Experimental and theoretical studies of the unimolecular decomposition of nitrosobenzene: High-pressure rate constants and the C-N bond strength

Article abstract of DOI:10.1021/jp9712258

The unimolecular decomposition of nitrosobenzene has been studied at 553-648 K with and without added NO under atmospheric pressure. Kinetic modeling of the measured C₆H₅NO decay rates by including the rapid reverse reaction and minor secondary processes yielded the high-pressure first-order rate constant for the decomposition C₆H₅NO → C₆H₅ + NO (1), k^∞₁ = (1.42 ± 0.13) × 10¹⁷ exp [-(55 060 ± 1080)/RT] s^-1, where the activation energy is given in units of cal/mol. With the thermodynamics third-law method, employing the values of k^∞₁ and those of the reverse rate constant measured in our earlier study by the cavity ring-down technique between 298 and 500 K, we obtained the C-N bond dissociation energy, D^○₀ (C₆H₅-NO) = 54.2 kcal/mol at 0 K, with an estimated error of ±0.5 kcal/mol. This new, larger bond dissociation energy is fully consistent with the quantum mechanically predicted value of 53.8-55.4 kcal/mol using a modified Gaussian-2 method. Our high-pressure rate constant was shown to be consistent with those reported recently by Horn et al. (ref 13) for both forward and reverse reactions after proper correction for the pressure falloff effect.

Full text of DOI:10.1021/jp9712258

J. Phys. Chem. A 1997, 101, 6043-6047
6043
Experimental and Theoretical Studies of the Unimolecular Decomposition of
Nitrosobenzene: High-Pressure Rate Constants and the C-N Bond Strength
J. Park, I. V. Dyakov, A. M. Mebel,† and M. C. Lin*
Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322
ReceiVed: April 9, 1997; In Final Form: June 17, 1997X
The unimolecular decomposition of nitrosobenzene has been studied at 553-648 K with and without added
NO under atmospheric pressure. Kinetic modeling of the measured C6H5NO decay rates by including the
rapid reverse reaction and minor secondary processes yielded the high-pressure first-order rate constant for
the decomposition C6H5NO f C6H5 + NO (1), k∞1 ) (1.42 ( 0.13) × 1017 exp [-(55 060 ( 1080)/RT] s-1,
where the activation energy is given in units of cal/mol. With the thermodynamics third-law method, employing
the values of k∞1 and those of the reverse rate constant measured in our earlier study by the cavity ring-down
technique between 298 and 500 K, we obtained the C-N bond dissociation energy, D° (C6H5-NO) ) 54.2
0
kcal/mol at 0 K, with an estimated error of (0.5 kcal/mol. This new, larger bond dissociation energy is fully
consistent with the quantum mechanically predicted value of 53.8-55.4 kcal/mol using a modified Gaussian-2
method. Our high-pressure rate constant was shown to be consistent with those reported recently by Horn et
al. (ref 13) for both forward and reverse reactions after proper correction for the pressure falloff effect.
I. Introduction
the Gaussian-2 method (G2M) recently developed by Mebel
and co-workers.14 The experimental and theoretical results are
presented below.
