Thermal rate constant for CN + H2/D2 → HCN/DCN + H/D reaction from T = 293 to 380 K

Article abstract of DOI:10.1021/jp980875o

The reaction rate constant for the cyano (CN) radical with hydrogen and deuterium has been determined over the temperature range 293-380 K. The CN radical was detected by time-resolved near-infrared absorption using the CN red system (A²Π ← X²Σ) (2,0) band near 790 nm. These measurements were carried out at low pressures of Ar or He as carrier gas. The diffusion rate of CN in these mixtures was inferred from the diffusion rate of HCN(000) determined using time-resolved infrared absorption of HCN(000) around 3.0 μm, simultaneously with the detection of CN. These measurements provide accurate thermal rate constant data that will enable a detailed comparison to be made between theoretical predictions and experimental measurements for this prototypical reaction system.

Full text of DOI:10.1021/jp980875o

J. Phys. Chem. A 1998, 102, 4585-4591
4585
Thermal Rate Constant for CN + H2/D2 f HCN/DCN + H/D Reaction from T ) 293 to
3
80 K
†
G. He, I. Tokue, and R. Glen Macdonald*
Argonne National Laboratory, Chemistry DiVision, 9700 South Cass AVe., Argonne, Illinois 60565
ReceiVed: January 23, 1998; In Final Form: April 16, 1998
The reaction rate constant for the cyano (CN) radical with hydrogen and deuterium has been determined over
the temperature range 293-380 K. The CN radical was detected by time-resolved near-infrared absorption
2
2
using the CN red system (A Π r X Σ) (2,0) band near 790 nm. These measurements were carried out at
low pressures of Ar or He as carrier gas. The diffusion rate of CN in these mixtures was inferred from the
diffusion rate of HCN(000) determined using time-resolved infrared absorption of HCN(000) around 3.0 µm,
simultaneously with the detection of CN. These measurements provide accurate thermal rate constant data
that will enable a detailed comparison to be made between theoretical predictions and experimental
measurements for this prototypical reaction system.
I. Introduction
sical trajectory calculations, again based on the recent global
surface. They also suggested that the surface could be modified
to obtain better agreement between theory and experiment.
The reaction of the cyano radical (CN) with H2
kR1
Earlier theoretical analysis of reaction R1 by Wagner and
Bair also used a comparison of theoretical rate constants for
CN + H2
8 HCN + H
(R1)
(R2)
6
reaction R1 and experimental values to refine the properties of
the transition state for the abstraction channel. These workers
carried out a detailed analysis of the saddle point properties for
reaction R1 using an ab initio generalized valence bond
configurational interaction (GVB-CI) and more refined calcula-
tions for the energetics of the reaction using a POL-CI
calculation. Using the theoretical predictions for the transition-
state structure, the temperature dependence of kR1 was calculated
using conventional transition-state theory. Good agreement with
experiment was obtained if the theoretically predicted barrier
and its deuterated analogue
kR2
CN + D2 8 DCN + D
are ideal systems to study the reaction dynamics of four-atom
systems. Over the past decade or so there has been an
1
increasing effort both experimentally and theoretically to probe
this system from a variety of perspectives. An important
experimental aspect of this problem is the determination of
-
1
-1
height of 6.0 kcal mol was reduced to 4.1 kcal mol .
2
accurate thermal rate constants for reactions R1 and R2, and
Although there are several recent studies7 of reactions R1
and R2 over wide temperature ranges, there still appears to be
some uncertainty as to the value of (R1) around room
-10
from the theoretical point of view, it is important to develop a
global potential energy surface (PES). This PES should describe
all the possible interactions that can occur in the four-atom
H-H-C-N system, i.e., the intermediates H2CN and HCNH
and both product channels, HCN + H and HNC + H. Such a
global PES has recently been developed for reaction R1 based
on accurate ab initio calculations of over 12 000 points in the
7
-13
temperature.
In light of the recent interest in adjusting the
new global PES according to the observed 300 K rate constant
3
data, it was felt that a new determination of the rate constant
for reactions R1 and R2 would be worthwhile. Furthermore,
7
-10,12
3
most recent
measurements of kR1 and/or kR2 at low
H-H-C-N configuration space. The temperature dependence
temperatures have been based on pulsed laser-induced fluores-
of the thermal rate constant was calculated using a quasiclassical
trajectory approach that completely accounted for the six degrees
of internal motion of the four-atom system on this global PES.
