured mass ranges are repeat-
edly scanned, usually 20-30 times to give a good statistical
average, and the mass intensities are recorded for data acquisi-
tion. Each mass signal is corrected for its small background
value recorded prior to start-up of mass flow. The chopping
and phase-sensitive detection ensures that we are sampling
species which have not made a collision after leaving the reactor.
Mass spectral calibration for a given 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
M
Experimental Section and Results
The VLPR system used for current measurements is the
same2 three-stage, all-turbo-pumped equipment we have used
for all previous experiments. It has been described in detail
0,21
2
4
earlier. However, the system parameters, the present experi-
mental sequence, and data processing are briefly summarized
below.
The thin Teflon-coated, cylindrical, thermostated flow cell
IM ) R F(M), where RM is the mass spectral efficiency for
3
3
reactor of volume Vr ) 217.5 cm is mounted on the top of the
mass M and F(M) ) flux/V in molecules/(cm ‚s) unit. This
r
main vacuum chamber. Gas inlets are affixed on the top of the
reactor preceded by resistive capillary flow subsystems cali-
brated for regulating the 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 the 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 5% Cl2/He
gas mixture inlet flow in the first series and then for a pure He
inlet in the second series of runs. The other supply line serves
for a 10% Cl2/He gas mixture inlet flow which provides the
Cl2 reactant concentration for reaction 1 in the reactor cell.
relationship is strictly linear in the mass flow range used as is
shown in Figure 1 for Cl analysis. The steady state concentra-
2
tion of M in the reactor cell then can be calculated from the
relation [M] ) F(M)/keM
.
The mass analyzer is very sensitive for the specific flux of
-10
Cl2. The slopes in Figure 1 give RCl ) (3.018 ( 0.036) × 10
2
-10
with 40 eV and (1.009 ( 0.015) × 10
with 20 eV electron
energies. Depending on the electron energy used, Cl2 undergoes
some fragmentation which produces Cl atom signals at masses
3
5 and 37. This fragmentation ratio is presented in Figure 2 as
a function of ionizing potential. The values at the two voltages
-2
of kinetic measurements are 0.67 × 10 with 20 eV and 3.56
-2
×
10 with 40 eV. These ratios are used for making corrections
At the bottom of the reactor, the gas escape orifice of 0.277
cm diameter (marked φ3 in our earlier studies) is used. With
the above reactor volume Vr, the first-order escape rate constant
to the mass signals of Cl atoms produced in reaction 1.
In the course of experimental measurements, the Cl flow
2
using a 5% Cl /He composition is started first through the newly
2
1
/2
for any component of mass M is given by keM ) 0.546(T/M)
coated microwave discharge inlet and the mass signal intensities
-1
s , where T is the absolute temperature. The reactor cell
operates in the Knudsen flow regime. The strictly controlled
gas inlet and outlet dynamics establish the well-defined steady
state flow conditions in the reactor. The uncertainty in flow is
less than 1%.
of the Cl isotopes (at 70, 72, and 74 amu) are repeatedly
2
11
recorded. This flow corresponds to [Cl ] ) 14.31 × 10
2
0
3
molecules/cm steady state concentration in the reactor cell.
