Determination of the rate constant and product channels for the radical-radical reaction NCO(X 2Π) + C2H5(X 2A″) at 293 K

Article abstract of DOI:10.1039/b701900a

The rate constant and product branching ratios for the reaction of the cyanato radical, NCO(X ²Π), with the ethyl radical, C ₂H₅(X ²A″), have been measured over the pressure range of 0.28 to 0.59 kPa and at a temperature of 293 ± 2 K. The total rate constant, k₁, increased with pressure, P(kPa), described by k₁ = (1.25 ± 0.16) × 10^-10 + (4.22 ± 0.35) × 10^-10 P cm³ molecule^-1 s^-1. Three product channels were observed that were not pressure dependent: (1a) HNCO + C₂H₄, k_1a = (1.1 ± 0.16) × 10^-10, (1b) HONC + C₂H₄, k_1b = (2.9 ± 1.3) × 10^-11, (1c) HCN + C ₂H₄O, k_1c = (8.7 ± 1.5) × 10 ^-13, with units cm³ molecule^-1 s^-1 and uncertainties of one-standard deviation in the scatter of the data. The pressure dependence was attributed to a forth channel, (1d), forming recombination products C₂H₅NCO and/or C₂H ₅OCN, with pressure dependence: (1d) k_1d = (0.090 ± 1.3) × 10^-11 + (3.91 ± 0.27) × 10^-10 P cm³ molecule^-1 s^-1. The radicals were generated by the 248 nm photolysis of ClNCO in an excess of C₂H ₆. Quantitative infrared time-resolved absorption spectrophotometry was used to follow the temporal dependence of the reactants and the appearance of the products. Five species were monitored, HCl, NCO, HCN, HNCO, and C ₂H₄, providing a detailed picture of the chemistry occurring in the system. Other rate constants were also measured: ClNCO + C ₂H₅, k₁₀ = (2.3 ± 1.2) × 10 ^-13, NCO + C₂H₆, k₂ = (1.6 ± 0.11) × 10^-14, NCO + C₄H₁₀, k₄ = (5.3 ± 0.51) × 10^-13, with units cm³ molecule^-1 s^-1 and uncertainties of one-standard deviation in the scatter of the data. the Owner Societies.

Full text of DOI:10.1039/b701900a

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Determination of the rate constant and product channels for the
2
2
radical–radical reaction NCO(X P) + C2H5(X A00) at 293 K
R. Glen Macdonald*
Received 7th February 2007, Accepted 11th April 2007
First published as an Advance Article on the web 1st May 2007
DOI: 10.1039/b701900a
The rate constant and product branching ratios for the reaction of the cyanato radical, NCO
2
2
(X P), with the ethyl radical, C2H5(X A00), have been measured over the pressure range of 0.28
to 0.59 kPa and at a temperature of 293 ꢀ 2 K. The total rate constant, k1, increased with
pressure, P(kPa), described by k1 = (1.25 ꢀ 0.16) ꢁ 10ꢂ10 + (4.22 ꢀ 0.35) ꢁ 10ꢂ10 P cm3
moleculeꢂ1 ꢂ1. Three product channels were observed that were not pressure dependent: (1a)
s
HNCO + C2H4, k1a = (1.1 ꢀ 0.16) ꢁ 10ꢂ10, (1b) HONC + C2H4, k1b = (2.9 ꢀ 1.3) ꢁ 10ꢂ11
,
(1c) HCN + C2H4O, k1c = (8.7 ꢀ 1.5) ꢁ 10ꢂ13, with units cm3 moleculeꢂ1 sꢂ1 and uncertainties
of one-standard deviation in the scatter of the data. The pressure dependence was attributed to a
forth channel, (1d), forming recombination products C2H5NCO and/or C2H5OCN, with pressure
dependence: (1d) k1d = (0.090 ꢀ 1.3) ꢁ 10ꢂ11 + (3.91 ꢀ 0.27) ꢁ 10ꢂ10 P cm3 moleculeꢂ1 sꢂ1
The radicals were generated by the 248 nm photolysis of ClNCO in an excess of C2H6.
Quantitative infrared time-resolved absorption spectrophotometry was used to follow the
temporal dependence of the reactants and the appearance of the products. Five species were
.
monitored, HCl, NCO, HCN, HNCO, and C2H4, providing a detailed picture of the chemistry
occurring in the system. Other rate constants were also measured: ClNCO + C2H5, k10 = (2.3 ꢀ
1.2) ꢁ 10ꢂ13 , NCO + C2H6, k2 = (1.6 ꢀ 0.11) ꢁ 10ꢂ14, NCO + C4H10, k4 = (5.3 ꢀ 0.51) ꢁ
10ꢂ13, with units cm3 moleculeꢂ1 sꢂ1 and uncertainties of one-standard deviation in the scatter of
the data.
be redistributed leading to isomerization and/or bond break-
I. Introduction
ing product channels. Radicals are reactive species, and direct
bimolecular metathesis reactions can occur without complex
formation. Thus, products can be formed by either a direct-
abstraction or an addition-elimination pathway, and it is not
generally easy to determine the dynamical route that produced
a particular product channel.
The chemical interaction of two radicals is a class of reactions
that plays an important role in combustion chemistry.1 Radical–
radical reactions can be either chain propagating or
terminating events. In addition, they can lead to the genera-
tion of new species increasing the complexity of the chemical
environment. The recombination of two radicals is directly
connected to the reverse bond dissociation reaction through
the equilibrium constant. In many cases, the study of the
dissociation reaction is easier from the viewpoint of the
recombination process because of the weaker temperature
dependence of recombination rate constants.2
Radical–radical interactions have several unique features.3
Firstly, the interaction of two species with unpaired electron
spins always involves the participation of at least two potential
energy surfaces (PESs) differing in spin multiplicity. If one of
the radicals possesses electron angular momentum, multiple
electronic manifolds for each spin manifold also result from
the interaction. Secondly, the PES corresponding to a bonding
interaction between the two radicals is attractive with no
potential energy barrier along the reaction coordinate forming
the recombination product. On this PES the system is chemi-
cally activated, and the energy in the newly forming bond can
Experimentally, the determination of a rate constant for a
radical–radical reaction requires the measurement of the con-
centration of two transient species, and if product branching
ratios are measured, the concentration of the products must be
determined as well. For some reactions, these difficulties have
been overcome, and real-time measurements of rate constants
and product branching ratios have been made. For example,
Knyazev and Slagle4 studied a variety of alkyl radical–radical
reactions, and in some cases, measured the product branching
ratios.5,6
Theoretically, the calculation of a recombination rate con-
stant requires a variational treatment,7 and a description of
the interaction between the two radicals in the region where
chemical and long range forces are similar in magnitude.
Recent calculations based on variable reaction coordinate
transition state theory (VRC-TST) by Klipenstein et al.8 have
elucidated alkyl radical recombination reactions. However,
the calculations do not address direct radical disproportiona-
tion or metathesis reactions that can also occur on PESs
without energy barriers. Metathesis reactions occur at closer
internuclear separations where chemical forces dominate. For
Chemistry Division, Argonne National Laboratory, 9700 South Cass
Avenue, Argonne, 60439-4831 Illinois, USA. E-mail:
rgmacdonald@anl.gov; Fax: (630) 252-9292
ꢃc
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Phys. Chem. Chem. Phys., 2007, 9, 4301–4314 | 4301

example, Harding et al.9 calculated the total addition and
abstraction rate constants as a function of temperature for the
reactions, O + C2H5 and O + C2H3.
generated by thermal decomposition of its trimer, and photo-
lyzed at 248 nm using a Lamda Physik model 203 Compex
excimer laser. At the entrance window to the reaction cham-
ber, the photolysis laser fluence was varied between 5 and
20 mJ cmꢂ2 in a beam with dimensions 5 ꢁ 2 cm.
The cyanato radical (NCO, X 2P) plays two important roles
in combustion chemistry,10 involving both NOX production
and abatement. The NCO radical is involved in the generation
of NOX by two mechanisms. These are the prompt production
of NOX, or the Fenimore mechanism11 and the production of
NOX from fuel fixed nitrogen sources. Both mechanisms are
initiated by CN radical chemistry,1 and the subsequent gen-
eration of NCO by the CN + O2 reaction. Although there is
considerable agreement between the predictions of various
combustion mechanisms and experiment regarding NOX
chemistry, there are still some areas of uncertainty.12,13 Two
NOX abatement strategies,1 the RaReNOX and NOXOUT
processes, involve NCO radical chemistry. These processes
are based on the addition of cyanic acid ((HONC)3) or urea
((NH2CO)) to combustion exhaust gases, respectively, and the
generation of HNCO leading to subsequent NCO chemistry
removing NOX.
The infrared probe laser was a Burleigh model 20 single-
mode color-center laser. The probe laser radiation was multi-
passed through the photolysis region using White cell optics.
The photolysis laser and probe laser were directly overlapped
using a UV-IR dichroic mirror placed at Brewster’s angle on
the optical axis of the White cell. At the opposite end, the
mirrors were protected from the UV laser radiation by a ZnS
flat at Brewster’s angle. The distance between these two optical
elements provided a base optical path length of 139 ꢀ 0.3 cm.
Most of the data were collected with a total optical path length
of 16.68 ꢀ 0.04 m.
