Rate constants for the thermal dissociation of N2O and the O(3P) + N2O reaction

Article abstract of DOI:10.1021/jp962416y

The thermal dissociation of N₂O in argon was investigated by monitoring the formation of O(³P) atoms in the reflected shock regime using atomic resonance absorption spectrophotometry (ARAS). The total density and [N₂O] ranges were, (2.6 × 10¹⁸)-(5.4 × 10¹⁸) molecules cm^-3 and (3.3 × 10¹²)-(7.9 × 10¹⁵) molecules cm^-3, respectively. Values for the bimolecular rate constant (131 points), derived under low-pressure limit conditions are given by the Arrhenius expression: k₁(T) = (1.18 ± 0.16) × 10^-9 exp[(-57820 ± 460 cal mol^-1)/RT] cm³ molecule^-1 s^-1 for the temperature range, 1195 ≤ T ≤ 2384 K. These results extend the low-temperature range of ARAS measurements of k₁ by about 200°C which is very significant in 1/T; and the value of the rate constant was extended by more than an order of magnitude. The present data were combined with previously published ARAS data to form a composite data set with a total of 278 points. Although systematic differences between the data of the various groups were discernible, all the data are well represented by the following Arrhenius equation: k₁(T) = (9.52 ± 1.07) × 10^-10 exp[(-57570 ± 390 cal mol^-1)/RT] cm³ molecule^-1 s^-1 for the temperature range, 1195 ≤ T ≤ 2494 K). Uncertainties in the Arrhenius expression are given at the one standard deviation level and the mean deviation of the experimental data from that predicted by the expression is ±26%. These results are compared to those from previous experimental studies. The rate of the reaction of O(³P) with N₂O was investigated experimentally and by kinetic modeling, but only over a limited temperature range, 1200 ≤ T ≤ 1400 K. Upper limit values of the overall rate constant for the O(³P) + N₂O reaction were estimated by a statistical technique. These values were about a factor of 10 lower (with an overall uncertainty of about a factor of three) than those calculated from the recommended Arrhenius expressions of Baulch et al. (1973), Hanson and Salimian (1984), and Tsang and Herron (1991).

Full text of DOI:10.1021/jp962416y

1104
J. Phys. Chem. A 1997, 101, 1104-1116
3
Rate Constants for the Thermal Dissociation of N2O and the O( P) + N2O Reaction
†
Stuart K. Ross, James W. Sutherland,* Szu-Cherng Kuo, and R. Bruce Klemm*
Department of Applied Science, BrookhaVen National Laboratory, Upton, New York 11973-5000
X
ReceiVed: August 8, 1996; In Final Form: NoVember 6, 1996
3
The thermal dissociation of N
2
O in argon was investigated by monitoring the formation of O( P) atoms in the
reflected shock regime using atomic resonance absorption spectrophotometry (ARAS). The total density and
1
8
18
-3
12
15
[
N
2
-3
O] ranges were, (2.6 × 10 )-(5.4 × 10 ) molecules cm and (3.3 × 10 )-(7.9 × 10 ) molecules
cm , respectively. Values for the bimolecular rate constant (131 points), derived under low-pressure limit
-
9
conditions are given by the Arrhenius expression: k
1
(T) ) (1.18 ( 0.16) × 10 exp[(-57820 ( 460 cal
for the temperature range, 1195 e T e 2384 K. These results extend the
low-temperature range of ARAS measurements of k by about 200 °C which is very significant in 1/T; and
-
1
3
-1 -1
mol )/RT] cm molecule
s
1
the value of the rate constant was extended by more than an order of magnitude. The present data were
combined with previously published ARAS data to form a composite data set with a total of 278 points.
Although systematic differences between the data of the various groups were discernible, all the data are well
-
10
represented by the following Arrhenius equation: k
1
(T) ) (9.52 ( 1.07) × 10
exp[(-57570 ( 390 cal
-1
3
-1 -1
mol )/RT] cm molecule
s
for the temperature range, 1195 e T e 2494 K). Uncertainties in the Arrhenius
expression are given at the one standard deviation level and the mean deviation of the experimental data
from that predicted by the expression is (26%. These results are compared to those from previous experimental
3
studies. The rate of the reaction of O( P) with N
2
O was investigated experimentally and by kinetic modeling,
but only over a limited temperature range, 1200 e T e 1400 K. Upper limit values of the overall rate
3
2
constant for the O( P) + N O reaction were estimated by a statistical technique. These values were about a
factor of 10 lower (with an overall uncertainty of about a factor of three) than those calculated from the
recommended Arrhenius expressions of Baulch et al. (1973), Hanson and Salimian (1984), and Tsang and
Herron (1991).
6
7,8
Introduction
chemiluminescence, gas chromatography, laser schlieren,9
1
0
11-15
2,16-17
UV-vis emission -absorption,
most recently, O-atom resonance absorption spectrophotometry
IR emission,
and
The thermal dissociation of N2O is of continuing interest,
both in experimental and theoretical chemistry, and in techno-
logical processes such as combustion in fluidized beds, combus-
1
8-22
1,2,23
(ARAS).
Other studies employed flow tube methods
along with analytical techniques such as FT-IR spectroscopy
and oxygen electrochemical analysis. As shown in Table 1,
there are significant differences in the bimolecular rate constant
expressions found, particularly among the activation energy
values, which range from about 48 to 62 kcal mol . The non-
ARAS results, in particular, show the widest variability in values
for the apparent activation energy and for individual values of
k1(T). In contrast, results from studies that employed the ARAS
technique display reasonably close agreement, especially a
1
,2
tion under fuel lean conditions, and propellant combustion.
1
-25
Consequently, there have been numerous experimental
and
studies to establish the kinetics and the dynamics
of this reaction. In addition, the kinetics of this system are
26-33
theoretical
-
1
3
4-36
discussed in several review articles.
Early studies of this unimolecular reaction established that it
proceeds Via a spin-forbidden, nonadiabatic pathway to form
3
O( P) atoms in preference to the spin allowed, but more
1
endothermic dissociation to form O( D) atoms:
1
8-22
narrow range in activation energies
clustering around 61 kcal mol .
with most values
-
1
1
+
1
+
3
N O( Σ ) + M f N ( Σ ) + O( P) + M
2
2
g
In their theoretical study, Cheng and Yarkony32 calculated
the potential energy surfaces involved and provided critical
information on the crossing surfaces linking the ground state
singlet to the three possible triplet states. These authors further
show that only the linear A′′ triplet state is important with state
to state crossing occurring at an energy level of about 58 kcal
mol above the ground state. This calculated energy level
should relate to the high-pressure activation energy for reaction
R1. If so, the value of 58 kcal mol would appear to be
somewhat small in relation to both the majority of the low-
-
1
∆rH° ) 39 kcal mol (R1)
0
1
+
1
+
g
1
N O( Σ ) + M f N ( Σ ) + O( D) + M
2
2
-
1
∆rH° ) 84 kcal mol (R1a)
0
-
1
Dissociation occurs as a result of collision induced vibrational
excitation of the singlet ground state to a critical “energy level”
from which intersystem crossing takes place to a triplet state,
which is predissociative.
Most of these investigations employed shock tubes together
-
1
3
4
-
1
pressure ARAS results (≈61 kcal mol ) and to the recently
1
5
∞
3-5
published value for the high-pressure limit, Ea ) 62.6 kcal
with various analytical techniques such as mass spectroscopy,
-
1
mol .
Fall-off behavior and the asymptotic approach to the high-
*
Authors to whom correspondence should be addressed.
Visiting Research Associate, permanent address: Department of
†
37
pressure limit is observed only at very high pressures.
Reported high-pressure studies are summarized in Table 2,
which includes results from studies by Allen et al., Olschewski
Chemistry, University of Aberdeen, Meston Walk, Aberdeen AB9 2UE,
Scotland, U.K.
X
2
Abstract published in AdVance ACS Abstracts, February 1, 1997.
S1089-5639(96)02416-4 CCC: $14.00 © 1997 American Chemical Society