The barrier height was adjusted from the ab initio value of 4.3
2
-
2 +
cence (LIF) of CN using the violet system, B Σ rX Σ (0-
), transition around 380 nm. In these measurements, the time
0
evolution of the CN radical was followed by varying the time
delay of the probe LIF laser following the pulsed laser
production of the CN radical from a suitable precursor. This
method is quite sensitive but requires very careful normalization
-
1
-1
kcal mol to 3.2 kcal mol in order to obtain agreement with
the average rate constant data for reaction R1 at 300 K. The
value of kR1 over the temperature range 200-3500 K was then
calculated and found to in good agreement with experiment.
This value for the barrier height for reaction R2 was also
1
3
of pulsed laser intensities. Balla and Pasternack monitored
the CN radical continuously using time-resolved infrared
absorption of the fundamental CN(V)1;J′) r (V)0;J′′) transition
near 5.2 µm using a tunable infrared lead salt laser spectrometer.
Although this is a direct method for detecting single rovibra-
tional levels of CN in a continuous fashion, the infrared
transition dipole moment of CN is small, and this method suffers
from a lack of sensitivity. Other approaches have been used to
detect the CN radical in a continuous time-resolved fashion,
4
suggested by Che and Liu from the determination of the
excitation function for reaction R2 in a molecular beam. In a
recent work Wang et al.5 again compared very detailed
molecular beam experiments with predictions from quasiclas-
†
Department of Chemistry, Niigata University, Faculty of Science,
Niigata 950-21, Japan.
S1089-5639(98)00875-5 CCC: $15.00 © 1998 American Chemical Society
Published on Web 05/22/1998

4
586 J. Phys. Chem. A, Vol. 102, No. 24, 1998
He et al.
2
but they have not been applied to the determination of kR1 or
kR2. Durant and Tully14 used a high-resolution continuous wave
density of 2-10 mJ/cm at a repetition rate of 1-5 Hz. As in
17
previous experiments, the rectangular shaped ArF laser beam
(
CW) ultraviolet dye laser to excite LIF of CN using the CN
propagated through the photolysis region with its long axis
perpendicular to the nominal flow direction of the TFR and the
split White cell mirror axis.
2
-
2
+
15
B Σ r X Σ (0-0) transition. Recently, Hall and Wu
detected CN in a continuous fashion using time-resolved
absorption on the CN red system, A Π r X Σ (2-0) band,
near 790 nm. This detection scheme was based on a high-
resolution tunable CW Ti-sapphire laser spectrometer. North
et al. have extended this technique to include time-resolved
FM-modulated absorption spectroscopy and applied this tech-
nique to a direct kinetic measurement of the reaction rate
constant for CN + C2H4.
2
2 +
Single rotational states of the CN radical were detected
using time-resolved near-infrared absorption spectroscopy on
2
2 +
the CN(A Π r X Σ ) (2,0) band near 790 nm. The room-
temperature external cavity diode laser was supplied by
Environmental Optical Sensors Inc. This laser reliably runs in
a single mode; nevertheless, the mode behavior was monitored
by a Burleigh 2 GHz free spectral range scanning Fabry-Perot
Etalon. The laser can be continuously tuned over several
nanometers without a mode hop. The laser bandwidth was less
than 5 MHz, much narrower than the thermal Doppler line width
of the CN radical. The laser wavelength was determined using
an evacuated Burleigh model IR-210 wavemeter.
1
6
In the present work, CN was detected in a continuous fashion
2
2 +
using direct absorption of CN on the A Π r X Σ (2-0)
transition at 790 nm. The laser source was a commercial
external cavity diode laser which has the advantage of narrow
bandwidth and tunability combined with low-amplitude fluctua-
tion noise. The sensitivity of the direct absorption technique
was improved by multipass optics to increase the absorption
path length. The CN radical was created by pulsed laser pho-
tolysis of (CN)2 at 193 nm, and its time evolution was followed
in low-pressure mixtures of H2 or D2 in inert gases to determine
kR1 and kR2.
White cell optics were used to multipass the probe laser
radiation through the photolysis region so that the nominal
absorption path length was 14 m. Both the excimer and probe
laser radiation were directly overlapped using a dichroic mirror
set at Brewster’s angle with respect to the probe laser polariza-
tion. Another optic, Pyrex or ZnSe, also inserted directly in
the optical path at Brewster’s angle, was used to absorb the
excimer laser radiation and prevent damage to the White cell
optics.
