Kinetics of phenyl radical reactions with propane, n-butane, n-hexane, and n-octane: Reactivity of C6H5 toward the secondary C-H bond of alkanes

Article abstract of DOI:10.1002/kin.10171

The kinetics of C₆H₅ reactions with n-C_nH_2n+2 (n = 3, 4, 6, 8) have been studied by the pulsed laser photolysis/mass spectrometric method using C₆H₅COCH₃ as the phenyl precursor at temperatures between 494 and 1051 K. The rate constants were determined by kinetic modeling of the absolute yields of C₆H₆ at each temperature. Another major product C₆H₅CH₃ formed by the recombination of C₆H₅ and CH₃ could also be quantitatively modeled using the known rate constant for the reaction. A weighted least-squares analysis of the four sets of data gave k (C₃H₈) = (1.96 ± 0.15) × 10¹¹ exp[-(1938 ± 56)/T], and k (n-C₄H₁₀) = (2.65 ± 0.23) × 10¹¹ exp[-(1950 ± 55)/T], k (n-C₆H₁₄) = (4.56 ± 0.21) × 10¹¹ exp[-(1735 ± 55)/T], and k (n-C₈H₁₈) = (4.31 ± 0.39) × 10¹¹ exp[-(1415 ± 65)/T] cm³ mol^-1 s^-1 for the temperature range studied. For the butane and hexane reactions, we have also applied the CRDS technique to extend our temperature range down to 297 K; the results obtained by the decay of C₆H₅ with CRDS agree fully with those determined by absolute product yield measurements with PLP/MS. Weighted least-squares analyses of these two sets of data gave rise to k (n-C₄H₁₀) = (2.70 ± 0.15) × 10¹¹ exp[-(1880 ± 127)/T] and k (n-C₆H₁₄) = (4.81 ± 0.30) × 10¹¹ exp[-(1780 ± 133)/T] cm³ mol^-1 s^-1 for the temperature range 297-1046 K. From the absolute rate constants for the two larger molecular reactions (C₆H₅ + n-C₆H₁₄ and n-C₈H₁₈), we derived the rate constant for H-abstraction from a secondary C-H bond, k_s-CH = (4.19 ± 0.24) × 10¹⁰ exp[-(1770 ± 48)/T] cm³ mol^-1 s^-1.

Full text of DOI:10.1002/kin.10171

Kinetics of Phenyl Radical
Reactions with Propane,
n-Butane, n-Hexane, and
n-Octane: Reactivity of C H5
6
Toward the Secondary C H
Bond of Alkanes
J. PARK, LIMING WANG, M. C. LIN
Department of Chemistry, Emory University, Atlanta, Georgia 30322
Received 12 May 2003; accepted 29 August 2003
DOI 10.1002/kin.10171
ABSTRACT: The kinetics of C H reactions with n-CnH
ied by the pulsed laser photolysis/mass spectrometric method using C H COCH as the
(n = 3, 4, 6, 8) have been stud-
6
5
2n+2
6
5
3
phenyl precursor at temperatures between 494 and 1051 K. The rate constants were deter-
mined by kinetic modeling of the absolute yields of C H at each temperature. Another ma-
6
6
jor product C H CH formed by the recombination of C H and CH could also be quanti-
6
5
3
6
5
3
tatively modeled using the known rate constant for the reaction. A weighted least-squares
1
1
analysis of the four sets of data gave k (C H ) = (1.96 ± 0.15) × 10 exp[−(1938 ± 56)/T],
3
8
1
1
11
and k (n-C H ) = (2.65 ± 0.23) × 10 exp[−(1950 ± 55)/T], k (n-C H ) = (4.56 ± 0.21) × 10
4
10
6 14
1
1
3
−1
exp[−(1735 ± 55)/T], and k (n-C H ) = (4.31 ± 0.39) × 10 exp[−(1415 ± 65)/T] cm mol
8
18
−
1
s
for the temperature range studied. For the butane and hexane reactions, we have also
applied the CRDS technique to extend our temperature range down to 297 K; the results
obtained by the decay of C H5 with CRDS agree fully with those determined by absolute
6
product yield measurements with PLP/MS. Weighted least-squares analyses of these two sets
1
1
of data gave rise to k (n-C H ) = (2.70 ± 0.15) × 10 exp[−(1880 ± 127)/T] and k (n-C H )
4
10
6 14
11
3
−1 −1
s for the temperature range 297–
=
(4.81 ± 0.30) × 10 exp[−(1780 ± 133)/T] cm mol
046 K. From the absolute rate constants for the two larger molecular reactions (C H + n-
1
6
5
C H and n-C H ), we derived the rate constant for H-abstraction from a secondary C H
6
14
8 18
10
3
−1 −1
bond, k
= (4.19 ± 0.24) × 10 exp[−(1770 ± 48)/T] cm mol
s
. ꢀC 2003 Wiley Period-
s-CH
icals, Inc. Int J Chem Kinet 36: 49–56, 2004
INTRODUCTION
Correspondence to: M. C. Lin; e-mail: chemmcl@emory.edu.