As will be discussed, the measurements on reaction 1 were
done at low C2H6 pressures, ranging from 0.1 to 0.39 Torr.
Higher C2H6 pressure experiments confirmed the measure-
ments at low C2H6 pressures, and provided a measurement of
the rate constant for the NCO + C2H6 reaction, k2. The
largest component in the gas mixture was generally N2O.
Separate experiments were also performed to measure the
absorption cross section for a rotational transition in the
HNCO fundamental n1 vibrational band. These experiments
were similar to those described in this section, and will be
discussed in section III. D.
The current work is a continuation of the study of the NCO
radical with simple alkyl radicals.14 The rate constant and
product yields for the NCO and C2H5 reaction:
NCO þ C2H5 ! HNCO þ C2H4
ð1aÞ
DHr0;0 ¼ ꢂ323:5 ꢀ 7 kJ molꢂ1
Time-resolved infrared absorption spectroscopy was used to
monitor the temporal behavior of each detected species. Probe
laser intensity fluctuations were the largest source of noise in
the experiment. These were reduced by splitting the probe laser
beam into equal intensity incident, I0, and transmitted, I,
beams. Each beam was detected by separate balanced InSb
detectors. The difference signal, I0 ꢂ I, was monitored by a
wideband differential amplifier to suppress common-mode
noise. A Con Optics Model Lass-II noise eater modulated
the intensity of the Kr+ ion laser that pumped the color-center
laser in a feedback-control loop using a signal from the I0
detector. Signal averaging, using a LeCroy Model 9410 digital
oscilloscope further enhanced the signal-to-noise of the data.
Thermal lensing and refractive index changes in the optical
elements exposed to the UV laser radiation induced back-
ground oscillations on the I signal channel. These were
removed by tuning to a nearby region of zero absorption
and acquiring a background trace. The true differential ab-
sorption signal was determined by subtraction. Data collection
was controlled by a laboratory computer.
! HOCN þ C2H4 DHr0;0 ¼ ꢂ221:0 ꢀ 8 kJ molꢂ1
ð1bÞ
! HCN þ H3CCHO DHr0;0 ¼ ꢂ294 ꢀ 11 kJ molꢂ1 ð1cÞ
! C2H5NCO=C2H5OCN
ð1dÞ
DHr0;0 ¼ ꢂ240=250 ꢀ 80 kJ molꢂ1
were measured at a temperature of 293 ꢀ 2 K and pressure
range of 2.1 to 4.5 Torr (1 Torr = 0.13332 kPa). The species in
bold in the above reaction scheme were detected, along with
HCl, using quantitative time-resolved infrared absorption
spectroscopy. The rate constants for channels 1a, 1b and 1c
were pressure independent while that for channel 1d was
pressure dependent.
II. Experimental
The apparatus and experimental procedure were the same as
described recently, and only a brief overview is given here.14–16
The reaction vessel was a vacuum-tight rectangular stainless-
steel box about 110 ꢁ 110 ꢁ 7 cm that was continuously
evacuated by a liquid-nitrogen-trapped mechanical pump. The
gasses used in the experiment were supplied by AGA, and were
used directly from their cylinders, with purities: Ar 99.9995%,
N2O 99.98%, C2H6 99.0%, O2 99.6%, and n-C4H10 99.95%.
The gases continuously flowed through the apparatus at a
total flow rate between 300 and 500 sccm. Their partial
pressures were determined from the total pressure and mea-
sured flow rates.
III. Results
A. Concentration determination: NCO,14 HCl,17 C2H4,18,19
and HNCO20
Each species was detected using isolated-rovibrational transi-
tions originating from their ground vibrational levels. For a
narrow-band source at frequency, n, the absorbance, ln(I0(n)/
I(n)), is related to the concentration of species X, [X], by the
Beer–Lambert law according to the product of path length,
absorption coefficient, s(n), and concentration.21 The s(n) is
The method of generating and measuring the partial pres-
sure of ClNCO has been described.16 Briefly, ClNCO was
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4302 | Phys. Chem. Chem. Phys., 2007, 9, 4301–4314

given by the product of the line strength, Sij, and the lineshape
function, g(n). At low pressures, pressure broadening can be
neglected, and g(n) is described by a normalized Doppler
profile. Thus, at the peak of an absorption line, the absorption
cross section, sXpk, is related to the product of Sij and the
inverse of the Doppler width. For the species detected in this
work, it was estimated that pressure broadening would reduce
sXpk by a few percent for pressures less than 5 Torr. The values
for sXpk and the spectroscopic transitions are summarized in
Table 1. Various spectral regions were scanned over for
signatures of other species such as C2H5, CH3, HNC, and
NH, but none were detected either because of spectral con-
gestion (C2H5 and CH3) and/or the species were not produced
either a reactant or a product.) are given by:
ClNCO 24ꢂ8!nm NCO þ Cl
Cl þ C2H6 ! HCl þ C2H5
NCO þ C2H5 ! products
ð7Þ
ð1Þ
NCO þ NCO ! N2 þ 2CO
NCO þ C2H6 ! HNCO þ C2H5
C2H5 þ C2H5 ! products
ð5Þ
ð2Þ
ð9Þ
in measurable concentrations (41 ꢁ 1010 molecules cmꢂ3
)
(HNC and NH).
C2H5 þ ClNCO ! NCO þ C2H5Cl
ð10Þ
X kdiꢂff!usion
ð11Þ
B. Reaction model
The complete reaction mechanism22–27 used to analyze the
experimental data is given in Table 2. The enthalpies of
formation28–34 at 0 K, DHf0,0, for the species in the model are
listed in Table 3. The number of reactions that essentially
accounted for all the chemistry in the system was smaller than
the number in Table 2. The reactions in which the fractional
integrated reaction contribution factors for a species were
greater than 0.01 (the fractional IRCFX is the fraction of the
total flux of X that passes through a reaction in which X is
The reaction numbers refer to the numbering in Table 2.
Several comments are in order about the rate constants used
in the data analysis. There have been several previous mea-
surements22,23,35 of k2 near 295 K ranging from 2.1 ꢁ 10ꢂ14 to
7.0 ꢁ 10ꢂ14 cm3 moleculeꢂ1 sꢂ1. The data were analyzed using
the slowest rate constant.22 This value is in close agreement
with the value of k2 equal to (1.6 ꢀ 0.11) ꢁ 10ꢂ14 cm3
moleculeꢂ1 sꢂ1 determined in the present work. For reaction
(9), both the rate constant and the branching between the
Table 1 Spectroscopic transitions and sXpk for the species detected in this work
Molecule
Upper level ’ (0. . .)
Wavelength/mm
sXpk/cm2 moleculeꢂ1
Ref.
NCO
HCl
(1011) Pe/f(12.5)
v = 1 R35(3)
v = 1 R35(6)
3.165073
3.354579
3.31737
3.147379
3.177556
2.816516
(3.13 ꢀ 0.12) ꢁ 10ꢂ19
(7.57 ꢀ 0.08) ꢁ 10ꢂ17
(2.65 ꢀ 0.03) ꢁ 10ꢂ17
(6.75 ꢀ 0.07) ꢁ 10ꢂ19
(1.38 ꢀ 0.014) ꢁ 10ꢂ18
(5.2 ꢀ 0.57) ꢁ 10ꢂ18
14
17
r
C2H4
n4 R70(7)
18, 19
r
n4 R4,0(4)
HNCOa
n1 qR0(16)
This work
a
This HNCO band has been assigned in ref. 20.
Table 2 Summary of the reactions and rate constants used to model the NCO + C2H5 system for 294 K
No.
Reactantsa
Products
k/cm3 moleculeꢂ1 sꢂ1 a
Ref.
b
b
b
b
1a
1b
1c
1d
2
3
4
5
6
NCO + C2H5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Diff.
HNCO + C2H4
HOCN + C2H4
HCN + C2H4O
C2H5NCO/C2H5OCN
HNCO + C2H5
Productsd
Optimized
Optimized
Optimized
Optimized
NCO + C2H6
NCO + C2H4
NCO + n-C4H10
NCO + NCO
NCO + Cl
Cl + C2H6
Cl + ClNCO
C2H5 + C2H5
(2.1 ꢀ 0.2) ꢁ 10ꢂ14
(2.85 ꢀ 0.22) ꢁ 10ꢂꢂ1312
(6.1 ꢀ 0.3) ꢁ 10
(5.0 ꢀ 2.0) ꢁ 10ꢂ12
(6.9 ꢀ 3.8) ꢁ 10ꢂ11
(5.5 ꢀ 0.2) ꢁ 10ꢂ11
(2.4 ꢀ 1.6) ꢁ 10ꢂ13
(2.4 ꢀ 0.42) ꢁ 10ꢂ11
(3.90 ꢀ 1.9) ꢁ 10ꢂ12
optimized
22c
23
23
24
16
25
16
26
e
HNCO + C4H9
N2 + 2CO
NCl + CO
HCl + C2H5
NCO + Cl2
n-C4H10
C2H4 + C2H6
NCO + C2H5Cl
Cl2 + N2
7
8
9a
9b
10
11
12
a
b
C2H5 + ClNCO
NCl + NCl
X
(8.1 ꢀ 1.8) ꢁ 10ꢂ12
measured/calculated
d
27
f
X
b
c
All reactions are second-order. Measured in this work. Measured in high C2H6 pressure experiments. Likely products H2CCH(NCO) +
e
HNCO f
pk
H. Measured in experiments used to determine s
. See text.