N2O Thermal Dissociation
J. Phys. Chem. A, Vol. 101, No. 6, 1997 1105
3
TABLE 1: Low-Pressure Rate Constant Expressions Determined by Shock Tube Techniques for N
2
O + M f N
2
+ O( P) + M,
M ) Ar
3
-1
(kcal mol-1
temperature (K)
pressure (Torr)
1350
A (cm molecule s-1
)
E
a
)
refs
Rate Expressions Determined Via ARAS
-
-
-
-
-
9
Roth and Just18b
Pamidimukkala et al.
1850-2500
1519-2408
1450-2200
1600-2500
1540-2500
2.40 × 10
2.23 × 10
2.40 × 10
1.66 × 10
2.76 × 10
61.206
62.040
59.465
60.470
52.542
9
19
9
20a
760-1350
760
Frank and Just
9
21a
Fujii et al.
10
22b a
Michael and Lim
Rate Expressions Determined Via Other Diagnostic Techniques
-
9
Jost et al.11
Olschewski et al.
1500-2500
1500-2500
1000-2000
1000-3000
1850-2536
2160-2500
1950-2800
2100-3200
1815-3365
1700-2400
1688-3113
1685-2560
1820-3170
80-250
1.66 × 10
8.32 × 10
8.32 × 10
7.80 × 10
4.90 × 10
8.32 × 10
1.91 × 10
4.50 × 10
2.36 × 10
6.47 × 10
5.25 × 10
6.15 × 10
7.30 × 10
60.999
57.998
57.001
58.000
52.367
58.000
48.639
54.016
51.282
57.365
55.834
54.966
56.001
5
-10
12
1140-2.28 × 10
-
-
-
-
-
-
-
-
-
-
-
10
10
10
10
10
10
10
10
10
10
10
13
30-200
Borisov and Skachkov
Soloukhin6
10
60-74
Baber and Dean
9
2-75
Dove et al.
15
37-77
Dean
16
77-238
304-380
112-744
228-4560
1290-3500
186-435
Dean and Steiner
24
Monat et al.
Endo et al.
28
15
Rohrig et al.
25
Sulzmann et al.
Zaslonko et al.
14
Rate Expressions Recommended in Review Articles
-
-
-
10
10
9
Baulch et al.34
Hanson and Salimian
Tsang and Herron
1300-2500
1500-2500
1000-2500
8.30 × 10
5.61 × 10
1.75 × 10
57.623
56.761
60.521
35 b
36 c
a
b
The values for A and E
rate expression recommended in ref 35, k
by using least-squares analysis to give a linear fit over the temperature range T ) 1500 - 2500 K. The rate expression recommended in ref 36,
a
given here were evaluated from the rate constant data of ref 22a for the experiments performed with Ar diluent. The
-
2.5
-1
3
-1 -1
1
(T) ) 1.15T
exp(-65.001 kcal mol /RT) cm molecule
s , T ) 1500 - 3600 K, was reevaluated
c
-
6
-0.73
-1
3
-1 -1
k
1
(T) ) 1.2 × 10
give a linear fit over the temperature range T ) 1000 - 2500 K. The expression tabulated here is for M ) Ar (corrected for collision efficiency:
Ar] ) [N ]/1.5).
T
exp(-65.001 kcal mol /RT) cm molecule
s , T ) 700 - 2500 K, was reevaluated by using least-squares analysis to
[
2
3
TABLE 2: High-Pressure Rate Constants for N
2
O + M f N
2
+ O ( P) + M
(s-1)
temperature (K)
pressure (Torr)
A
∞
E
a
(kcal mol-1
)
refs
2
5
11
12
1400-2500
1250-1800
1780-2300
1103-1173
1600-2000
(6.08 × 10 )-(2.28 × 10 )
1.26 × 10
59.5
52.8
57.6
56.02
62.61
Olschewski et al.
3
3
10 a
11
38
(5.32 × 10 )-(7.60 × 10 )
9.3 × 10
1.7 × 10
5.3 × 10
1.3 × 10
Verem’ev et al.
3
4
39
(1.52 × 10 )-(1.55 × 10 )
Zuev et al.
3
3
10 a
12
2
(1.14 × 10 )-(7.98 × 10 )
Allen et al.
2
5
15
(2.28 × 10 )-(3.42 × 10 )
R o¨ hrig et al.
a
This value has been corrected for collision efficiency: [Ar] ) [N
2
]/1.5.
et al.,12b and Rohrig et al., along with those from two other
15
At high concentrations of N2O and where substantial decom-
position takes place, the following additional reactions may also
become significant:
3
8,39
34-36
investigations
and three review articles.
The recent
study of Rohrig et al.15 reports results that cover an exceptionally
wide range in total pressure (argon buffer gas, about 0.3-450
atm) and, although there is considerable scatter in the data, the
derived activation energy for the rate constant at the high-
pressure limit implies that the singlet-triplet crossing occurs
3
O( P) + NO + Ar f NO + Ar
(R3)
2
3
O( P) + NO f O + NO
(R4)
(R5)
2
2
-
1
at about 63 kcal mol above the singlet ground state. This
∞
-1
value for Ea , which is some 3.4 kcal mol higher than that
NO + N O f NO + N
2 2 2
reported previously1
2b,34-36
(59.6 kcal mol ) and adopted in
-1
3
theoretical calculations, would appear to support the consensus
ARAS value for Ea of about 61 kcal mol . However, Rohrig
et al. report an Arrhenius Ea value of 55.8 ( 1 kcal mol
O( P) + O + Ar f O + Ar
(R6)
(R7)
2
3
o
-1
1
5
o
-1
NO + O f NO + O
3 2 2
for the temperature range 1688-3113 K, in good agreement
with the values given in refs 34-36. Clearly, a precisely defined
kinetic expression for the low-pressure rate constant is required
to test future unimolecular calculations and for modeling of
combustion systems.
Few values for the rate constants of reactions R2a and R2b
have been reported. The reaction is relatively slow, and until
recently, both channels were thought to be of nearly equal
-
10
3
-1
importance, k2a ) 1.1 × 10 exp(-13400/T) cm molecule
-
1
-10
exp(-14100/T) cm3
s
(refs 35 and 36), k2b ) 1.7×10
molecule
evidence for this conclusion is sparse.
A full description of N2O thermal decomposition requires that
reactions R2a and R2b be considered along with reaction R1,
particularly at low temperatures:
-
1
-1
s
(refs 35 and 36), although the experimental
3
4-37
However, a recent
study has reported significantly different rate constant expres-
40
-
11
sions for the two channels: k2a ) (4.8 ( 15%) × 10
exp-
3
O( P) + N O f NO + NO
(R2a)
(R2b)
3
-1 -1
2
(-11650/T) cm molecule
s
(1680 e T e 2430 K, 0.7-
-
12
exp(-5440/T) cm3
1
.0 atm) and k2b ) (2.3 ( 25%) × 10
3
O( P) + N O f N + O
-1 -1
2
2
2
molecule
s
(1940 e T e 3340 K, 0.9-2.0 atm). Values

1106 J. Phys. Chem. A, Vol. 101, No. 6, 1997
Ross et al.
of the bimolecular rate constant calculated from these equations
at high temperatures, e.g., around 2000 K, agree with those from
34-36
the recommended expressions,
but there are significant
differences when the expressions are extrapolated to the
important range of practical combustion systems, 1000 e T e
2
1
500 K. This observation was noted already by Allen et al.
in a recent paper on a variable pressure flow study of nitrous
oxide. Specifically, they concluded (from detailed kinetic
modeling calculations in their experimental temperature range
1103 e T e 1173 K) that values of the overall rate constant
for the O + N2O reactions obtained by extrapolating the
expression of Davidson et al.4 were too large. The low
0
-1
activation energy for reaction R2b of 10.8 kcal mol determined
4
0
by Davidson et al. is the primary reason for the large overall
k2 value at lower temperatures. These recent values also raise
2,15
questions about the stoichiometric number
assumed in a
previous study of N2O dissociation.1
2b
In the present study, an O-atom spectrophotometer was cali-
brated. Bimolecular rate constant values for reaction R1 were
determined over the temperature range 1195 e T e 2384 K,
taking into account absorption of resonance and nonresonance
light by N2O. These values were then combined with the indi-
vidual data points from previous ARAS investigations to give
a composite bimolecular rate constant expression (1195 e T e
Figure 1. Typical transmission signal observed for the thermal
decomposition of N
2
O in the reflected shock regime: P
1
) 15.64 Torr,
18
-3
M
s
) 2.998, T
5
-
) 2163 K, F
5
) 3.32 × 10 molecules cm , and XN O
2
6
)
2.727 × 10
.
(Vt volts), then ABSt, the absorbance at time t, is given by eq
2
494 K). Kinetic modeling was employed to demonstrate that
1
:
the present results are not consistent with recommended values
for k2 (k2a + k2b). A statistical approach was used to evaluate
the data of seven runs to derive estimated upper limit values
for k2 over the temperature range 1200 e T e 1400 K.
ABS ) ln[I f/(I f - (I - I ))] ) -ln(1 - (V - V )/V f)
t
o
o
o
t
o
t
o
(1)
It is assumed that the Beer-Lambert law (ABS ) RlC) holds,
2
-1
where R is the O-atom absorption coefficient (cm molecule ),
l is the path length (the diameter of the shock tube, 6.02 cm),
Experimental Section
-3
and C is the O-atom concentration (molecules cm ).
The base line level Io ) Vo is usually taken as the signal
level in the reflected regime immediately following the passage
of the shock front past the observation window. At very high
temperatures, where it can be obscured by the fast formation
of atoms, the base line is determined from corresponding absorb-
ance values associated with compression ratios measured at
lower temperatures with appropriate concentrations of reactant
mixtures. Where the rate constants were derived from the initial
linear slope of the O-atom absorbance vs time, the base line
could be easily determined with sufficient accuracy by extrapo-
lation.
The shock tube apparatus, its operation, and its subsequent
modifications have been fully described elsewhere.4
1-46
In the
present study, the shock tube was operated in the thermal
mode.46 ARAS
41,47
was used to monitor changes in the
3
concentration of O( P) atoms.
The temperature (T5), density (F5), and pressure (P5) in the
reflected shock regime were calculated using ideal shock theory
from the measured values of the incident shock velocity, the
test gas composition, the initial temperature, and the initial
4
1,48,49
pressure.
Vibrational equilibrium was assumed to be
complete. When necessary, boundary layer effects were cor-
rected for by a procedure that made use of the adiabatic equation
of state and of the experimental measurements of the pressure
changes occurring in the sample after passage of the incident
and reflected shock waves.41 Uncertainties in determining Mach
numbers ranged from 0.5 to 1% leading to corresponding
uncertainties in T5 and F5 of 1-2%.
O-atom Calibration. The O-atom spectrophotometer was
calibrated by completely dissociating N O at known mole frac-
2
-
6
-6
tions (1.040 × 10 e XN2O e 9.740 × 10 ) in argon over the
temperature range 1932 e T e 2384 K. A typical transmit-
tance-time profile from a calibration run is shown in Figure 1,
the initial voltage signal rapidly decreasing with time after the
passage of the reflected shock, to reach a constant level, corre-
sponding to the final concentration of O-atoms when N2O has
fully dissociated. Experimental conditions are chosen so that
secondary reactions are negligible, and therefore the final con-
centration of O-atoms [O]∞ is equal to the initial concentration
of N2O. A calibration plot can then be constructed that shows
the relationship between absorbance and O-atom concentration.
Results from a total of 71 calibration runs are listed in Table
The resonance lamp was operated at a pressure of 10 Torr
with a mixture of 0.0862% of O2 in He and a microwave power
42-45
level of about 100 W. An O-atom filter,
which consisted
of a second microwave discharge in a flowing mixture of 9.54%
O2 in He that was maintained at 8 Torr, was located between
the lamp and the shock tube window. A vacuum UV CaF2
window, placed in the optical path between the filter and the
shock tube window, allowed transmission of the O-atom
resonance triplet lines, centered at 130.4 nm, but effectively
blocked the lower lying resonance line emissions from H and
N atoms. The photomultiplier housing was purged by a steady
flow of N2. When the voltage signal from the photomulti-
plier was measured with the filter discharge on and off, the
fraction of incident resonance radiation was determined. If f is
the fraction of resonance radiation, Io is the total incident
intensity (Vo volts) and It is the transmitted intensity at time t
3
and plotted in Figure 2. The Beer-Lambert law holds up to
absorbance values of approximately 0.67 (see Figure 2, inset),
but at higher concentrations increasing curvature is observed.
Over the total absorbance range, 0-1.1, the data are fitted by
the polynomial of degree 2:
8
13
[
O] ) 8.127 × 10 + (2.457 × 10 )(ABS) +
12 2
-3
(6.123 × 10 )(ABS) atoms cm (2)