II. Experimental Section
The basic experimental apparatus has been described in
previous works.1
7,18
The photolysis laser introduced a small instantaneous baseline
shift, presumably from a refractive index change induced in one
of the optical elements. To account for this, a time-resolved
absorption profile was obtained with the probe laser tuned to
the peak of an absorption feature, signal averaged for 100-
Briefly, the transverse flow reactor (TFR)
consists of a stainless steel chamber which contains a Teflon
box of dimensions 100 × 100 × 5 cm. The TFR was evacuated
by a liquid nitrogen trapped 25 cfm mechanical pump to a
pressure of a few milliTorr. The leak rate of the TFR was less
than 1 mTorr/min. To reduce gas consumption and provide a
constant pumping speed during an experiment, a small orifice
was placed between the mechanical pump and the TFR.
The temperature of the TFR was controlled by circulating
hot silicone oil (a NestLab model HT-200 hot oil bath) through
copper tubing folded back and forth over the top and bottom
surface of the inner Teflon box. Five thermocouples, four of
which were inserted in wells in the Teflon box using silicone
thermal grease and the fifth was suspended directly in the gas
stream, were used to monitor the gas temperature. About 5%
of the optical path was in regions not directly heated by the
circulating hot oil system. Heating tape was used to heat these
side-arm chambers containing the White cell optics to the
temperature of the reaction region.
5
00 shots using a LeCroy model 9410 digital oscilloscope, and
then a background profile was recorded and signal averaged
with the probe laser frequency detuned several line widths from
the peak. These two curves, signal + background and back-
ground, were transferred to a laboratory computer and subtracted
to produce a time-resolved CN(V)0;J) absorption profile. The
reaction rate constants for (R1) and (R2) are small, and the
observed first-order exponential decay times ranged from 100
-1
to 5000 s so that in order to avoid distortions of these profiles
from low-frequency filtering they were collected in a dc mode.
As a result, the initial I0 was recorded simultaneously with the
absorption profile using the pretrigger feature of the digital
oscilloscope, and the absorbance, ln(I0/I), vs time profiles could
be directly calculated.
The laser intensity was detected using a New Focus Si PIN
photodiode. Care was taken so that the detector was not satu-
rated by the probe laser power. The time response of the Si
diode was 100 MHz, but in most of the experiments, the
frequency response was limited to the range dc to 3 MHz using
a Krohn-Hite model 3944 electronic filter.
The laboratory PC computer that was used to generate the
absorbance profiles and data analysis was also used to provide
appropriate timing pulses for the data collection sequence and
necessary voltages to scan the diode laser.
A separate high-vacuum system was used to control the flow
of the various gases into the TFR. The Ar, He, and H2 were
all supplied by AGA Gas and were research grade, 99.9995%
pure. The D2 (research grade, 99.5% pure) and (CN)2 (research
grade, 98.5% pure) were supplied by Matheson. The (CN)2
was purified by pumping on at -78 °C. The gases were
continuously flowed through the TFR and their partial pressures
determined from the known flow rates and total pressure in the
TFR, as determined by an Edwards model 600 pressure
transducer. All except the (CN)2 flow meters were carefully
calibrated. In early experiments, calibrated Gilmont rotometers
were used to measure the Ar or He and H2/D2 flow rates, but at
low flow rates of He or H2 the readings required a long time to
stabilize. To overcome this problem, the rotometers were
replaced by M.K.S. model 0258 electronic mass flow meters,
which were again carefully calibrated.
The apparatus and gas handling system were specifically
designed for a flowing gas setup. As a result, the appropriate
experimental pressure range was 2-15 Torr; however, at the
higher pressures the diffusion rate becomes very slow, and
increasing the pumping speed results in rapid consumption of
(CN) and D . Hence, most of the data reported in this work
2
2
The CN radical was produced by the photolysis of (CN)2 at
93 nm using a Lumonics model 740 excimer laser. All the
experiments were carried out with the photolysis laser power
were obtained with a total gas pressure around 4 Torr. At this
pressure, diffusion can contribute to the first-order decay rates.
To a first-order approximation, the diffusion constant for CN
1

CN + H2/D2 f HCN/DCN + H/D
J. Phys. Chem. A, Vol. 102, No. 24, 1998 4587
Figure 1. (a) Absorbance of CN(V)0;J)9.5) as a function of time
Figure 2. (a) Absorbance of CN(V)0;J)8.5) as a function of time
for a temperature of 328 K; PH2 ) 3.046, PAr )1.803, and P(CN)2
)
for a temperature of 293 K; P ) 0.780, P ) 3.178, and P
)
D2
He
(CN)2
0
.0083 Torr. The solid line is the single-exponential decay fit for the
0.0023 Torr. The solid line is the single-exponential decay fit for the
rate determined in Figure 2(b). (b) Determination of kCN for the
absorbance profile in Figure 2(a). A linear least-squares fit gives k
rate determined in Figure 1(b). (b) Determination of kCN for the
absorbance profile in Figure 1(a). A linear least-squares fit gives kCN
CN
3
-1
2
-1
)
(4.292 ( 0.003) × 10 s
.