Contract grant sponsor: Department of Energy.
The reactivity of C6H5 radicals toward C H bonds
in hydrocarbons is not only fundamentally rele-
vant, but also practically important for quantitative
Contract grant number: DE-FG02-97-ER14784.
ꢀ
c 2003 Wiley Periodicals, Inc.

50
PARK, WANG, AND LIN
understandingoffossilfuelcombustion. Inourtwosep-
arate series of studies on the kinetics and mechanisms
of C6H5 reactions employing the cavity ringdown spec-
trometric (CRDS) technique [1–8] and the pulsed laser
photolysis/mass spectrometric (PLP/MS) methods [9–
under the present conditions determined by NO titra-
tion was found to be 63% of the dissociated acetophe-
none. C6H5COCH3 carried by an excess amount of
He was premixed in corrugated stainless steel tub-
ing with CnH2n+2 before being introduced into the
Saalfeld-type quartz reactor [18]; the products of the
photo-initiated reaction were supersonically sampled
and ionized by electron-impact ionization. The abso-
lute concentrations of the products were determined by
the standard calibration mixtures. The mole fractions
of C6H5COCH3 and alkanes were typically <0.1% and
0–65%, respectively. The typical concentration profiles
of the C6H6 and C6H5CH3 products as functions of
temperature are shown in Fig. 1 and Table I. Kinetic
modeling of the absolute concentrations of C6H6 and
C6H5CH3 provides reliable determination of the rate
constant for the following reactions:
1
5], with some of the studies aided by quantum chemi-
cal calculations [4,6,13,14], we have quantitatively es-
tablished the reactivity of the phenyl radical toward a
variety of chemical bonds and functional groups.
In general, C6H5 is considerably more reactive than
CH3 and larger alkyl radicals [16,17]. For the C H
bonds in alkanes, the activation energies for the ab-
straction of a primary C H bond by C6H5 from C2H6
−
1
and neo-C5H12 are 4.4 and 3.8 kcal mol , respectively,
−1
which are ∼9 kcal mol lower than the correspond-
ing CH3 reactions. For the abstraction of the t-C H
bond from isobutane and 2,3-dimethyl butane by C6H5,
the activation energies are lowered to 3.0 and 2.0 kcal
−
1
−1
C H + n-C H
→ C H + n-C H
(1)
(2)
6
5
n
2n+2
6
6
n
2n+1
mol , respectively, which are again ∼6.0 kcal mol
lowerthanthosefromthecorrespondingCH3 reactions.
Another interesting aspect of C6H5 reactions with
alkanes is that the rate constant per C H bond for C2H6
and neo-C5H12 is approximately the same over the
temperature range studied, 565–1000 K, whereas the
rate constant per t-C H for the reactions with isobu-
tane, 2,3-dimethylbutane and 2,3,4-trimethyl pentane
increases significantly with the molecular size of the
alkane [8]. The observation was attributed in part to
the greater accessibility of the H-atoms as the carbon
chain length lengthens.
C6H5 + CH3 → C6H5CH3
In this study, we examine the effect of molecular size
and the length of the carbon chain on the reactivity of
the C6H5 radical toward the s-C H bonds from C3H8
to n-C8H18.