N2O Thermal Dissociation
J. Phys. Chem. A, Vol. 101, No. 6, 1997 1107
TABLE 3: Calibration Data for the O-Atom Photometera
b
c
/Kd
O)e
b
c
/Kd
5 2
F (N
O)e
P
1
/(Torr)
M
s
F
5
T
5
ABS
∞
F
5
(N
2
P
1
/(Torr)
M
s
F
5
T
5
ABS
∞
-
6
X
3.300
N O ) 1.040 × 10
2
1
1
5.11
5.11
2.947
2.959
3.173
3.181
2092
2110
0.13
0.13
15.06
2.996
3.200
2159
0.13
3.328
3.308
-
6
X
N O ) 1.058 × 10
2
1
1
1
1
5.07
5.07
5.00
4.89
2.971
2.936
2.887
2.963
3.200
3.160
3.108
3.151
2114
2075
2008
2106
0.13
0.14
0.14
0.14
3.386
3.343
3.288
3.334
15.08
15.06
14.85
15.06
2.925
2.983
3.016
2.957
3.158
3.202
3.189
3.185
2056
2132
2173
2095
0.13
0.14
0.13
0.14
3.341
3.388
3.374
3.370
-
6
X
5.370
N O ) 1.655 × 10
2
1
5.53
2.929
3.245
2069
0.21
15.63
2.824
3.172
1932
0.20
5.250
-
6
X
N O ) 2.014 × 10
2
1
1
1
1
5.00
5.08
5.06
5.07
2.892
2.884
2.921
2.937
3.112
3.126
3.153
3.165
2014
2000
2050
2072
0.27
0.26
0.26
0.25
6.268
6.296
6.350
6.374
14.98
15.03
15.06
3.004
3.019
2.948
3.204
3.228
3.173
2159
2179
2086
0.27
0.27
0.26
6.453
6.501
6.390
-
6
X
7.486
7.572
N O ) 2.322 × 10
2
1
1
5.06
5.00
3.025
3.095
3.224
3.261
2198
2296
0.26
0.27
15.03
15.02
2.860
3.021
3.083
3.212
1976
2192
0.26
0.27
7.159
7.458
-
6
X
N O ) 2.404 × 10
2
1
1
1
1
5.06
4.98
5.05
0.30
2.897
3.030
2.864
3.143
3.125
3.209
3.087
2.266
2024
2204
1984
2361
0.29
0.30
0.29
0.22
7.513
7.714
7.421
5.447
15.02
15.04
15.00
15.08
3.157
3.165
3.053
3.082
3.312
3.328
3.234
3.272
2383
2391
2235
2276
0.28
0.28
0.29
0.30
8.001
7.963
7.774
7.866
-
6
X
9.479
8.874
N O ) 2.727 × 10
2
1
1
5.74
5.65
3.118
2.903
3.476
3.254
2305
2029
0.32
0.32
14.91
15.64
2.973
2.998
3.158
3.324
2122
2163
0.32
0.32
8.612
9.065
-
6
X
9.926
9.954
N O ) 3.150 × 10
2
1
1
4.94
5.15
2.967
2.924
3.151
3.160
2120
2063
0.37
0.36
15.14
2.921
3.157
2059
0.37
9.945
-
6
X
N O ) 3.266 × 10
2
1
1
5.05
5.09
3.011
3.028
3.212
3.225
2178
2206
0.39
0.36
10.490
10.533
14.99
15.02
3.027
2.873
3.200
3.092
2208
1995
0.37
0.39
10.451
10.098
-
6
X
N O ) 4.120 × 10
2
1
1
5.02
5.03
3.107
2.965
3.278
3.171
2311
2116
0.48
0.49
13.505
13.065
15.23
15.05
2.947
3.108
3.198
3.288
2091
2311
0.50
0.47
13.176
13.547
-
6
X
N O ) 5.191 × 10
2
1
1
1
5.04
5.02
5.13
3.035
3.032
3.033
3.270
3.239
3.239
2182
2194
2213
0.59
0.60
0.58
16.974
16.814
16.184
15.06
15.03
2.879
2.983
3.107
3.188
2001
2139
0.60
0.57
16.128
16.549
-
6
X
N O ) 5.807 × 10
2
1
1
4.98
5.02
3.034
3.029
3.220
3.223
2205
2200
0.66
0.67
18.699
18.716
14.92
15.07
3.056
2.843
3.221
3.079
2237
1954
0.64
0.67
18.704
17.880
-
6
X
N O ) 7.755 × 10
2
1
1
1
4.88
5.29
5.05
2.995
3.000
2.935
3.185
3.273
3.171
2142
2150
2063
0.86
0.84
0.86
24.700
25.382
24.591
15.02
15.41
2.914
3.106
3.153
3.384
2030
2295
0.86
0.83
24.451
26.243
-
6
X
N O ) 9.740 × 10
2
1
1
5.33
5.08
2.995
2.990
3.287
3.230
2137
2131
1.00
1.00
32.015
31.460
f
15.03
15.17
3.047
2.891
3.259
3.155
2211
2006
0.97
1.06
31.743
30.730
-6
X
N O ) 3.956 × 10
2
1
1
1
5.85
5.87
5.80
2.957
3.086
2.945
3.366
3.477
3.381
2087
2262
2051
0.49
0.50
0.49
1.332
1.376
1.338
15.76
15.32
15.23
3.091
3.174
3.174
3.451
3.436
3.404
2270
2376
2384
0.51
0.50
0.50
1.365
1.359
1.347
a
Unless otherwise stated, the N
O sample was of 99.99% purity. b The uncertainty in measuring the Mach number is typically about (0.7% at
c 18 d
2
-3
the one standard deviation level. Units of density are 10 molecules cm
1.5%. Units of density are 10 molecules cm . The N
.
The uncertainty in temperature is estimated to be no more than
e
12
-3 f
(
2
O sample for these data was of 99.999% purity.
15
2
-1
The mean deviation of the experimental data points from
those predicted by this expression is (3.2%.
10- cm atom showing, as expected, that there is appreciable
self-absorption and pressure broadening in the lamp. This ab-
sorption coefficient is assumed to be constant over the total ex-
perimental temperature range of 1195 e T e 2384 K. There
were no significant changes in the values of the O-atom con-
centrations when they were calculated by eq 2. Six of the
In general, rate constants in this study were evaluated only
from absorbance data obtained in the concentration range over
which the Beer-Lambert law held. From the zero constrained
-
14
plot, Figure 2 (inset), a value for Rl of (3.66 ( 0.06) × 10
3
-1
-6
cm atom was determined, independent of temperature over
the experimental range of 1932 e T e 2384 K. This value of
Rl corresponds to an O-atom absorption coefficient of 6.08 ×
calibration runs (XN O ) 3.956 × 10 ), listed in Table 3 and
2
shown in Figure 2 as filled circles, were performed using a
separate source of N2O (M. G. Products, stated purity of