) (4.98 ( 0.04) × 10 s
.
and HCN in nonpolar environments should be similar. In this
laboratory there is the capability to detect the time dependence
of vibrational levels of HCN in the infrared region around 3.0
µm. A Burleigh model FCL-20 single-mode color center laser
was used to monitor HCN(000) produced in reaction R1. Both
the CN reactant and HCN product could be detected simulta-
neously. These experiments will be described in detail in
another work, but for the present it should be noted that the
diffusion rate constants for HCN in mixtures of He-H2 and
Ar-H2 were measured directly.
by the direct experimental measurements of diffusion using the
HCN(000) measurements.
18,19
A typical absorbance temporal profile for the removal of CN-
(V)0;J)9.5) in H2-Ar mixtures at a temperature of 328 K is
shown in Figure 1a, and the determination of kCN from these
data is shown in Figure 1b. A similar absorbance profile for
the removal of CN(V)0;J)8.5) in D2-He mixtures is shown
in Figure 2a for a temperature of 293 K, and the determination
of kCN from this absorbance trace is shown in Figure 2b. As is
evident from Figures 1b and 2b, the data were well described
by single-exponential decay rates. This was generally the case
for all the data collected in this work, except for low partial
pressures of reactants when sometimes the decay curves could
be described by two decaying exponential terms. In these cases,
the appearance of a second exponential term was likely due to
1
9
III. Results and Discussion
The bandwidth of the probe diode laser radiation was much
narrower than the thermal Doppler width of the CN transitions
so that the Beer-Lambert law was obeyed, and a plot of
absorbance, A ) ln(I0/I), against time is a direct measure of the
temporal concentration profile of CN, [CN] (where the square
brackets refer to concentration). At the low initial concentra-
20
the appearance of multiple diffusion modes. Also, in some
cases an induction period, due to rotational relaxation, persisted
for several microseconds but was of short enough duration as
not to influence the determination of the first-order decay rates.
1
1
tions of CN used in the present experiments (<7 × 10
-
3
molecules cm ) secondary reactions can be ignored, and the
first-order decay of CN, kCN , represents the sum of all removal
processes for the CN radicals, i.e., reaction with H2 or D2,
reaction with any impurities such as O2 or a hydrocarbon
background, and removal by diffusion. To minimize the
influence of these possibilities, the first-order removal rates for
If the removal of CN by diffusion is described by a single
diff
first-order decay rate, k , at a constant total pressure, then
CN
2
0
Blanc’s law relates the diffusion rate constant to a linear
function of the partial pressures of the components in the
mixture, i.e.
CN were measured as a function of pressure of H2 (PH ) or D2
2
P
at a constant total pressure. Under these circumstances, the
second-order rate constant for reaction R1 or R2 can be obtained
from the slope of the first-order rates plotted against PH or PD
X2
PM
1
diff
CN
)
+
(3)
D
DM
k
X2
2
2
at constant total pressure. The intercept provides the influence
of impurity reactions and diffusion. This treatment assumes of
course that the change in reactant partial pressure changes only
the reaction rate; however, at low total pressures and especially
for Ar as the carrier gas, the diffusion rate constant also depends
on gas composition so that the diffusion rate should be
subtracted from kCN before plotting the data. The estimates for
the diffusion rate of CN in the various mixtures were provided
where X2 is either H2 or D2, M is either Ar or He, and DX2,M is
the corresponding diffusion coefficient of CN in the pure gas
X2 or M at the pressure PX2/M. With the present geometry the
diffusion process was complicated, and at long times (>1 ms)
there were two measurable diffusion rate constants, describing
20
five low-order diffusion modes. However, the faster diffusion
rate (motion parallel to the short dimension of the rectangular

4588 J. Phys. Chem. A, Vol. 102, No. 24, 1998
He et al.
shaped excimer laser beam) was about 9 times larger than the
smaller one (motion parallel to the long dimension). The faster
diffusion rate constant was assumed to dominate, and the smaller
one was neglected so that the diffusion process could be
described by a first-order rate process.
The diffusion process was studied by monitoring HCN(000)
at times from 1 to 80 ms following the photolysis laser pulse.
