Study of the Reaction Cl + Ethyl Formate at 700-950 Torr and 297 to 435 K: Product Distribution and the Kinetics of the Reaction C2H5OC(=O) → CO2 + C2H5

Article abstract of DOI:10.1021/acs.jpca.6b02767

The kinetics and mechanism of the reaction of atomic chlorine with ethyl formate [Cl + CH₃CH₂O(C=O)H, reaction 1] have been examined. These experiments were performed at pressures of 760-950 Torr and temperatures from 297 to 435 K. Reactants and products were quantified by gas chromatography-flame ionization detector (GC/FID) analysis. The initial mixture contained ethyl formate, Cl₂, and N₂. Cl atoms were generated by UV photolysis of this initial mixture at 360 nm, which dissociates Cl₂. The rate constant of reaction 1 was measured at 297 K relative to that of the reaction Cl + C₂H₅Cl (reaction 2), yielding the rate constant ratio k₁/k₂ = 1.09 ± 0.05. The final products formed from reaction 1 are ethyl chloroformate, 1-chloroethyl formate, and 2-chloroethyl formate. These products result from the reactions with Cl₂ of the three free radicals formed by H atom abstraction from ethylformate in reaction 1. Based on the molar yields of these three chlorinated products, the yields of the three radicals formed from reaction 1 at 297 K are (25 ± 3) mole percent of CH₃CH₂O(C=O); (67 ± 5) mole percent of CH₃CHO(C=O)H; and (8 ± 2) mole percent of CH₂CH₂O(C=O)H. A second phase of this experiment measured the rate constant of the decarboxylation of the ethoxy carbonyl radical [CH₃CH₂O(C=O) → CO₂ + C₂H₅, reaction 4] relative to the rate constant of its reaction with Cl₂ [CH₃CH₂O(C=O) + Cl₂ → CH₃CH₂O(C=O)Cl + Cl, reaction 3a]. Over the temperature range 297 to 404 K at 1 atm total pressure, this ratio can be expressed by k₄/k_3a = 10^23.56±0.22 e^{-(12700±375)/RT} molecules cm^-3. Estimating the value of k_3a (which has not been measured) based on similar reactions, the expression k₄ = 5.8 × 10¹² e^-(12700)/RT s^-1 is obtained. The estimated error of this rate constant is ± a factor of 2 over the experimental temperature range. This rate expression is compared with recent ab initio calculations of the decarboxylation of the analogous methoxy carbonyl radical.

Full text of DOI:10.1021/acs.jpca.6b02767

Article
pubs.acs.org/JPCA
Study of the Reaction Cl + Ethyl Formate at 700−950 Torr and 297 to
435 K: Product Distribution and the Kinetics of the Reaction
C2H5OC(O) → CO2 + C2H5
E. W. Kaiser*
Department of Natural Sciences, University of Michigan-Dearborn, 4901 Evergreen Road, Dearborn, Michigan 48128, United States
ABSTRACT: The kinetics and mechanism of the reaction of atomic chlorine with ethyl formate
[Cl + CH3CH2O(CO)H, reaction 1] have been examined. These experiments were performed at
pressures of 760−950 Torr and temperatures from 297 to 435 K. Reactants and products were
quantified by gas chromatography−flame ionization detector (GC/FID) analysis. The initial
mixture contained ethyl formate, Cl2, and N2. Cl atoms were generated by UV photolysis of this
initial mixture at 360 nm, which dissociates Cl2. The rate constant of reaction 1 was measured at 297
K relative to that of the reaction Cl + C2H5Cl (reaction 2), yielding the rate constant ratio k1/k2 =
1.09
0.05. The final products formed from reaction 1 are ethyl chloroformate, 1-chloroethyl
formate, and 2-chloroethyl formate. These products result from the reactions with Cl2 of the three free radicals formed by H
atom abstraction from ethylformate in reaction 1. Based on the molar yields of these three chlorinated products, the yields of the
three radicals formed from reaction 1 at 297 K are (25 3) mole percent of CH3CH2O(CO); (67 5) mole percent of
CH3CHO(CO)H; and (8 2) mole percent of CH2CH2O(CO)H. A second phase of this experiment measured the rate
constant of the decarboxylation of the ethoxy carbonyl radical [CH3CH2O(CO) → CO2 + C2H5, reaction 4] relative to the
rate constant of its reaction with Cl2 [CH3CH2O(CO) + Cl2 → CH3CH2O(CO)Cl + Cl, reaction 3a]. Over the
0.22
375)/RT
temperature range 297 to 404 K at 1 atm total pressure, this ratio can be expressed by k4/k3a = 1023.56
e−(12700
molecules cm−3. Estimating the value of k3a (which has not been measured) based on similar reactions, the expression k4 = 5.8 ×
1012 e−(12700)/RT s−1 is obtained. The estimated error of this rate constant is a factor of 2 over the experimental temperature
range. This rate expression is compared with recent ab initio calculations of the decarboxylation of the analogous methoxy
carbonyl radical.