EXPERIMENTAL
The experimental apparatus and kinetic data acqui-
sition by pulsed laser photolysis/mass spectrometry
(PLP/MS) have been discussed in detail in our previ-
ous studies [9–15]. The key aspects of PLP/MS and the
complementary technique, cavity ringdown spectrom-
etry (CRDS [1–8]) which was employed to extend the
temperature range of the butane and hexane reactions
down to 297 K, are briefly summarized below.
PLP/MS
Figure 1 Typical concentration profiles for the C6H5 +
The detail of PLP/MS has been described in a recent
review on the technique [9]. The C6H5 radical was
generated by the pulsed photolysis of C6H5COCH3 at
C3H8 reaction as functions of temperature (a), and C3H8
concentration (b). (a) +, C6H6 (exp);
◦
, C6H6 (model); ∇,
C6H5CH3 (exp); ꢀ, C6H5CH3 (model). (b) ꢁ, C6H6 (exp);
1
93 nm. The conversion of acetophenone was in the
∇, C H CH (exp);solidcurve, C H (model);dashedcurve,
6
5
3
6 6
range of 45–65%. The amount of the C6H5 formed
C6H5CH3 (model).

PHENYL RADICAL REACTIONS WITH PROPANE, n-BUTANE, n-HEXANE, AND n-OCTANE
51
a
b
c
Table I Experimental Conditions , Product Yields , and Modeled Rate Constants in the PLP/MS Experiment
at the Temperatures Studied
[C6H6]t
[C7H8]t
−
k1 10
10
Temp (K)
[C6H5]0
1.13
[C6H5COCH3]0
1.54
[CnH2n+2]0
C3H8]
Exp
Model
Exp
Model
[
4
5
6
6
7
8
9
9
94
67
31
72
80
08
23
98
2105.26
0.32
0.45
0.49
0.56
0.67
0.69
0.76
0.78
0.80
0.45
0.49
0.52
0.54
0.55
0.32
0.45
0.49
0.56
0.68
0.69
0.76
0.78
0.80
0.45
0.49
0.53
0.54
0.56
0.30
0.29
0.27
0.27
0.23
0.24
0.19
0.18
0.18
0.30
0.28
0.29
0.26
0.26
0.35
0.34
0.32
0.31
0.26
0.25
0.19
0.16
0.15
0.30
0.27
0.26
0.24
0.25
0.36
0.71
0.86
1.12
1.82
1.92
2.62
2.82
3.08
1.68
1.95
2.43
2.22
2.55
1
051
7
8
8
9
9
85
58
90
43
86
1.13
1.02
1.54
1.73
1052.63
[n-C4H10]
5
5
6
7
7
8
8
8
9
31
95
45
38
89
38
68
91
53
619.78
0.22
0.28
0.32
0.37
0.41
0.42
0.46
0.48
0.48
0.55
0.22
0.28
0.32
0.37
0.41
0.42
0.46
0.48
0.48
0.55
0.29
0.29
0.29
0.28
0.27
0.26
0.25
0.28
0.24
0.21
0.33
0.32
0.28
0.30
0.29
0.26
0.21
0.27
0.29
0.20
0.75
1.11
1.46
2.03
2.56
2.66
3.22
3.45
3.55
4.82
1
046
[n-C6H14]
6
6
7
7
8
8
8
8
9
9
9
33
98
45
69
20
43
85
99
46
53
82
1.10
1.51
323.21
0.44
0.47
0.51
0.51
0.45
0.48
0.48
0.50
0.51
0.52
0.54
0.56
0.44
0.47
0.51
0.51
0.45
0.47
0.48
0.50
0.51
0.52
0.54
0.56
0.29
0.28
0.27
0.27
0.29
0.28
0.28
0.27
0.27
0.26
0.25
0.24
0.33
0.32
0.30
0.30
0.27
0.23
0.26
0.25
0.23
0.21
0.23
0.22
3.09
3.65
4.47
4.61
5.53
5.95
6.20
6.65
7.03
7.34
8.13
8.83
1
038
[n-C8H18]
5
6
7
8
7
7
8
9
9
95
78
60
07
03
79
66
26
78
2.14
0.85
3.72
2.02
421.05
0.66
0.73
0.78
0.82
0.30
0.32
0.35
0.54
0.55
0.66
0.73
0.79
0.82
0.30
0.33
0.36
0.55
0.56
0.57
0.55
0.52
0.52
0.35
0.30
0.26
0.24
0.23
0.60
0.60
0.59
0.58
0.23
0.23
0.22
0.15
0.13
4.10
5.32
6.35
7.02
2.35
2.85
3.45
9.72
10.2
421.05
a
All conditions are given in m Torr.
b
c
Product yields were measured at t = 8 ms. Typically 2–3 runs were carried out for each temperature.