At these long times, vibrational relaxation of the whole HCN
vibrational manifold was complete as can be inferred from the
known vibrational relaxation rate constants of many highly
21
excited HCN levels by H2 and also from experiments carried
out in this laboratory.18 Furthermore, the decay of HCN(001)
was observed to be complete before the time scale for diffusion
became important. Thus, at these long times the HCN(000)
level was proportional to the thermalized HCN product from
reaction R1, and its time behavior was not perturbed by
vibrational relaxation processes. The diffusion coefficients of
CN and HCN should be similar. Virtually all the data for the
measurement of kR2 were obtained in He-D2 mixtures for which
the diffusion rate for CN should be approximately constant
22
because of the constant effective mass for this gas combination.
Simple temperature and mass dependencies predicted by ideal
gas kinetic theory were used to extend the determination of the
diffusion rate constants to temperatures greater than 294 K and
other gas compositions. The majority of the rate constant mea-
diff
surements were made using He as the carrier gas, and kCN was
diff
-1
almost constant. At most kCN varied from 100 to 300 s for
the CN in the Ar-H2 mixtures used in this work, and the direct
correction for diffusion decreased the measured rate constants
by up to 5% for some experiments.
Figure 3. (a) Confirmation that the thermocouples gave the correct
gas temperature. A wavelength scan over two pairs of high and low
rotational states of CN(V)0) is shown. The measurements were carried
out at a total pressure of He of 3.86 Torr. The data were collected with
a boxcar delay of 15 µs, and gate width of 1.0 µs and averaged for 30
shots per frequency interval. (b) A Boltzmann plot of the peaks in Figure
A possible complicating reaction could be the attack of H
atoms on (CN)2 to regenerate CN radicals
3
(a), fit to Gaussian profiles, to determine the rotational temperature
of the reacting CN radical. The data were normalized for fluctuations
in the excimer laser power, S. The three thermocouples nearest the
reaction zone gave readings of 362.2, 363, and 365 K so there is good
agreement between the determination of T by the thermocouple and
spectroscopic techniques.
H + (CN) f
2
-
1
HCN + CN (∆H ) +41.4 ( 5.0 kJ mol ) (R3)
0
where the ∆H0 has been evaluated from recent data.23,24 If
reaction R3 occurred by a single-step process, then even though
the reaction is substantially endothermic, it could become
important with increasing temperature if the A factor for the
rate constant was large. Fortunately, Phillips25 has studied this
reaction at 300 K and found that the rate constant for the
used just to dissociate the (CN)2 molecule. The largest
perturbation to the gas temperature, at the maximum photolysis
laser energy and largest [(CN)2], can be estimated to be only
0.02 K. Much larger uncertainties in the gas temperature arise
from the thermal inertia of the inner Teflon box. The TFR
apparatus was not designed for very carefully temperature-
controlled experiments so that the gas temperature could be
different from that recorded by the thermocouples. Five
calibrated thermocouples were arranged so that two monitored
the temperature of the box near the gas inlet and outlet, two
monitored the temperature directly over the photolysis region,
and one was suspended directly in the center of the gas stream
a few centimeters downstream from the photolysis region, well
isolated from the walls. The readings from the two thermo-
couples directly above the reaction zone and the one directly
in the gas stream were always within several kelvin of each
other at the highest temperatures, and this was taken as a
measure of the uncertainty in the temperature.
-
15
3
disappearance of H atoms was small, k ) 1.5 × 10
cm
-
1 -1
molecule at a pressure of 1 Torr. These experiments also
s
verified that the mechanism of H atom removal did not occur
through reaction R3 but by complicated multistep three-body
processes originally proposed by Abers et al.11 Furthermore,
there was no detectable production of CN radicals at long times
in the CN + H2 system so that the influence of this reaction
path was negligible.
