Kinetics and thermochemistry of the reversible combination reaction of the phenoxy radical with NO

Article abstract of DOI:10.1021/jp972576p

The kinetics of association reaction of the phenoxy radical with NO were studied by flash photolysis coupled with UV absorption spectrometry. The influence of resonance stabilization energy of radicals on R-NO bond dissociation energy was also analyzed. B

Full text of DOI:10.1021/jp972576p

©
Copyright 1998 by the American Chemical Society
VOLUME 102, NUMBER 1, JANUARY 1, 1998
ARTICLES
Kinetics and Thermochemistry of the Reversible Combination Reaction of the Phenoxy
Radical with NO
Florence Berho, Fran c¸ oise Caralp, Marie-Th e´ r e` se Rayez, and Robert Lesclaux*
Laboratoire de Physico-Chimie Mol e´ culaire, UniVersit e´ Bordeaux I, UMR 5803 CNRS,
3
3405 Talence Cedex, France
Emil Ratajczak
Department of Physical Chemistry, Wroclaw UniVersity of Medicine, Pl. Nankiera 1, 50-140 Wroclaw, Poland
X
ReceiVed: August 7, 1997; In Final Form: October 22, 1997
The kinetics of the association reaction of the phenoxy radical with NO were investigated using a flash
photolysis technique coupled to UV absorption spectrometry. This yielded k(C
6
H
5
O + NO) ) (1.65 ( 0.10)
-
12
3
-1 -1
×
10 cm molecule s , with no significant temperature effect over the temperature range 280-328 K.
Experiments were performed at atmospheric pressure, and theoretical calculations using the RRKM method
showed that the rate constant is at the high-pressure limit above ≈50 Torr for temperatures below 400 K.
Upon increasing the temperature, the reaction was found to be reversible, and the equilibrium kinetics have
been studied at seven temperatures between 310 and 423 K. The equilibrium constant can be expressed as
3
-1
ln(K
c
/cm molecule ) ) -(63.3 ( 1.0) + (10 140 ( 1000)K/T. Thermodynamic treatment of the data by
-
1
the Third Law method of analysis yielded ∆H°298 ) (-87.3 ( 8.0) kJ mol (yielding ∆H°
0
) (-83.8 (
O(NO)) ) (51.5 ( 8.0) kJ mol ), corresponding to the calculated ∆S°298
-164.9 ( 8.0) J mol K . All spectroscopic parameters necessary for RRKM calculations and for the
-
1
-1
8.0) kJ mol and ∆H°f,298(C
6
-1
H
5
)
-
1
(
entropy determination using statistical thermodynamics were calculated using both semiempirical (MNDO)
and DFT methods. Influence of the resonance stabilization energy of radicals on R-NO bond dissociation
energy is discussed.
Introduction
with molecular oxygen, forming the phenoxy radical and
initiating a chain reaction through O atom production.1 The
The oxidation of aromatic hydrocarbons in the gas phase is
now becoming a topical issue, as such compounds are exten-
sively used as additives in lead-free gasoline because of their
high octane value. Nevertheless, few kinetic data are available
concerning the reactions of the phenoxy radical (C6H5O), which
is a key intermediate in the oxidation of small aromatic
compounds. For instance, the high-temperature oxidation of
benzene initiated by reaction with atoms (O or H) or radicals
phenoxy radical is also an intermediate in the oxidation of other
aromatic compounds, such as phenol and benzaldehyde. There-
fore, kinetic data are necessary for better understanding and
modeling of the oxidation processes of aromatic hydrocarbons.
1,2
Studies of association reactions with hydrogen atoms and
3
,4
methyl radicals (yielding phenol and anisole or cresols,
respectively) have been reported. Concerning the association
reaction with NO, only one combined experimental and
(OH or CH3) yields the phenyl radical C6H5, which can react
5
theoretical study has been performed. In the present work,
the equilibrated reaction between C6H5O and NO has been
investigated above 310 K.
*
Corresponding author. E-mail: lesclaux@cribx1.u-bordeaux.fr.
Abstract published in AdVance ACS Abstracts, December 1, 1997.
X
S1089-5639(97)02576-0 CCC: $15.00 © 1998 American Chemical Society
Published on Web 01/01/1998

2
J. Phys. Chem. A, Vol. 102, No. 1, 1998
Berho et al.
C H O + NO + M a C H O(NO) + M (1, -1)
6
5
6
5
The results were obtained from kinetic simulations of phenoxy
radical decay traces recorded using the flash photolysis tech-
nique. The equilibrium constant was determined as a function
of temperature, from 310 to 423 K, to derive the thermochemical
parameters, the enthalpy and entropy changes, for reaction 1.
These values were obtained using both Second and Third Law
thermodynamic analysis. Quantum calculations were used for
the determination of structural parameters of C6H5O and C6H5O-
(NO), including the three possible isomers of C6H5O(NO)
resulting from the resonant structure of the phenoxy radical.