Cl2 for comparison to the rate constant ratios k1/k2 determined
at ambient temperature using the same reference compound by
Balaganesh et al.1 and by Wallington et al.2 In addition, the
yields of the free radical product channels 1a-1c are determined
experimentally from the yields of the chloride products (ethyl
chloroformate, 1-chloroethyl formate, and 2-chloroethyl
formate) formed by reactions 3a−3c.
1. INTRODUCTION
In a recent publication,1 the overall rate constant of the reaction
of Cl with ethyl formate [Cl + CH3CH2O(CO)H, reaction
1] was measured as a function of temperature relative to that of
the reaction of Cl with C2H5Cl (reaction 2). The yield of each
of the three abstraction product channels for reaction 1 was
estimated using ab initio calculations in that publication. These
calculations indicated that the major product channel was that
represented by reaction 1b, which contributed 66.9% to the
overall reaction rate constant at 298 K. Channel 1a contributed
33%, and channel 1c was predicted to contribute 0.1% to the
total rate constant:
CH3CH2OC(O) + Cl2 → CH3CH2OC(O)Cl + Cl
(3a)
CH3CHOC(O)H + Cl2 → CH3CHClOC(O)H + Cl
(3b)
CH3CH2OC(O)H + Cl → CH3CH2OC(O) + HCl
CH2CH2OC(O)H + Cl2 → CH2ClCH2OC(O)H + Cl
(1a)
(3c)
CH3CH2OC(O)H + Cl → CH3CHOC(O)H + HCl
Finally, the rate constant of reaction 4, the decomposition
(decarboxylation) of the ethoxy carbonyl radical formed in
reaction 1a [CH3CH2OC(O)] to CO2 and CH3CH2, is
determined relative to that of its reaction with Cl2 (reaction 3a)
over the temperature range 297−404 K. The relative rate
constant ratio, k4/k3a is obtained by measuring the molar yields
(1b)
CH3CH2OC(O)H + Cl → CH2CH2OC(O)H + HCl
(1c)
C2H5Cl + Cl → Products
(2)
In the current experiments, the overall rate constant of
reaction 1 is measured relative to that of reaction 2 at 297 K
using the relative rate method. These experiments are
performed in mixtures of ethyl formate, ethyl chloride, and
Received: March 16, 2016
Revised: April 16, 2016
© XXXX American Chemical Society
A
DOI: 10.1021/acs.jpca.6b02767
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The Journal of Physical Chemistry A
Article
of the ethyl chloride and ethyl chloroformate products formed
by reactions 5 and 3a, respectively.
from the mean. During a reaction, a portion of the unreacted
mixture in a storage flask was placed into the high-temperature
reactor at a pressure of ∼760 Torr. The mixture was then
irradiated for a chosen time, and a sample of the contents was
withdrawn into the gastight syringe using the vacuum manifold,
after removing a small amount to purge the low temperature
dead volume. Only one irradiation was possible per sample
placed into the reactor for the high temperature experiments
because of the substantial pressure loss during sampling.
Identification and GC calibration of ethyl formate (Sigma-
Aldrich 99%) and the product ethyl chloroformate (Sigma-
Aldrich 99%), formed by reaction 1a followed by reaction 3a,
were carried out by injecting a known concentration of the pure
species into the GC in the presence of the internal calibration
species. This provides a determination of the retention time
and relative GC/FID response of the two species. The molar
responses of both ethyl formate and ethyl chloroformate were
the same within experimental error. The retention time of ethyl
formate was 6.00 min, and that of ethyl chloroformate was 8.35
min.