3
−1 −1
In units of cm mol
s
.

52
PARK, WANG, AND LIN
as has been demonstrated previously for C6H5 reac-
tionswithH2 [12], CH4 [13], C2H6 andneo-C5H12 [15],
i-C4H10 [8], and CH2O [14]. All the reactions, except
C2H6 and neo-C5H12, have been corroborated by re-
sults with different methods, pyrolysis/FTIR spectrom-
etry and shock tube studies for H2 and CH4 reactions
-3.8
(a)
-
-
-
4.0
4.2
4.4
[
[
12,13] and CRDS for i-C4H10 [8] and CH2O reactions
14].
-4.6
-
-
4.8
5.0
[C H10] = 0
4
CRDS
[C4H10] = 7.5 Torr
0.0
0.2
0.4
0.6
0.8
1.0
The CRDS method measures the decay times of the
injected probing photons in the absence (t ) and the
time (msec)
0
c
presence (tc) of absorbing species. These photon decay
1
000
900
00
700
(
b)
times can be related to the concentration of the species
T =297K
T =375K
ꢁ
at time t after its generation by the Eq. (I),
8
ꢀ
ꢁ ꢂ
ln 1/tc − 1 t = C − kꢁtꢁ
0
(I)
c
6
5
00
00
where C = ln(B[A]0), B is a constant related to the
length of the absorbing medium, index of refraction of
the medium, cavity length, extinction coefficient, etc.,
400
[
A]0 is the initial concentration of the C6H5 radical,
3
2
00
00
11
−3
ꢁ
which is estimated to be ∼5 × 10 particles cm . k
is the pseudo-first-order decay constant of C6H5 in the
presence of a known, excess amount of a molecular
reactant, n-CnH2n+2.
0
2
4
[
6
8
10
C H10] (Torr)
4
Figure 2 (a) Typical pseudo-first order decay plots at 375
0
c
ꢁ
The slopes of the ln(1/tc − 1/t ) vs. t plots as illus-
ꢁ
K; (b) k vs. [C4H10] for the C6H5 + C4H10 reaction studied
trated in Fig. 2a for the reaction of C6H5 with n-C4H8
yield the pseudo-first-order rate coefficients, k , for the
by CRDS.
ꢁ
decay of C6H5 in the presence of known, excess RH
lized using ethanol as solvent and vacuum-dried before
use. n-C6H14, n-C8H18, and C6H5COCH3 were puri-
fied by trap-to-trap distillation using appropriate slush
baths. The C3H8 and n-C4H10 reactants (Aldrich, 99%
purity) and Ar and He carrier gases (Specialty Gases,
99.999%purity)wereusedwithoutfurtherpurification.
concentrations as specified in the caption of the figure.
ꢁ
A standard plot of k vs. n-C4H8 concentration is shown
in Fig. 2b, which gives the averaged second-order rate
ꢁ
ꢁ
constant k from its slope according to the relationship
0
ꢁꢁ
k = k + k [RH]
(II)
x
0
where k is the radical decay constant in the absence
of the molecular reactant [RH] due to the loss of the
radical by diffusion away from the probing beam and
recombination reactions (e.g., C6H5 + NO and C6H5
RESULTS AND DISCUSSION
Rate Constant Determination by PLP/MS
+
C6H5).
The PLP/MS technique with acetophenone as the C6H5
source has been employed to determine the reaction
rates of the C6H5 + n-CnH2n+2 (n = 3, 4, 6, 8) reac-
tions in the temperature range 494–1051 K, using the
procedure previously employed in our studies of the re-
actions with H2 [12], CH4 [13], C2H6 and neo-C5H12
[15], and i-C4H10 [8] and CH2O [14].