Nitrosobenzene (C6H5NO) is a convenient thermal1-3 and
photolytical4-10 source of phenyl radical. The rate constant for
the unimolecular decomposition of nitrosobenzene, C6H5NO f
C6H5 + NO (1), was first measured by Choo et al. employing
the very-low-pressure pyrolysis (VLPP) method.11 Their ex-
trapolated high-pressure rate constant by means of the Rice-
Ramsperger-Kassel-Marcus (RRKM) theory, k∞1 ) 2.5 ×
1015 exp(-24 660/T) s-1, has provided the widely accepted
C-N bond dissociation energy D2°98 (C6H5-NO) ) 51 ( 1 kcal/
mol.12
Recently, the unimolecular decomposition of C6H5NO was
studied by Horn et al.13 in shock waves in the 800-1000 K
temperature range at pressures between 0.9 and 4.4 atm. Their
first-order rate constant obtained near 2 atm can be represented
by k1 ) 1015.29(0.53e-(24720(1110)/T s-1, which appears to be in
accord with the extrapolated result of Choo and co-workers.11
Horn et al.13 have also measured the rate constant for the
association of C6H5 with NO near 10 Torr in the 420-820 K
range using a fast-flow reactor under pseudo-first-order condi-
tions. Their result is in close agreement with that of Yu and
Lin obtained by the cavity ring-down (CRD) method.6
In order to extend the range of temperature beyond that
employed in our phenyl kinetic studies with the CRD technique,
300-523 K,4-10 we utilized C6H5NO as the thermal source of
C6H5 in the temperature range 553-648 K with and without
added NO. For providing a more accurate prediction of C6H5
concentration, we have carried out a series of measurements
for the rate constant of the C6H5NO decomposition reaction by
Fourier transform infrared (FTIR) spectrometry. The study was
performed under atmospheric conditions, and its result reveals
that the activation energy for the decomposition reaction is
higher by as much as 6 kcal/mol than those reported earlier.11,13
In order to confirm this surprising finding, we performed a high-
level ab initio molecular orbital (MO) calculation, employing
II. Experimental and Computational Procedures
A. Experiment. The rate constant for the unimolecular
decomposition of C6H5NO was measured at temperatures
between 553 and 648 K at atmospheric pressure in a static
reactor using the pyrolysis-FTIR (Fourier transform infrared)
spectrometric method.15-17 Pyrolysis was carried out in a 270
cm3 quartz reactor, housed in a double-walled cylindrical oven.
The reactor was heated by adjusting the current through the
heater, and the current was controlled by a temperature controller
(OMEGA CN 9000). The temperature was measured with a
type K thermocouple, located in the center of reactor bulb, with
an accuracy and reproducibility of 1 K.
The concentrations of the reactants/products of unpyrolyzed
and pyrolyzed samples were taken and analyzed by an FTIR
spectrometer (Mattson Instruments, Polaris) with a resolution
of 4 cm-1. The concentrations of C6H5NO and NO ranged from
0.07 to 0.10% and 0.00 to 0.45%, respectively, with Ar dilution
to atmospheric pressure. The concentrations of C6H5NO and
NO were calibrated with standard mixtures at pressures near
those of expanded, pyrolyzed samples. Calibration curves were
plotted in terms of concentration versus absorbance at 1113.0
cm-1 for C6H5NO and 1905.8 cm-1 for NO.
C6H5NO (Aldrich) was purified by recrystallization using
ethanol, followed by vacuum distillation at 273 K to remove
the ethanol solvent. NO (Matheson Gas Products) was purified
by vacuum distillation through a silica gel trap at 195 K. Before
use, the trap was preheated and diffusion-pumped overnight at
420 K to remove any condensed water. Ar (99.9995%,
Specialty Gases) was used without further purification.
B. Computation. In order to confirm the measured high-
pressure activation energy for the C6H5NO dissociation reaction,
we have performed ab initio molecular orbital calculations for
the C6H5NO ) C6H5 + NO system using a modified G2M.14
The geometries of C6H5NO, C6H5, and NO have been optimized
using the hybrid density functional B3LYP method18,19 with the
6-31G(d) basis set.20 Vibrational frequencies, calculated at the
† Present address: Institute of Atomic and Molecular Sciences, Academia
Sinica, P.O. Box 23-166, Taipei 10764, Taiwan.
* Key correspondent. Email: chemmcl@emory.edu.
X Abstract published in AdVance ACS Abstracts, August 1, 1997.
S1089-5639(97)01225-5 CCC: $14.00 © 1997 American Chemical Society

6044 J. Phys. Chem. A, Vol. 101, No. 34, 1997
Park et al.