Then the microwave generator is turned on and its power is
adjusted to total dissociation of Cl observed by the disappear-
2
The gas mixture leaves the reactor cell through the exit orifice
in the form of an effusive molecular beam. 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 mass spectrometer and the mass
ance of Cl2 mass signals and their replacement by Cl atom and
HCl signals. The total balance of Cl2 decomposed and Cl +
HCl formed has been studied in detail earlier using absolute
22
mass signal intensity measurements. The experimentally found
mass conservation relations have shown a (2% scatter at most
which sets RCl ) RHCl within the same uncertainty.22

Reaction of Hydrogen Atoms with Molecular Chlorine
J. Phys. Chem. A, Vol. 104, No. 4, 2000 779
a
TABLE 2: Initial and Final Steady State Concentrations of
2
Cl Reactant and of Cl and HCl Products
[
Cl]
0
) 10.22, [HCl]
∆[Cl]b
0
) 10.16
∆[HCl]b
[Cl]
[Cl
0
) [HCl]
0
) 0
no. [Cl ]
2 0
[Cl
2
]
2
]
[Cl] [HCl]
1
2
3
4
5
6
7
3.54
5.16
7.70
2.66
4.00
6.16
8.71
0.67
0.83
1.11
1.45
1.66
1.85
1.97
0.70
0.85
1.08
1.36
1.66
1.89
2.01
2.68 0.61 0.63
4.00 0.79 0.81
6.16 1.01 1.05
8.65 1.35 1.35
14.48 1.69 1.70
18.56 1.89 1.88
24.10 2.11 2.10
10.63
16.66 14.24
21.62 18.90
27.09 24.12
a
All concentrations are in units of 1011 particles/ cm3. b ∆[X] ) [X]
0
-
[X] , where X ) Cl or HCl.
supply line, a gradually increasing flow of the 10% Cl2/He gas
composition can be introduced which corresponds to the Cl2
initial concentrations given in the second column of Table 2.
The actual concentration of Cl2 as well as the increases in Cl
and HCl concentrations were measured in each step. Because
of a relatively large HCl concentration, corrections for HCl
2
4
fragmentation were also made to the Cl atom signals.
After the Cl2 gas composition in the microwave discharge
line was replaced by pure He flow, the whole procedure was
repeated with the same steps of [Cl2]0, but with zero [Cl]0 and
[
HCl]0 initial concentrations. These results are given in the
Figure 1. Mass 70 signal intensities (in arbitrary units) of Cl
2
recorded
second part of Table 2.
at various specific flow rates of 10.00% Cl /He mixture using 20 and
2
The amounts of Cl and HCl products formed in reaction 1
are equal within an average (2% scatter and are independent
of their initial values as shown in Table 2. On combining the
steady state kinetic equations for Cl2 consumption with those
for formation of Cl or HCl, the kinetic mass balance gives the
following equalities:
4
0 V ionization energies.
∆
[Cl ]k ) ∆[Cl]keCl ) -∆[HCl]keHCl
(3)
2
eCl2
where ∆[Cl2] ) [Cl2]0 - [Cl2]. This balance is shown in Figure
indicating that the Cl2 reactant consumption and product
3
recovery according to reaction 1 is better than 97% in our
experimental system. Note that these equalities rule out any loss
of HCl by wall reactions or production of Cl by reaction 2.
With the single reaction 1 established, the steady state H atom
consumption kinetics is given by
(
[H] - [H])k ) k [H][Cl ]
0 eH 1 2
Upon substituting k1[H][Cl2] ) ∆[Cl]keCl from the steady state
kinetics of Cl formation and [H] ) ∆[Cl2]keCl2/k1[Cl2] from the
steady state kinetics of Cl2 consumption, we obtain
∆
[Cl2]
k1
k k
1 eCl
)
[H] -
∆[Cl]
(4)
0
[Cl2]
keCl2
k k
eH eCl2
Figure 2. Cl
2
fragmentation (in percentage) as a function of electron
which is a convenient form to determine both k1 and [H]0 values.
Plotting values of ∆[Cl2]/[Cl2] against ∆[Cl] according to eq
1
2
3
energy measured with 1.574 × 10 molecules/(cm ‚s) specific flow
rate of Cl . Solid circles represent average values of various flow rate
2
4
, a good linear relationship, presented in Figure 4, is obtained,
measurements calculated from the data of Figure 1.
-11
3
where rate constant k1 ) (0.96 ( 0.04) × 10 cm /(molecule‚
s) is calculated from the slope, and [H]0 ) (4.85 ( 0.11) ×
There is no Cl but always HCl signal in full mass balance
with Cl2 at the start-up of the microwave generator. Over a 1-2
h period, the Cl/HCl ratio increases until it reaches a permanent
value of about 50% which is usually maintained for about 40-
1
0
3
1
0
atoms/cm is found from the ratio of intercept to slope.