1108 J. Phys. Chem. A, Vol. 101, No. 6, 1997
Ross et al.
Figure 3. Schematic of transmission changes observed when a high
Figure 2. Calibration data. Solid line is fit of the polynomial of degree
-
2
concentration (XN2O ) 2.0 × 10 ) N
2
O mixture is shocked. (a) Solid
8
13
12
2
2
, [O] ) 8.127 × 10 + (2.457 × 10 )(ABS) + (6.123 × 10 )(ABS)
VAC
lines are signal levels in evacuated shock tube: V
T
, O-atom filter
off and V NR, O-atom filter on. (b) Corresponding signal levels in
shock tube filled with N O mixture. Note high voltage on photomul-
-3
atoms cm , to absorbance data from 0 to 1.1: open circle, data from
purified 99.99% N O, filled circle, data from purified 99.999% N O.
Inset: solid line is the linear least-squares fit of the Beer-Lambert
VAC
2
2
2
tiplier tube has been increased. (c) Signal levels observed when mixture
is shocked: solid lines are observed signals and dashed lines are
corresponding signal levels with filter on; they are not observed and
must be calculated, see text. Superscripts: VAC, evacuated shock tube;
AT, ambient temperature; I, incident regime; R, reflected regime.
Subscripts: T, total signal, filter off and NR, nonresonance signal,
filter on.
-
14
3
-1
expression, ABS ) Rl[O], where Rl ) 3.66 × 10 cm atom , over
1
3
-3
the absorbance range 0-0.6 ≡ 0-1.7 × 10 atoms cm
.
99.999%). These points were in excellent agreement with the
other calibration data. It was observed that the calibration of
the lamp was reproducible over a long period of time provided
that the lamp operating conditions were the same and that the
lamp was tuned and conditioned after each shutdown period.
In experiments where the light fraction at room temperature
was deliberately changed by altering the lamp operating
conditions, it was shown that, for the high-temperature runs,
calibration and kinetic data were independent of the light
fraction. From these observations, it can be inferred that the
O-atom filter technique worked efficiently and that the measure-
ments were not dependent of the output characteristics of the
lamp. As part of the experimental procedure, the calibration
was checked periodically by performing measurements at
temperatures of about 2100 K, where N2O completely dissoci-
ates during the observation time.
perturbations have even a more minor effect on the accuracy
of the rate constant determination, especially when compared
to the typical errors that result from the uncertainties in
determining the temperature, pressure, and density in the
reflected regime.
Nitrous oxide, however, is a relatively strong absorber of both
the resonance and nonresonance wavelengths to which the
50
typical solar blind photomultiplier is sensitive. Neglect of this
absorption, particularly at the higher concentrations required for
the lower temperatures in this study, can lead to serious errors
in the determination of absorbance values and, hence, of O-atom
concentrations and rate constants. The simplest method to take
this effect into account is to determine the light fraction in the
reflected regime directly by carrying out the same experiment,
with and without the filter on, in separate but identical shocks.
Unfortunately, as is well-known, it is characteristic of the shock
tube technique that identical shocks cannot be generated
consistently; exact conditions of temperature and density in the
reflected regime are notoriously difficult to duplicate on demand.
Hence, the following experimental procedure was devised. A
series of experiments with N2O/Ar mixtures of appropriate
compositions were carried out with the filter on, i.e., with only
nonresonance light being transmitted through the shock tube.
From the changes in transmittance and [N2O] resulting from
successive incident and reflected shock compressions, a calibra-
tion curve was constructed for absorbance of nonresonance light
by N2O, ABSNR vs ∆[N2O], where ∆[N2O] is the difference
between N2O concentration in the incident and reflected shock
regime and that at ambient temperature prior to shock process-
ing. This procedure is presented schematically in Figure 3,
Molecular Absorption at High Concentrations of N2O.
Incident radiation from resonance H and O-atom lamps contains
a significant fraction of nonresonance light that can range from
1
0 to 35% depending on lamp operating conditions. The
resonance light fraction f, necessary for the calculation of
absorbance and atom concentration, is usually determined at
ambient temperature for the evacuated shock tube as has been
previously described.41 In general, the absorption coefficients
of molecular components at resonance wavelengths are very
much less than those of the H and O-atoms, ranging from
-
18
-20
2
-1
10
-10 cm molecule . These values are to be compared
-
13
-14
2
-1
to absorption coefficients of 10 -10
cm atom for H
-14
-15
2
-1
atoms and 10 -10 cm atom for O-atoms observed with
typical resonance lamps. Careful tuning of the microwave
cavity, the lamp design itself, and appropriate choice of
operating conditions enable bright, stable, and reproducible
plasmas that emit 75-90% of incident resonance light to be
formed. The use of a solar blind photomultiplier further
minimizes the effect of absorption of nonresonance radiation
by molecular components. Usually in the typical ARAS shock
tube experiment, the small perturbations in the value of the light
fraction, caused by light absorption by the molecular components
of the mix, are not significant and thus the light fraction is little
changed in the reflected regime. Moreover, these small
R
AT
R
I
AT
where ABS NR ) ln(V NR/V NR) and ABS NR ) ln(V NR/
I
V NR). The symbols are defined as follows: (superscripts) AT,
ambient temperature; I, incident regime; R, reflected regime;
and VAC, shock tube under vacuum; and (subscripts) NR,
nonresonance radiation and T, total (nonresonance + resonance
radiation).

N2O Thermal Dissociation
J. Phys. Chem. A, Vol. 101, No. 6, 1997 1109
TABLE 4: Absorbance Data: Nonresonance Light (O-Atom
Filter On)
TABLE 5: Effect of Changing Light Fraction Value on Rate
Constants
VATNRa
VINRb
VRNRc ABSINRd ∆[N
O]e ABSRNRf ∆[N
O]g
light fraction
light fraction
percent
change
2
2
(uncorrected, fAT) (corrected, fCORR
)
a
T (K)
X
N O
2
3
3
2
5
5
5
5
5
5
5
4
4
2
2.83 28.02 24.07 0.1584
5.21 30.88 27.00 0.1312
6.00 24.78 23.57 0.0480
2.36 44.97 38.80 0.1521
2.38 44.77 38.45 0.1570
4.59 48.61 42.85 0.1160
5.61 50.41 45.25 0.0982
6.76 50.68 44.93 0.1133
7.19 51.29 45.64 0.1089
8.12 53.37 48.24 0.08537
7.78 43.88 39.56 0.08517
5.91 42.81 39.10 0.06995
7.65 26.31 24.62 0.04968
1.864
1.511
0.3659
1.825
1.641
1.079
0.8663
1.034
0.3104
0.2655
0.0980
0.2997
0.3092
0.2421
0.2062
0.2337
0.2256
0.1865
0.1889
0.1606
0.1161
5.035
4.035
0.9801
5.174
4.643
3.090
2.447
2.763
2.724
2.028
2.010
1.622
1.015
-
-
-
-
-
4
4
4
3
3
1500 2.403 × 10
1378 2.403 × 10
1409 4.176 × 10
1425 1.000 × 10
1322 2.000 × 10
0.65
0.63
0.64
0.62
0.69
0.62
0.58
0.56
0.50
0.38
5.3
8.1
16.0
33.0
150.0
a
Percentage change in rate constants (as presented in Table 7) that
employed the correct light fraction.
1.012
0.7159
0.7100
0.5673
0.3765
R
appropriate voltage level for nonresonance light V NR in the
reflected regime could be determined. The value of V NR for
each experiment was calculated from the measured V T, the
AT
AT
a
base line before the shock (see Figure 3), by making use of the
light fraction f previously determined for the particular mix
Initial voltage level at room temperature before shock compression;
b
AT
units are mV. Voltage level after incident shock compression; units
are mV. Voltage level after reflected shock compression; units are
c
at ambient temperature. Hence, from the experimentally
d
mV. Nonresonance absorbance after incident shock compression;
R
determined V T value, the correct light fraction for the reflected
ABSINR ) ln(V NR/V NR). Change in N
AT
I
e
O concentration after incident
2
regime could be calculated. In summary, the light fraction for
-
3
15 f
shock compression; units are molecules cm × 10 . Nonresonance
VAC
VAC
VAC
VAC
R
AT
the evacuated shock tube f
) (V
T - V
NR)/V
T, was
absorbance after reflected shock compression; ABS NR ) ln(V NR
/
R
g
measured. The shock tube was then filled, and the light fraction,
V
NR). Change in N
units are molecules cm × 10 .
2
O concentration after reflected shock compression;
-
3
15
AT
AT
AT
AT
f
) (V T - V NR)/V T, was measured at ambient temper-
ature for the particular mix. The mixture was shocked and the
correct value for the light fraction in the reflected regime, fCORR
R
R
R
)
(V T - V NR)/V T, calculated by the above procedure.
Absorbance values were then calculated in the usual manner
from eq 1.
Depending upon the mole fraction of N2O and the temper-
ature, the resonance light fraction decreased in going from
vacuum to sample at ambient temperature to sample in the
reflected regime. The effect of typical changes in the light
fraction on the measured rate constant values for five examples
are listed in Table 5. Use of the corrected light fraction fCORR
always leads to larger absorbance values, i.e., larger concentra-
tion of O-atoms, and thus to an increase in the value of the
derived rate constant. This effect is most pronounced for results
obtained at low temperatures where high concentrations of N2O
were generally employed.
Materials. The helium and argon were of stated purity of
9
9.9999% (M. G. Industries). The two nitrous oxide samples
(99.99% and 99.999%, M. G. Industries) were further purified
by the freeze-pump-thaw technique at 78 K. The 0.0862%
O2/He and 9.54% O2/He mixtures (both were 99.999% purity
O2 and 99.9999% purity He, M. G. Industries) were used directly
from cylinders without further purification.
Figure 4. Calibration curve for determination of the nonresonant light
2
absorbance by N O. Solid line is fit of the polynomial of degree 2,
-
2
-17
ABSNR ) 1.744 × 10 + (9.674 × 10 )(∆[N
2
O]) - (7.857 ×
-
33
2
1
0
)(∆[N
2
O]) , to experimental data over ∆[N
2
O] range of (0.37-
1
5
-3
5
.2) × 10 molecules cm (Table 4); open circle, data from incident
Results and Discussion
regime; filled circle, data from reflected regime.
The N2O + M(Ar) Reaction. As discussed in the Introduc-
tion, the rate constant for reaction R1 has been demonstrated
to be in the low-pressure limit for pressures e6 atm. Since the
present experiments were performed at pressures below 1 atm,
the data were computed as second-order rate constants.
Kinetic Analysis: First-Order Method. At high temperatures
(T > 1900 K) the reaction goes to completion within the
experimental observation time, and the low-pressure unimo-
2
The calibration data are listed in Table 4 and shown in Figure
. This procedure was necessary only for the low end of the
4
temperature range (1195 e T e 1602 K), where higher mole
fractions of N2O were required to obtain adequate O-atom
absorbances. It was assumed that the absorption coefficient for
N2O for nonresonance light was constant. A polynomial fit to
the data gave the following expression for ABSNR, which is a
function only of ∆[N2O]:
lecular rate, first order in [Ar] and [N O] , is then given by
-2
-17
-d[N O] /dt ) d[O] /dt ) k [Ar][N O]
t
(4)
ABSNR ) 1.744 × 10 + (9.674 × 10 )(∆[N O]) -
2
t
t
1
2
2
-
33
2
(
7.857 × 10 )(∆[N O]) (3)
2
Hence, k1 can be determined from the slope of the first-order
plot,
The mean deviation of the experimental points from this fit
was (4.0%. From this equation, ABSNR could be calculated
for any value of ∆[N2O] in the reflected regime; hence from
ln([O] - [O] ) ) -kobst + ln[O]∞
(5)
∞
t
R
AT
the Beer-Lambert law, V NR ) V NR exp(-ABSNR), the
where kobs ) k1[Ar].