ꢃc
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Phys. Chem. Chem. Phys., 2007, 9, 4301–4314 | 4303

Table 3 Summary of the DH0f,0 of the species in the NCO + C2H5
reaction model
constants were calculated for all species using the method
developed by Fuller et al.,38 and normalized to the observed
diffusional loss rate constant for HCl. This procedure gave
diffusional rate constants for the monitored stable species,
HNCO, HCN and C2H4, within about 10% of their measured
values, and provided good estimates for the unobserved
species. The diffusional loss rate constants for NCO and
C2H5 radicals were assumed to be the same as HNCO and
C2H4, respectively.
Species
DH0f,0(X)/kJ molꢂ1
Ref.
2
NCO(X P)
128 ꢀ 0.8
119.62 ꢀ 0.008
132 ꢀ 4
28
29
Cl(2 Pu)
2
C2H5(X A00)
30
This work
This work
C2H5NCO
C2H5OCN
NCl(X3Sꢂ)
C2H6
20 ꢀ 80a
10 ꢀ 80a
325 ꢀ 5
31
30
16
29
28
28
32
29
32
33
ꢂ68.2 ꢀ 0.3
53 ꢀ 30
ClNCO
HCl
HNCO
HOCN
C2H4
ꢂ91.992 ꢀ 0.006
ꢂ115.5 ꢀ 0.8
ꢂ12.9 ꢀ 1
61 ꢀ 1
C. Determination of rate constants and product branching
ratios
All rate constants were determined as described in recent
works.14,16 A single rate constant, in the reaction model of
Table 2, noted by ‘‘optimized’’ in column 5, was varied until
the sum of the squares of the residuals, w2X, between the
experimental temporal concentration profiles of X and the
model simulation was minimized. The fitting procedure also
returned an estimate of the confidence limits in the value of the
rate constant at the 68% level in the goodness-of-fit.
CO
HCN
ꢂ113.8 ꢀ 0.2
132 ꢀ 4
H3CC(H)O
C2H3NCO
C4H10
ꢂ166 ꢀ 2b
120c
ꢂ97.5 ꢀ 2
ꢂ112.1 ꢀ 1d
66.5d
30
34
34
34
b
C2H5Cl
1-C4H9
2-C4H9
a
70d
Estimated from theoretical calculations, see section III. F. DHf0,298
c
and corrected to 0 K. Estimated from the C–N bond energy
Reaction (10) is analogous to the C2H5 + Cl2 reaction. Its
inclusion in the reaction scheme improved the model fits to the
NCO profile at long times. Three species were sensitive to the
value of k10, NCO, HNCO and C2H4, but only the NCO and
C2H4 profiles were used in the data analysis for k10 because
their peak absorption coefficients (Table 1) were better deter-
mined. The procedure adopted to determine the optimum
value of k10 was similar to that described previously.16 With
k1a fixed by fitting the HNCO profile, a value of k10 was
chosen and each rate constant, k1 and k1b, was varied to define
a minimum in w2NCO(k1, k10) and wC H 2(k1a+1b, k10), respec-
C2H3NO2. DH0f,298
.
d
recombination and disproportionation channels have been
established.5 Fortunately, k9 is a factor of ten smaller than
k1 so that reaction (9) is a minor removal process for C2H5.
The rate constant for reaction (7) is sufficiently large that the
ethyl radicals are produced over a time-scale of a few tens of
microseconds, and no other reactions contribute to the Cl
atom loss. Hence, the initial concentrations of NCO and Cl are
accurately determined by the initial HCl concentration.
When radicals are generated by photolysis, there is always
the concern that excess energy will be deposited into vibra-
tional motions of the products, and influence the subsequent
kinetics. Using a recent estimate16 of the bond dissociation
energy of ClNCO to be 195 kJ molꢂ1, there are 288 kJ molꢂ1
of excess energy to be distributed between the relative transla-
tional motion of Cl and NCO and the internal energy in NCO.
At a few Torr total pressure, translational and rotational
energy are quickly thermalized, and only vibrational energy
in NCO is of concern. The real extent of vibrational excitation
in NCO is unknown but vibrational relaxation is rapid in
NCO even in collisions with inert gases.36 In the experiments
reported here, N2O was the predominant carrier gas, and it is
an efficient relaxation partner for vibrationally excited NCO.37
Therefore, the vibrational energy levels of NCO are equili-
brated to the temperature of the bath gas after a short
induction period. There is no internal energy excitation in
the C2H5 radical because reaction (7) is only slightly exother-
mic (DH0f,0 = ꢂ11.2 kJ molꢂ1).
2
4
tively. The value of k10 was incremented and the procedure
repeated, until w2NCO(k1, k10) and wC H 2(k1a+1b, k10) were
2
4
defined as functions of k10. The resulting parabolic curves
were fit to a second-order polynomial to determine the values
of k10 that minimized w2NCO(k1, k10) and wC H 2(k1a+1b, k10).
2
4
Usually, the plot defining w2NCO(k1, k10) had the larger curva-
ture and hence smaller uncertainty in the estimate of k10. The
optimum value of k10 was taken as a weighted average of the
two values, where the weights were the reciprocal of the 68%
goodness-of-fit limits. The final values of k1 and k1a+1b were
determined by refitting the NCO and C2H4 profiles using this
best estimate of k10.
In an initial attempt to fit all the data, i. e. at low (o0.39 Torr)
and high (41.0 Torr) C2H6 pressures, the following strategy
HNCO
pk
was adopted: s
was treated as a variable because of its
large uncertainty (Table 1), reaction k1b was not included in
the reaction mechanism, and k2 was fixed at the value in Table
HNCO
2. No consistent values for k1a or s
were found that
pk
described the complete data set, over this wide variation in
C2H6 pressures (0.1 to 3.3 Torr). To deal with this, an alternate
HNCO
The reaction time-scale is several milliseconds so that diffu-
sion is an important removal process. The diffusional loss
process is complicated by the geometry of the system, and two
first-order rate constants differing in magnitude by about a
factor of ten, describe the loss by diffusion.14 Only the largest
diffusional rate constant was considered in the data analysis of
the first 5 ms of the concentration profiles. Binary diffusion
strategy was adopted: s
was fixed at the value reported
pk
in Table 1, reaction (1b) was added to the mechanism, and k2
was treated as a variable in analyzing the high C2H6 pressure
experiments but fixed to the value in Table 2 in the analysis of
low C2H6 pressure experiments. For the analysis of the low
C2H6 pressure experiments, the HNCO temporal concentra-
tion profile was used to determine k1a by minimizing wH2 NCO
ꢃc
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4304 | Phys. Chem. Chem. Phys., 2007, 9, 4301–4314

with k1 and k10 fixed at the values determined by analyzing the
NCO and C2H4 profiles, as discussed. With k1a known, k1b
2
was found by minimizing wC H as a function of k1b. In a
2
4
similar fashion, k1c was determined by fixing the other rate
constants and finding the minimum in w2HCN as a function of
k1c. The rate constant for channel (1d), k1d, was determined by
subtracting the sum of the other three channel rate constants
from k1.
Typical experimental temporal concentration profiles are
shown in Fig. 1 to 4. In each figure, panel (a) corresponds to
the experimental profiles for NCO and HCl and panel (b)
corresponds to the product profiles, C2H4, HNCO, and HCN.
The open symbols are the experimental data shown every 10th
point, the lines (dashed and solid) are the optimized fits to the
appropriate species, and the dotted lines denote zero concen-
trations. The determination of k1 and the product branching
ratios were made under the conditions of low C2H6 pressures,
as illustrated in Fig. 1 and 2. These experimental conditions
Fig. 2 (a) Typical experimental temporal concentration profiles for
NCO (J) and HCl (,) observed at high total pressure and low PC H
.
6
2
The data points are shown every 10th point. The curves are calculated
model profiles for NCO (—) and HCl (ꢄ ꢄ ꢄ) using the optimum rate
constants: k1 = (3.8 ꢀ 0.5) ꢁ 10ꢂ10 cm3 moleculeꢂ1 sꢂ1 and k7 = (5.0
ꢀ 1.0) ꢁ 10ꢂ11 cm3 moleculeꢂ1 sꢂ1, and k10 = (1.0 ꢀ 1.0) ꢁ 10ꢂ13 cm3
moleculesꢂ1 sꢂ1. (b) Same as (a) except for C2H4 (n), HNCO(&), and
HCN (ꢅ). The curves are the model profiles for HNCO (ꢄ ꢄ ꢄ), C2H4
(—), and HCN (-ꢄ ꢄ ꢄ-): k1a = (1.3 ꢀ 0.3) ꢁ 10ꢂ10, k1b = (3.1 ꢀ 0.3) ꢁ
10ꢂ11, and k1c = (1.0 ꢀ 2.0) ꢁ 10ꢂ13 cm3 moleculeꢂ1 s.ꢂ1 The
conditions of the experiment were PN O = 3.82, PAr = 0.384, PC H
2
2
6
= 0.172 and PClNCO = 0.013 Torr at a temperature of 293 K.
and rate constant measurements are summarized in Table 4
and shown in Fig. 5.