Discussion
5
0 h which is the service life of the H3PO4 coat. In the present
The presence of background hydrogen in kinetic systems
using microwave or RF discharge H atom generation is well-
known. With [H]0 , [Cl2]0 conditions, a low permanent inlet
case, the permanent ratio of ICl/(ICl + IHCl) is 0.502 from which
the initial steady state Cl concentration is calculated as [Cl]0 )
1
2
3
2
F(Cl2)ICl/(ICl + IHCl)keCl. This value, along with [HCl]0, is given
concentration of hydrogen, usually [H]o e 10 atoms/cm , can
in the first part data head of Table 2. Through the separate
be maintained by the microwave decomposition of impurities

780 J. Phys. Chem. A, Vol. 104, No. 4, 2000
Dobis and Benson
measurements. This is in sharp contrast with the moving inlet
flow systems, where under such initial conditions, pseudo-first-
order kinetics is employed.
The kinetic balance of Cl2 consumption and product forma-
tions expressed by eq 3 indicates that no wall removal of free
atoms exists in our system. The experimental evidence for the
absence of Cl atom wall recombination is the complete
dissociation of Cl2 achieved by microwave discharge. Theoreti-
cally, there are three kinds of atom removal to be considered in
the H/Cl2 reaction system:
2
Cl f Cl2
(w1)
H + Cl f HCl
H f H2
(w2)
(w3)
2
Reaction w1 is the fastest one and should be accounted for in
5
all cases when [Cl2] e [H]. Ambridge et al. have included this
surface reaction in their kinetic scheme. Reaction w2 is
2
5
considered to be fast and should be taken into account when
[
Cl2] . [H], that is, when the kinetics is measured by the loss
6
Figure 3. Mass flow balance between Cl
2
consumption and Cl atom
of H atoms. Wagner et al. neglected this surface reaction which
or HCl formation rates in the H/Cl two-component system plotted
according to eq 3. Solid circles represent the measurements with pure
He flow in the discharge tube (microwave on), while open circles denote
2
they justified by referring to the direct measurements of Spencer
and Glass. But the low kw value in the reaction system of
26
Spencer and Glass is due to the applied halocarbonwax coat.
This may hint some overshoot in the reported6 k1 value.
Similarly, the observed wall reaction rates of refs 7 and 12 can
be attributed to reaction w2. The same experimental system used
measurements started with initial conditions of [Cl] ) (10.22 ( 0.21)
0
1
1
11
3
×
10 and [HCl]
0
) (10.16 ( 0.25) × 10 molecules/cm .
12
by Michael et al. shows no wall removal of H atom by reaction
w3 when it is used for the chlorine-free kinetic study of the H
2
7
+
C2H4 f C2H5 reaction. In any case, when surface reaction
w1 is observed, (w2) should also be taken into account, but it
was omitted from the overall mechanism of Ambridge et al.5
In our Teflon-coated reactor cell, surface reactions w1 and
w2 would conflict with the linear relationships shown in Figures
3
and 4. Only the hypothetical, sole existence of reaction w3
would still preserve these linear relationships, not changing eq
, but altering eq 4 to
3
∆
[Cl2]
k1
k k
1 eCl
)
[H] -
∆[Cl]
keCl2(keH + kw3)
(5)
i
[Cl2]
keCl2
where [H]i ) [H]okeH/(keH + kw3). Equation 5 would lead to
higher k1 values and to lower values of [H]0. In our VLPR
system the absence of surface reaction w3 was tested earlier28
using the same Teflon-coated reactor cell and different exit
orifice sizes. Surface reaction w3 is the most unlikely process
in any H/Cl2 experimental system. None of the studies compiled
in Table 1 have considered it. In our system, wall reaction w3
would be expected to be accompanied by wall reaction w2. This
would upset the flow balance given by eq 3, especially in the
first series of runs, where high initial Cl concentration is used.