Figure 1. Typical decay traces recorded at 240 nm following the flash
2 2
photolysis of Cl /phenol/NO/N mixtures at room temperature and
1
4
atmospheric pressure: (a) absence of NO; (b) [NO] ) 3.3 × 10
-
3
14
-3
molecule cm ; (c) [NO] ) 8.2 × 10 molecule cm The solid lines
are simulations of the data.
deuterium lamp, passed once through the cell and was then
directed onto a monochromator (2 nm resolution)/photomulti-
plier unit. The signal was then digitized and transferred to a
computer for averaging and further data analysis. Kinetic
simulations were performed by numerical integration and fitted
to the averaged decay traces using nonlinear least-squares
analysis.
In addition, kinetic studies were performed on the association
of phenoxy radicals with NO at lower temperatures (T ) 280-
3
28 K, P ) 760 Torr, M ) N2), where the association and
dissociation components of the decay could be separated during
the approach to equilibrium. The kinetics of the phenoxy self-
reaction, which are necessary to fully characterize the chemical
system at low NO concentrations and when reaction 1 is
equilibrated, are reported separately.6
To introduce phenol in the gas mixture, nitrogen was slowly
flowed through a glass tube whose walls were coated with solid
phenol. The phenol concentration was monitored by its
-
18
2
-1 6
Experimental Section
absorption at λ ) 275 nm (σ ) 6.20 × 10 cm molecule )
and that of molecular chlorine at λ ) 330 nm (σ ) 2.56 ×
All experiments were performed using the flash photolysis
technique, coupled to UV absorption spectrometry, to monitor
radical concentrations in real time. This technique has been
-19
2
-1 8
10
cm molecule ). Concentrations were adjusted such that
the conversion of chlorine atoms into phenoxy radicals was total
and very fast (5-20 µs) compared to the phenoxy reaction time
7
described in detail previously and can be briefly summarized
(
>10 ms). Typically, concentrations of reactants were (units
as follows.
-
3
14
of molecule cm ): [phenol] ) (2-6) × 10 , [Cl2] ) (3-9) ×
Phenoxy radicals were produced by flash photolysis of Cl2/
phenol/N2 mixtures
1
5
14
1
0 , [NO] ) (0.7-15) × 10 , resulting in initial radical
13 -3
concentrations of (0.3-2) × 10 molecule cm .
Cl + hν f 2Cl
(2)
(3)
Nitrogen (AGA Gaz Sp e´ ciaux, purity > 99.995%), oxygen
AGA Gaz Sp e´ ciaux, purity > 99.995%), phenol (Aldrich,
2
(
Cl + C H OH f HCl + C H O
99+%), molecular chlorine (Messer, 5% in N2, purity > 99.9%),
and nitric oxide (AGA Gaz Sp e´ ciaux, 0.96% in N2, purity >
99.9%) were used without further purification.
6
5
6
5
-
10
3
-1 -1 1
with k3 ) 2.4 ×10
cm molecule s . Recently, this
reaction has been shown to be a clean source of phenoxy
1
radicals.
Results
All experiments were performed at atmospheric pressure (760
10 Torr) and in the temperature range 280-423 K. The
desired temperature was controlled to within (3 K by either
flowing thermostated water in an outer jacket surrounding the
cylindrical reaction cell (4 cm i.d., 70 cm length) or by heating
in an oven for temperatures above 370 K.
Decay traces corresponding to the phenoxy radical self-
reaction were recorded at 240 nm and at each temperature
(
investigated, both to measure the initial radical concentration,
using the previously determined UV absorption cross sections,6
and to characterize the chemical system in the absence of NO
(Figure 1a).
The photolyzing light was provided by an argon flash lamp.
A Pyrex tube was used to filter out radiation of λ < 280 nm in
order to prevent any photodissociation of phenol during the
flash. Gas mixtures were prepared using calibrated flow
controllers, and the total gas flow was adjusted so that the
reaction cell was replenished between each flash to prevent any
secondary photodissociation of reaction products.
The study of the phenoxy radical self-reaction is reported in
a separate publication. The system was analyzed using the
following simple reaction mechanism:
6
Cl + C H OH f HCl + C H O
(3)
(4)
(5)
6
5
6
5
2
C H O f product
6 5
Phenoxy radical concentrations were monitored by UV
absorption spectrometry at λ ) 240 nm. According to the
6
C H O + Cl f C H O(Cl) + Cl
6 5 2 6 5
phenoxy UV spectrum determined previously, this wavelength
appeared to be the most appropriate for kinetic studies by
providing good signal-to-noise ratios and low residual absorption
due to reaction products. The analysis beam, generated by a
The product of reaction 4 is probably a dimer that rearranges
to give dihydroxybiphenyl isomers. The product of reaction
9

Reaction of the Phenoxy Radical with NO
J. Phys. Chem. A, Vol. 102, No. 1, 1998 3
TABLE 1: Reaction Mechanism and Parameters Used in Simulations of Decay Traces Recorded at 240 nm (P ) 760 Torr, M )
2
N )
3
-1
reaction
+ hν f 2Cl
Cl + C OH f HCl + C
O + C O f products
O + Cl f C
O + NO f C
O(NO) f C
k/cm molecule s-1
ref
Cl
2
-
10
6
H
5
6
H
5
O
2.4 × 10
(1.44 ( 0.16) × 10 exp[(631 ( 37)K/T]
(1)
(6)
(6)
-
10
C
6
C
6
C
6
C
6
H
H
H
H
5
5
5
5
6 5
H
2
-
14 a
6
H
5
O(Cl) + Cl
O(NO)
O + NO
1 × 10
-
12
6
H
5
(1.65 ( 0.1) × 10
(this work)
(this work)
(8)
b
6
H
5
k
-1
-
6
-2.6
Cl + NO + M f ClNO + M
k(T) ) 6.07 × 10 × T
at 760 Torr
-
12 a
C
6
H
5
O + C
6
H
5
O(NO) f products
4.5 × 10
absorption cross sections
(this work)
-
17
2
-1
σ(C
σ(C
σ(C
6
6
6
H
H
H
5
5
5
O) ) 2.55 × 10 cm molecule
-18 2
-1
O(NO)) ) 5.0 × 10 cm molecule
-
19
2
-1
OH) ) 5.0 × 10 cm molecule
σ(Cl
2
) is negligible at 240 nm
a
No significant variation with T could be detected in the temperature range investigated. b
1 c c
-1 ) k /K , with ln(K
/cm molecule-1) ) -(63.3 (
3
k
1
.0) + [(10 140 ( 1000)K/T] (this work).