1110 J. Phys. Chem. A, Vol. 101, No. 6, 1997
Ross et al.
It already has been shown that for the present ARAS lamp,
the Beer-Lambert law (ABS ) Rl[O]) holds up to absorbance
values of about 0.7, and over this range, eq 5, on substitution,
is transformed to
ln(ABS - ABS ) ) -kobst + ln ABS∞
(6)
∞
t
or, in the exponential form,
ABS ) ABS (1 - exp(-kobst))
(7)
t
∞
Figure 5 shows a typical absorbance-time plot, corresponding
to the transmittance trace illustrated in Figure 1. The solid line
through the data points is the fit to the first-order buildup
equation (eq 7):
ABS ) 0.32(1 - exp((-5925 ( 26)t))
(8)
t
-
1
where ABS∞ ) 0.32, kobs ) 5925 ( 26 s , and [Ar] ) 3.324
1
8
-3
-15
3
×
10 molecules cm ; hence, k1 ) 1.78 × 10
cm
Figure 5. Plot of the absorbance buildup corresponding to the
transmission signal of Figure 1: Open circle, experimental data points;
solid line, fit of first-order equation, ABS ) ABS (1 - exp(kobst)),
-
1 -1
molecule s . Values of kobs were obtained from linear least-
squares fitting of eq 7 and are listed in Table 6 together with
the corresponding values of k1.
Kinetic Analysis: Initial Slope Method. At temperatures
lower than about 1900 K, there was insufficient time to observe
complete N2O dissociation. On the other hand, given the time
resolution and sensitivity of the apparatus, conditions could be
readily chosen so that only a negligible fraction of N2O was
decomposed in the time frame of the experiment, and thus
t
∞
-
1
where kobs ) 5925 s , ABS
∞
) 0.32, k
1
) kobs/[M], [M] ≡ F
5
) 3.324
18
-3
×
10 molecules cm . Inset: plot of residuals. Here, time ) 0
corresponds to the passage of the reflected shock by the observation
window.
observed, and no evidence of complex kinetics was apparent.
This was as expected from results of simulation studies.
Experimental values of k1(T) were independent of changes in
[
N2O]t = [N2O]o at all times. The rate constants could then be
[
1
N2O], which was varied by more than a factor of 5 ((3.3 ×
determined from the initial slopes of the absorbance-time
1
2
13
0 )-(1.8 × 10 )). This is further evidence that the first-
profiles:
order decay of N2O was free from the influence of secondary
reactions.
-
d[N O] /dt ) d[O] /dt ) (dABS /dt)/Rl ) k [N O] [Ar]
2 t t t 1 2 o
The total densities F5(Ar) for the kinetic data reported in
(
9)
18
Tables 6 and 7 vary by a factor of 2.1 from (2.6 × 10 )-(5.4
1
8
-3
×
10 ) molecules cm . No systematic pressure dependence
and
of the bimolecular rate constant k1 was observed; thus, it was
dABS /dt ) k Rl[Ar][N O]
o
(10)
concluded that these experiments were performed in or near to
t
1
2
1
8-22
the low-pressure limit. Other workers,
using the O-atom
Hence,
ARAS technique to investigate N2O thermal decomposition,
have reached similar conclusions, and in the study of Frank
ABS - ABS ) k Rl[Ar][N O] (t - t )
(11)
18
t2
t1
1
2
o
2
1
and Just, experiments were extended to much higher total
1
8
18
-3
densities ((4.2 × 10 )-(36.1 × 10 ) molecules cm ) than
where t1 and t2 are the arbitrary observation times.
The linear graph of ABSt vs time (typical examples are shown
those employed in the present study.
To check for impurity effects, experiments were also per-
formed using a second source of N2O that had a stated
purity of 99.999%. The kinetic results obtained over the
temperature range 1400 e T e 2384 K and the calibration
results were in excellent agreement with those from the
experiments that employed 99.99% purity N2O (see Figures 2
and 7).
-
1
in Figure 6) will have a slope (ABS s ) ≡ k1[N2O]o[Ar]Rl;
hence, k1 can be calculated by dividing by the known concentra-
-
14
3
tions of N2O and Ar and the value of Rl (3.66 × 10
cm
-
1
atom ), which is assumed to be independent of temperature.
Slopes were determined by the linear least-squares method, and
the calculated k1 values are listed in Table 7.
Arrhenius Expressions. This study. An Arrhenius plot of
the kinetic data (131 points) from this study, listed in Tables 6
and 7, are shown in Figure 7. Over the temperature range 1195
e T e 2384 K, and with total densities ranging from (2.266 ×
Composite Data Set. The ARAS technique was employed
previously by five groups to determine the unimolecular
dissociation of N2O in argon mixtures in the low-pressure limit.
In Figure 8, the previous ARAS data appear to agree well with
one another and with the present results for k1(T). Therefore,
the results from this study were combined with the ARAS data
18
18
-3
1
0 )-(5.393 × 10 ) molecules cm , the data were well
represented by the Arrhenius expression:
1
8c
sets of Roth and Just (1498 e T e 2245 K), Pamidimukkala
-
9
k (T) ) (1.18 ( 0.16) × 10 exp[(-57820 (
19
20b
1
et al. (1519 e T e 2408 K), Frank and Just (1389 e T e
2
60 cal mol )/RT] cm molecule s-1 (12)
-1
3
-1
21b
210 K), Fujii et al. (1602 e T e 2421 K), and Michael and
4
2
2b
Lim (1546 e T e 2494 K) to obtain a composite ARAS
data set of 278 data points, equal weight being given to each
data point. Since tabulated data for k1(T) were not given in
The uncertainties are given at the 1σ standard deviation level,
and the mean deviation of experimental data from the expression
is (24%.
1
8c,20b,21b,22b
four of the five previous ARAS studies,
this is the
In those experiments performed at high temperatures (1932
e T e 2384 K), first-order kinetic behavior was always
first evaluation to make a detailed comparison among these
studies. Linear-least squares analysis (Figure 8) results in the