In the present study, two pulsed lasers were em-
ployed for the pump and probe processes. A Lambda
Physik EMG 102 excimer laser operating at 248 nm
was used to photodissociate C6H5NO (nitrosoben-
zene), which was placed on a sealed, fritted glass disk
and carried into the reactor via a mixing tube with Ar.
The measured absolute yields of C6H6 for the reac-
tions with C3H8, n-C4H10, n−6H14, and n-C8H18 re-
actions and that of C6H5CH3 from the C6H5 + CH3
reaction can be readily modeled using the SENKIN
program [19] with the mechanism presented in
Chemicals
The radical sources and molecular reactants were pur-
chased from Aldrich. Nitrosobenzene was recrystal-

PHENYL RADICAL REACTIONS WITH PROPANE, n-BUTANE, n-HEXANE, AND n-OCTANE
53
a
Table II Reactions and Rate Constants Used in the Modeling of the C H + CnH
(n = 3, 4, 6, 8) Reactions in the
6
5
2n+2
PLP/MS Experiment
Reactions
A
n
Ea
Ref.c
b
1
1
1
1
2
3
4
5
6
7
a. C6H5 + C3H8 → C6H6 + C3H7
b. C6H5 + C4H10 → C6H6 + C4H9
c. C6H5 + C6H14 → C6H6 + C6H13
d. C6H5 + C8H18 → C6H6 + C8H17
1.96E+11
2.65E+11
4.56E+11
4.31E+11
1.38E+13
1.39E+13
2.12E+16
1.00E+13
1.00E+13
1.00E+13
0.0
0.0
0.0
0.0
0.0
0.0
3850
3780
3450
2820
46
111
620
0
This work
This work
This work
This work
c
. C6H5 + CH3 → C6H5CH3
c
c
. C6H5 + C6H5 → C12H10
. CH3 + CH3(+M) → C2H6(+M)
. C6H5 + CnH2n+1 → Cn+6H2n+6
. CH3 + CnH2n+1 → Cn+1H2n+4
. CnH2n+1 + CnH2n+1 → C2nH4n+2
−1.0
d
d
d
0.0
0.0
0.0
0
0
a
n
3
−1
−1
−1
Rate constants are defined by k = AT exp(−E
a
/RT ) and in units cm , mol , and s ; E
can be found in Ref. [13].
a
is given in units of cal mol ; additional
reactions involving C , C CH , and C COCH
6
H
6
6
H
5
3
6
H
5
3
b
11
Read as 1.96 × 10 .
c
Ref. [13].
d
Assumed.
Table II to give the rate constants for the present se-
ries of reactions:
26
(a)
2
2
2
2
2
5
4
3
2
1
C6H5 + n-CnH2n+2 → C6H6 + n-CnH2n+1
(1)
Kinetically modeled values of k1 summarized in
Table I are also graphically presented in Fig. 3a. Least-
squares analyses [20] of these rate constants in units
3
−1 −1
s gave rise to the following Arrhenius
of cm mol
equations:
11
k (C3H8) = (1.96 ± 0.15) × 10
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
×
exp[−(1938 ± 56)/T ] (III-a)
1000/T (K)
11
k (n-C4H10) = (2.65 ± 0.23) × 10
26
(
b)
×
exp[−(1950 ± 55)/T ] (III-b)
2
2
2
2
2
5
4
3
2
1
11
k (n-C6H14) = (4.56 ± 0.21) × 10
×
exp[−(1735 ± 55)/T ] (III-c)
11
k (n-C8 H18) = (4.31 ± 0.39) × 10
×
exp[−(1415 ± 65)/T ] (III-d)
where the errors represent 1ꢀ, reflecting only the scat-
ters of data listed in Table I.
20
1
9
It is particularly worthwhile to note that the modeled
yields of C6H5CH3 using k2 determined in our pre-
vious studies [8,12,13], agree closely with measured
values as illustrated in the Table I. As the yields of
C6H5CH3 depend strongly on the initial concentrations
of CH3 and C6H5 (which were assumed to be the same
as the amount of C6H5NO determined by NO titra-
tion for each experimental run), the close agreement in
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
1
000/T (K)
Figure 3 (a) Arrhenius plot of the rate constants for the
C6H5 + C3H8 (ꢂ), n-C4H10 (ꢁ), n-C6H14 ( ), and n-C8H18
∇) reactions by PLP/MS. (b) Comparison of the rate con-
stants for the C6H5 + n-C4H10 (ꢁ) and n-C6H14 ( ) by
PLP/MS with those for the C H + n-C H (ꢃ) and n-
◦
(
◦
6
5
4 10
C6H14 ( ) by CRDS.