A sample of 2-chloroethyl formate was also available from
Sigma-Aldrich, but this compound was provided at a purity
stated to be “as is” with the predominant impurity being ethyl
formate, according to the GC analysis herein. In this case, no
calibration of the GC/FID sensitivity was possible but the
retention time of 2-chloroethyl formate was observed to be 9.62
min. 1-chloroethyl formate was not available commercially and
neither its retention time nor its GC/FID sensitivity could be
determined directly. The retention time of this species was
deduced from the GC trace during a photolysis experiment.
When irradiation of the unreacted mixture was complete, ethyl
chloroformate and 2-chloroethyl formate were observed at 297
K. A third GC peak, which was the predominant product peak,
was also observed at a retention time of 8.42 min. This peak
was assigned to the 1-chloroethyl formate product.
In calculating the product molar yields, the assumption is
made that the molar GC/FID responses of all three products
are identical to that of ethyl formate. This was verified
experimentally for ethyl chloroformate as stated above. The
following observations lend support for this assumption in the
cases of 1- and 2-chloroethyl formate. In previous experiments
using this GC/FID instrument, the response factors of several
chlorinated versus nonchlorinated species were measured.
These observations showed that CH3Cl had the same response
factor as CH4; C2H5Cl the same as C2H6; and CH3CHO the
same as CH3COCl. In every case, substitution of a single Cl for
a hydrogen atom produced no measurable change in the FID
response to within 3%. This lends support to the assumption
that 1- and 2-chloroethyl formate will have essentially the same
FID response as ethyl formate, and this assumption will be used
to calculate yields of these products.
One problem occurred during these experiments that has not
been observed previously with analyses using this GC/FID
system. When using the high-temperature reactor, the
composition of the unreacted mixture in the storage flask
used to fill that reactor is analyzed. This composition
measurement provides the unreacted composition in the high
temperature reactor, because the contents of the unreacted
mixture cannot be analyzed after filling. To test this
assumption, the high temperature reactor was filled and
sampled without irradiation. In the past, this sample always
matched the composition in the storage flask to within the
experimental error of approximately 1.0%. For ethyl formate,
CH3CH2OC(O) → CH3CH2 + CO2
(4)
CH3CH2 + Cl2 → CH3CH2Cl + Cl
(5)
Gas-phase decarboxylation reactions of the type represented by
reaction 4 are potentially important in the combustion of
biodiesel fuels containing ester components.3 Its methyl
analogue (CH3OC(O) → CH3 + CO2) has been studied
extensively in theoretical calculations as summarized by
McCunn et al.,4 Bell et al.5 and Tan et al.6 Although
experimental rate constant data are available for the
decarboxylation of larger organic carbonyl radicals in solution
(see refs 7−9 and references therein), direct measurements of
the rate constant for the decomposition of a gas-phase
alkoxycarbonyl radical have not been made to my knowledge.
To attempt to fill this gap, a relative rate measurement of the
rate constant ratio k4/k3a is described herein over the
temperature range 297−404 K at ∼1 atm total pressure.
While the rate constant k3a has not been measured, it can be
estimated from similar, although not identical, types of
reactions, as will be discussed in Section 3.3.
2. EXPERIMENT
The gas chromatography−flame ionization detector (GC/FID)
analysis has been described in detail previously.10 Briefly, a
spherical (500 cm3), Pyrex reactor was used for ambient-
temperature measurements. The relative rate constant experi-
ments were performed using initial mixtures of Cl2 (purity
=99.7%), ethyl formate (99%), and C2H5Cl (99.5%) [the
kinetic reference species], diluted by N2 (99.999% min). These
mixtures were prepared by partial pressure using a vacuum
manifold. Freeze/thaw degassing cycles were performed on
condensable reactants. In addition, CF2Cl2 (99%) was included
in the reaction mixtures for internal calibration of the GC
samples. This molecule does not react with Cl and is thermally
stable at the maximum temperature and reaction time of these
experiments.11
Chlorine atoms were generated by irradiation of the
unreacted mixture with UV light peaking near 360 nm from a
single Sylvania F6T5 BLB fluorescent lamp. After irradiation for
a chosen time at ambient temperaure, a portion of the contents
of the 500 cm3 reactor was removed into a 2.5 cm3 gastight
syringe set to 1 cm3 (Hamilton) using the vacuum manifold.
The sample was analyzed by injection into the injector port
(373 K) of the gas chromatograph. The presence of the internal
calibration species, CF2Cl2, permitted corrections to be made
for uncertainty in the precise amount of sample injected into
the GC using the syringe. The mixture in the 500 cm3 reactor
was then irradiated for additional times, and these additional
samples were analyzed. All ambient temperature experiments in
this reactor were carried out at a total pressure of ∼950 Torr.