TABLE 1: Summary of the Experimental Conditionsa and
Rate Constants for the C6H5NO Decompostion Reaction at
the Temperatures Studiedb
temp (K)
[C6H5NO]0
[NO]0
k1 (s-1
)
553
563
583
592
598
599
603
608
573
588
605
620
623
623
635
638
645
648
650
1.64 × 10-8
1.61 × 10-8
1.56 × 10-8
1.18 × 10-8
1.17 × 10-8
1.17 × 10-8
1.53 × 10-8
1.15 × 10-8
1.30 × 10-8
1.51 × 10-8
1.45 × 10-8
1.45 × 10-8
1.42 × 10-8
1.45 × 10-8
1.44 × 10-8
1.24 × 10-8
1.71 × 10-8
1.22 × 10-8
1.69 × 10-8
0
0
0
0
0
0
0
0
(2.91 ( 0.28) × 10-5
(5.72 ( 0.58) × 10-5
(2.72 ( 0.36) × 10-4
(6.06 ( 0.74) × 10-4
(1.25 ( 0.66) × 10-3
(1.08 ( 0.40) × 10-3
(1.75 ( 0.11) × 10-3
(2.21 ( 0.09) × 10-3
(1.29 ( 0.19) × 10-4
(4.35 ( 0.58) × 10-4
(2.28 ( 0.36) × 10-3
(6.52 ( 0.36) × 10-3
(4.69 ( 0.24) × 10-3
(6.65 ( 0.24) × 10-3
(1.83 ( 0.36) × 10-2
(1.97 ( 0.24) × 10-2
(3.81 ( 0.36) × 10-2
(2.76 ( 0.36) × 10-2
(5.60 ( 0.36) × 10-2
5.23 × 10-8
6.08 × 10-8
7.81 × 10-8
7.81 × 10-8
5.74 × 10-8
9.88 × 10-8
12.9 × 10-8
8.40 × 10-8
12.9 × 10-8
8.27 × 10-8
17.9 × 10-8
Figure 1. Time-resolved concentration decay profiles of nitroso-
benzene: (O) T ) 592 K without added NO; (b) T ) 650 K with NO
added; (solid line) modeled result at 592 K with k1 ) 6.06 × 10-4 s-1
;
a The concentration units are in mol/cm3. b All experiments were
performed at 1 atm total pressure with Ar as diluent. The error represents
(dashed line) modeled result at 650 K without added NO using k1 )
5.60 × 10-2 s-1; (dotted line) modeled result at 650 K with NO added
using k1 ) 5.60 × 10-2 s-1
.
1σ.
TABLE 2: Reactions and Rate Constantsa for the Modeling
of the Nitrosobenzene Decomposition
B3LYP/6-31G(d) level, were used for zero-point-energy (ZPE)
corrections, thermal corrections, and Gibbs free energy calcula-
tions.
reactionsb
A
Ea
ref
The energies were refined at various levels of theory, such
as MP2/6-31G(d,p), MP2/6-311G(d,p), MP2/6-311+G(3df,2p),20
and coupled-cluster21 RCCSD(T)/6-31G(d,p) as well as
RCCSD(T)/6-311G(d,p). The most accurate energies were
obtained by using the G2M(rcc,MP2*) and G2M(RCC,MP2)
schemes,14,22 where
1. C6H5NO f C6H5 + NO
-1. C6H5 + NO f C6H5NO
2. C6H5 + C6H5 ) C12H10
1.42E+17d 55 060 this work
2.69E+12 -860 6
1.39E+13
4.90E+12
111 31
3. C6H5 + C6H5NO f C12H10NO
-3. C12H10NO f C6H5NO + C6H5
-68 31
5.00E+14 45 000 c
4. C6H5 + C6H5NO f C12H10 + NO 5.00E+12
5. C12H10NO + C6H5 f C12H10N + 1.00E+13
C6H5O
4500 c
0 c
E[G2M(RCC,MP2)] ) E[RCCSD(T)/6-311G(d,p)] +
E[MP2/6-311+G(3df,2p)] - E[MP2/6-311G(d,p)] +
∆E(HLC,RCC) + ZPE
6. C12H10N + NO f C12H10NNO
1.00E+13
0 c
a Rate constants are defined by k ) A exp(-Ea/RT) and in units of
cm3, mol, and s; Ea is in units of cal/mol. b The equal sign represents
that the modeling was carried out for both forward and reverse
directions. The arrow represents the forward direction only. c Assumed.
d Read as 1.42 × 1017.