N2O Thermal Dissociation
J. Phys. Chem. A, Vol. 101, No. 6, 1997 1111
+ O( P) + Ar: First-Order Analysisa
3
TABLE 6: Rate Constant Data for the Reaction N
2
O + Ar f N
2
b
c
/Kd
e
f
b
c
/Kd
e
k f
P
1
/(Torr)
M
s
F
5
T
5
k
obs
k
1
P
1
/(Torr)
M
s
F
5
T
5
k
obs
1
-
6
X
N2O ) 1.040×10
12.9 15.06
13.7
1
1
5.11
5.11
2.947
2.959
3.173
3.181
2092
2110
4080
4356
2.996
3.200
2159
5455
17.0
-
6
X
N O ) 1.058×10
2
1
1
1
1
5.07
5.07
5.00
4.89
2.971
2.936
2.887
2.963
3.200
3.160
3.108
3.151
2114
2075
2008
2106
2934
2853
2395
3230
9.17
9.03
7.71
15.08
15.06
14.85
15.06
2.925
2.983
3.016
2.957
3.158
3.202
3.189
3.185
2056
2132
2173
2095
2144
3299
4455
3453
6.79
10.3
13.9
10.2
8.38
-
6
X
X
N O ) 1.655 × 10
2
1
5.53
2.929
3.245
2069
3223
9.93
15.63
2.824
3.172
1932
1402
4.42
-
6
N O ) 2.014 × 10
2
1
1
1
1
5.00
5.08
5.06
5.07
2.892
2.884
2.921
2.937
3.112
3.126
3.153
3.165
2014
2000
2050
2072
1852
1706
2312
2469
5.95
5.46
7.33
7.80
14.98
15.03
15.06
3.004
3.019
2.948
3.204
3.228
3.173
2159
2179
2086
4869
4164
2784
15.2
12.9
8.77
-
6
X
X
X
X
X
X
X
N O ) 2.322 × 10
2
1
1
5.06
5.00
3.025
3.095
3.224
3.261
2198
2296
6711
14307
20.8
43.9
15.03
15.02
2.860
3.021
3.083
3.212
1976
2192
1553
6441
5.04
20.1
-
6
N O ) 2.404 × 10
2
1
1
5.06
4.98
2.897
3.030
3.125
3.209
2024
2204
1960
7888
6.27
15.05
2.864
3.087
1984
2053
6.65
24.6
-
6
N O ) 2.727 × 10
2
1
1
5.74
5.65
3.118
2.903
3.476
3.254
2305
2029
16708
2064
48.1
14.91
15.64
2.973
2.998
3.158
3.324
2122
2163
3957
5925
12.5
17.8
6.34
-
6
N O ) 3.150 × 10
2
1
1
4.94
5.15
2.967
2.924
3.151
3.160
2120
2063
4274
3457
13.6
10.9
15.14
2.921
3.157
2059
3713
11.8
-
6
N O ) 3.266 × 10
2
1
1
5.05
5.09
3.011
3.028
3.212
3.225
2178
2206
5899
8497
18.4
26.4
14.99
15.02
3.027
2.873
3.200
3.092
2208
1995
8659
1274
27.1
4.12
-
6
N O ) 4.120 × 10
2
1
1
5.02
5.03
3.107
2.965
3.278
3.171
2311
2116
14700
4532
44.8
14.3
15.23
15.05
2.947
3.108
3.198
3.288
2091
2311
3555
13716
11.1
41.7
-
6
N O ) 5.191 × 10
2
1
1
1
5.04
5.02
5.13
3.035
3.032
3.033
3.270
3.239
3.239
2182
2194
2213
7765
7897
7305
23.8
24.4
22.6
15.06
15.03
2.879
2.983
3.107
3.188
2001
2139
1318
5054
4.24
15.9
-
6
X
N O ) 5.807 × 10
2
1
1
4.98
5.02
3.034
3.029
3.220
3.223
2205
2200
8405
7973
26.1
24.7
g
14.92
15.07
-6
3.056
2.843
3.221
3.079
2237
1954
9651
1662
30.0
5.4
X
N O ) 3.956 × 10
2
1
1
1
1
5.85
5.87
5.80
5.55
2.957
3.086
2.945
2.832
3.366
3.477
3.381
3.188
2087
2262
2051
1928
2624
9749
2729
767
7.80
15.76
3.091
3.174
3.174
3.451
3.436
3.404
2270
2376
2384
12825
18648
18230
37.2
54.2
53.6
28.0
8.07
2.41
15.32
15.23
a
Unless otherwise stated, the N
O sample was of 99.99% purity. b The uncertainty in measuring the Mach number is typically about (0.7% at
c 18 d
2
-3
the one standard deviation level. Units of density are 10 molecules cm
Units of kobs are s . Units of k
. The uncertainty in temperature is estimated to be (1.5% or less.
e
-1
f
-16
3
-1 -1 g
1
are 10 cm molecule
s
.
2
The N O sample for these data was of 99.999% purity.
following Arrhenius expression for the temperature range 1195
e T e 2494 K:
temperatures below 1500 K. Rate constant determinations for
k1(T) were extended to just below 1200 K by making use of
the correction procedure developed to take into account the
significant molecular absorption of both resonance and non-
resonance light by high concentrations of N2O.
-
10
k (T) ) (9.52 ( 1.07)×10 exp[(-57570 (
1
-1
3
-1 -1
3
90 cal mol )/RT] cm molecule s (13)
In Figure 9, these low-temperature measurements are seen
to be in agreement with the (non-ARAS) rate constant data of
The mean deviation of the composite data set from eq 13 is
1
2a
(26% (at the 1σ-level). The tightness of this fit may be
Martinengo et al. (4 points over the temperature range 1320
1
b
contrasted to the systematic differences in the Arrhenius
parameters between the individual ARAS data sets, which are
readily discernable (values listed in Table 1). This work,
therefore, further emphasizes that rate constants should be
measured over as wide a temperature range as possible and that
care should be taken to collect sufficient data points, especially
in shock tube experiments.
e T e 1440 K) and Glarborg et al. (4 points over the
temperature range 1200 e T e 1348 K). However, the non-
2
3
ARAS data of Loirat et al. (not shown) do not agree.
The six ARAS/shock tube studies that comprise the composite
data set, employed total pressures from about 1 to 3 atm. The
excellent agreement of these results over such a wide temper-
ature range (1195 e T e 2494 K) is consistent with our previous
conclusion (Viz. Introduction) that reaction R1 is indeed in the
low-pressure limit under the conditions of these studies. The
It is evident from Figure 8 that, prior to the present study,
few ARAS measurements of k1(T) have been reported at

1112 J. Phys. Chem. A, Vol. 101, No. 6, 1997
Ross et al.
then increasing the temperature from 1200 to 2500K would lead
o
-1
to a decrease in Ea of only a few kcal mol . Also, even close
to the high-pressure limit, where it is well established that the
∞
Ea is the difference between the average energy of the reacting
levels from which intersystem crossing occurs and the average
3
0
thermal energy of the molecule, there is no evidence of
1
2b,15
curvature in the Arrhenius behavior.
Finally, it may be
possible that, at the highest temperatures, there is a small
contribution from the more endothermic adiabatic dissociation
1
process that leads to O( D). In the high-pressure limit, the
unimolecular rate expression for this reaction should have an
-
1
o
activation energy of about 84 kcal mol (∆H0 ) 83.93 kcal
-
1
mol , ref 9)as well as a preexponential factor that could
increase by a factor of approximately 1000. The corresponding
activation energy and preexponential factor for the low-pressure
limit are difficult to estimate in the absence of a detailed
unimolecular calculation. However, in the case of CH4 dis-
sociation, the activation energy in the low-pressure limit is lower
-
1
than the endothermicity by about 18 kcal mol .
O( P) + N2O Reaction. The rate constants for the O + N2O
3
reactions R2a and R2b are difficult to measure experimentally
because the overall reaction is very slow. Table 8 lists the rate
expressions for reactions R2a and R2b recommended in three
3
4-36
review articles
(including the recent recommendation of
3
6
Tsang and Herron) along with the expressions reported by
Davidson et al. (where rate constants were derived from
measured O2 and NO profiles).
4
0
The sensitivity of the O-atom ARAS technique lends itself
to simplified kinetics and to a more direct method for determin-
ing the value for the overall rate constant, k2(k2a + k2b). Analysis
of the reaction sequence R1, R2a, and R2b leads to the following
kinetic equations:
d[O] /dt ) k [N O][Ar] - k [N O][O]
t
t
1
2
2
2
)
k [N O][Ar](1 - (k + k )[O] /k [Ar])
(14)
1
2
2a
2b
t
1
Under the present experimental conditions, it is readily shown
that reactions R3-R7 can be neglected. On integration, the
following expression for the buildup of the O-atom concentration
is obtained:
Figure 6. Examples of observed linear absorbance buildup plots at
low temperatures. (a) P
1
) 15.55 Torr, M
s
) 2.509, T
5
) 1557 K, F
5
1
8
-3
-4
)
2.949 × 10 molecules cm , XN O ) 2.625 × 10 . Solid line:
2
-
1
-14
linear fit, gradient ) 551 ( 0.57 ABS s , and k
1
) 551/(3.66 × 10
-1 -1
[O] ) k [Ar]/k (1 - exp(-k [N O]t))
(15)
t
1
2
2
2
1
8
14
-18
3
×
2.949 × 10 × 7.741 × 10 ) ) 6.59 × 10 cm molecule
s .
1
8
(b) P
1
) 30.53 Torr, M
s
) 2.253, T
5
)1260 K, F
5
) 5.025 × 10
where k2 ) k2a + k2b.
-
3
-4
molecules cm , XN O ) 9.925 × 10 . Solid line: linear fit, gradient
2
Kinetic modeling showed that deviation from initial linearity
should be clearly observable over the temperature range 1200
e T e 1400 K when recommended rate constants were
employed. It was also shown that a high [N2O] was required
in order to obtain a sufficiently rapid buildup of [O] to enable
curvature to be observed in the available experimental time
frame (see eqs 14 and 15). Figure 10 shows the data from an
experimental run at 1395K together with the results of two
-
1
-14
18
)
132 ( 0.52 ABS s , k
1
) 132/(3.66 × 10 × 5.025 × 10
-1 -1
×
1
5
-19
3
4
.987 × 10 ) ) 1.44 × 10
cm molecule
s . Insets: plots of
residuals.
individual data points of Rohrig et al.,15 determined by
monitoring IR emission from N2O at 4.5 µm, are also in
excellent agreement with the corresponding values calculated
from eq 13. The deviations of their individual data points from
those calculated ranged from -33% to +3% with a mean value
of -14%. Moreover, these results are in agreement with the
5
1
simulations (using the CHEMKIN routine) that used the
36
recommended values of k2 from Tsang and Herron and from
12b
40
low-pressure data of Olschewski et al. (when account is taken
Davidson et al. Clearly the experimental data do not show
of the uncertainty in the assumed stoichiometry2 ).
,15
the curvature that is evident in the simulations. All the
experimental data in this investigation display similar behavior,
and thus the present results do not support the use of k2 values
as large as those employed in the simulations. This suggests
that k2 must be even smaller than the recommended value of
Over the temperature range 1195 e T e 2494 K, there is no
discernible curvature in the Arrhenius plot of the ARAS data,
12b
Figure 8, in agreement with the findings of Olschewski et al.,
assuming that the stoichiometric number for the reaction is
independent of temperature. An accurate temperature depen-
dence of the low-pressure rate constant is difficult to predict
without a detailed unimolecular calculation. However, if it is
assumed that the rate of intersystem crossing of energized
molecules is independent of energy (the Lindemann-Hinshel-
wood model), or that it has a very narrow energy distribution,
36
Tsang and Herron and those of refs 34 and 35 (Table 8), since
all three give very similar k2 values over the temperature range
of interest. Even though there is no evidence of strong curvature
(as in the Figure 10 simulations) in any of the experimental
initial-rate-data runs, upper limit values for k2 can be estimated
using the statistical approach described below.