A comparison between Fig. 1a and 2a shows that in the
higher-pressure experiment NCO decays faster, although the
initial NCO concentration is slightly larger. The rate constant
analysis bears this observation out; k1 is a factor 1.52 larger for
a pressure change from 2.11 to 4.38 Torr. As can be seen from
Table 4 and Fig. 5a, k1 and k1d were pressure dependent but
the other rate constants were independent of pressure (Fig. 5b
and c).
Fig. 1 (a) Typical experimental temporal concentration profiles for
NCO (J) and HCl (,) observed at low total pressure and low PC H
.
In Fig. 1a and 2a, the model calculated HCl profiles were
generated by determining optimum values for k7 instead of the
value listed in Table 2. Under high PC H conditions, Fig. 2a
2
6
The data points are shown for every 10th point. The curves are the
calculated model profiles for NCO (—) and HCl (ꢄ ꢄ ꢄ) using the
optimum rate: k1 = (2.5 ꢀ 0.3) ꢁ 10ꢂ10 cm3 moleculeꢂ1 sꢂ1 and k7
2
6
and 4a, the appearance rate of HCl was too large to provide an
= (5.0 ꢀ 0.4) ꢁ 10ꢂ11 cm3 moleculeꢂ1
s
ꢂ1, and k10 = (2.9 ꢀ 1.0) ꢁ
estimate for k7. The analysis for k7 yielded a value of (4.7 ꢀ
10ꢂ13 cm3 moleculesꢂ1 ꢂ1. (b) Same as (a) except for C2H4(n),
s
0.26) ꢁ 10ꢂ11 cm3 moleculeꢂ1
s
ꢂ1, where the uncertainty is
HNCO(&), and HCN (B). The curves are the model profiles for
HNCO (ꢄ ꢄ ꢄ), C2H4 (—), and HCN (-ꢅ-) using the optimum rate
one-standard deviation from the average, which is about 15%
less than the more precise measurements of Pilgrim et al.25 No
attempt was made to provide an improved measurement for
k7. The C2H6 flow meter was used to cover the complete flow
range of C2H6 (up to 400 sccm) and for low C2H6 pressures
constants: k1a = (1.2 ꢀ 0.12) ꢁ 10ꢂ10, k1b = (1.7 ꢀ 0.5) ꢁ 10ꢂ11
,
and k1c = (6.9 ꢀ 2.2) ꢁ 10ꢂ13 cm3 moleculeꢂ1
s
ꢂ1. The conditions of
the experiment were PN O = 1.82, PAr = 0.190, PC H = 0.149 and
2
2
6
PClNCO = 0.0078 Torr at a temperature of 293 K.
ꢃc
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Fig. 4 (a) Typical experimental temporal concentration profiles for
NCO (J) and HCl (,) observed at high total pressure and high PC H
Fig. 3 (a) Typical experimental temporal concentration profiles for
.
6
2
NCO (J) and HCl (r) observed at low total pressure and high PC H
.
The data points are shown every 10th point. The curves are the model
profiles for NCO (—) and HCl (ꢄ ꢄ ꢄ). For k2 = 1.6 ꢁ 10ꢂ14 cm3
moleculesꢂ1 sꢂ1, the optimum value for k1 was (3.3 ꢀ 0.7) ꢁ 10ꢂ10 cm3
moleculesꢂ1 sꢂ1. (b) Same as (a) except for C2H4 (n) and HNCO (&).
The curves are the model profiles for HNCO (ꢄ ꢄ ꢄ) and C2H4 (—) using
the optimum rate constants for each channel: k1a = (1.2 ꢀ 0.11) ꢁ
10ꢂ10, k1b = (3.9 ꢀ 0.5) ꢁ 10ꢂ11 cm3 moleculeꢂ1 s.ꢂ1 The conditions
of the experiment were PC H = 1.78, PN O = 1.75, PAr = 0.38, and
2
6
The data points are shown every 10th point. The curves are calculated
model profiles for NCO (—) and HCl (ꢄ ꢄ ꢄ). For k2 = 1.6 ꢁ 10ꢂ14 cm3
moleculesꢂ1 sꢂ1, the optimum value for k1 was (2.2 ꢀ 0.6) ꢁ 10ꢂ10 cm3
moleculesꢂ1 sꢂ1. (b) Same as (a) except for C2H4 (n) and HNCO (&).
The curves are the model profiles for HNCO (ꢄ ꢄ ꢄ) and C2H4 (—) using
the optimum rate constants: k1a = (9.3 ꢀ 0.11) ꢁ 10ꢂ11, k1b = (1.9 ꢀ
0.3) ꢁ 10ꢂ11 cm3 moleculeꢂ1
s
ꢂ1. The conditions of the experiment
2
6
2
were PC H = 1.55, PAr = 0.166, and PClNCO = 0.005 Torr, at a
PClNCO = 0.01 Torr, at a temperature of 294 K.
2
6
temperature of 293 K.
small C2H6 flows resulted in a larger uncertainty in the C2H6
partial pressure. None of the rate constant determinations for
reaction (1) depended on the accuracy of the C2H6 pressure
measurement.
and 2b, the rise in the experimental HCN profile is faster than
the model predictions. Similar behavior was observed for the
HCN/HNC product channels in the NCO + CH3 reaction.14
In this case, this was attributed to rapid vibrational relaxation
of excited HCN/HNC bending modes populating the ground
vibrational level. Likely, the situation is similar for reaction
(1). Note the better agreement for the appearance of HCN at
higher N2O pressure, Fig. 2b compared to Fig. 1b, supports
this speculation.
It can be seen from Fig. 1b and 2b that the concentration of
C2H4 is slightly larger than the concentration of HNCO,
indicating another source of C2H4 besides reaction (1a). This
other source was attributed to reaction (1b). When k1b was
included in the reaction scheme, the calculated temporal
concentration profiles for HNCO and C2H4 were in good
agreement with the experimental profiles over the complete
observation time-scale. This was also the case under high C2H6
pressure conditions, as seen in Fig. 3b and 4b. Note too, there
is a difference in the shape of the C2H4 and HNCO profiles due
to their slightly different chemistry. The model calculations
reproduce this difference quite well.
There is considerable excess energy released in reaction (1),
and it is likely that some of this energy was deposited as
vibrational energy in the products. Indeed, in the similar Cl +
C2H5 - HCl + C2H4 reaction, the vibrational energy dis-
tribution in the HCl product has been measured39 and vibra-
tionally excited C2H4 has been observed.40 An initial
population inversion, indicated by negative absorption signals,
was observed near time equal to zero on the HNCO profiles,
but its duration was only a few microseconds. If vibrational
relaxation were slow, the concentration and rate of appear-
ance of the probed species would be underestimated. For a
polyatomic molecule, the slowest vibrational relaxation step is
The only product observed for channel (1c) was HCN with
the C2H4O coproduct assumed to be CH3CHO, the most
exothermic channel. This channel accounted for less than
0.4% of the product yield for reaction (1), and only a few
measurements were made on its yield. As can be seen in Fig. 1b
ꢃc
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Table 4 Summary of the experimental conditions and rate constant determinations for conditions with low C2H6 pressures
Partial pressure/Torr
Rate constants/cm3 moleculeꢂ1 sꢂ1
[NCO]a
1013
PN O
PAr
PC H
6
PClNCO
k1 (10ꢂ10
)
k1a (10ꢂ10
)
k1b (10ꢂ11
)
k1c (10ꢂ13
)
k10 (10ꢂ13
)
2
2
1.76
1.76
1.77
1.78
1.83
1.83
1.83
1.83
1.83
3.23
3.23
3.83
3.83
3.83
3.83
3.86
3.86
3.86
Average
0.187
0.188
0.189
0.189
0.188
0.188
0.189
0.190
0.190
0.401
0.401
0.386
0.386
0.386
0.386
0.389
0.389
0.389
0.148
0.148
0.150
0.150
0.0964
0.0964
0.0943
0.0950
0.0950
0.318
0.318
0.173
0.173
0.173
0.173
0.175
0.175
0.175
0.0059
0.0076
0.0089
0.0078
0.010
0.010
0.011
0.0075
0.0075
0.014
0.014
0.013
0.013
0.013
0.013
0.0089
0.0089
0.0089
0.630
0.667
1.06
2.8(.13)b
2.6(.3)
2.8(.2)
3.0(.35)
2.0(.5)
2.4(.3)
2.4 (.2)
1.8(.23)
2.5(.3)
3.1(.15)
3.0(.2)
3.5(.4)
3.8(.48)
3.8(.35)
4.0(.6)
4.2(.7)
3.4(.25)
1.21(.02)
1.03(.03)
1.15(.05)
1.27(.07)
0.87(.17)
0.95(.15)
1.1(.2)
0.87(.4)
1.16(.12)
1.0(.05)
0.98(.08)
1.13(.3)
1.28 (.3)
1.19(.05)
1.42( .06)
1.43(.06)
1.20( .04)
1.31(.02)
1.14
3.4(.5)
3. 6(.5)
2.5(.6)
2.2(.6)
3.7(.8)
3.4(.7)
2.8(.65)
1.7(.5)
1.7(.5)
3.0(.35)
3.0(.3)
2.9(.3)
3.1(.30)
1.3(.25)
0.58(.2)
2.4(.75)
3.0(.7)
2.7(.65)
2.9
2.0 (1.0)
5.8(4.0)
1.0 (1.0)
0.5( 2.0)
3.7( 3.7)
2.2 (2.0)
1.5(1.0)
4.9 (3.0)
2.9(2.9)
0.5(1.5)
2.0(1.5)
1.0 (1.0)
1.0 (1.0)
3.4(1.3)
1.0(1.0)
1.5(1.5)
6.0(2.5)
4.6 (3.0)
2.3
1.25
0.907
0.907
0.883
1.35
1.30
1.03
1.00
1.77
1.70
0.909
0.849
0.860
0.866
0.844
7.3(2.3)
6.9(2.0)
10. (2.0)
3.8(.30)
9.8(1.8)
c
8.7
1.5
c
Standard deviation
0.17
1.3
1.2
a
b
Units molecules cmꢂ3
.