∆E(HLC,RCC) ) -5.25nâ - 0.19nR in mhartree
In order to isolate the unimolecular decomposition rate of
nitrosobenzene, we carried out kinetic chemical modeling for
each experimental run to account for the competing secondary
reactions. The decomposition rate of nitrosobenzene was
obtained by fitting the calculated concentrations to our experi-
mentally measured values. The experimental conditions and
kinetically modeled data are summarized in Table 1. The
reaction mechanism used for kinetic modeling is presented in
Table 2. The Arrhenius plot of the modeled unimolecular
decomposition rate constants is presented in Figure 2 and
compared with previously reported data.11,13 A weighted least-
squares analysis of our data covering the 553-648 K temper-
ature range gave rise to the expression k∞1 ) (1.42 ( 0.13) ×
1017 exp[-(55 060 ( 1080)/RT] s-1, where R ) 1.987 cal/(mol
K).
B. Theoretical C-N Bond Energy. The calculated energies
of C6H5NO, C6H5, and NO are shown in Table 3, and the
molecular parameters for these species are presented in Table
4. The geometry optimization of C6H5NO was carried out
without symmetry constraints and was converged to a planar
structure. As shown in Figure 3, the structure of C6H5NO is
stabilized by the O‚‚‚H hydrogen bond between the oxygen of
the NO group and a neighboring H. We discussed the optimized
geometry of the phenyl radical in an earlier paper.25 At the
B3LYP level with ZPE corrections the C-N bond dissociation
E[G2M(rcc,MP2*)] ) E[RCCSD(T)/6-31G(d,p)] +
E[MP2/6-311+G(3df,2p)] - E[MP2/6-31G(d,p)] +
∆E(HLC,rcc) + ZPE
∆E(HLC,rcc) ) -4.93nâ - 0.19nR in mhartree
Here, nR and nâ are the numbers of R and â valence electrons,
respectively. The G2M approach is expected to provide the
bond dissociation energies with an accuracy of 1-2 kcal/mol.
GAUSSIAN 9423 and MOLPRO-9624 programs were employed
for the computations.
III. Results
A. Kinetic Data. The rate constant for the unimolecular
decomposition of C6H5NO was measured by monitoring the
decay of nitrosobenzene concentration as a function of time.
At higher temperatures, we added NO into the gas mixture to
decrease the decomposition rate of nitrosobenzene. In the NO-
added experiments, the [NO]/[C6H5NO] ratio varied randomly
from 4 to 10 with one [NO] at each temperature. The
temperature range was limited by the measurability of the decay
rate with and without NO, varying from ∼10 min to ∼10 h
(overnight). Typical time-resolved concentration decay profiles
of nitrosobenzene are shown in Figure 1.

Unimolecular Decomposition of Nitrosobenzene
J. Phys. Chem. A, Vol. 101, No. 34, 1997 6045
with minor contribution from the reaction of C6H5 with C6H5NO
producing biphenyl nitroxide,
C6H5 + C6H5NO f (C6H5)2NO
(2)
whose rate constant has been determined in this laboratory.31
In principle, the nitroxide thus formed can react with an
additional phenyl radical to produce C6H5O and (C6H5)2N. Both
are thermally stable.