5, C6H5O(Cl), represents the three possible isomers correspond-
ing to the three resonance structures of the phenoxy radical.
The values of the parameters used in simulations are listed
in Table 1. It must be stressed that the absorption cross section
values assigned to the products of reactions 4 and 5 to
characterize the residual absorption have no individual meaning,
as they strongly depend on the value assigned to k5, which bears
6
a large uncertainty factor of about 3. Nevertheless it was shown
that those parameters, characterizing the residual absorption,
were of negligible importance in the determination of the kinetic
parameters and equilibrium constant of reaction 1.
A. Kinetics of the Association Reaction 1.
C H O + NO + M f C H O(NO) + M
(1)
6
5
6
5
I
Figure 2. Plot of the measured pseudo-first-order rate constant k )
1
Decay traces were recorded by photolyzing Cl2/phenol/NO
mixtures, diluted in nitrogen as carrier gas, at 760 Torr and in
the temperature range 280-328 K. In the presence of NO, the
phenoxy decay rate was significantly increased (Figure 1b,c),
compared to the decay rate observed in the absence of NO
k
[NO] against NO concentration, derived from experimental data
collected at room temperature and atmospheric pressure.
TABLE 2: Temperature Dependence of k
1
12
3
-1
T/K
k
1
/10- cm molecule s-1
no. of expts
(
Figure 1a). All experiments were performed under pseudo-
2
80
1.76 ( 0.10
1.70 ( 0.10
1.67 ( 0.05
1.54 ( 0.20
10
10
9
first-order conditions, using an excess of NO. The concentration
293
310
328
1
4
of NO was varied over the range (0.7-3.5) × 10 molecule
-3
10
cm , which resulted in pseudo-first-order rate constants varying
by a factor of about 5 at each temperature.
thus is not significant. Consequently, the proposed value of k1
for the temperature range investigated is the average of the
values given in Table 2:
Simulations of decay traces were performed using a reaction
mechanism that included reaction 1, between C6H5O and NO,
in addition to reactions 3-5, which characterized the chemical
system in the absence of NO (Table 1). The pseudo-first-order
-12
k1 ) (1.65 ( 0.1) × 10
cm molecule s-1
3
-1
I
rate constant, k ) k1[NO], was optimized for each concentration
of NO, and the value of k1 was obtained from the plot of kI
against [NO]. The plot resulted in a straight line passing through
the origin, within experimental uncertainties, showing that
experimental conditions were appropriate (Figure 2). The rate
constant k1 was derived from the slope of the straight lines
obtained at each temperature investigated. The results are
reported in Table 2, along with the statistical uncertainties.
A slight decrease of the rate constant is observed upon
increasing the temperature, resulting in the following rate
expression:
Measurements of k1 could only be performed at temperatures
lower than 330 K. At 280 and 293 K, only k1 was necessary to
properly simulate the decay traces, whereas at 310, 320, and
3
28 K the occurrence of the equilibrium could not be ignored.
The value of k-1 had to be included in the reaction mechanism
for an accurate analysis of decay traces. At higher temperatures,
k1 could no longer be measured because decay rates became
too fast as higher concentrations of NO had to be used to prevent
the equilibrium from being shifted toward the reactants. As
explained below, only the ratio k1/k-1 could be used in the
determination of the equilibrium constant.
A pressure effect can be expected for association processes
with low reaction enthalpy such as reaction 1, as shown below.
To estimate if any pressure effect could be observed in the
pressure range covered by our experimental setup (30-760
Torr), the pressure dependence of k1 was estimated using RRKM
k1 ) (1.70 ( 0.1) × 10 12(T/298)-(0.79(0.20) cm
-
3
molecule- s-1 (280 < T < 328 K)
1
However, the observed variation of k1 with temperature is of
the order of the magnitude of experimental uncertainties and

4
J. Phys. Chem. A, Vol. 102, No. 1, 1998
Berho et al.