Regardless of the Cl2/H ratio, there are no wall reactions w1-
Figure 4. Relative Cl
plotted according to eq 4. The slope and intercept are proportional to
and [H] , respectively. Symbols of measurements are the same as in
Figure 3.
2
consumption versus Cl or HCl formation rates
k
1
0
8
w3 observed when the reactor surface is coated with boric acid,
1
0,11
23
13
phosphoric acid,
halocarbonwax, or treated with HF.
(
mostly water) of the carrier gas7,10,23 He or Ar. In our system
The sole existence of reaction 1 in our system is indicated
by the experimentally well-established mass balance expressed
by eq 3 and presented in Figure 3. Two earlier publications5
examined the experimental mass balances in the H + Cl2
this background hydrogen content can be well measured by Cl2
titration according to reaction 1. Because of the nature of the
VLPR system as used here, both the steady state initial
concentration of the hydrogen atom and rate constant k1 can be
determined in one series of experiments. This is a consequence
of the fact that, although the ratio of initial concentrations [Cl2]0/
,13
5
reaction system. Ambidge et al. found that the ∆[H]/∆[Cl2]
ratio decreases with increasing [Cl2]0/[H]0 and approaches 2
asymptotically, while ∆[HCl]/∆[H] increases with the same ratio
of reactants and approaches 1, but no Cl atom product was
detected. With high initial ratios of reactants [Cl2]0/[H]0, these
[H]0 varies between 7 and 56, the kinetics can still be measured
under real second-order conditions using absolute concentration

Reaction of Hydrogen Atoms with Molecular Chlorine
J. Phys. Chem. A, Vol. 104, No. 4, 2000 781
results lead to a chlorine balance: 2∆[Cl2] ) ∆[HCl]. Assuming
a reaction mechanism which consists of reactions 1 and 2, the
total wall recombination of Cl, and the homogeneous quenching
of HCl(V) with Cl2, a varying H atom consumption stoichiometry
TABLE 3: Transition State Entropy Calculation for the A
‡
Factor of Reaction 1 Using H + Cl
2
T [HSCl] Model
Reactiona
q
partial contributions (eu)
∆
298
S
p
(bent, 120°)
5
was deduced. Its value changes from 1 to 2 with increasing
model reaction
translation
-27.1
0.4
1.4
0.6
-0.6
0.0
[
Cl2]0/[H]0. The problem with this mechanism is that the
29
spin, electronic
rotation
quenching of HCl(V) with Cl2 is a very slow process (about 4
orders of magnitude slower than with H atom), and therefore
its rate is insignificant in the 1-8 ms reaction time scale. It
will not establish a steady state HCl(V) concentration in
S-Cl, stretch (565 cm-1), RC
H‚S, stretch (1800 cm-1)
H‚S‚Cl, bend (900 f 500 cm-1)
0.5
-18.8
5
competition with reaction 2 as claimed by the authors.
total
1
3
Stedman et al. found a consumption balance of reactants
[H] + ∆[H2] ) ∆[Cl2], where the H2 consumption arises from
a
Entropy of HSCl (S°model ) 59.6 eu) is calculated by bond
∆
37
1
1
additivity according to /
2
H
2
2 2
S + / SCl T HSCl isodesmic,hypo-
thetical reaction. b RC ) reaction coordinate.
the reaction of vibrationally excited hydrogen:
TABLE 4: Transition State Entropy Calculation for the A
Cl + H (V) f HCl + H
(6)
2
‡
Factor of Reaction 1 Using H + Cl
2
T [Cl
2
] Model
Reaction
This reaction is exothermic for V g 1, and it becomes the H
q
partial contributions (eu)
∆
298
S
p
(bent, 120°)
atom chain recovery step of the entire mechanism with an
model reaction
translation
spin, electronic
symmetry
-27.4
0.1
estimated rate constant1 of k6 ∼ 1.5 × 10 cm /(molecule‚
s) for H2(V)1) reaction. Active H2(V) is formed in the
microwave or RF discharge process30 by partial excitation of
ground electronic state H2. Its concentration may be as high as
3,19
-12
3
1.4
1.4
0.7
5.3
-0.6
0.5
0.0
rotation (2-D)
rotation (1 - D)
1
5% of the total H2 passed through the microwave discharge
Cl-Cl, stretch (565 cm 1), RCa
-
13
area. Considering the Cl atom removal, reaction 6 is now
indistinguishable from the wall recombination of Cl. Since the
only effective quencher in these fast flow systems is product
HCl, the overall mechanism is further complicated by
H‚Cl‚Cl, bend (900 f 500 cm 1)
-
-1
H‚Cl, stretch (2000 cm
)
total
-18.6
a
RC ) reaction coordinate.