The addition of NO to this highly diluted C6H5NO system
(%C6H5NO e 0.05) enhances reaction -1 and minimizes the
contribution from the secondary and tertiary reactions alluded
to above. Figure 1 illustrates the pronounced effect of NO
inhibition on the rate of C6H5NO decomposition. At 650 K,
the half-life of C6H5NO is ∼10 s; the addition of 1.8 × 10-7
mol/cm3 of NO lengthens its half-life to 500 s. Kinetic modeling
of the decay of C6H5NO, with the inclusion of the secondary
and tertiary reactions as summarized in Table 2, enables us to
quantitatively obtain the unimolecular decomposition rate
constant under the atmospheric pressure of Ar (which corre-
sponds to the high-pressure limit as indicated by Figure 5):
Figure 2. Arrhenius plot of nitrosobenzene unimolecular decomposi-
tion reaction: (3) ref 13; (4) this work with NO added; (O) this work
without NO added; (dotted line) ref 11; (solid line) this work according
to eq II.
k∞1 ) (1.42 ( 0.13) × 1017 exp[-(55 060 ( 1080)/RT] s-1
energy was calculated to be 53.2 kcal/mol. The RCCSD(T)
approximation gives values in the 49-51 kcal/mol range. The
MP2 energies are much higher and are not reliable because of
the enormous spin contamination of the UHF wave function
for C6H5.25 The G2M(rcc,MP2*) and G2M(RCC,MP2) meth-
ods gave close values of 53.8 and 55.4 kcal/mol, respectively.
We consider the latter result to be the most accurate one in the
present study. After inclusion of the thermal correction for room
temperature, we obtained the value of 56.5 kcal/mol for the
C-N bond dissociation energy at 298 K.
(II)
This result, extrapolated to the 800-1000 K region, lies between
those of Choo et al.11 and Horn and co-workers.13 The deviation
between our values and Horn’s results stems from the effect of
pressure falloff on Horn’s shock tube data (Vide infra).
The activation energy for the decomposition process, 55.1
kcal/mol, is very close to the C-N bond energy of C6H5NO
presented in the preceding section, 56.5 kcal/mol at 298 K. The
measured activation energy is slightly lower than the bond
dissociation energy and is consistent with the negative activation
energy, -0.86 kcal/mol, determined for the recombination of
C6H5 and NO by the cavity ring-down technique.6 The rate
constant for the recombination reaction measured at 20-120
Torr Ar pressure in the 298-500 K range was found to be6
In order to confirm the result, we also performed the
calculation of the enthalpy change for the following isodesmic
reaction:
C6H5NO + H2 f C6H6 + HNO
k∞-1 ) 1012.43(0.06 exp[+(860 ( 220)/RT] cm3/(mol s) (III)
At the G2M(RCC,MP2) level, the reaction was calculated to
be thermoneutral, ∆H0° ) 0.0 kcal/mol. After adding the thermal
corrections, we found ∆H° ) -0.8 kcal/mol. With the
The combination of this reverse rate constant with the equilib-
rium constant obtained by the ab initio calculation presented in
the preceding section yields the expression
298
experimental heats of formation at 298 K for C6H6 and HNO,
19.8 and 25.5 kcal/mol,26,27 respectively, we calculated ∆H°f,298
for C6H5NO as 46.1 kcal/mol. Finally, on the basis of the
experimental ∆H°f,298 for NO (21.6 kcal/mol)28 and C6H5 (81.2
kcal/mol),29 the C-N bond dissociation energy at 298 K is
calculated to be 56.7 kcal/mol. Thus, the dissociation energies
calculated by the two different approaches are in close agree-
ment. These values are also in good accord with the predicted
result of Melius, 57.6 kcal/mol at 298 K, with the BAC-MP4
method.30
k∞1 ) k∞-1/Keq ) 9.2 × 1016 exp[-55 230/RT] s-1 (IV)
This result is in excellent agreement with the measured value
given by eq II, as also illustrated in Figure 4.