Elevated temperature experiments were performed over the
range 297−435 K using a ∼ 40 cm3, cylindrical, Pyrex reactor
(26 mm ID × ∼7 cm length) with a thermocouple well along
the axis and a Teflon-sealed, glass stopcock attached to a Pyrex
capillary tube at the end opposite the thermocouple well. This
reactor was placed inside a tube oven, whose lid remained open
approximately 6 mm to allow radiation from the fluorescent
lamp to enter. The calibration of the chromel−alumel
thermocouple was checked in ice and boiling water. The
temperature along the axis of the reactor was uniform to 1 K
B
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this was not the case. When the unreacted mixture was placed
in the reactor in limited tests and sampled without being
irradiated, the ethyl formate signal was 7
5% larger than
observed by analyzing the unreacted mixture in the storage
flask. The cause of this effect is unknown, but it undoubtedly
causes additional error in determining the product yields. In all
product yield calculations, the initial mole fraction of ethyl
formate was assumed to be 1.07 times that measured in the
flask containing the initial mixture.
3.0. RESULTS AND DISCUSSION
3.1. Rate Constant of Reaction 1. In a brief set of
experiments, the rate constant of reaction 1 (Cl + ethyl
formate) was measured at 297 K and ∼950 Torr relative to that
of reaction 2 (Cl + ethyl chloride) for comparison to two
previous relative rate measurements of k1/k2.1,2 Table 1
Table 1. Initial Conditions and Results for Measurements of
the Rate Constant of Reaction 1 Relative to That of Reaction
2 in N2 at 297 K and 950 Torr (Data Plotted in Figure 1)
Figure 1. Plot of the log10 of the fractional consumption of ethyl
formate versus that of the reference compound ethyl chloride. The
slope of the resultant line = k1/k2 = 1.09 0.025, where the error limit
represents the statistical 2σ from a least-squares fit. Because the data
a
b
b
b
data
tirr
Cl2
C2H5Cl
(ppm)
EF
C2H5Cl /
t c
k /
1d
c
set (sec) (ppm)
(ppm) C2H5Cl0
EFt/EF0
k2
are very limited, a larger error limit k1/k2 = 1.09
0.05 is more
1a
1b
1c
2a
2b
3
2
4
1056
188
74
0.663
0.396
0.217
0.841
0.513
0.657
0.372
0.195
0.843
0.518
0.0714
1.02
1.07
1.07
0.99
0.99
1.08
appropriate.
6
measurements, not to provide a more accurate measurement of
k1/k2, and, therefore, limited data were taken.
∼2
8
719
241
123
23
3.2. Experimental Product Yields. Table 2 presents
selected experiments during which the yields of the three stable
products formed by reaction 1 followed by reaction 3 (ethyl
chloroformate, 1-chloroethyl formate, and 2-chloroethyl
formate) were determined. No ethyl chloride was present in
these mixtures because the rate constant of reaction 1 was not
being determined. These products are formed from the reaction
of the molecular chlorine present in the initial mixture with the
free radical species produced by the H atom abstraction
reactions 1a−1c. The yields of the free radical species can be
determined from the yields of the three chlorides produced
quantitatively from them by reactions 3a−3c. This table
presents the initial reactant concentrations present in each
mixture, the reactor temperature and pressure, and the
irradiation time. The number designations again indicate
experiments having the same initial mixture, while the letter
designations indicate different irradiation times. The fractional
consumption of the ethyl formate (EFt/EF0) is also presented
in Table 2. The molar percentage yields of each of the three
chloride products (100[moles product]/[moles of ethyl
formate consumed]) are tabulated along with the C2H5Cl
molar yield, which is formed from the C2H5 radicals produced
by the decarboxylation of the C2H5OC(O) radical at
elevated temperature via reaction 4. These yields are labeled
raw yields in subsequent discussions and have been corrected
for secondary consumption as described below. Because the
C2H5OC(O) radical begins to decompose according to
reaction 4 at elevated temperature, the actual yield of the
C2H5OC(O) radical produced by reaction 1a is obtained
from the sum of the molar yields of the C2H5Cl and
C2H5OC(O)Cl product species. This sum is also presented
in Table 2. Reaction 4 will be discussed in detail in section 3.3.