H (V) + HCl f HCl(V) + H2
(7)
2
linear Arrhenius function
-
11
an energy transfer process which then enhances reaction 2. The
k1 ) (7.2 ( 0.7) × 10 exp(-1200 ( 100)/RT (8)
31
known rate constant of reaction 2 involving HCl(V)1) as
-
12
3
excited reactant is 7 × 10
cm /(molecule‚s) and 4 times
between 252 and 730 K based on optimized PES calculation
RT in cal/mol). This would exactly reproduce our experimental
rate constant at 298 K, although we have some reservations
concerning the steep angular dependence of the TS energy
barrier. It starts from a very low barrier at collinear TS geometry
Table 4 of ref 31). This function is remarkably different from
those obtained with LEPS or semiempirical ”diatomics-in-
molecule” PES calculation. The reaction free-energy criterion
used in the canonical variation theory imposes a compensation
between the Arrhenius parameters when applied to thermal rate
constant calculations.
A reliable empirical approximation of the experimental A1
factor can be performed by estimating the entropy of activation
S using the entropy change of a suitable model reaction and
3
2
higher with HCl(V)2) as reactant. Higher excitations (V > 2)
would further increase the rate of reaction 2 and, with the
contribution of energy transfer process 7, it may become a
moderate side process for H atom consumption especially under
(
[
H]0 ∼ [Cl2]0 conditions.
(
Because of the fast rate of reaction 1, all discharge flow
33
systems have to use fast linear flow velocities (∼15-95 m/s)
and short injector position displacement (∼1-15 cm) to ensure
a short contact time (∼1-15 ms). In this short time scale the
perturbations by reactions 2, 6, and 7, as well as the mixing
time of reactants, should be taken into account. These experi-
mental difficulties, together with the lack of a clear-cut reaction
mechanism, may lead to those large discrepancies presented in
Table 1 in the kinetic investigations of this apparently simple
elementary reaction. In comparison, the long residence time
35
36
q
∆
correcting it with partial entropy contributions for perturbations
and changes in the degrees of freedom:
37
(0.6-0.9 s) of the VLPR system ensures thermalized conditions
and the excellent mass balance of Cl2 consumption with Cl and
HCl product formation indicate the sole existence of reaction 1
in our system.
q
∆
S° ) (S°
- S° - S° ) +
∑∆S°(corrections)
model
H
Cl
2
(9)
The exoergic character of reaction 1 has attracted a number
of authors to perform ab initio potential energy surface (PES)
calculations. High-level, large basis set computations of the
where
33
∆S°(corrections) ) ∆S°(transl) + ∆S°(rot) +
barrier height support a 1.40-1.45 kcal/mol activation energy
with collinear or slightly bent (170°) transitions state (TS)
configuration. They also reproduce the exoergicity of the
reaction within (1 kcal/mol. With similar PES and London-
Eyring-Polanyi-Sato (LEPS) empirical surface calculations,
Gonzales et al.34 have computed thermal rate constants for
reaction 1 using the variational transition state theory with
semiclassical tunneling corrections. They found a satisfactory
∑
∆S°(vib) + ∆S°(electronic) + ∆S°(symmetry) (10)
The right side terms of eq 10 can be calculated using known
thermochemical functions. The results of such calculations are
summarized in Table 3 using the hypothetical model reaction
H + Cl2 f [HSCl] , and in Table 4 using an H atom insertion
model reaction H + Cl2 f [Cl2] . Summing up the partial
37
‡
‡

782 J. Phys. Chem. A, Vol. 104, No. 4, 2000
Dobis and Benson
contributions for corrections, the two model calculations give
the TS entropy change in good agreement.