6 5
TABLE 3: Molecular Parameters for the Phenoxy Radical and (C H O(NO) Isomers
Vibrational Frequencies (cm-1)
NO:
phenoxy:
1992
195, 380, 444, 485, 531, 598, 657, 795, 806, 811, 921, 973, 986, 994, 1018, 1098, 1175, 1176, 1289, 1353, 1433,
458, 1498, 1565, 1604, 3192, 3199, 3214, 3224, 3227
69, 133, 160, 293, 362, 423, 465, 536, 608, 635, 704, 751, 791, 844, 904, 932, 965, 992, 1020, 1053, 1108, 1191,
198, 1246, 1345, 1363, 1503, 1536, 1649, 1654, 1804, 3189, 3198, 3210, 3221, 3223
27, 62, 172, 273, 342, 405, 455, 489, 518, 573, 607, 739, 761, 799, 881, 967, 986, 993, 1020, 1031, 1163, 1192,
207, 1246, 1321, 1406, 1453, 1599, 1679, 1708, 1765, 3136, 3180, 3189, 3207, 3216
33, 49, 194, 278, 333, 419, 457, 464, 540, 578, 610, 772, 777, 794, 871, 935, 987, 1011, 1021, 1033, 1159, 1192,
1
(C H
6
(C H
6
(C H
6
5
5
5
O(NO) isomer 1:
O(NO) isomer 2:
O(NO) isomer 3:
1
1
1225, 1272, 1370, 1416, 1419, 1661, 1672, 1708, 1761, 3083, 3178, 3179, 3209, 3210
Rotational Constants (cm-1)
NO
1.6805
C
6
C
6
C
6
C
6
H
H
H
H
5
5
5
5
O
0.1836
0.1655
0.0829
0.1389
0.0926
0.0328
0.0543
0.0358
0.0616
0.0280
0.0376
0.0312
O(NO) isomer 1
O(NO) isomer 2
O(NO) isomer 3
Parameters Used in RRKM Calculations
) (-83.8 ( 8.0) kJ mol- (this work)
1
∆
H°
0
Lennard-Jones Parameters
N
3.68
91.5
2
C
6
H
5
O(NO)
5.0
σ (Å)
/k
ꢀ
400
Figure 3. Falloff curves for the reaction C
6
H
5
O + NO + M f C
6 5
H O-
(NO) + M resulting from RRKM calculations performed at different
5
temperatures. 9, b, experimental data (this work); O, calculated data.
calculations at 298, 328, and 423 K. The parameters necessary
to perform calculations (∆H°0, structural parameters) were
determined as explained in the next section and given in Table
3
. The falloff curves calculated at each temperature are
-
12
represented in Figure 3, using âc ) 0.2 and k∞ ) 1.8 × 10
3
-1 -1
cm molecule s , independent of temperature. On the basis
of these results, it can be concluded that any pressure depen-
dence would be too small to be experimentally observable in
the pressure range considered, whatever the temperature, below
4
23 K. As a consequence, no experiments were performed at
pressures lower than 760 Torr, and it is concluded that the
reported values of k1 correspond to the high-pressure limit.
B. Equilibrium and Thermodynamics of the Reaction
System 1, -1. 1. Experimental Determination of the Equi-
librium Constant.
Figure 4. Typical decay traces recorded at 240 nm following the flash
photolysis of Cl /phenol/NO/N mixtures at 328 K and atmospheric
pressure: (a) absence of NO; (b) [NO] ) 6.92 × 10 molecule cm
2
2
1
4
-3
;
16
-3
(
c) [NO] ) 1.54 × 10 molecule cm . The solid lines are simulations
C H O + NO + M a C H O(NO) + M (1, -1)
6
5
6
5
of the data.
As stated above, at temperatures higher than 310 K, decay traces
could not be simulated without taking into account the dis-
sociation of C6H5O(NO) (reaction -1). The experimental decay
traces began to exhibit kinetic profiles indicative of the
establishment of an equilibrium (Figure 4b). Two regimes
became apparent, the first one dominated by the rapid associa-
tion of phenoxy radicals with NO and the second one corre-
sponding to the absorption signal resulting from the establish-
ment of the phenoxy radical and C6H5O(NO) concentrations at
equilibrium. Upon increasing the temperature toward the upper

Reaction of the Phenoxy Radical with NO
J. Phys. Chem. A, Vol. 102, No. 1, 1998 5
TABLE 4: Temperature Dependence of the Equilibrium
products of reaction 7 are a phenoxy dimer and NO, but we
have no evidence for the formation of such products.
The equilibrium constant was measured between 310 and 423
K for 7-10 different concentrations of NO at each temperature.
The results are given in Table 4, along with the experimental
conditions.
2. Quantum Calculations. The thermochemical parameters
of reaction 1, enthalpy and entropy changes, can be derived
from the above experimental determination of the temperature
dependence of the equilibrium constant, using either the Second
or Third Law thermodynamic analysis. The former only
requires experimental data whereas the latter also requires the
calculated value of the entropy change of reaction 1. Both
methods were used in this work, and the results are reported
below. All spectroscopic and structural parameters necessary
to calculate the entropy change of reaction 1 were derived from
quantum calculations.