•

54
PARK, WANG, AND LIN
the yields of C6H5CH3 between experiment and mod-
eling suggests that the yields of C6H6 measured can
provide a reliable determination of the abstraction rate
constants.
The result of our sensitivity analysis shown in Fig. 4
using the SENKIN program indicates that the con-
centration of C6H6 varied positively and strongly with
k1, but negatively and strongly with k2 and k3, and
C6H5CH3 varied positively and strongly with k2, but
negatively and strongly with k1 and k3, as we had ob-
served in our previous studies on several systems as
alluded to above.
obtain the bimolecular rate constant for the reactions
with C4H10 and C6H14.
Table III summarizes the bimolecular rate constants
for the three reactions obtained by CRDS. These re-
sults together with the kinetic data obtained by PLP/MS
technique are graphically presented in Fig. 3b. As is ev-
ident from the figure, the results obtained by absolute
product yield measurements with PLP/MS agree fully
with those determined by the decay of C6H5 by CRDS.
Weighted least-squares analyses [20] of these individ-
ual data convoluting the scatters in the pseudo-first-
order and second-order rate constant determinations
gave rise to
Rate Constant Determination by CRDS
11
k (n-C4H10) = (2.70 ± 0.15) × 10
For the butane and hexane reactions, we have also ap-
plied the CRDS technique to extend our temperature
range down to 297 K to corroborate the two comple-
mentary techniques developed for C6H5 kinetic mea-
surements [7,9].
×
exp[−(1880 ± 127)/T ] (IV-a)
1
1
k (n-C6H14) = (4.81 ± 0.30) × 10
×
exp[−(1780 ± 133)/T ] (IV-b)
3
−1 −1
A typical set of pseudo-first-order plots, ln(1/tc −
in units of cm mol
s for the temperature range
0
c
1
/t ) vs. time for C4H10, is presented in Fig. 2a. The
297–1046 K.
slopes of these plots give the apparent decay constants
ꢁ
(
k ) for the specific concentrations of the molecular
Kinetics of the C H + sec-CH Bond
6
5
reactants present in the system. From the slope of the
second-order plot at each temperature (Fig. 2b), we
In Fig. 5, we compare the calculated single secondary
C H rate constants, ks-CH, for the four systems with
our previously reported single primary C H abstrac-
1
0.40± 0.06
0
.7
.6
.5
.4
.3
.2
.1
.0
0.1
0.2
0.3
tion rate constant kp-CH = 10
102)/T )] cm mol [15]. The rate constant per
s-CH bond, k , was obtained by
exp[−(1790 ±
(a)
3
−1 −1
s
0
0
1
s-CH
0
0
ks-CH = (kalkane − 6 × kp-CH)/Ns-CH
0
where Ns-CH is the number of s-CH bonds, 2, 4, 8,
and 12 for C3H8, n-C4H10, n-C6H14, and n-C8H18,
0
0
5
-
-
2
3
-
Table III Bimolecular Rate Constants of C H
Reactions with n-C4H10 and n-C6H14 Measured
6
5
(
b)
a
0
.8
.6
.4
.2
.0
0.2
0.4
0.6
2
by the CRDS Technique
0
3
−1 −1 b
s )
Reactant
T (K)
[RH] (Torr)
k (cm mol
0
8
9
9
9
n-C4H10
297
0–9.63
0–8.42
0–8.80
0–7.50
0–1.19
0–1.26
0–1.13
0–0.78
(5.25 ± 0.98) × 10
(1.04 ± 0.22) × 10
(1.03 ± 0.20) × 10
(1.74 ± 0.20) × 10
0
3
31
350
75
0
3
-
3
1
9
n-C6H14
298
334
(1.38 ± 0.43) ×10
(2.04 ± 0.28) × 10
(3.20 ± 0.48) × 10
(5.15 ± 0.52) × 10
9
9
9
-
3
3
59
91
-
0
2
4
6
8
10
time (msec)
a
All experiments were carried out with total pressure of 40 Torr
10 and 10 Torr for n-C
The uncertainties represent 1ꢀ, evaluated by weighted least-
squares analysis.