An important experimental parameter in this reaction system
is the temperature. Small uncertainties in the determination of
the gas temperature can cause large variations in the observed
rate constants because of the relatively large activation barrier
for reactions R1 and R2. In principle, the laser photolysis
process itself could perturb the gas temperature by depositing
energy into the internal degrees of freedom and/or the transla-
tional motion of the photolysis products; however, in the present
experiments this effect was quite minor. The small absorption
To further verified that the gas temperature was correctly
given by these three thermocouples, the rotational temperature
2
of the reacting CN was measured directly. The CN A Π r
2
X Σ (2,0) is especially suited for this purpose because the R1
-
19
2 13
cross section of (CN)2 at 193 nm (1.1 × 10
cm ) and low
bandhead is conveniently located near the peak of the Boltzmann
distribution for the temperatures of the experiment, and transi-
tions for both high and low rotational states lie within a small
frequency range of each other. A typical scan over several low
and high rotational transitions is shown in Figure 3a, and a
partial pressures of (CN)2 (P(CN) < 0.01 Torr) resulted in less
2
than 0.5% of the initial photolysis energy (a maximum of 50
mJ) being absorbed. Furthermore, because of the large bond
dissociation energy24 of (CN)2, about 90% of this energy was

CN + H2/D2 f HCN/DCN + H/D
J. Phys. Chem. A, Vol. 102, No. 24, 1998 4589
reaction chamber was not designed to be a high-vacuum
apparatus so that a small concentration of impurity could
contribute to the removal of CN radicals if the reaction rate
-
11
3
constant were large enough, e.g. O2, kRO ) 2.5 × 10
cm
2
-
1
-1
26
molecules
s
at T ) 294 K. The CN + O2 reaction could
account for a large fraction of the observed intercepts in Figures
4
and 5 if there was a background pressure of ∼1 mTorr of air
either due to a vacuum leak or from outgassing. In later
experiments, when the diffusion rates of HCN were determined
using the infrared laser source, it was discovered that a
background reaction produced predominately HCN. Thus, the
nature of the apparent background reaction is unclear, but it
does not influence the kinetic measurements reported on here.
Further discussions of these experiments will be presented in
Figure 4. First-order rate constants, as shown in Figure 1(b), are plotted
as a function of PH2 for a temperature of 328 K. The diffusion rate of
1
9
another work.
CN in H
2
-Ar mixtures was subtracted from each of the first-order
It is interesting to note that the results reported here were
independent of which rotational state of the CN(V)0;J) was
monitored. This of course is to be expected because rotational
relaxation should proceed much more rapidly than reaction but
in many cases has not been verified experimentally.
decay rates so that the intercept represents the influence of a background
reaction of CN. The uncertainty in each first-order rate constant is within
the symbols. The linear least-squares fit to the data gives kR1 ) (4.5 (
-
14
3
-1 -1
0
.05) × 10 (cm molecule
s ).
There could be several possible complications from the pho-
tolysis of (CN)2 at 193 nm besides a rise in the gas temperature,
namely, the production of electronically and/or vibrationally
excited CN products. Fortunately, these effects have been
investigated previously. The lowest-lying excited electronic
2
state of CN is the A Π state, but it is not energetically accessible
2
4
by a one-photon process at 193 nm. About 13% of the initial
2
7,28
CN radicals are produced in the CN(V)1) level.
However,
the presence of CN(V)1) will have little effect on the measure-
ment of the reaction rate constants determined by monitoring
CN(V)0). Assuming that the total removal rate for CN(V)1)
is larger than that for CN(V)0), the production of CN(V)0) by
vibrational relaxation from CN(V)1) would appear as a small
rising exponential term in the complete time description of CN-
(
V)0) with a preexponential factor at least 7 times smaller than
Figure 5. First-order rate constants as shown in Figure 2(b) are plotted
as a function of P 2 for a temperature of 293 K. The diffusion rate of
CN in D -He mixtures should be approximately independent of the
the term describing CN(V)0) decay. As is evident from Figures
1a and 2a, no such term was detected. Furthermore, previous
workers
H2 and D2 systems and found the decay of CN(V)1) slightly
larger than CN(V)0) and attributed this decay to reaction of
vibrationally excited CN. A similar conclusion was reached in
D
2
mixture and was not subtracted out from the first-order rate constants
so that the intercept contains contributions from diffusion and the CN
background reaction. The uncertainty in each first-order rate constant
is within the symbols. The linear least-squares fit to the data gives kR2
7,10
have monitored CN(V)1) decay in both the CN +
-
15
3
-1 -1
)
(7.6 ( 0.2) × 10 (cm molecule
s ).
3
recent theoretical investigations of reaction R1.
Boltzmann plot of these data is shown in Figure 3b. The slope
of the least-squares fit gave a direct measurement of the
rotational temperature of the reacting CN radical and was in
agreement with the average temperature of the three thermo-
couples closest to the reaction zone. Other direct measurements
of the gas temperature were found to be in good agreement with
the average temperature given by these three thermocouple
measurements. It was concluded that the gas temperature was
well represented by the thermocouple readings with a maximum
uncertainty of (2 K.
The determination of the second-order rate constants by
plotting the first-order decay rates as a function of reactant
partial pressure minimizes the influence of any impurity on the
rate constant determination. As long as an impurity is not
introduced along with the variation in the gas flow rates, but
arises from a background contamination in the vacuum system,
its influence is accounted for by this measurement method.