(4) Davidov, R. S.; Lee, R. A.; Armstrong, D. A. J. Chem. Phys. 1966,
5, 3364.
4
(5) Ambidge, P. F.; Bradley, J. N.; Whytock, D. A. J. Chem. Soc.,
Correcting the overall entropy change in Tables 3 and 4 from
Faraday Trans. 1 1976, 72, 1157.
(6) Wagner, H. G.; Welzbacher, U.; Zellner, R. Ber. Bunsen-Ges. Phys.
Chem. 1976, 80, 902.
-10
3
pressure to concentration unit, A1 ) (1.60 ( 0.48) × 10 cm /
(molecule‚s) is obtained. It is more than twice the value derived
(
7) Bemand, P. P.; Clyne, M. A. A. J. Chem. Soc., Faraday Trans. 2
977, 73, 394.
8) Dodonov, A. F.; Lavrovskaya, G. K.; Morozov, I. I.; Ulbright, R.
from ab initio calculations in eq 8, but in good agreement with
the experimental values of refs 6 and 7. This A1 factor and the
measured k1 rate constant yields the activation energy E1 ) 1.68
1
(
T.; Tal’roze, V. L.; Lyubimova, A. K. Kinet. Catal. 1970, 11, 677. Albright,
R. G.; Dodonov, A. F.; Lavrovskaya, G. K.; Morosov, I. I.; Tal’roze, V. L.
J. Chem. Phys. 1969, 50, 3632.
(
0.18 kcal/mol which is in good agreement with the activation
energies in Table 1. Empirically estimated A factors computed
by the above methods have never shown discrepancies greater
than a factor of 2 and we estimate the uncertainty as a factor of
(9) Bykhalo, I. B.; Filatov, V. V.; Gordon, E. B.; Perminov, A. P. Russ.
Chem. Bull. 1994, 43, 1637.
(10) Kita, D.; Stedman, D. H. J. Chem. Soc., Faraday Trans. 2 1982,
8, 1249.
11) Jaffe, S.; Clyne, M. A. A. J. Chem. Soc., Faraday Trans. 2 1981,
7, 531.
12) Michael, J. V.; Lee, J. H. Chem. Phys. Lett. 1977, 51, 303.
(13) Stedman, D. H.; Steffenson, D.; Niki, H. Chem. Phys. Lett. 1970,
7
7
1
.5 leading to the uncertainties listed above.
(
A linear model of the TS would lead to a replacement of the
rotational mode by a doubly degenerated bending mode at about
(
-
1
5
1
0
00 cm , yielding an A factor 10-fold smaller, A1 ) 1.6 ×
cm /(molecule‚s). The activation energy would than be
.28 kcal/mol. Both A1 and E1 are well below all of the values
-
11
3
7, 173.
0
(
14) Jardine, D. K.; Ballash, N. M.; Armstrong, D. A. Can. J. Chem.
973, 51, 656.
15) Ambidge, P. F.; Bradley, J. N.; Whytock, D. A. J. Chem. Soc.,
Faraday Trans. 1 1976, 72, 2143.
1
measured and would seem to rule out a linear transition state.
(
(
16) Weston, E. R. J. Phys. Chem. 1979, 83, 61.
Conclusions
(17) Miller, J. C.; Gordon, R. J. J. Chem. Phys. 1981, 75, 5305.
A low, permanent H atom inlet flow is produced by the
operation of the phosphoric acid coated microwave discharge
tube of the VLPR system. This background [H]0 concentration
in the system can be determined by Cl2 titration.
(18) Benson, S. W.; Cruickshank, F. R.; Shaw, R Int. J. Chem. Kinet.
969, 1, 29.
1
(19) Baulch, D. L.; Duxbury, J.; Grant, S. J.; Montague, D. C. J. Chem.