Constant for Reactions 1, -1
[
NO]/1015
molecule
cm
no.
of
expts
K
c
/cm3
molecule
-
3
-1
/atm-1
(6.48 ( 2.20) × 105
T/K
K
p
-
-
-
-
-
-
-
14
14
14
15
16
17
17
3
3
3
3
3
4
4
10 0.12-0.71 (2.74 ( 0.90) × 10
20 0.11-0.70 (1.47 ( 1.20) × 10
28 0.07-0.30 (1.18 ( 0.35) × 10
47 0.14-0.67 (1.78 ( 0.48) × 10
70 0.33-0.46 (3.22 ( 0.97) × 10
9
(3.36 ( 2.70) × 105 10
(2.65 ( 0.80) × 105
(3.76 ( 1.01) × 104 10
(6.40 ( 1.90) × 103
(6.64 ( 1.00) × 102 10
(1.89 ( 0.58) × 102
7
8
03 3.0-9.4
(3.65 ( 1.00) × 10
23 10.0-34.7 (1.10 ( 0.33) × 10
7
limit, large concentrations of NO had to be used and the first
part of the signal described above became so fast that it could
not be observed anymore. Thus, only the postequilibrium part
of the decay signal could be recorded.
Using a large excess of NO, a residual absorption was
observed (Figure 4c), indicating that the absorption of the adduct
had to be taken into account when simulating decay traces. This
residual absorption was used to estimate the absorption cross
The entropy was calculated for each species involved in the
reaction, even though the NO and C6H5O entropy values can
be easily determined. Nevertheless, they were calculated using
the same method as for C6H5O(NO), expecting the errors to
cancel to some extent when calculating ∆S. The C6H5O(NO)
species has three isomers
-
18
2
section of the adduct: σ(C6H5O(NO)) ) 5.0 × 10
cm
-
1
molecule at 240 nm. No significant variation of this value
could be observed when changing the temperature. The excess
of NO had to be large enough to ensure that the equilibrium
was completely shifted toward the formation of the adduct
C6H5O(NO). However, at such high NO concentrations, the
reaction of chlorine atoms with NO
Cl + NO + M f ClNO + M
(6)
had to be taken into account as it competes with the reaction of
Cl atoms with phenol, forming phenoxy radicals. Omitting
reaction 6 in simulations would have resulted in overestimating
the initial radical concentration of phenoxy radicals. The
occurrence of reaction 6 was most significant at the highest
temperatures investigated, where high NO concentrations had
to be used (Table 4) and resulted in up to 20% of chlorine atom
loss.
resulting from the combination of NO with either the benzenoid
structure a (giving isomer 1) or quinoid structures b and c
(giving isomers 2 and 3) of the phenoxy radical. Furthermore,
each isomer can undergo subsequent rearrangements to yield
the following three compounds:
The equilibrium constant was obtained by measuring the ratio
of the association and dissociation rate coefficients (Kc ) k1/
k-1). At the lower end of our temperature range (T < 330 K),
where NO concentrations were low, decay traces included the
association step (Figure 4b) and simulations consisted of
optimizing both k1 and k-1 as individual parameters. At higher
temperatures, where NO concentrations were high, the associa-
tion step became too fast and simulations consisted of optimizing
the ratio k1/k-1 directly.
However, it is likely that such internal rearrangements, which
require significant activation energy, would not take place during
the reaction time scales of interest in this work. In addition,
they must be irreversible as the above products are more stable
than the C H O(NO) isomers. Consequently, they cannot be
The postequilibrium decay of the signal was found to be
slightly faster than that calculated by only considering the
phenoxy radical self-reaction. A loss other than radical
recombination was clearly increasing the phenoxy decay rate,
either directly or indirectly through adduct removal. A similar
behavior of the postequilibrium signal has already been observed
6
5
involved in the equilibrium, and the entropy was only calculated
for the C H O(NO) isomers 1, 2, and 3. It should be noted
6
5
1
0
in previous studies of association reactions with NO.
A
that if the above rearrangements were to occur at a rate
significantly high to perturb the equilibrium, the postequilibrium
decay would have been much faster than that actually observed.
Quantum calculations were performed using density func-
tional theory (DFT), with Becke’s three-parameter function11
and the nonlocal correlation provided by the LYP expression
reaction of the phenoxy radical with the adduct C6H5O(NO)
was considered to be representative of this additional chemistry:
C H O + C H O(NO) f products
(7)
6
5
6
5
1
2
This reaction was added to the reaction mechanism, and
adjusting its rate constant to fit the post-equilibrium decay
(B3LYP). This method is implemented in the Gaussian94
1
3
computational package.
The double-ú 6-31G(d) basis set
-
12
3
-1 -1
yielded: k7 ≈ 4.5 × 10
cm molecule s , with no clear
including the polarization function has been used. This choice
was made as this method is known to give reliable structures,
vibrational frequencies, and energies for stable systems. The
calculated vibrational frequencies, for nitric oxide, the phenoxy
temperature dependence. It must be emphasized that such a
reaction is always too slow to perturb the equilibrium and hence
to affect any determination of the equilibrium constant. Possible

6
J. Phys. Chem. A, Vol. 102, No. 1, 1998
Berho et al.