Numbers in parentheses are the uncertainties at the 68% level of confidence in the goodness-of-fit. Pressure dependent.
the relaxation of the lowest energetic level, a V–R,T process;
higher vibrational levels rapidly equilibrate by V–V pro-
cesses.41 In the present experiments, the bath gas was either
N2O, C2H6 or both, and both molecules have vibrational
energy levels lower in energy or nearly so than the lowest
vibrational energy level in HNCO, n5 = 574 cmꢂ1, and C2H4,
determined under low C2H6 pressures, and the final k2 value
determined. The experimental conditions and results of this
analysis are summarized in Table 5.
A notable feature of the results summarized in Table 4 and
illustrated in Fig. 5a is the pressure dependence of k1. Over this
pressure range k1 is described by (1.25 ꢀ 0.16) ꢁ 10ꢂ10 + (5.63
n
10 = 826 cmꢂ1. Thus, vibrational relaxation is expected to be
ꢀ 0.47) ꢁ 10ꢂ11 P(Torr) cm3 moleculesꢂ1
s
ꢂ1. The pressure
facile for each molecule in collisions with N2O or C2H6. The
HNCO molecule is a transient species, and no information on
the vibrational relaxation of HNCO was found. However,
except for the high frequency n1 mode in HNCO, its vibra-
tional frequencies are similar to NCO, and the vibrational
relaxation of HNCO should be similar to NCO.36,37 Vibra-
tional relaxation in C2H4 has been investigated,42,43 and the
V–T, R relaxation of the lowest excited vibrational level was
found to be rate limiting. Yaun and Flynn have measured the
V–T, R rate constant of C2H4 with C2H6 to be 2.8 ꢁ 10ꢂ12 cm3
moleculeꢂ1 sꢂ1. As is evidenced in Fig. 1b to 4b, there was no
difference in the appearance rate of C2H4 or HNCO as a
function of total pressure or C2H6 partial pressure, so that
vibrational energy redistribution in C2H4 and HNCO was
rapid on the time-scale of the reactions producing them.
Comparing the NCO profiles for low (Fig. 1a and 2a) and
high (Fig. 3a and 4a) C2H6 pressure experiments, immediately
reveals the influence of reaction (2). At high C2H6 pressure
(Fig. 3a and 4a), the NCO profiles are more exponential in
appearance. As already noted, there is considerable uncer-
tainty in the reported22,23,35 values for k2; thus, the consistency
of the measurements made under low C2H6 pressures was
examined by analyzing the high C2H6 pressure experiments to
determine k2 independently. Under these conditions, the pro-
cedure used to determine k1 and k2 was similar to that
described in the determination of k10. However, both wN2 CO
(k1, k2) and w2HNCO(k1, k2) curves had very small curvatures;
hence, the range of acceptable values of k1 and k2 was broad.
Generally, a value of k1 was found that agreed with k1
dependence is due to the recombination channel and k1d is
given by (0.090 ꢀ 1.3) ꢁ 10ꢂ11 + (5.21 ꢀ 0.36) ꢁ 10ꢂ10
P(Torr) cm3 moleculesꢂ1 ꢂ1. As is evident from Table 4 and
s
shown in Fig. 5b, k1a and k1b were pressure independent, and
have the values (1.14 ꢀ 0.17) ꢁ 10ꢂ10 and (2.9 ꢀ 1.3) ꢁ 10ꢂ11
cm3 moleculeꢂ1 sꢂ1, respectively, where the uncertainty is one-
standard deviation from the average, 1s. Fig. 5c shows the
measurements for k1c, and within the scatter of the data, k1c
appears to be pressure independent with a value of (8.7 ꢀ 1.5)
ꢁ 10ꢂ13 cm3 moleculeꢂ1
s
ꢂ1. The last column of Table 4 lists
the measurements of k10 to be (2.3 ꢀ 1.2) ꢁ 10ꢂ13 cm3
moleculeꢂ1 sꢂ1 with uncertainty of 1s.
At high C2H6 pressures, independent measurements were
made of k1, k1a, and k1b (Table 5) that were in good agreement
with those made at low C2H6 pressures (Table 4). However,
there was a high degree of correlation between k1 and k2, and
the high C2H6 pressure measurements were not considered as
reliable as the low pressure ones. The value found for k2 is
summarized in the last column in Table 5 and is (1.6 ꢀ 0.11) ꢁ
10ꢂ14 cm3 moleculeꢂ1
s
ꢂ1, where the uncertainty is 1s.
HNCO
pk
D. Determination of r
In order to determine the product branching into channel (1a),
it is necessary to measure the absorption coefficient for a
suitable spectroscopic transition in HNCO. However, the
generation of pure samples of HNCO is not straightforward.24
Thus, HNCO was generated in situ from the reaction of NCO
+ n-C4H10 using ClNCO as the NCO precursor. The initial
ꢃc
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Phys. Chem. Chem. Phys., 2007, 9, 4301–4314 | 4307

radicals was suppressed by the addition of excess O2, as done
by Maricq et al.40 At the O2 pressures used in the experiment,
the rate of reaction (18) was sufficiently rapid that reactions
(12), (13) and (14) made no significant contributions to the
removal of NCO. Reaction (15) is a potential loss process for
NCO that might not generate HNCO. The butylperoxide
radical could decompose to the corresponding alkene +
HO2 products; however, no information was found on this
pathway and it was not included in the mechanism.
HNCO
The determinations of k4 and s
were made in an
pk
iterative manner. The first estimate of k4 was made using the
HNCO
NCO profile. A value for s
was then found by varying
pk
HNCO
s
pk
to minimize w2HNCO for the model and experimental
HNCO profiles generated using the estimate of k4 given from
the NCO profile analysis. The value of k4 was then revised by
fitting the new HNCO experimental profile generated with the
HNCO
pk
HNCO
pk
estimate of s
. Further iterations in s
and k4
resulted in changes of less than 2%. Values of k4 determined
by fitting the NCO profile were usually about 10% larger than
those determined fitting the HNCO profile. This was attrib-
uted to the loss of NCO by reaction (4) before vibrational
equilibration of NCO was complete. Under conditions of
vibrational disequilibrium, monitoring only the ground state
of NCO is not a true measure of the total NCO concentration.
Evidence for this comes from the systematic under prediction
of the initial NCO concentration determined by extrapolating
the NCO profile back to time zero compared to the initial
NCO concentration determined from the HCl profile.
Typical experimental profiles for HCl, HNCO, NCO, and
their model simulations are shown in Fig. 6, and the experi-
mental conditions and results are summarized in Table 7. Fig.
6a shows the initial 10 ms of the HCl profile and 450 ms of the
HNCO profile. The model calculations presented in the figure
HNCO
reflect the last iteration to determine k4 and s
using the
pk
Fig. 5 (a) Summary of the determination of the k1 (’) and k1d (&)
as a function of the total pressure. Only the low PC H data, Table 4,
HNCO profile. For this calculation, k15 was set to 1.0 ꢁ
2
6
10ꢂ12 cm3 moleculeꢂ1 ꢂ1. With this value of k15, the fraction
s
were used to determine the rate constants associated with reaction (1).
The error bars are the uncertainty in the optimized values of k1 at the
68% confidence level. The pressure dependence was allocated to the
recombination channel. The lines are a linear fit to the data points.
(b) Similar to (a) except a summary of the determination of the
optimum values for k1a (K) and k1b (J). The dashed lines are the
average values listed in Table 4 and the error bar attached to the lines
the standard deviation. (c) Similar to (a) and (b) except for the
determination of k1c (m). Although there is an apparent pressure
dependence on k1c, the scatter is too large to be conclusive.
on NCO removed by reaction 15 was 7 ꢁ 10ꢂ4 but increased to
0.033 for k15 equal to 5.0 ꢁ 10ꢂ11 cm3 moleculeꢂ1 sꢂ1. Similar
behavior was found in the simulations of the other experi-
mental runs. It is unlikely that k15 would be substantially
larger than k4 and it, therefore, had a small effect on the
HNCO
measurement of s
.
pk
From Table 7, the value of k4 determined fitting the NCO
profile was (5.7 ꢀ 0.86) ꢁ 10ꢂ13 cm3 moleculesꢂ1 sꢂ1 and that
determined fitting the HNCO profile was (5.3 ꢀ 0.51) ꢁ
10ꢂ13 cm3 moleculesꢂ1 ꢂ1, where the uncertainty is 1s. The
s
radical concentration was again determined from the HCl
concentration generated in the Cl + n-C4H10 reaction. The
rate constant for the NCO + n-C4H10 reaction is sufficiently
large23 that all the NCO radicals can be scavenged in a few
hundred microseconds at modest pressures of n-C4H10, mini-
mizing secondary loss processes. The complete reaction
mechanism44–47 used in the data analysis is given in Table 6.