N2O Thermal Dissociation
J. Phys. Chem. A, Vol. 101, No. 6, 1997 1113
+ O( P) + M: Initial Rate Analysisa
3
TABLE 7: Rate Constant Data for the Reaction N
2
O + M f N
2
b
c
d
/(Ke)
ratef
g
b
c
d
/(Ke)
ratef
g
P
1
M
s
F
5
T
5
k
1
P
1
M
s
F
5
T
5
k
1
-
6
X
112
23.6
N O ) 1.04 × 10
2
1
1
5.11
5.49
2.947
2.804
3.173
3.126
2092
1906
431
87.6
15.11
2.959
3.181
2110
410
106
-
-
6
6
X
22.0
N2O ) 1.655 × 10
1
1
1
5.44
5.07
5.32
2.750
2.748
2.671
3.067
2.989
2.959
1838
1837
1744
125.5
154
X
19.5
N2O ) 2.404 × 10
-
6
X
4.02
N O ) 3.15 × 10
2
40.6
14.81
2.776
2.959
1873
207
20.5
-
6
X
91.0
110
29.5
12.8
N O ) 4.120 × 10
2
1
1
1
1
1
5.23
5.03
5.32
5.88
5.57
2.947
2.965
2.798
2.750
2.585
3.198
3.171
3.091
3.157
2.925
2091
2116
1896
1836
1639
1404
1671
426
193
48.8
14.73
2.466
2.630
2.519
2.584
2.643
2.858
3.132
3.120
1503
1692
1562
1638
4.60
38.4
21.9
38.4
0.437
3.11
1.48
2.62
14.97
17.09
16.62
3.77
-
6
X
44.8
80.9
138
48.9
1.48
1.89
N O ) 5.807 × 10
2
1
1
1
1
1
1
5.09
5.79
5.39
5.07
5.09
5.06
2.834
2.916
2.946
2.843
2.543
2.621
3.073
3.293
3.233
3.079
2.792
2.868
1944
2048
2089
1954
1589
1680
897
1863
3075
987
24.5
33.0
15.14
15.80
14.97
14.96
15.14
2.641
2.681
2.736
2.722
2.626
2.904
3.068
2.962
2.948
2.902
1703
1754
1819
1801
1696
103
5.74
5.79
17.2
13.5
2.44
116
320
249
60.3
-
6
X
1.07
N O ) 9.760 × 10
2
1
5.05
2.494
2.827
1549
30.5
15.26
2.536
2.835
1570
34.8
92.0
1.21
-
4
4
4
X
N O ) 2.403 × 10
2
3
3
0.58
0.12
2.317
2.481
5.107
5.327
1335
1519
51.1
1330
0.0223
0.533
30.23
16.10
2.352
2.464
5.116
2.888
1378
1500
0.0399
0.902
661
-
X
N O ) 2.548 × 10
2
3
2
2.73
5.53
2.265
2.402
5.318
4.433
1297
1439
66.1
231
0.0251
0.126
27.17
27.65
2.347
2.339
4.681
4.759
1358
1346
44.9
53.0
0.0220
0.0251
-
X
N O ) 4.176 × 10
2
2
2
2
2
2
1
5.34
5.53
5.50
5.45
5.39
4.91
2.562
2.344
2.374
2.389
2.490
2.423
4.748
4.371
4.426
4.449
4.630
2.742
1602
1362
1393
1409
1519
1470
3326
123
198
398
1865
468
0.965
0.0421
0.0661
0.131
0.569
0.407
15.03
2.435
2.375
2.391
2.339
2.289
2.756
2.725
2.711
5.110
5.393
1484
1421
1441
1355
1294
732
0.631
0.266
0.350
0.0376
0.0234
15.08
14.95
29.89
32.31
302
393
150
104
-
4
3
3
3
X
N O ) 9.925 × 10
2
2
2
8.88
5.30
2.342
2.275
4.994
4.216
1344
1282
212
92.8
0.0234
0.0204
30.53
2.253
5.025
1260
132
0.0150
-
X
0.216
0.149
N O ) 1.010 × 10
2
1
1
5.05
5.36
2.381
2.335
2.729
2.734
1425
1381
594
413
15.09
24.08
2.286
2.277
2.633
3.997
1333
1285
126
102
0.0492
0.0173
-
X
N O ) 1.482 × 10
2
2
1
0.97
9.42
2.226
2.215
3.437
3.314
1227
1254
42.1
74.9
0.00657
0.0148
19.78
2.154
3.284
1195
27.3
0.00467
-
X
N O ) 2.000 × 10
2
1
1
2
7.34
9.13
2.81
2.310
2.227
2.201
3.085
3.285
3.790
1344
1265
1232
237
168
124
0.0341
0.0212
0.0118
17.82
19.58
2.357
2.289
3.217
3.457
1395
1322
336
189
0.0444
0.0216
-
3
X
N O ) 2.014 × 10
2
15.48
2.270
2.705
1307
247
0.0458
15.71
2.278
2.736
1324
262
0.0475
h
-4
X
N O ) 2.625 × 10
2
1
1
1
1
5.55
5.53
5.53
5.48
2.509
2.431
2.348
2.464
2.949
2.863
2.768
2.871
1557
1479
1400
1521
551
160
49.9
377
0.659
15.46
15.04
15.37
2.399
2.390
2.382
2.800
2.724
2.783
1452
1442
1429
190
155
93.6
0.252
0.217
0.126
0.203
0.0678
0.476
h
-6
X
11.0
N O ) 3.956 × 10
2
15.64
2.750
3.131
1823
156
a
Unless otherwise stated, the N
2
O sample was of 99.99% purity. b Units are in Torr. c The uncertainty in measuring the Mach number is typically
d
18
-3 e
about (0.7% at the one standard deviation level. Units of density are 10 molecules cm
.
The uncertainty in temperature is estimated to be no
f
-1
g
3
-1 -1
-17
O][Ar]). h The N
more than (1.5%. Units of rate are ABS s
.
Units of k
1
are cm molecule s ×10 ; k
1
) rate/(Rl[N O sample for these
2
2
data was of 99.999% purity.
Criteria. It was evident from the modeling studies that the
O-atom buildup is most sensitive to the influence of reaction
R2 (R2a + R2b) at low temperatures and for large mole
fractions of N2O. The following criteria were chosen for
selecting data to analyze so that a consistent statistical approach
could be employed in determining an upper limit for k2: (i)