TABLE 5: Calculated Entropies Using DFT and MNDO
Methods and Calculated ∆S°298 for Reaction 1
DFT
MNDO
S°298 (J mol K-1
-
1
)
S°298 (J mol K-1
-1
)
NO
210.5
314.8
360.4
377.0
376.5
210.0
318.0
366.0
369.0
370.0
C
C
C
C
6
6
6
6
H
H
H
H
5
5
5
5
O
O(NO) 1
O(NO) 2
O(NO) 3
S°298 (J mol K-1)a
-
1
-164.9
-162.0
∆
a
Calculated for isomer 1.
radical and the three isomers are reported in Table 3. They
agree satisfactorily with those already reported and calculated
using other methods.1
4-16
For the phenoxy radical, our theoreti-
cal results for the vibrational frequencies are in good agreement
with the experimental data available to date.17,18 The values of
S°298 derived from these optimized molecular structures are
given in Table 5. They were confirmed using the MNDO
semiempirical method,19 combined with the gradient minimiza-
tion algorithm AMPAC20 (also reported in Table 5).
In addition, DFT results confirmed previous calculations
(
using ab initio MP4(SDQ)/6-31G(d)//HF and isodesmic cor-
5
rections), showing that isomer 1 is more stable than isomers 2
-
1
and 3 by about 30 kJ mol . This led us to consider that only
the reaction forming isomer 1 should be taken into account in
the determination of the equilibrium parameters. Thus, ∆S°298
was calculated using the entropy of isomer 1 (which is not
significantly different from the entropy of other isomers), giving
for reaction 1:
S°298 ) -(164.9 ( 8.0) J mol K-1
-
1
∆
Figure 5. Van’t Hoff plots for the equilibrated reaction 1: dashed
line, Second Law analysis; solid line, Third Law analysis.
Errors were estimated from uncertainties in parameters used in
calculations and, in particular, on the lowest vibrational frequen-
cies.
A better accuracy is generally provided by the Third Law
method, which consists of calculating the value of ∆S°298 using
statistical thermodynamics, as detailed above, and deriving
Note that the calculated value is consistent with other
theoretical and experimental similar determinations of ∆S°298
concerning the association reactions of the allyl and benzyl
∆
∆
H°298 from the experimental values of the equilibrium constant.
H°298 was thus determined from a linear least-squares analysis,
-
1
radicals with NO, (-154.0 ( 9.0) and (-159.0 ( 9.0) J mol
-
1
10
K
respectively. As the similar bond (RO-NO) is formed
this time constrained to pass through the calculated value of
S°298 (Figure 5b). This method yields ∆H°298 ) -(87.3 (
in the reaction, a value close to that found here for reaction 1
can be reasonably expected.
∆
-1
-1
-1
3
.0) kJ mol for ∆S°298 ) -(164.9 ( 8.0) J mol K , the
3. Thermochemical Parameters of Reaction 1. The enthalpy
errors being estimated by combining the uncertainty in the
calculated ∆S°298 value and the experimental uncertainty (1σ)
in the equilibrium constant. In this case, possible errors on Kc
and entropy change of reaction 1 were first determined by a
Second Law analysis by plotting the experimental values of ln
Kp, listed in Table 4, against 1/T (Van’t Hoff plot) as shown in
Figure 5a (dashed line). The slope and intercept of a linear
regression analysis yielded
measurements result in an overall uncertainty on the Third Law
-1
∆
H value of 8.0 kJ mol .
A noticeable difference is observed between the values of
H°298 determined by the Second and Third Law analysis,
∆
-
1
∆
H°298 ) -(80.8 ( 3.0) kJ mol
-1
(-80.8 ( 8.0) and (-87.3 ( 8.0) kJ mol , respectively, but it
can be considered that the two values agree within experimental
and calculated uncertainties. In particular, in the case of the
Second Law analysis, the temperature range explored for
measurements of the equilibrium constant is too narrow to result
in good accuracy in the value of ∆H determined. This is well
illustrated by ignoring the Kp values obtained at the lowest
temperatures (310 and 320 K), where the accuracy is the poorest
(due to the low dissociation rate of C6H5O(NO)). Indeed,
omitting these two measurements, the “second law values” are
in very good agreement with the “third law values”. It should
be stressed, in addition, that the difference observed between
and ∆S°298 ) -(146.3 ( 8.0) J mol K-1 (errors 1σ)
-1
Considering the possible errors on Kc measurements (see
Discussion below), we estimate that overall uncertainties in the
-
1
experimental (Second Law) ∆H and ∆S values are 8.0 kJ mol
-
1
-1
and 20.0 J mol K , respectively. The corrections that were
applied to derive ∆H°298 and ∆S°298 by taking into account their
variation with temperature were found to be smaller than 1%
over the temperature range of interest (310-423 K). This was
expected as the temperature range investigated was not much
above room temperature.
-
1
-1
the experimental and calculated ∆S (= 18.6 J mol K ) is
As the equilibrium constant was determined over a narrow
temperature range, the accuracy of these results is questionable.
much larger than the possible error on the calculated value
-
1
-1
(estimated to be less than 8.0 J mol K ). The only way to

Reaction of the Phenoxy Radical with NO
J. Phys. Chem. A, Vol. 102, No. 1, 1998
7
fit the calculated ∆S value to the experimental one would be to
assign an unrealistic degree of looseness to the torsion modes
in C6H5O(NO). This indicates that the “second law value”
derived from all measurements is indeed too small.