The products of reaction (4) have not been conclusively
established but a recent study23 of the yield of HNCO from the
reaction of NCO with a variety of alkanes and alkenes
provides strong evidence that HNCO is the dominant channel.
Both reactions (4) and (16) produce 1-C4H9 and 2-C4H9
radicals (Table 6) so that the reaction of NCO with these
value from the HNCO profile analysis was taken as the more
reliable measurement. There is only one previous measure-
ment of k4. Park and Hershberger23 found k4 equal to
(6.1 ꢀ 0.3) ꢁ 10ꢂ13 cm3 moleculesꢂ1 sꢂ1 at 296 K, and within
the scatter of the measurements, the agreement is good.
E. Reaction contribution factor analysis
It is important to have some measure of the influence an
individual reaction has on the chemistry in a chemical reaction
mechanism. One useful measure is a reaction contribution
factor analysis48 particularly when both concentrations and
rate constants are important. An IRCF analysis was done for
ꢃc
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4308 | Phys. Chem. Chem. Phys., 2007, 9, 4301–4314

Table 5 Summary of the experimental conditions and rate constanta determinations for conditions of high C2H6 pressure
Rate constants/cm3 moleculeꢂ1sꢂ1 c
k1 (10ꢂ10 k1a (10ꢂ10 k1b (10ꢂ11
Partial pressure/Torr
[NCO]
(1012 b
PC H
PN O
PAr
PClNCO
)
)
)
)
k1d (10ꢂ10
)
k2 (10ꢂ14
)
2
6
2
1.55
1.55
3.25
1.55
1.55
3.15
1.03
1.55
1.75
0.0
0.0
0.0
0.0
0.0
0.0
2.44
1.94
1.78
0.161
0.161
0.338
0.166
0.166
0.349
0.394
0.387
0.383
005
8.51
4.80
8.40
9.20
9.31
2.5 ꢀ 0.40
2.2 ꢀ 0.30
2.7 ꢀ 0.80
1.7 ꢀ 0.3
2.2 ꢀ 0.50
3.1 ꢀ 0.5
2.3 ꢀ 0.4
2.2 ꢀ 0.4
0.91 ꢀ 0.10
1.1 ꢀ 0.1
0.92 ꢀ 0.5
1.08 ꢀ 0.11
0.91 ꢀ 0.09
1.0 ꢀ 0.15
1.2 ꢀ 0.08
1.1 ꢀ 0.1
1.2 ꢀ 0.1
1.0
2.8 ꢀ 0.40
1.0 ꢀ 0.30
0.0
2.2 ꢀ 0.6
1.9 ꢀ 0.30
2.0 ꢀ 0.4
0.7 ꢀ 0.6
1.7 ꢀ 0.8
3.9 ꢀ 0.4
1.7
1.3
1.1
1.8
0.43
1.1
1.9
1.1
1.6
1.7
1.6
1.4
1.6
1.4
1.4
1.4
1.6
1.6
0.11
0.005
0.005
0.005
0.005
0.010
0.006
0.006
0.01
20.3
5.42
5.27
4.73
0.988
1.8
3.3 ꢀ 0.7
d
d
Average
Standard deviation
0.11
0.14
a
b
c
k10 was fixed at 2.3 ꢁ 10ꢂ13 cm3 moleculeꢂ1 sꢂ1
.
Units molecule cmꢂ3
. The uncertainties are the 68% level of confidence in the goodness-of-
d
fit. Pressure dependent.
every model simulation. An example of an IRCF analysis for
the experiment illustrated in Fig. 1 is shown in Fig. 7. The
IRCFXs are expressed as a fraction of the total amount of
species ꢁ produced or removed in the system. As indicated by
made using a commercial program (HyperChem).49 This
program could also be used to calculate the energy and
physical properties of the lowest excited triplet states of these
molecules. The calculations were made at the 6-311++G**/
MP2 level of theory; thus, the uncertainty in the calculations is
large (ꢀ 80 kJ molꢂ1). The vibrational frequencies were
calculated using a smaller basis set at the 6-311G*/MP2 level
of theory. The results of the electronic structure calculations
are summarized in Table 8.
the IRCFNCO and IRCFC H plots in Fig. 7a and b, reaction
(1) accounted for nearly 80% of the total removal of both
NCO and C2H5, and only small fractions were removed by
diffusion and reaction (9). Under low C2H6 pressure condi-
tions, reaction (2) accounted for about 10% of the total
removal of NCO and production of C2H5, as indicated in
Fig. 7. The general behavior of the ICRFXs, as outlined in
Fig. 7 was observed in all the experiments.
2
5
IV. Discussion
A. The recombination channel, 1d
F. Theoretical estimates of the bond dissociation energies of
C2H5–NCO and C2H5–OCN
Troe’s description2 of a high-pressure recombination rate
constant, krec,N, was used to provide a theoretical estimate
for k1d. In this formulation, krec,N is given by:
The recombination channel accounts for over half of the
products in reaction (1), but neither possible recombination
product was detected in the present experiments. A theoretical
estimate of the rate constant for this channel would be an
important clue as to the dynamics of reaction (1). Further-
more, no experimental measurements or theoretical estimates
could be found for the heat of formation for either C2H5NCO
or C2H5OCN. Thus, electronic structure calculations of the
bond energy and vibrational frequencies of both isomers were
QꢆcentFAꢆMe
1
kT
h
h2
QelðABÞ
ꢆ
3=2
krec;1
¼
ð
Þ
2pmkT
QelðAÞ QelðBÞ QvrðAÞ QvrðsBÞ
DE0z
kT
ðE1Þ
b
r
ꢁ P Qꢆj P Qꢆm expð ꢂ
Þ
where k, h, and T have their usual meaning, m is the reduced
mass, Qel(X) is the electronic partition function of X, Q*cent is a
Table 6 Summary of the reactions and rate constants used to model the NCO + n-C4H10 system at 294 K
No.
Reactants
Products
k/cm3 moleculeꢂ1 sꢂ1
Ref.
a
4a
4b
5
12a
12b
13
14
15
16a
16b
17a
17b
18
NCO + n-C4H10
-
HNCO + 1-C4H9
HNCO +2-C4H9
N2 + 2CO
HNCO + C4H8
C4H9NCO
Products1
Products2
Products3
HCl + 1-C4H9
HCl + 2-C4H9
C8H18
Optimizeda
a
NCO + NCO
NCO + C4H9
-
-
-
-
-
-
-
-
-
-
-
Diff.
(5.0 ꢀ 2.ꢂ01)1ꢁ 10ꢂ12
5.0 ꢁ 10
24
Guess
2.0 ꢁ 10ꢂ10
NCO + C4H8
NCO + C8H18
NCO + C4H9O2
Cl + n-C4H10
1.0 ꢁ 10ꢂ10
Guess
Guess
Varied
44
2.0 ꢁ 10ꢂ10
(1.0 to 50) ꢁ 10ꢂ12
(6.2 ꢀ 0.7) ꢁ 10ꢂ11
(1.5 ꢀ 0.2) ꢁ 10ꢂ10
(1.7 ꢀ 0.2) ꢁ 10ꢂ11b
(3.2 ꢀ 0.4) ꢁ 10ꢂ12b
1.4 ꢁ 10ꢂ11c
n-C4H9 + n-C4H9
45, 46
47
C4H10 + C4H8
C4H9O2
c
C4H9 + O2
X
19
X
Measured/calculated
a
b
The distribution of 1-C4H9 and 2-C4H9 radicals as in reaction (16). k17 was assumed to be the same for all C4H9 isomeric combinations.
k18 was assumed the same for all C4H9 isomers.
c
ꢃc
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Phys. Chem. Chem. Phys., 2007, 9, 4301–4314 | 4309

centrifugal pseudo-partition function, F*AME is a factor cor-
recting for the rotation character of the disappearing oscilla-
tors, s* is the effective symmetry number at the transition
state, Qvr(X) is the rovibrational partition function of X, Qj* is
the vibrational partition function for the conserved modes of
*
AB, Qm is the vibrational partition function for the transi-
tional modes, and DE0z is the lowest threshold energy for
recombination. The new bond is described by Morse potential
energy parameters and an interpolation parameter, a, describ-
ing the transformation of rotational degrees of freedom
in the radical fragments into transitional modes of the new
molecule.
In a systematic study, Cobos and Troe50 found that values
of a/b equal to 0.46 ꢀ 0.09 provided agreement between
calculated and experimental values of krec,N for over 26
systems. The theoretical estimates of krec,N for reaction (1d)
are reported in Table 9 for a/b equal to the average and the
plus and minus limits found by Cobos and Troe. Even though
the experimental rate constants are in the fall-off region at a
pressure of 4.5 Torr, the values of k1d (Fig. 5a) are about a
factor of five larger than the theoretical estimates for a/b =
0.55 (Table 9). An increase in either the bond dissociation
energy by a 100 kJ molꢂ1 or the a/b ratio to 1.1 only increases
the calculated value of krec,
by a factor of two, and is
N
still more than a factor of two smaller than the experimental
value.