Shown in the figure are the extrapolated high-pressure rate
constants of Choo et al.11 obtained by the VLPP method at 763-
953 K and that of Horn et al.13 measured in shock waves at
800-1000 K. The latter set of data obtained at 0.9-4.4 atm
was extrapolated to the high-pressure limit with our high-
pressure Arrhenius parameters by the RRKM theory employing
the specific rate constant approximated by32
Using the G2M(RCC,MP2) energy and the molecular pa-
rameters of C6H5NO, C6H5, and NO shown in Table 4, we
calculated the equilibrium constant for the C6H5 + NO )
C6H5NO reaction. In the temperature range 300-1000 K, it
can be fitted by the following Arrhenius expression:
kE ) A∞F(E - E∞)/hF(E)
(V)
Keq ) 2.93 × 10-5 exp(56 093/RT) cm3/mol
(I)
where F(E) represents the density of the state of C6H5NO at
energy E and F(E-E∞), that of C6H5NO with energy above the
decomposition threshold, which is approximated by E∞ ) 55.1
kcal/mol (in lieu of the bond dissociation energy of 0 K, 55.4
kcal/mol). The extrapolation was made with the equation k1∞
) kP1/R, where R is the theoretically predicted falloff ratio,
(kP/k∞)T, at pressure P and temperature T, using the RRKM
IV. Discussion
In the temperature range studied, 553-648 K, the decay of
C6H5NO was found to be dominated by unimolecular decom-
position and negatively affected by its reverse reaction:
1
1
theory. Under the conditions employed by Horn et al.13 (T )
C6H5NO h C6H5 + NO
(1),(-1)

6046 J. Phys. Chem. A, Vol. 101, No. 34, 1997
Park et al.
TABLE 3: Total Energies of C6H5NO, C6H5, and NO (hartrees) and the C-N Bond Dissociation Energy in C6H5NO (kcal/mol),
Calculated at Various Levels of Theory
level of theory
C6H5NO
C6H5
NO
∆E(C-N)
B3LYP/6-31G(d)
MP2/6-31G(d,p)
MP2/6-311G(d,p)
MP2/6-311+G(3df,2p)
RCCSD(T)/6-31G(d,p)
RCCSD(T)/6-311G(d,p)
G2M(rcc,MP2*)
-361.539 80
-360.462 15
-360.604 92
-360.826 48
-360.549 68
-360.693 81
-360.918 78
-360.926 54
-231.561 28
-230.775 01
-230.858 86
-231.000 53
-230.888 71
-230.969 76
-231.098 61
-231.100 29
-129.888 16
-129.553 59
-129.617 82
-129.692 83
-129.573 93
-129.640 12
-129.734 43
-129.737 98
53.2
80.3
77.0
80.0
51.1
49.1
53.8
55.4
G2M(RCC,MP2)
TABLE 4: Molecular Parameters of C6H5NO, C6H5, and NO, Calculated at the B3LYP/6-31G(d) Level
species
i
Ii (10-40 g cm2)
νj (cm-1
)
C6H5NO
A
B
C
161.2
515.5
676.7
118,251,258,423,449,477,625,682,695,782,
836,872,963,995,1015,1019,1045,1105,
1138,1195,1207,1347,1380,1499,1518,1599,
1653,1665,3191,3204,3211,3221,3230
401,428,601,619,672,722,815,890,958,986,
988,1023,1058,1081,1182,1183,1313,1342,
1473,1485,1592,1646,3173,3179,3192,3194,3205
1984
C6H5
NO
A
B
C
A
B
C
134.8
151.0
285.7
16.5
16.5
0.0
Figure 4. Comparison of the nitrosobenzene decomposition rate after
high-pressure-limit correction by the RRKM theory: (2) k∞-1 (ref 6)/
Keq; ([) k∞ (ref 13)/Keq; (0) ref 13; (O) this work; (dotted line) ref
11; (solid -li1ne) this work according to eq II. The pressure-dependent
data of ref 13 have been extrapolated to their high-pressure limits, as
described in the text.
Figure 3. Molecular structures of C6H5NO, C6H5, and NO calculated
with the B3LYP/6-31G(d) method.