This allows us to conclude that the Third Law analysis gives
the more reliable results. Thus, our recommended values of
temperature dependence found in this work is quite close to
5
-0.61
that reported by Yu et al. (T
from 293 to 373 K).
According to the RRKM calculations, the rate constant
reported for k1 corresponds to the high-pressure limit. However,
at pressures lower than 50 Torr, the reaction is definitely in the
falloff region and the pressure dependence of k1 must be taken
into account, particularly upon increasing the temperature above
room temperature.
The equilibrium constant was measured as a function of
temperature with an accuracy that could not be better than 30%
as estimated from the scatter of results (Table 4). The accuracy
was the poorest at the lowest temperatures of this study where
the reverse rate constant became too low and thus of reduced
importance in simulations. This has led us to conclude that
the Second Law method could not yield sufficient accuracy for
the ∆H determination and only a Third Law analysis could yield
reliable results.
∆
H°298 and ∆S°298 are
-
1
∆
H°298 ) -(87.3 ( 8.0) kJ mol
and ∆S°298 ) -(164.9 ( 8.0) J mol K-1
-
1
The corresponding Van’t Hoff plot is represented by the solid
line in Figure 5a,b. Note that it still fits the experimental data
quite satisfactorily. The variation of Kc, derived from the above
recommended parameters, can be expressed as:
Possible systematic errors on the equilibrium constant would
arise from errors on the parameters used in simulations. Some
of these parameters, σ(C6H5O), σ(C6H5OH), σ(C6H5OCl), the
rate constant and product absorption cross section of the C6H5O
+ C6H5O reaction, are those used to fit the decay traces recorded
in the absence of NO and their associated uncertainties should
not introduce significant errors. The same situation should
prevail for σ(C6H5O(NO)) which is determined in the presence
of a large excess of NO. However, under such conditions, the
loss of chlorine atoms by reaction with NO cannot be taken
into account accurately, thus introducing an uncertainty in σ-
3
-1
ln(K /cm molecule ) ) -(63.3 ( 1.0) +
c
[(10 140 ( 1000)K/T]
The enthalpy of formation of C6H5O(NO) at 298 K could
also be estimated using our ∆H°298 value and those of NO and
C6H5O (90.8 and 48.0 kJ mol respectively
-
1
21-23
)
-
1
∆
H°f,298(C H O(NO)) ) 51.5 ( 8.0 kJ mol
6
5
the most likely structure of C6H5O(NO) being that of isomer 1,
as explained above.
H°0 for reaction 1 could also be estimated at -83.8 ( 8.0 kJ
mol using ∆H°298 and the structural parameters given in Table
. This value of ∆H°0 was used in the RRKM calculations
(C6H5O(NO)). It was estimated that this error was minor
compared to the 30% statistical uncertainty on Kc measurements
at each temperature. As mentioned above, no significant error
could result from the occurrence of the reaction between C6H5O
and C6H5O(NO) and from the slow isomerization of C6H5O-
∆
-1
3
reported above.
(NO).
As already stressed, the determination of the thermochemical
Discussion
parameters, using the Second Law method of analysis, is of
poor accuracy. Nevertheless, it is shown that the most accurate
values of the equilibrium constant yield a ∆H°298 value in quite
good agreement with the Third Law analysis. Thus we have
considered the Third Law values as being of greater accuracy
compared to those obtained by the Second Law method, which
gives for ∆S°298 a value difficult to account for. In addition,
the entropy change of reaction 1 was calculated using different
methods, and the results were in satisfactory agreement (see
Table 5). As a result, we can consider that our combined
experimental and theoretical approach has provided reliable
values of the thermochemical parameters for reaction 1. There
are no direct measurements in the literature, but the enthalpy
change of reaction 1 can be compared with the results of
theoretical calculations
The experimental work reported in this paper was focused
on the determination of the rate constant and equilibrium
constant of the association reaction of the phenoxy radical with
NO. The mean rate constant found in the temperature range
-
12
3
-1 -1
2
80-328 K, k1 ) (1.65 ( 0.1) × 10 cm molecule s , is
in good agreement with the recent determination of Yu et al.
-12
3
-1 -1
5
of k1 ) 1.45 × 10 cm molecule
s
at room temperature.
It should be noted that this value is significantly lower than the
rate constant values generally observed for radical combination
-11
3
-1 -1
reactions with NO, (1-2) × 10 cm molecule
s
for both
R- and RO-type radicals.24 This particular behavior of the
C6H5O + NO reaction can be related to its smaller enthalpy
change compared to that of similar reactions of alkyl and alkoxy
radicals, these being generally 70-80 kJ mol- higher. A
similar trend was observed in the case of the benzyl and allyl
radicals, which are also resonance stabilized, resulting in smaller
enthalpy changes for their association reactions with NO, of
1
-1
5
∆
H° ) -71.1 kJ mol
(Yu et al.)
0
-
1
-1
10
12
-
123 ( 5 kJ mol and -110 ( 5 kJ mol respectively.