Typical second-order plots for the data sets from which Figures
The results for the determination of kR1 and kR2 are presented
in Figures 6 and 7 and summarized in Tables 1 and 2,
respectively. A motivating factor in carrying out these experi-
ments was to provide a reliable value for kR1 and kR2 near room
temperature, and a detailed summary of the available data for
kR1 and kR2 is given in Table 3. The average of the rate
constants determined in the present experiments at T ) 293 K
-
14
3
-1 -1
is given by kR1 ) (2.50 ( 0.26) × 10
cm molecule
s
-
15
3
-1 -1
and kR2 ) (7.5 ( 0.75) × 10
cm molecule s. The error
bars include one standard deviation from the average of several
measurements at T ) 293 K and an estimate of a systematic
error of (5% error from determination of the various partial
pressures. Near 300 K, the rate constants for the CN + H2 and
D2 reactions determined in the present work are in good
7
,8,10,13
agreement with several recent determinations,
values are now well established.
and these
As is evident from Figures 1b and 2b, the uncertainty in the
determination of each first-order decay rate was quite small;
however, the overall scatter in the data was larger than expected
considering the excellent signal-to-noise of the individual decay
curves. One contributing factor to this scatter is the uncertainty
in the gas temperature. Using simple Arrhenius parameters for
1
and 2 were taken are shown in Figures 4 and 5, respectively.
The nonzero intercept in Figures 4 and 5 indicates that indeed
diff
there was a background reaction of CN because kCN has been
subtracted from the first-order decays, as described. The

4590 J. Phys. Chem. A, Vol. 102, No. 24, 1998
He et al.
TABLE 1: Summary of the Reaction Rate Constant
Measurements for the CN + H Reaction
2
1
4
P
tot
k × 10
T (K) carrier gas (Torr) (cm molecule s-1
3 -1
)
(1 std deva
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
93
93
93
93
93
93
93.5
93.5
94
94
94
94
14.5
15
16
18
25
Ar
4.0
4.0
4.0
4.0
3.7
3.7
4.0
3.6
3.2
5.7
3.8
4.0
4.5
3.5
7.9
4.0
3.6
3.7
5.0
1.9
3.9
5.0
3.4
7.6
4.0
4.0
4.0
3.9
4.0
4.1
4.0
2.49
2.38
2.45
2.63
2.51
2.37
2.25
2.61
2.57
2.48
2.60
2.68
3.67
3.79
3.76
3.74
4.35
4.24
4.49
5.22
6.14
5.96
6.13
7.61
7.02
6.85
8.40
8.10
8.14
8.54
0.12
0.21
0.17
0.11
He
He
He
He
He
pure H
Ar
He
He
Ar
Ar
Ar
Ar
Ar
He
Ar
He
Ar
Ar
Ar
Ar
Ar
Ar
0.078
0.053
0.019
0.058
0.047
0.039
0.050
0.043
0.05
0.033
0.056
0.28
0.092
0.073
0.054
0.14
2
27.5
27.5
29
38
48
0.44
0.083
0.098
0.40
0.26
0.26
0.19
0.23
0.44
0.19
Figure 6. Summary of the available data for the determination of the
reaction rate constant as a function of temperature. The lines
51
CN + H
2
354
355
355
367
367
367
1
0
are from the fits to the complete data set of Sun et al. and Sims et
He
He
He
He
He
He
He
8
al. determined over a much wider temperature range. The error bars
are all (σ for the slope to plots such as shown in Figure 4 except for
8
the work of Sims et al. in which the error bars represent (2σ and an
estimate of systematic errors.
3
3
69
80
10.7
0.33
a
(
1σ uncertainty in the least-squares fit for the slope of kCN vs P 2
H
.
TABLE 2: Summary of the Reaction Rate Constant
Measurements for CN + D
2
1
4
P
tot
k × 10
T (K) carrier gas (Torr) (cm molecule s-1
3 -1
)
(1 std deva
2
2
3
3
3
3
3
3
3
3
3
93
93
20
21
21
21
39
43
55
66
79
He
Ar
He
He
He
Ar
He
He
He
He
He
4.2
3.9
4.0
4.2
4.2
6.0
4.0
4.0
4.0
3.9
4.0
0.749
0.759
1.53
1.38
1.22
1.20
1.98
2.21
2.70
2.97
3.73
0.028
0.024
0.22
0.072
0.10
0.083
0.093
0.10
0.15
0.20
0.17
a
D
(1σ uncertainty in the least-squares fit for the slope of kCN vs P 2.
experiments this effect was eliminated by waiting for a
sufficiently long time for the gas to equilibrate. At a total flow
rate of 400 sccm the TFR volume was replaced in about a
minute. Data were generally collected after waiting at least five
pump-out decay times, ensuring that the gas mixture was evenly
distributed throughout the TFR volume. No other systematic
trends were evident.