Fig. 6 (a) Typical concentration temporal profiles for HCl (,) and
HNCO
HNCO (&) used to determine s
for the n1 qR0(16) transition.
The experimental points are shown every 10th point. The curves are
pk
The value of krec,N could be increased if the electronic
degeneracy factor in eqn (E1) was larger than the statistical
value of 1/8. This would require the participation of the triplet
spin manifold in the reaction dynamics. There are several ways
this could occur. By direct recombination into the triplet
manifold followed by intersystem crossing (ISC) to the ground
state, as suggested by Smith51 or indirectly by increasing the
effective density of states due to the mixing of the singlet and
triplet manifolds by the spin–orbit interaction in NCO. This
mechanism was proposed by Sims and Smith52 to account for
the larger than expected recombination rate constant for CN
and NO radicals. However, neither of these mechanisms is
likely to be operative in the NCO + C2H5 system. The initial
approach of the two radicals on the C2H5NCO/OCN (a3A00)
the model simulations for HNCO (—) and HCl (–ꢄ ꢄ ꢄ-). The HNCO
pk
HNCO
profile was fit by varying k4 and s
as described in the text. For
this experiment k4 was found to be (5.8 ꢀ 0.3) ꢁ 10ꢂ13 cm3 moleculeꢂ1
pk
sꢂ1 and s
was (5.12 ꢀ 0.05) ꢁ 10ꢂ18 cm2 moleculeꢂ1. For this
HNCO
simulation, k15 was 1.0 ꢁ 10ꢂ12 cm3 moleculeꢂ1 sꢂ1. The conditions of
the experiment were PO = 2.62, Pn-C H = 1.011, PAr = 0.401, and
2
4
10
PClNCO = 0.014 Torr at 294 K. (b) Same as (a) except the experimental
profile for NCO (&) is shown. The model NCO (—) profile using k4
determined in (a). The value of k4 that was found by fitting the NCO
profile was (6.7 ꢀ 0.4) ꢁ 10ꢂ13 cm3 moleculeꢂ1
pk
s
ꢂ1, and the initial
HNCO
value of s
was (5.09 ꢀ 0.1) ꢁ 10ꢂ18 cm2 molecule.ꢂ1 The model
C4H9 (ꢄ ꢄ ꢄ) profile and indicates how effective reaction (15) is at
scavenging the butyl radicals. The model profile for C4H9O2 (- ꢄ ꢄ ꢄ -).
HNCO
pk
Table 7 Summary of the experimental conditions and results for the determination of s
and k4 using the model chemistrya in Table 6
Partial pressure
k4/cm3 moleculesꢂ1 sꢂ1
HNCO
pk
PO
Pn-C H
NCO (1012 b
)
NCO profile (10ꢂ13
)
HNCO profile (10ꢂ13
)
s
(10ꢂ18 c
)
2
4
10
2.301
2.70
1.65
1.93
1.45
0.487
4.51
7.24
3.08
5.51
9.13
2.92
3.33
3.86
5.10
8.84
4.8
5.7
4.7
5.3
6.5
5.2
5.3
6.8
4.9
5.9
7.3
6.7
5.4
5.7
ꢀ0.86
4.7
5.1
5.0
4.8
6.1
5.5
5.2
4.9
4.9
5.3
6.0
5.8
5.0
5.3
ꢀ0.51
5.9
4.7
5.7
5.7
4.7
5.7
5.6
4.3
4.8
5.0
4.7
5.1
5.7
5.2
ꢀ0.53
1.76
1.90
3.00
0.370
0.267
0.654
2.62
1.01
18.0
9.33
4.71
Average
Standard deviation
a
b
c
The reported determinations were obtained with k15 equal to 1.0 ꢁ 10ꢂ12 cm3 moleculeꢂ1 sꢂ1
.
Units, molecules cmꢂ3 Units, cm2 moleculeꢂ1
. .
ꢃc
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Table 9 Estimates for krec,N for the NCO + C2H5 reaction produ-
cing C2H5NCO or C2H5OCN (X1A0) at 300 K
k
rec, N/cm3 moleculeꢂ1 sꢂ1
Product
a/b = 0.46
a/b = 0.55
a/b = 0.37
C2H5NCO
C2H5OCN
1.9 ꢁ 10ꢂ11
3.8 ꢁ 10ꢂ11
7.7 ꢁ 10ꢂ12
1.4 ꢁ 10ꢂ11
3.3 ꢁ 10ꢂ11
4.2 ꢁ 10ꢂ12
orbitals are orthogonal. High-level electronic structure calcu-
lations on the excited states of the related H + NCO system
concur with these simple arguments.53
It has been recognized that the long-range portion of the
PES between two radicals can play an important part in the
reaction dynamics.54 In this region, the various forms of
angular momentum start to couple to the collision frame.
For atoms with electronic angular momentum reacting with
molecules or radicals, theoretical calculations by several
groups have shown that non-adiabatic transitions can occur
in the van der Waals region of the PES if the spin–orbit
splitting of the atom is smaller than the van der Waals well
depth. Schatz and coworkers55,56 illustrated this for Cl(2 P) +
HCl reaction by artificially adjusting the spin–orbit constant in
the chlorine atom. Similarly, Takayanagi et al.57 conducted
high level, MRCI cc-pVDZ and cc-pVTZ, theoretical calcula-
tions on the 5 doublet PESs for the N(2D) + C2H2 reaction,
and calculated the rate constant as a function of temperature.
They concluded that non-adiabatic effects induced at large
internuclear separations increased the effective electronic de-
generacy for the reaction. The relationship between spin–orbit
splitting and van der Waals well depth is further illustrated by
the theoretical calculations by Yagi et al.58 on the O(3P) +
2
CH3(X A200) reaction. They showed that non-adiabatic tran-
Fig. 7 An IRCF analysis plotted as a fraction of the total removal
(negative) and total production (positive) fluxes for each major species
in reaction (1) under conditions of low total pressure and low PC H
sitions did not play a direct role in the reaction dynamics. For
this system, the fine-structure splittings in the O atom are
comparable to the van der Waals well depth.
2
6
corresponding to the experiment in Fig. 1. (a) NCO. (b) C2H5. (c)
C2H4. (d) HNCO.
The enhancement of the electronic degeneracy factor by the
long range mixing of electronic states could be important in
radical–radical reactions involving the NCO radical. For this
mechanism to be operative the important parameter appears
to be the ratio of the spin–orbit constant to the van der Waals
PES is likely repulsive because of the similar orbital and spin
alignments; thus, direct recombination on this PES is unlikely.
The theoretical calculations reported in section IV F placed
the energy of the triplet state for either isomer higher in energy
than the energy asymptote of the products. At best, the triplet
state density will be low in this region and not enhance the
density of states. No information about the C2H5NCO/OCN
(b3A0) PES is available except to note that the bonding
interaction will be even smaller because the two radical
2
well depth. For linear NCO(X P), the fine-structure splitting
is 95.6 cmꢂ1; however, NCO is subject to the Renner–Teller
effect and the electronic angular momentum is quenched as the
molecule bends. Thus, the effective spin–orbit constant in the
NCO + C2H5 system could be smaller in bent configurations
involving the NCO molecular frame enhancing non-adiabatic
effects. Theoretical calculations on the quenching of NCO
electronic angular momentum in the presence of species
possessing unpaired electrons will need to be done to deter-
mine if this mechanism is possible.
Table 8 Theoretical estimates of the bond energies and morse para-
meters for the dissociating bonds C2H5–NCO and C2H5–OCN produ-
cing NCO + C2H5
Dissociation energyꢂ1
B. Abstraction or complex formation, channels (1a) and (1b)
Isomer
(D)a (X1A0)/kJ mol
bb/Aꢂ1
nD/cmꢂ1
As is evident from Fig. 5b, k1a and k1b are independent of
pressure within the scatter in the data, and suggests that these
two product channels could be produced in a direct bimole-
cular collision encounter. The radical orbital on NCO has
predominantly N atom p-orbital character so that the
C2H5–NCO
C2H5–OCN
a
240
250
2.63
3.91
778
1176
Calculated at the 6-311++G*/MP2 level of theory and corrected for
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
b
zero point energy. Morse parameter, b ¼ 2 p2m=Dh2.
ꢃc
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dominant abstraction product would be expected to be the
HNCO + C2H4 product channel as observed.
similar to the a-hydrogen migration in the C2H5O2 adduct
alluded to in the previous paragraph. A four-centered transi-
tion state involving NCCC atoms has been discovered to be
the lowest energy pathway in the NCO + C2H2 reaction.62
If channel (1a) is indeed an abstraction process, the inter-
action of NCO with C2H5 must be substantially different from
the interaction with C2H6, especially on a per H atom basis.
The temperature dependence22 of k2 has been measured. If it is
represented by a simple Arrhenius expression, the Arrhenius
factor is 1.0 ꢁ 10ꢂ11 and the activation energy is 15.9 kJ
molꢂ1. This activation energy is in excellent agreement with a
theoretical calculation for the barrier height.59 At room tem-
perature, on a per hydrogen atom basis, the NCO abstraction
rate of a hydrogen atom from C2H5 compared to C2H6 is 1.3 ꢁ
104 times larger; however, a reduction of the barrier height to
zero can only account for a factor of 5.9 ꢁ 102 in the reactivity.