Figure 4 Sensitivity analyses for C6H6 (a) and C6H5CH3
b) in the C6H5 + C6H14 reaction at 899 K. Reaction condi-
tions are given in Table II.
for n-C
4
H
6 14
H .
b
(

PHENYL RADICAL REACTIONS WITH PROPANE, n-BUTANE, n-HEXANE, AND n-OCTANE
55
2
2
2
2
2
1
1
4
3
2
1
0
9
8
The rate constant of per s-CH from the C6H5 + n-
C6H14, and n-C8H18 reactions by PLP/MS and that
from the n-C6H14 reaction by CRDS is presented in
Fig. 5(b). The three sets of the data agree within the
combined errors as indicated. A weighted least-squares
analysis from individual measurements gives the fol-
lowing expression:
(
a)
1
0
ks-CH = (4.19 ± 0.24) × 10 exp[−(1770 ± 48)/T ]
(
V)
0.8
1.0
1.2
1.4
1.6
1.8
2.0
3
−1 −1
s for the temperature range
in units of cm mol
1
000/T (K)
2
97–1038 K. Comparison of ks-CH calculated at 300
8
9
2
2
2
2
2
1
1
1
4
and 1000 K using Eq. (V), 1.15 × 10 and 7.14 × 10
(
b)
3
−1 −1
cm mol
s
, respectively, with the values given
3
2
1
0
9
8
7
7
by kp-CH for the same temperatures, 6.44 × 10 and
9
3
−1 −1
s , suggests that s-CH bonds
4.19 × 10 cm mol
of alkanes are 1.7 times more reactive than the p-CH
bonds toward C6H5 radicals, independent of tempera-
ture in the range of 300–1000 K.
To understand the possible steric effect, calculations
are underway to obtain theoretical rate constants for H-
atom abstraction by C6H5 from C2H6 to n-C6H14, in-
cluding molecules containing t-CH bonds, by the den-
sity functional theory; hopefully a reasonable trend can
be established from such calculations even at a semi-
quantitative mechanistic level.
0
.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
1000/T (K)
Figure 5 (a) Arrhenius plot of the rate constant per s-CH
bond obtained by the C6H5 + C3H8 (dashed line with large
error), n-C4H10 (ꢁ), n-C6H14 (ꢂ), and n-C8H18 (
◦
) rate
constants. Dot-dashed line, total primary C H abstraction
rate constant for six primary C H bonds Ref. [15]. (b) Ar-
rhenius plot of the rate constant per s-CH bond obtained by
CONCLUSION
The kinetics of the C6H5 reactions with n-CnH2n+2
the n-C6H14 (ꢂ) and n-C8H18 (
◦
) rate constants by PLP/MS
(n = 3, 4, 6, 8) have been measured by the pulsed
technique and by the n-C6H14 (ꢀ) by CRDS technique.
laser photolysis/mass spectrometry (PLP/MS) employ-
ing acetophenone as the radical source. Kinetic mod-
eling of the benzene formed in these systems over the
temperature range 494–1051 K allowed us to reliably
determine the total rate constants for H-abstraction re-
actions. For the butane and hexane reactions, we have
also applied the CRDS technique, using nitrosoben-
zene as the radical source, to extend our temperature
range down to 297 K. The results of these C6H5 decay
measurements quantitatively corroborate the PLP/MS
data.
Comparison of the rate constants for H-abstraction
from the secondary CH bonds, evaluated from the ap-
proximation, ks-CH = (kalkane − 6 × kp-CH)/Ns-CH, us-
ing our previously reported single primary C H ab-
straction rate constant, indicates that the rate constants
per s-CH bond for the four reactions increase with
the molecular size up to hexane, reflecting the likely
effect of steric hindrance by the less reactive neigh-
boring CH3 groups in the smaller alkanes. The values
respectively. The results shown in Fig. 5a reveal a
strong dependence of ks-CH on molecular size until the
number of s-CH bonds Ns-CH ≥ 8 (i.e., ≥n-C6H14).