The FID sensitivities for neither CH3CHClOC(O)H nor
CH2ClCH2OC(O)H could be determined. It is assumed
that they are identical to that of ethyl formate based on the
discussion in the Experiment section.
7
1548
157
0.0871
a
b
Time of irradiation in the 500 cm3 reactor. Initial mole fractions of
reactants. EF = ethyl formate. Data points with same number but
different letter designation were obtained from the same initial
mixture. Ratio of the final (t) to the initial (0) concentrations after
irradiation is complete. Ratio of the rate constant for reaction of Cl
c
d
with ethyl formate to that for reaction with C2H5Cl.
presents the initial reactant concentrations and values of ct/c0
for both ethyl formate and ethyl chloride after irradiation for a
time t. In Table 1, each numbered data set was obtained from
the same initial mixture placed into the 500 cm3 reactor. In the
case of data set 1, this mixture was irradiated three times
successively, resulting in the three total irradiation times
represented by the letter designations 1a, 1b, and 1c for data set
1 in Table 1. The total irradiation time for each data point is
presented as tirr in the table. The three data sets (1, 2, and 3)
were obtained on three separate days spanning a month and
show satisfactory consistency. The initial concentrations of the
reactants also varied across the data sets with no significant
change in the measured rate constant ratios.
According to the equation for relative rate determinations:
log10{[ethyl formate]t/[ethyl formate]0}/log10{[ethyl chlori-
de]t/[ethyl chloride]0} = k1/k2. The subscript t represents the
mole fraction after irradiation for time t, and subscript 0
represents the initial mole fraction. Figure 1 presents a log−log
plot of the six data points presented in Table 1 at 297 K. The
slope of the least-squares fit to the data points is calculated to
be 1.09 0.05, where the error limit includes the statistical 2σ
for the six data points ( 0.025) plus an additional factor of 2
because the data set is very limited. The value of k1/k2 agrees
satisfactorily with that determined by Balaganesh et al.1 (k1/k2
= 1.19 0.09) and by Wallington et al.2 (k1/k2 = 1.13 0.10).
This rate constant measurement was performed primarily to
show that the current experiments agreed with the previous
C
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Table 2. Results and Initial Conditions for Selected Experiments in the Study of the Products Formed during Reaction 1 (Cl +
a
ethyl formate)
b
b
b
c
d
d
d
e
e
e
e
f
g
tirr
Data (sec)
T
P
EF
EF0
Cl2
[Cl2]av
C2H5Cl
(%)
EClF
(%)
1-ClEF
(%)
2-ClEF
(%)
C2H5Cl +
ΣC
k4/k3a
e
(K) (torr)
/EF0
(ppm)
(ppm)
(ppm)
EClF (%)
(%) molecules cm−3
h
h
h
h
1
lost
2.3
4.8
1.8
15
40
80
30
53
75
32
75
120
13.5
21
37
18
38
60
8
297
297
950
950
0.484
0.524
0.277
0.469
0.83
0.63
0.27
0.74
0.50
0.40
0.80
0.42
0.28
0.88
0.76
0.35
0.67
0.48
0.21
0.72
0.22
0.35
200
214
444
724
392
673
647
648
456
436
399
427
398
387
416
372
354
431
433
404
371
361
347
761
710
∼0.24
∼0.15
∼0.16
∼0.22
1.68
1.56
1.62
3.34
3.85
3.75
9.18
12.4
11.8
19.0
15.9
14.6
16.8
18.7
18.9
17.6
21.2
20.7
19.3
19.7
19.8
20.2
20.2
18.4
19.4
15.1
16.6
16.4
7.5
51.5
61.6
67.5
51.4
51.4
46.5
54.3
38.8
47.4
47.9
35.0
51.0
49.0
56.4
40.4
44.0
38.1
46.4
55.9
48.0
56.7
48.5
5.8
7.5
19.5
19.7
19.8
20.4
21.9
20.0
21.0
18.5
20.5
20.2
16.7
21.2
19.9
26.9
21.4
20.6
19.8
21.7
21.6
23.0
26.1
20.7
76.8
89
1.38 × 1014
1.44 × 1014
1.65 × 1014
2.00 × 1014
8.12 × 1014
8.42 × 1014
7.60 × 1014
2.07 × 1015
1.91 × 1015
1.94 × 1015
1.02 × 1016
1.00 × 1016
1.04 × 1016
1.72 × 1016