1114 J. Phys. Chem. A, Vol. 101, No. 6, 1997
Ross et al.
Figure 7. Arrhenius plot of the 131 data points (listed in Tables 5
Figure 9. Arrhenius plot of all data (286 points): s, is the linear
3
-10
and 6) for the reaction N
temperature range 1195 e T e 2384 K. Solid line: linear least-squares
2
O + Ar f N
2
+ O( P) + Ar over the
least-squares fit, where k
( 370 cal mol )/RT] cm molecule
1
(T) ) (9.45 ( 1.00) × 10 exp[(-57540
-
1
3 -1 -1
s ; O, this study (1195-2384
-9
-1
fit, where k
RT] cm molecule
9.999% N O.
1
(T) ) (1.18 ( 0.16) × 10 exp[(-57820 ( 460 cal mol )/
K); 1, Pamidimukkala et al. (1519 e T e 2408 K); 4, Michael and
Lim (1546 e T e 2494 K); 0, Fujii et al. (1602 e T e 2421 K); (,
Frank and Just (1389 e T e 2210 K); 3, Roth and Just (1498 e T
Pound 2245 K); 9, Glarborg et al. (1200 e T e 1348 K); b,
Martinengo et al. (1320 e T e 1440 K).
3
-1 -1
2
s . Open circle: 99.99% N O and filled circle:
9
2
3
TABLE 8: Rate Expressions for the O( P) + N
2
O Reaction
temperature
K)
rate expression
3
(cm molecule s-1
-1
)
refs
(
-10
1
1
1
200-2000 k2a ) 1.7 × 10 exp(-14100/T) Baulch et al.34
-
10
k2b ) 1.7 × 10
exp(-14100/T)
200-4100 k2a ) 1.1 × 10 exp(-13400/T) Hanson and Salimian35
-
10
-
10
k2b ) 1.7 × 10
exp(-14100/T)
200-4100 k2a ) 1.1 × 10 exp(-13400/T) Tsang and Herron36
-
10
-
10
k2b ) 1.7 × 10
exp(-14100/T)
-
11
1
1
680-2430 k2a ) 4.8 × 10 exp(-11650/T) Davidson et al.40
-
12
940-3340 k2b ) 2.3 × 10
exp(-5440/T)
for selecting 2σ is discussed below). The value of k2 was then
determined by using a nonlinear least-squares routine (Leven-
5
2
berg-Marquardt method ) to fit eq 15 to the data in each of
the experimental runs. These k2 values, corresponding to the
upper limit in our evaluation, are listed in Table 9. These results
clearly show that, over the narrow temperature range 1200 e T
e 1400 K, the estimated rate constant values for k2 (the sum of
k2a and k2b) are consistently lower than those calculated from
Figure 8. Arrhenius plot of the composite O-atom ARAS data set
(
278 points) for the low pressure rate constant, M ) Ar: s, is the
-
10
36
linear least squares fit, where k
5
e T e 2384 K); 1, Pamidimukkala et al. (1519 e T e 2408 K); 4,
Michael and Lim (1546 e T e 2494 K); 0, Fujii et al. (1602 e T e
1
(T) ) (9.52 ( 1.07) × 10 exp[(-
the recommended expression of Tsang and Herron. Values
-
1
3
-1 -1
7570 ( 390 cal mol )/RT] cm molecule
s
; O, this study (1195
of k2 ranged between about 4 and 32 times lower than the
recommended ones. Even though there is large uncertainty (see
further discussion below) in the k2 values derived here, we
believe these results show that, over the temperature range of
the measurements, k2 is about an order of magnitude smaller
than that calculated from the expressions of Tsang and Herron.36
The uncertainties in the upper limit values for k2 that were
derived here are directly related to the perturbation of k1 by
+2σ. The 2σ level was selected because it always lead to
observable curvature in the nonlinear fit to the absorbance data.
At the 1σ level, curvature was just discernable and, at the 3σ
level, the extent of curvature was very severe. These variations
in the perturbation lead to about 0.5 times and 1.5 times the
derived k2 values, or an uncertainty of about 50% for the
individual determinations. However, the scatter in the k2 values
is obviously greater than the estimated uncertainty level. We
believe the large scatter is due to systematic error caused by
modulation in the output of the resonance lamp. This “ripple”
may result in data with random scatter or with slightly concave
2
421 K); (, Frank and Just (1389 e T e 2210 K) ; 3, Roth and Just
(1498 e T e 2245 K).
low temperatures, to maximize the influence of reaction R2 Vis-
a-Vis reaction R1; (ii) observation times (which depend on shock
quality and lamp stability) greater than about 2ms, in order to
increase the possibility of detecting the effect of k2; and (iii)
-
3
high [N2O], with XN O greater than about 1 × 10 , to allow
2
sufficient buildup of the [O] at low temperatures. These criteria
limited evaluation to seven runs over the approximate temper-
ature range 1200 e T e 1400 K.
Method of Analysis and Estimates of k2. For each of the seven
runs that met the criteria discussed above, values of k2 were
derived using the following procedure. First, k1 and the standard
deviation (σ) were determined by using a linear least-squares
fit to the data in each of the experimental runs. This value of
k1 was increased by 2σ for the estimation of k2 (the rationale

N2O Thermal Dissociation
J. Phys. Chem. A, Vol. 101, No. 6, 1997 1115
result but prefer the value recommended in the evaluation by
3
5
Hanson and Salimian.
Conclusions
Shock tube experiments were performed, with sensitive
ARAS detection of oxygen atoms, to measure the rate constant
for N2O thermal dissociation at the low-pressure limit over the
temperature range 1195 e T e 2384 K. A procedure to correct
for molecular absorption of resonance and nonresonance light
by N2O allowed rate constant measurements to be extended by
almost 200° to just below 1200 K, which is significant in terms
of 1/T. Also, by extending measurements down to 1200 K,
this work provides ARAS data for reaction R1 that, for the first
time, overlap with previous studies that employed nonshock tube
techniques. The present determinations at low temperatures
demonstrate agreement with those reported by Martinengo et
1
2a
1b
al. and Glarborg et al. but not with the data of Loirat et
2
3
al.
2
Figure 10. Influence of the O + N O reaction: comparison of
The ARAS rate data from five independent studies in five
laboratories were combined with the present data for reaction
R1 and represented by the Arrhenius expression,
experimentally observed buildup of O-atom concentrations with
those predicted by appropriate kinetic modeling at T ) 1395 K. Also,
1
8
-3
P
X
)
1
) 17.82 Torr, M
s
) 2.357, F
5
) 3.217 × 10 molecules cm
,
-
3
N O ) 2.00 × 10 . Solid line is the linear least-squares fit, where k
1
2
-
19
3
-1 -1
-10
4.44 × 10 cm molecule
s
. For the dashed line, k
1
) 4.44 ×
k1(T) ) (9.52 ( 1.07) × 10- exp[(-57570 (
-
19
3
-1 -1
-14
3
-1 -1
1
0
cm molecule
s
and k
2
) 1.43 × 10 cm molecule
s
cm
1
3
-1 -1
3
6
-19
3
(Tsang and Herron ). For the dotted line, k
1
) 4.44 × 10
390 cal mol )/RT] cm molecule s (13)
-
1
-1
-14
3
-1 -1
molecule
et al. ).
s
and k
2
) 5.79 × 10 cm molecule
s
(Davidson
4
0
over the temperature range 1195 e T e 2494 K, where
uncertainties are given at the 1σ level. The mean deviation of
the composite data set from the Arrhenius expression (eq 13)
is (26% at the 1σ level. Values of k1(T), calculated from eq
13, are in reasonably close agreement with those derived from
3
TABLE 9: Rate Constant Data for the Reaction O( P) +
2
N O
2
k (Tsang
and Herron)/k
2
a
σb
c
d
T (K)
X
2
N O
∆t (ms)
k
1
k
2
3
4
35
the evaluations of Baulch et al. and Hanson and Salimian.
-
-
-
-
-
-
-
3
4
3
3
3
4
3
1
1
1
1
1
1
1
254 1.482 × 10
260 9.925 × 10
265 2.000 × 10
322 2.000 × 10
344 2.000 × 10
344 9.925 × 10
395 2.000 × 10
3.192 1.48 6.43 5.4
2.704 1.50 5.80 1.6
2.584 2.12 13.16 9.6
2.252 2.16 10.20 13.1
2.815 3.41 12.10 3.2
1.896 2.34 8.69 23.5
2.345 4.44 13.36 8.5
8.8
31.7
5.4
6.3
31.0
4.2
The recommended expression of Tsang and Herron36 diverges
from eq 13, and at 1200 K their value for k1(T) is about 50%
lower than that derived from the composite of the ARAS data.
We recommend the Arrhenius expression, eq. 13, derived from
fitting the composite ARAS data set of 278 points because of
the good agreement among these data and because the ARAS
technique is a direct method with very high detection sensitivity
for determining [O] and because it is free from the influence of
secondary reactions. In contrast, the other shock tube studies
employed diagnostic techniques with relatively low detection
sensitivity for [N2O]. Therefore, in their analyses, these studies
required complex kinetic modeling to extract values for k1(T)
and the overall stoichiometry was either not considered or an
assumed value was used.
16.8
a
are cm molecule s-1 × 10-19. b The standard deviation
3
-1
Units of k
1
3
in k
molecule
1
from the linear fit of the [O] versus time data. Units are cm
-
1
-1
-22
c
3
-1 -1
-16
s
× 10
.
Units of k
2
are cm molecule
s
× 10
;
d
the uncertainty in each determination is about 50%. Ratio of the rate
3
6
constant derived from the expression of Tsang and Herron to the rate
constant estimated in the present study.
or slightly convex curving O-atom buildup plots. For data with
concave curvature, the derived values for k2 were always too
low (e.g., the values at 1260 and 1344 K/#1) and (conversely)
for data with convex curvature, the derived values for k2 were
always too high (e.g., the values at 1322 and 1344 K/#2). The
magnitude of this effect depends upon the O-atom buildup plots.
In some cases, this effect was less than or about the same as
the uncertainty in the individual determinations (e.g., the values
at 1254, 1265, and 1395 K). In other cases, the effect was
somewhat larger, say, about the same or as much as double the
uncertainty in the individual determinations. Therefore, the
values listed in Table 9 represent relatively crude estimates for
the upper limit of k2. At the most, however, we believe these
values are not in error by more than about a factor of 3; and we
therefore conclude that k2 is much smaller than the value
Kinetic simulations, taken together with our experimental
3
observation that the buildup of O( P) atoms was linear over
3
6
about 2 ms, clearly show that the recommended overall rate
3
constant for the O( P) + N2O reaction is much too large. Upper
limit values for k2 were estimated from the data for seven
experimental runs. Over the temperature range 1200 e T e
1400 K, the present upper limit for k2 is about an order of
magnitude smaller than the recommended value of Tsang and
3
6
Herron with an uncertainty factor of about 3. This result,
therefore, suggests that further work will be required to establish
accurate rate constants and the branching fraction for the reaction
3
of O( P) with N2O.
36
recommended by Tsang and Herron. There is an even more
serious difference between the upper limit value for k2, derived
here, and the value for k2 computed from the expressions
reported by Davidson et al.40 The identification of this difference
may not be important, however, because in the work reported
by Rohrig et al.,15 these authors not only question their ref 40
Acknowledgment. We thank Professors W. Fujii and P.
Roth and Drs. P. Frank, P. Glarborg, and J. V. Michael for
providing tabulated data of their published results. This work
was supported by the Chemical Sciences Division, Office of
Basic Energy Sciences, U.S. Department of Energy, under
Contract No. DE-AC02-76CH00016.

1116 J. Phys. Chem. A, Vol. 101, No. 6, 1997
Ross et al.
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