Phys. Ref. Data 1981, 10, 1, Suppl.1.
(20) Dobis, O.; Benson, S. W. J. Phys. Chem. 1997, 101, 1305 (Table
An excellent balance is found between the Cl2 consumption
and the Cl as well as the HCl formation kinetics under steady
state flow conditions. It indicates the sole existence of reaction
1).
(
(
(
21) Dobis, O.; Benson, S. W. J. Phys. Chem. 1995, 99, 4986.
22) Dobis, O.; Benson, S. W. J. Am. Chem. Soc. 1991, 113, 6377.
23) Seeley, J. V.; Jayne, J. T.; Molina, M. J. Int. J. Chem. Kinet. 1993,
1
in our system without any perturbation from reactions of
2
5, 571.
vibrationally excited secondary products. This is due to the
relatively long residence time in the reactor cell which allows
the thermalization of HCl(V). Since the kinetic investigation is
performed under real second-order kinetics, both the rate
constant and the initial H atom concentration can be determined
(24) Dobis, O.; Benson, S. W. Int. J. Chem. Kinet. 1987, 19, 691.
(25) Galante, J. J.; Gislason, E. A. Chem. Phys. Lett. 1973, 15, 231.
(26) Spencer, J. E.; Glass. G. P. J. Phys. Chem. 1975, 79, 2329.
(27) Barker, J. R.; Kiel, D. G.; Michael, J. V.; Osborne, D. T. J. Chem.
Phys. 1970, 52, 2079.
(28) Mitchell, T. J.; Gonzales, A. C.; Benson, S. W. J. Phys. Chem.
1955, 99, 16960. Vasileides, S.; Benson, S. W. Int. J. Chem. Kinet. 1997,
9, 915.
-
11
3
in one series of measurements as k1 ) (0.96 ( 0.04) × 10
2
3
10
cm /(molecule‚s) and [H]0 ) (4.85 ( 0.11) × 10 atoms/cm .
Both values are independent of the initial Cl and HCl concentra-
tions.
(
(
29) Leone, S. R. J. Phys. Chem. Ref. Data 1982, 11, 953.
30) Polanyi, J. C.; Sadowski, C. M. J. Chem. Phys. 1962, 36, 2239.
Heidner III, R. F.; Kasper, J. V. V. J. Chem. Phys. 1969, 51, 4163.
31) Arnoldi, D.; Wolfrum, J. Ber. Bunsen-Ges. Phys. Chem. 1976, 80,
92.
(
8
Acknowledgment is made to the donors of the Petroleum
Research Fund administered by the American Chemical Society,
for the support of this research.
(
(
32) Macdonald, R. G.; Moore, C. B. J. Chem. Phys. 1980, 73, 1681.
33) Vincent, M. A.; Connor, J. N. L.; Gordon, M. S.; Schatz, G. C.
Chem. Phys. Lett. 1993, 203, 415. Wisscher, L.; Dyall, K. G. Chem. Phys.
Lett. 1995, 239, 181.
(
34) Gonzales, M.; Hijazo, J.; Novoa, J. J.; Sayos, R. J. Chem. Phys.
References and Notes
1
998, 108, 3168.
(
1) Cohen, N.; Jacobs, T. A.; Emanuel, G.; Wilkins, R. L. Int. J. Chem.
Kinet. 1969, 1, 551.
2) Anlauf, K. G.; Horne, D. S.; Macdonald, R. G.; Polanyi, J. C.;
Woodall, K. B. J. Chem. Phys. 1972, 57, 1561.
3) Klein, F. S.; Wolfsberg, M. J.Chem. Phys. 1961, 34, 1494.
(35) Levine, R. D.; Bernstein, R. B. Molecular Reaction Dynamics and
Chemical ReactiVity; Oxford University Press: New York, 1987; p 141.
(36) Truhlar, D. G.; Garrett, B. C. Acc. Chem. Res. 1980, 13, 440.
(37) Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New
York, 1976; pp 37, 151.
(
(