2.21 × 1016
1.91 × 1016
3.88 × 1016
4.22 × 1016
4.22 × 1016
4.54 × 1016
2a
2b
3
8.1
95.4
78.2
82.5
74.1
84.3
64.4
75.1
76.8
59.3
89.2
78.0
96.6
72.8
72.5
65.3
78.4
88.8
85.0
95.2
81.5
297
320
322
321
335
335
335
367
366
366
383
383
383
401
402
400
403
404
434
950
710
760
760
760
720
760
760
725
765
660
720
770
760
780
720
760
770
210
205
703
474
6.4
4a
4b
4c
5a
5b
5c
6a
6b
6c
7a
7b
7c
8a
8b
8c
10a
10b
11
9.2
7.6
9.0
237
214
212
103
458
431
443
388
7.1
9.2
8.7
7.6
8.8
11.3
9.1
8.1
7.9
13.8
11.0
10.3
7.9
5.5
6.0
2.9
3.0
10.3
11.3
14.0
14.4
12.3
2.7
206
206
790
445
5.4
37
60
4.9
5.63 × 1016
i
i
0
a
EF = ethyl formate; EClF = ethyl chloroformate; 1-ClEF = 1-chloroethyl formate; 2-ClEF = 2 chloroethyl formate. All of the data points used to
b
c
determine k4/k3a are included in this table. tirr (sec) = irradiation time in sec. T = reactor temperature; P = reactor pressure. Fractional
consumption of ethyl formate during irradiation. Initial mole fractions of ethyl formate and Cl2. [Cl2]av represents the average Cl2 mole fraction
which accounts for loss during irradiation (see text). Raw product yields in mole percent corrected for secondary consumption. Not corrected to
d
e
100% total carbon yield (see Section 3.2). Note C2H5Cl + EClF represents the yield of the ethyloxy carbonyl radical [C2H5OC(O)] produced in
f
g
h
reaction 1. Total apparent carbon recovery in mole percent. k4/k3a = [C2H5Cl][Cl2]av/[EClF] (see text). Approximate C2H5Cl yield near noise
i
limit. Data points not included in the fit to the data in Figure 4. No ECF visible above the noise in GC trace. Therefore, k4/k3a cannot be
determined.
The molar yields of the chlorinated products presented in
Table 2 have been corrected for secondary consumption by
chlorine atoms using a chemical model entered into the
Acuchem kinetics solver.12 The rate constants for the reactions
of Cl with ethyl chloroformate, 1-chloroethyl formate, and 2-
chloroethyl formate necessary to calculate this correction have
not been determined previously. Therefore, approximate rate
constants for the reaction of Cl with ethyl chloroformate (k6)
and with 2-chloroethyl formate (k7) relative to that of ethyl
formate were determined in a single experiment at 297 K.
The rate constant of 1-chloroethyl formate with Cl (k8)
could not be determined since the compound was not available
commercially as stated in the Experiment section. The rate
constant ratios determined at 297 K are k6/k1 = 0.25 0.06;
uncertainty in the secondary consumption correction is
estimated to produce errors less than the experimental data
scatter. Note that data points 4a and 4c in Table 2 have very
different fractional consumptions of ethyl formate (0.83 and
0.27, respectively). The product yields are identical to within
experimental error, providing support for the validity of the
secondary consumption corrections.
As shown by data points 1−3 at 297 K in Table 2, the total
carbon recovery in these ambient-temperature experiments is
between 77% and 95%. The near 100% carbon recovery
supports the assumption that the GC/FID response of all three
products is equal to that of ethyl formate. In the high
temperature reactor, the carbon recovery varies from 60% to
90%, somewhat lower than at ambient temperature probably
because of uncertainty in measuring the initial mole fraction of
ethyl formate as discussed in the Experiment section.
Figure 2 presents the measured raw product yields, corrected
for secondary consumption as described above in this section,
and the total carbon recovery determined in these experiments.