Theaveragedabsoluterateconstantat1000Kincreases
9
3
−1 −1
9
from 1.6 × 10 cm mol
s
for C3H8 to 3.8 × 10
for n-C4H10, and 7.0 × 10 cm mol
for n-C6H14, approximately 2:4:8. A similar strong
3
−1 −1
9
3
−1
cm mol
s
−
1
s
molecular size dependence was noted in the C6H5 + t-
CH bonds [8], but not in the reaction with the p-CH
bonds of C2H6 and neo-C5H12 [15]. However, the ks-CH
for n-C8H18 (Ns-CH = 12) is quite close to the value for
n-C6H14 (Ns-CH = 8). These data suggest that the rates
of the s-CH reactions in C3H8 and n-C4H10 are influ-
enced rather strongly by the accessibility of C6H5 to the
small secondary H atoms in the presence of the large
number of the less reactive CH3-bonds, particularly in
the C3H8 reaction (i.e., steric hindrance).

56
PARK, WANG, AND LIN
of both hexane and octane reactions covering the
75–1050 K range provides the rate constant per s-
9. Park, J.; Lin, M. C. Recent Research Development
in Physical Chemistry, Transworld Research Network:
India, 1998, 2, 965.
2
10
CH bond, ks-CH = (4.19 ± 0.24) × 10 exp[−(1770
3
−1 −1
s . This result suggests that
10. Park, J.; Lin, M. C. J Phys Chem A 1997, 101, 5.
±
48)/T ] cm mol
1
1
1. Park, J.; Lin, M. C. J Phys Chem A 1997, 101, 14.
2. Park, J.; Dyakov, I. V.; Lin, M. C. J Phys Chem A 1997,
C6H5 is 1.7 times more reactive to a secondary CH
bond than to a primary CH bond in alkanes.
101, 8839.
13. Tokmakov, I. V.; Park, J.; Gheyas, S.; Lin, M. C. J Phys
Chem A 1999, 103, 3636.
BIBLIOGRAPHY
14. Choi, Y. M.; Xia, W. S.; Park, J.; Lin, M. C. J Phys Chem
A 2000, 104, 7030.
1
2
. Yu, T.; Lin, M. C. J Phys Chem 1995, 99, 8599.
. Yu, T.; Lin, M. C. J Am Chem Soc 1993, 115,
15. Park, J.; Gheyas, S.; Lin, M. C. Int J Chem Kinet 2001,
33, 64.
4
371.
. Yu, T.; Lin, M. C. J Am Chem Soc 1994, 116,
571.
. Yu, T.; Lin, M. C.; Melius, C. F. Int J Chem Kinet 1994,
6, 1096.
16. Baulch, D. L.; Cobos, C. J.; Cox, R. A.; Esser, C.; Frank,
P.; Just, Th.; Kerr, J. A.; Pilling, M. J.; Troe, J.; Walker,
R. W.; Warnatz, J. J Phys Chem Ref Data 1992, 21, 411.
17. Tsang, W.; Hampson, R. F. J Phys Chem Ref Data 1986,
15, 1087.
3
4
9
2
5
6
. Park, J.; Lin, M. C. J Phys Chem A 1997, 101, 14.
. Park, J.; Chakraborty, D.; Bhusari, D. M.; Lin, M. C.
J Phys Chem A 1999, 103, 4002.
. Park, J.; Lin, M. C. Cavity-Ring-Down Spectrometry-
A New Technique for Trace Absorption Measurements;
ACS Publication Series 720; American Chemical Soci-
ety: Washington, 1999; Ch. 13, p. 196.
18. Wyatt, J. R.; DeCorpo, J. J.; McDowell, W. V.; Saafeld,
F. E. Rev Sci Instrum 1974, 45, 916.
19. Luts, A. E.; Lee, R. K.; Miller, J. A. SENKIN: A
FORTRAN Program for Predicting Homogeneous Gas-
Phase Chemical Kinetics with Sensitivity Analysis;
Sandia National Laboratories Report No. SANDIA 89-
8009, 1989.
7
8
. Park, J.; Gheyas, S. I.; Lin, M. C. Int J Chem Kinet 1999,
20. Cvetanovic, R. J.; Singleton, D. L.; Paraskevopoulos, G.
J Phys Chem 1979, 83, 50.
3
1, 645.