-1
and ∆H° ) -80.6 kJ mol
-
0
The corresponding rate constants were found to be 9 × 10
16
-12
3
-1 -1
10
and 7 × 10 cm molecule
s
respectively. The question
(Glenewinkel-Meyer et al.)
of the resonance stabilization of these radicals is discussed
below.
to be compared to our value, derived from experimental
-
1
The rate constant k1 was found to decrease slightly upon
measurements (∆H°0 ) -83.8 ( 8.0 kJ mol ). The value of
Glenewinkel-Meyer et al. agrees with our value within combined
uncertainties whereas that of Yu et al. appears too low.
The bond dissociation energy (BDE) of phenoxy-NO is the
lowest measured to date for a bond between a radical and NO.
A few values are shown for comparison in Table 6. It is more
-
0.79
increasing temperature, with a T
temperature dependence.
However, as stressed above, the temperature range investigated
is too narrow to expect an accurate determination of such a weak
temperature dependence, which may be accounted for by
uncertainties. This has led us to only report the average value
of k1 in the temperature range investigated. Nevertheless, the
-
1
than 80 kJ mol smaller than BDE values generally observed

8
J. Phys. Chem. A, Vol. 102, No. 1, 1998
Berho et al.
TABLE 6: Resonance Stabilization Energies and R-NO
(5) Yu, Y.; Mebel, M.; Lin, M. C. J. Phys. Org. Chem. 1995, 8, 47.
(6) Berho, F.; Lesclaux, R. Chem. Phys. Lett., in press.
Bond Dissociation Energies for a Few Typical Radicals
(
7) Lightfoot, P. D.; Lesclaux, R.; Veyret, B. J. Phys. Chem. 1990,
4, 700.
8) de More, W. B.; Sander, S. P.; Golden, D. M.; Molina, M. J.;
1
BDE(R-NO)/kJ mol-1
R
RSE/kJ mol-
ref
9
(
CH
t-C
CF
CCl
3
172
167
167
125
123
110
87
(29)
(30)
(29)
(26)
(10)
(10)
Hampson, R. F.; Kurylo, M. J.; Howard, C. J.; Kolb, C. E.; Ravishankara,
A. R. Chemical Kinetics and Photochemical Data for Use in Stratospheric
Modeling. NASA-JPL Publication, 92-20, Pasadena, CA, 1990.
4
H
9
3
3
(
9) Ye, M.; Schuler, R. H. J. Phys. Chem. 1989, 93, 1898.
10) Boyd, A. A.; Nozi e` re, B.; Lesclaux, R. J. Phys. Chem. 1995, 99,
0815.
a
6
C H
5
CH
2
52.3
62.8
83.7
(
a
CH
2
CHCH
5
2
1
b
6
C H
O
(this work)
(
11) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
a
Reference 28. b Reference 27.
(12) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. 1988, B37, 785.
(
13) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.;
Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Peterson, G. A.;
Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V.
G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.;
Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.;
Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomberts, R.; Martin, R. L.;
Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-
Gordon, M.; Gonzales, C.; Pople, J. A. GAUSSIAN 94, Revision C.2;
Gaussian, Inc.: Pittsburgh, PA, 1995.
for alkyl and fluorinated alkyl radicals. The particular case of
CCl3 has already been discussed in previous publications.
10,25,26
This low BDE(phenoxy-NO) must be related to the strong
resonance stabilization energy (RSE) that has been determined
-
1 27
for the phenoxy radical, 83.7 kJ mol . It should be noted
that the difference in BDEs for R-NO bonds between those of
alkyl radicals and those of resonance-stabilized radicals, such
as benzyl, allyl, and phenoxy, is very close to the RSE of the
latter radicals, as shown in Table 6. In addition, note that the
differences between BDEs are almost exactly the same as the
difference in RSEs for these radicals.
(
(
14) Qin, Y.; Wheeler, R. A. J. Chem. Phys. 1995, 102 (4), 1689.
15) Qin, Y.; Wheeler, R. A. J. Am. Chem. Soc. 1995, 117, 6083.
(16) Glenewinkel-Meyer, T.; Crim, F. F. J. Mol. Struct.: THEOCHEM
1995, 337, 209.
(17) Tripathi, G. N. R.; Schuler, R. H. J. Chem. Phys. 1984, 81, 113.
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(20) AMPAC 5.2, 1994, Semichem**, 7128 Summit, Shawnee, KS,
The high resonance stabilization energy associated to the
phenoxy radical must be related to the absence of reaction that
66216.
(21) Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Frurip, D. J.;
McDonald, R. A.; Syveruid, A. N. J. Phys. Chem. Ref. Data 1985, 14,
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(22) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin,
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6
was observed between this radical and O2. Because of this
high RSE it is likely that this radical may not even form a stable
peroxy radical (phenoxy-O2).
1
(
Acknowledgment. The authors thank A. A. Boyd for his
help in the preparation of the manuscript and the Ministry of
Environment and the European Community (Copernicus Pro-
gram) for financial support.
Th.; Kerr, J. A.; Pilling, M. J.; Troe, J.; Walker, R. W.; Warnatz, J. J.
Phys. Chem. Ref. Data 1992, 21, 411.
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(25) Masanet, J.; Caralp, F.; Jemi-Alade, A. A.; Lightfoot, P. D.;
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2
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(
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(
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(
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