800-1000 K, P ) 0.9-4.4 atm Ar), the values of R lie between
0.46 and 0.85 with a strong pressure dependence, as illustrated
by the pressure falloff plots in Figure 5. The extrapolated values
of Horn et al.13 agree reasonably with our results extrapolated
to their temperature region. The result of Choo et al.,11 however,
is noticeably higher than our and Horn’s values.
with the combination of individual rate constant k∞-1 reported
by Yu and Lin6 and k∞1 given by eq II for the temperature range
of 300-500 K. The results of this evaluation for ∆H° with the
0
calculated Gibbs energy function, -(G°T - H°)/RT, employing
0
Also shown in Figure 4 are the calculated rate constants,
k∞1 ) k-∞1/Keq, using the measured reverse rate constants k-∞1 by
Yu and Lin6 as well as Horn et al.13 with the equilibrium
constant Keq given by eq I. With the exception of the highest
temperature point, Yu and Lin’s values correspond to the high-
pressure limits. For the highest-T (500 K) result, the falloff
ratio was calculated to be R ) 0.95, which was used in the
extrapolation as described above. The results of Horn et al.,13
measured at 10 Torr total pressure, are well into the falloff
region, with R ) 0.99-0.23 in the 420-820 K range. The
data presented in Figure 4 have been approximately corrected
for the pressure effect.
the molecular parameters presented in Table 4, are summarized
in Table 5. The averaged value of ∆H°0, 54.2 kcal/mol with an
estimated total error of (0.5 kcal/mol arising from the scatters
of the forward and reverse rate constants, agrees excellently
with theoretical values 53.8 and 55.4 kcal/mol based on the two
different schemes of G2M calculations. The predicted values
are expected to have an uncertainty of 1-2 kcal/mol, as
indicated earlier.
V. Conclusion
Our study of the thermal decomposition of C6H5NO in the
553-648 K temperature range under atmospheric conditions
by FTIR spectrometry gave rise to the high-pressure first-order
rate constant for the decomposition process, C6H5NO f C6H5
In order to obtain reliable experimental values of the enthalpy
change for reaction 1, we have employed the thermodynamics
third-law method33 using the equilibrium constant, calculated

Unimolecular Decomposition of Nitrosobenzene
J. Phys. Chem. A, Vol. 101, No. 34, 1997 6047
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33, 439.
(13) Horn, C.; Frank, P.; Trauter, R. S.; Schaug, J.; Grotheer, H.-H.;
Just, Th. 26th Symp. (Int.) Combust., [Proc.], in press
(14) Mebel, A. M.; Morokuma, K.; Lin, M. C. J. Chem. Phys. 1995,
103, 7414.
Figure 5. Effect of pressure on the first-order rate coefficient, k1, at
the two temperatures indicated.
(15) He, Y.; Kolby, E.; Shumaker, P.; Lin, M. C. Int. J. Chem. Kinet.
1989, 21, 1015.
(16) Aldridge, K. H.; Liu, X; Lin, M. C.; Melius, C. F. Int. J. Chem.
Kinet. 1991, 23, 947.
(17) Diau, E. W. G.; Halbgewachs, M. J.; Smith, A. R.; Lin, M. C. Int.
J. Chem. Kinet. 1995, 27, 855.
(18) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648; (b) Ibid. 1992,
96, 2155; (c) Ibid. 1992, 97, 9173.
(19) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785.
(20) Hehre, W.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio
Molecular Orbital Theory; Wiley: New York, 1986.
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321.
TABLE 5: Calculated Values of ∆H° by the Third-Law
0
with the Calculated Gibbs Energy Function
b
temp (K)
k-1 (cm3/mol s)a
k1 (s-1
)
∆H°(kcal/mol)
0
298
323
350
388
388
388
423
463
1.13 × 1013
1.11 × 1013
9.40 × 1012
8.37 × 1012
1.02 × 1013
1.11 × 1013
6.38 × 1012
9.13 × 1012
8.19 × 1012
5.89 × 10-24
7.87 × 10-21
5.89 × 10-18
1.37 × 10-14
1.37 × 10-14
1.37 × 10-14
5.05 × 10-12
1.45 × 10-9
1.21 × 10-7
54.40
54.38
54.24
54.10
54.25
54.32
53.81
54.04
500
average value
53.86
54.16 ( 0.22
a Data of Yu and Lin, ref 6. b Calculated by eq II.