Figure 7. Same as Figure 6 except all the data for the determination
of the CN + D
2
reaction rate constant are shown.
this reaction,8,10 it can be shown that an uncertainty of (1 K at
3
00 K and (2 K at 380 K leads to an uncertainty in the rate
constant of 2% and 3%, respectively. One systematic trend that
was observed was a slight rise in the temperature of the gas
mixture with increasing mole fraction of H2/D2. Even at the
highest temperatures, this effect was small, about a degree, but
was unlikely to introduce a systematic error into the data
reduction because this effect was within the temperature
uncertainty of (2 K. In preliminary experiments, it was
observed that if sufficient time was not allowed for complete
equilibration of the gas mixture throughout the TFR reaction
volume, erratic results were obtained. However, in later
The results of this work and other data7,8,10,13 should provide
a reliable database for a comparison with theoretical predictions
of the rate constants for the CN + H2 and D2 reactions. This
in turn will allow for a better theoretical description of this
reaction system both in terms of refinements to the PES and
also with respect to refinements in the dynamical descriptions
leading to rate constant predictions.
The use of direct, long path, time-resolved absorption of CW
laser diode radiation is a sensitive method to study the chemical
reactions of radicals. The narrow line width, tunability, and

CN + H2/D2 f HCN/DCN + H/D
J. Phys. Chem. A, Vol. 102, No. 24, 1998 4591
TABLE 3: A Summary of the Measurements for the CN +
supported by the U.S. Department of Energy, Office of Basic
Energy Sciences, Division of Chemical Sciences, under contract
No. W-31-109-ENG-38.
2 2
H /D Rate Constants near 300 K
1
4
a
k
R1 × 10
uncertainty
(×10 )
T (K)
technique (cm molecule s-1
3
-1
)
14
ref
References and Notes
CN + H
1.2
2
2
95
00
CW abs
0.2
11
(1) Bowman, J. M.; Schatz, G. C. Annu. ReV. Phys. Chem. 1995, 46,
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(2) Yang, D. L.; Lin, M. C. In The Chemical Dynamics and Kinetics
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b
(
B r X )
c
3
2
2
2
2
2
2
2
LIF
1.6
2.45
2.6
2.40
2.55
1.59
2.51
2.50
0.3
0.5
12
7
13
8
8
9
d
95 ( 4 LIF
98
94.5
96.5
95
e
IR abs
0.1
f
(3) ter Horst, M. A.; Schatz, G. C.; Harding, L. B. J. Chem. Phys.
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LIF
LIF
LIF
LIF
0.36
1
0.2f
(
(
4) Che, D.-C.; Liu, K. Chem. Phys. 1996, 207, 367.
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0.06
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h
93 ( 1 CW abs
(
(A r X)
(
(
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0.85
0.72
0.86
0.75
2
2
2
2
2
96
98
99
LIF
IR abs
LIF
0.06f
0.4
0.23
8
13
10
this work
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(
h
93 ( 1 CW abs
0.075
(A r X)
a
σ unless indicated otherwise. b CN monitored by time-resolved
absorption spectroscopy on the violet B r X system. CN monitored
by LIF using the violet B r X system. Uncertainty (2σ. e CN
monitored by time-resolved infrared absorption spectroscopy on the
CN IR fundamental. Uncertainty (2σ and an estimate of systematic
errors. CN monitored by time-resolved absorption spectroscopy on
1
7
65.
c
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d
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f
g
h
the red A r X system. Uncertainty (1σ and an estimate of systematic
(
errors.
1
(
18) Bethardy, G. A.; Northrup, F. J.; He, G.; Tokue, I.; Macdonald, R.
low-amplitude fluctuation noise of these devices make external
cavity CW laser diodes ideal light sources. The narrow line
width ensures that even in congested spectral regions absorption
features of single rovibrational states can be resolved easily.
As well, the narrow line width also ensures that the absorbance
is a direct measure of the population in a single rotational state
in accordance with the Beer-Lambert law. These laser sources
when coupled with high speed and low noise detectors are also
capable of measuring reaction rate constants over a wide range
of time scales, from 100 MHz to dc. All these attributes are
particularly true for the detection of the CN radical using the A
r X (2, 0) transition at 790 nm.
G. J. Chem. Phys., submitted for publication.
(
(
19) He, G.; Tokue, I.; Macdonald, R. G. J. Phys. Chem. A, in press.
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(
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25.
(
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(
(
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Acknowledgment. The authors wish to thank Dr. A. F.
Wagner for many stimulating discussions. This work was
3421.