The remaining enhancement of the abstraction efficiency by a
factor of 20 could be due to a larger acceptance angle for the
NCO + C2H5 reaction or the dynamical role played by the
energy released in the formation of the more stable C2H4
molecule rather that the C2H5 radical. This is in contrast to the
usual view of abstraction reaction dynamics being governed by
repulsive energy release between the breaking bond fragments
such as occurs the related Cl(2P) + C2H6.60
D. Estimated uncertainties in k1, k1a and k1a + k1b
The uncertainties in the rate constants are directly related to
the factors that determine the concentrations of the various
species monitored in the experiment, either directly by a
concentration measurement or indirectly through the uncer-
tainties in the rate constants used to the model analysis. The
uncertainty in the concentration measurement of each ob-
served species is given by the sum of the uncertainties in the
absorption coefficient (Table 1) and the path length, which is
small, ꢀ 0.2% (section II). The uncertainties in the concentra-
tion measurements introduced by the uncertainties in the rate
constants used in the model calculations were estimated using
the results of the IRCFX analysis for each experiment (Fig. 7),
as described in several recent works.16,63, To a good approx-
imation, the propagation error in a specific rate constant is
given by the fraction of the total removal flux for that specific
reaction times the rate constant uncertainty.
The formation of channels (1a) and (1b) could also result
through complex formation if isomerization and bond break-
ing occur before collisional stabilization. The formation of a
complex would be dominated by the initial overlap of the half-
occupied p-orbitals on the carbon and nitrogen atoms; how-
ever, this interaction would lead to a b-H atom transfer and
the preferential formation of HOCN + C2H4 products rather
than the observed HNCO + C2H4 ones. For the isoelectronic
reaction, O2 + C2H5 - C2H4 + HO2, theoretical calcula-
tions61 have revealed that the dominant low temperature
pathway is a concerted-elimination route through a five-
membered ring intermediate formed from the initial C2H5O2
adduct. A similar reaction path from a H3CH2ꢄ ꢄ ꢄNCO inter-
mediate by a six-membered ring intermediate would produce
HOCN + C2H4 products. If the initial interaction involved a
H3CH2ꢄ ꢄ ꢄOCN adduct, this concerted-elimination pathway
The IRCF analysis in Fig. 7 is typical of the experimental
conditions used to measure k1. There were only four reactions
contributing to NCO kinetics beside reaction (1), reactions (2),
5, (10) and kNdiffCO. The uncertainty in k2 was taken to be ꢀ15%
based on the difference between the value used to analyze the
data (Table 2) and the value measured in this work (Table 5).
At low pressures of C2H6, reaction (2) contributed about 10%
to the total removal of NCO; thus, the uncertainty in k2
contributed about ꢀ1.5% to the systematic uncertainty in
the determination of k1. Reactions (5) and (10) are production
processes but contributed less than 5% to the total NCO
production flux, and hence, contributed about ꢀ3% each to
the uncertainty in k1. Assuming the uncertainties in the
parameters used to define the NCO concentration were dis-
tributed randomly, they contributed a total systematic uncer-
tainty of ꢀ7% to the determination of k1.
would lead to HNCO
+ C2H4 products. From an
H3CH2ꢄ ꢄ ꢄNCO adduct, the abstraction of an a-hydrogen
atom to form HNCO followed by a hydrogen atom transfer
from the methyl group to form C2H4 would have a significant
energy barrier. This pathway is similar to the formation of the
OH + CH3CHO channel in the O2 + C2H5 reaction by a-
hydrogen atom migration and decomposition from the initial
C2H5O2 adduct. Calculations61 show that this pathway has a
larger barrier than the concerted-elimination pathway.
The concentration of C2H5 was not directly monitored in
the experiment, but was established by the initial radical
concentration and the kinetic model. The initial NCO and
C2H5 radical concentrations were determined from the HCl
profile, contributing a systematic uncertainty of ꢀ1% due to
HCl
the uncertainty in s
(Table 1). The reactions contributing
pk
directly to the C2H5 concentration besides reaction (1) were
C2H5
reactions (2), (9), (10), and kdiff
. The uncertainties in the
individual reactions are listed in Table 2 and can be combined
with the IRCF C H from Fig. 7 to provide an overall estimate
of the uncertainty in the C2H5 concentration, and hence
contributing an uncertainty of ꢀ7% to k1, coincidentally the
same as for NCO.
2
5
C. Channel (1c)
The only observed product from channel (1c) was HCN. The
coproduct was assumed to be the most stable one, CH3CHO.
The HNC isomer of HCN, was not observed. Clearly, the
formation of HCN + CH3CHO in reaction (1) requires
isomerization and bond breaking from a C2H5ꢄ ꢄ ꢄNCO/OCN
intermediate. A plausible pathway is a-hydrogen migration to
the carbon atom of OC0N by the formation of a four-mem-
bered ring transition state followed by C0–O bond cleavage
giving HCN and H3CHO products. This pathway is again
Other factors effecting the measurements such as pressure
broadening, flow and total pressure measurements, and the
uncertainty in tuning to the maximum of an absorption
feature were small or contribute to the random scatter in the
measurements of k1. This random scatter was taken from
Table 4 to be ꢀ13%. Assuming the individual errors were
distributed randomly, the systematic and random errors were
ꢃc
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4312 | Phys. Chem. Chem. Phys., 2007, 9, 4301–4314

combined to give an estimated uncertainty in k1 of ꢀ16%,
including both systematic and random errors.
The participation of electronically excited states in the
reaction dynamics was examined. A possible mechanism caus-
ing the large rate constant for reaction (1) could be the mixing
of triplet and singlet manifolds at long range due to the
spin–orbit interaction in NCO, thus leading to an enhanced
electronic degeneracy factor for the reaction.
A similar analysis as outlined above can be used to estimate
the contribution of systematic and random errors in the
measurements of k1a and k1b. Both HNCO and C2H4 were
removed by diffusion with an experimental uncertainty of ꢀ
10% (section III. B). Reaction (2) produced HNCO with an
uncertainty in k2 of ꢀ15%, as discussed. There were no
significant reactions producing C2H4 (Fig. 7c). The largest
Acknowledgements
uncertainty in analyzing the HNCO profile resulted from the
HNCO
This work was performed under the auspices of the Office of
Basic Energy Sciences, Division of Chemical Sciences, Geo-
sciences, and Biosciences, US Department of Energy, under
contract number DE-AC02-06CH11357.
uncertainty of ꢀ11% in the value of s
(Table 1). The
pk
C2H4
spk
is better known and has an uncertainty of ꢀ1% (Table
1). The uncertainties in the determination of the HNCO and
C2H4 concentrations were calculated to be ꢀ12 and ꢀ4%,
respectively. However, the determination of k1a and k1a + k1b
relied on the NCO and C2H5 concentrations as well, contri-
buting uncertainties of ꢀ7% each. Again, combing these
uncertainties with a random scatter of ꢀ16% in k1a and
k1a + k1b (Table 4), the resultant random and systematic
errors in k1a and k1a + k1b, were ꢀ22% from the HNCO
profile analysis for k1a and ꢀ19%, if the C2H4 profile had been
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V. Summary
The rate constant for the NCO + C2H5 reaction was mea-
sured over a pressure range of 2.1 to 4.4 Torr at a temperature
of 293 ꢀ 2 K, and found to increase with increasing pressure.
Over this pressure range k1 is represented by (1.25 ꢀ 0.16) ꢁ
10ꢂ10 + (3.3 ꢀ 0.47) ꢁ 10ꢂ11 P(Torr) cm3 moleculesꢂ1 sꢂ1
(Fig. 5a), where the uncertainties are the standard deviation in
the fit parameters. The combined systematic and random error
in the measurements in k1, was estimated to be ꢀ16% at the 1s
level.
19 HITRAN 2004 edition, http://cfa-www.harvard.edu/hitran/; L. S.
Rothman, D. Jacquemart, A. Barbe, D. C. Benner, M. Birk, L. R.
Brown, M. R. Carleer, C. Chackerian, Jr, K. Chance, L. H.
Coudert, V. Dana, V. M. Devi, J.-M. Flaud, R. R. Gamache, A.
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The rate constants for the three pressure independent
channels (Fig. 5b and c) were measured to be: 1a (HNCO +
C2H4), k1a = (1.1 ꢀ 0.16) ꢁ 10ꢂ10 cm3 moleculeꢂ1
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rate constants: k2 = (1.6 ꢀ 1.1) ꢁ 10ꢂ14 cm3 moleculeꢂ1 sꢂ1
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k4 = (5.3 ꢀ 0.51) ꢁ 10ꢂ13 cm3 moleculeꢂ1
s =
ꢂ1, and k10
(2.3 ꢀ 1.2) ꢁ 10ꢂ13 cm3 moleculeꢂ1 sꢂ1, where the uncertainty
is 1s.
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dominance of channel (1a) suggest that these two channels
proceed by in a direct bimolecular collision and are the result
of an abstraction process rather than complex formation.
ꢃc
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4314 | Phys. Chem. Chem. Phys., 2007, 9, 4301–4314