(22) Liu, R.; Morokuma, K.; Mebel, A. M.; Lin, M. C. J. Phys. Chem.
1996, 100, 9314.
(23) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.;
Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, 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.; Gomperts, R.; Martin, R. L.;
Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-
Gordon, M.; Gonzalez, C.; Pople, J. A. GAUSSIAN 94, Revision B.2;
Gaussian, Inc.: Pittsburgh, PA, 1995.
(24) MOLPRO is a package of ab initio programs written by H.-J.
Werner and P. J. Knowles, with contributions from J. Almlo¨f, R. D. Amos,
M. J. O. Deegan, S. T. Elbert, C. Hampel, W. Meyer, K. Peterson, R. Pitzer,
A. J. Stone, P. R. Taylor and R. Lindh.
(25) Mebel, A. M.; Lin, M. C.; Yu, T.; Morokuma, K. J. Phys. Chem.,
in press.
(26) CRC Handbook of Chemistry and Physics, 74th ed.; Lide, D. R.,
Ed.; Chemical Rubber: Boca Raton, FL, 1993.
(27) Dixon, R. N. J. Chem. Phys. 1996, 104, 6905. The value given at
0 K, 26.29 ( 0.06 kcal/mol, was corrected for the thermal effect. The 298
K value, 25.5 kcal/mol, is very close to 25.4 + 0.6/-0.1 kcal/mol,
recommended by W. R. Anderson (CPIA Pub. No. 606, Vol. II, p 205,
1993).
(28) Chase, M. W., Jr.; Davles, C. A.; Downey, J. R., Jr.; Frurip, D. J.;
McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables. J. Phys.
Chem. Ref. Data 1985, 14, Suppl. 1.
+ NO (1), k∞1 ) (1.42 ( 0.13) × 1017 exp[-(55 060 ( 1080)/
RT] s-1. The combination of this new result with that reported
earlier by Yu and Lin for the reverse process (-1) obtained by
the cavity ring-down technique yielded with the third-law
method the C-N bond dissociation energy D°0 (C6H5-NO) )
54.2 ( 0.5 kcal/mol. This result, after thermal correction to
298 K, is 4 kcal/mol higher than the accepted value, 51 ( 1
kcal/mol.12 Our higher value is fully consistent with the result
of high-level ab inito MO calculations, 53.8-55.4 kcal/mol,
based on a modified Gaussian-2 method.14 Furthermore, our
high-pressure rate constant k∞1 was found to be in good
agreement with the results of k1 and k-1, reported by Horn and
co-workers,13 after appropriate corrections were made for the
pressure falloff effect.
Acknowledgment. We acknowledge the support received
from the Department of Energy, Office of Basic Energy
Sciences, Division of Chemical Sciences, through Contract DE-
FGO5-91ER14191. The authors are thankful to the Cherry L.
Emerson Center for Scientific Computation for the use of
various programs and computing facilities. Helpful discussion
with Dr. C. F. Melius is much appreciated.
(29) Davico, G. E.; Bierbaum, V. M.; Depuy, C. H.; Ellison, G. B.;
Squires, R. R. J. Am. Chem. Soc. 1995, 117, 2590.
(30) Melius, C. F. BAC-MP4 Heats of Formation and Free Energies,
April 25, 2993 (private communication).
(31) Park, J.; Lin, M. C. J. Phys. Chem. 1997, 101A, 14.
(32) Frost, W. J. Phys. Chem. 1972, 76, 342
References and Notes
(1) Lin, C.-Y. Ph.D. Dissertation, The Catholic University of America,
Washington, DC, 1987.
(33) Pitzer, K. S. Thermodynamics, 3rd ed.; 1995; McGrawHill: New
York, p 114.