The line through each set of individual product data represents
a least-squares fit to those points. For these plots, the data
scatter is relatively large. A substantial contribution to this
uncertainty likely results from the scatter in the total carbon
recovery, which in turn reflects the uncertainty in the initial
ethyl formate mole fraction in the reactor as discussed at the
end of the Experiment section.
and k7/k1 = 0.27
0.06. The rate constant ratio k8/k1 was
assumed to be equal to k7/k1. for the purpose of calculating the
correction for secondary consumption. Approximate relative
rate ratios were also determined at 410 K for ethyl
chloroformate and for 2-chloroethyl formate during a single
experiment. The results showed that k6/k1 at 297 and 410 K
were identical to within experimental error. The ratio k7/k1 =
(0.34
0.1) at 410 K was slightly higher than at 297 K
(although indistinguishable within the error limits), and k8/k1
was again assumed equal to k7/k1 at 410 K. For the purpose of
correcting for secondary consumption, both k7/k1 and k8/k1
were set equal to 0.34 at all temperatures at and above 400 K
and 0.25 for temperatures below 400 K. Because the secondary
corrections are typically <20% (maximum correction =35%),
In Figure 3, the consumption of ethyl formate is assumed to
be equal to the sum of the product mole fractions, thereby
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each chlorinated product is again fitted to a least-squares
expression shown by the solid colored lines.
The yields of the precursor radicals formed by reactions
1a−1c predicted by Balaganesh et al.1 are shown by the dashed
lines in Figure 3 using the same color code. The predicted yield
of the CH3CHOC(O)H radical [67%] at 298 K agrees well
with the measured yield of 1-chloroethyl formate [67 5%].
The predicted yield of the CH3CH2OC(O) radical [33%] is
in reasonable agreement with the [25
3%] yield of ethyl
chloroformate measured herein. The small experimental
temperature dependencies for the CH3CHClOC(O)H and
CH3CH2OC(O)Cl yields are also similar to those predicted
for their free radical precursors by Balaganesch et al. However,
the yield predicted for the CH2CH2OC(O)H radical [0.11%
at 298 K] by Balaganesh et al is nearly a factor of 100 smaller
than the [8
2%] yield measured experimentally for
CH2ClCH2OC(O)H. The predicted yield seems low for
abstraction of a hydrogen atom from a CH3 group. As an
example, site specific rate constants have been measured for the
reaction Cl + CH3CH2OH by Taatjes et al.13 At 295 K, the
ratio of the rate constants for abstraction at the two ethyl group
Figure 2. Plot of the raw (corrected for secondary consumption but
not corrected to 100% carbon recovery) molar yield of the chlorinated
products from reaction 1 as a function of reciprocal temperature from
297 to 434 K. Red symbols represent 2-chloroethyl formate; blue
symbols represent ethyl chloroformate; and green symbols represent
1-chloroethyl formate. The black symbols represent the total carbon
recovery in mole percent for each experiment.
sites is observed to be kCH3/kCH2 = 0.075
0.02, while no
measurable reaction occurs at the hydroxyl hydrogen. While
ethanol is not structurally identical to ethyl formate, it does
contain an ethoxy group as does ethyl formate. If we assume
that the ethoxy groups behave similarly in the two molecules
regarding their site specificity toward Cl atom abstraction, the
ratio in ethyl formate would also be of the order of kCH3/kCH2
=
0.075 0.02 = k1c/k1b. Based on the yield of 1-chloroethyl
formate determined herein (67%), we would predict that the
yield of 2-chloroethyl formate will be (0.075 0.02) × 67 = (5
1.4)%, indicating that abstraction at the 2-ethyl position
should not be negligible. In addition, in a measurement of the
product branching fraction for the reaction Cl + CH3OC(O)
H Wallington et al.14 observed that 45% occurred by hydrogen
abstraction from the methyl group and 65% by abstraction of
the formyl hydrogen. This result also shows that abstraction
from a primary hydrogen is not likely to be negligibly small.
One previous measurement of the product yields formed
from channels 1a−1c of reaction 1 carried out at 298 K has
been published using totally different chemistry to trap these
radicals.15 These authors determined that 62 7% of reaction 1
proceeded through channel 1b in good agreement with the data
in Figure 3 and 44 5% through channel 1a, which is larger
than measured herein. These authors did not observe any
products attributable to channel 1c, but they stated that (2
1)% of reaction 1 could proceed by 1c based on the measured
yields and error limits of the products observed from channels
1a and 1b quoted above. Their method of obtaining this
estimate for the yield from channel 1c was not described.
3.3. Decomposition Rate Constant of CH3CH2OC(O).
The ethoxy carbonyl radical [CH3CH2OC(O)] formed by
reaction 1a has two subsequent reaction channels that form
final products under the experimental conditions tested. It can
react with molecular chlorine in the mixture to form
CH3CH2OC(O)Cl via reaction 3a, or it can decompose at
elevated temperature to CO2 and ethyl radicals by reaction 4.
The ethyl radicals formed in the decarboxylation reaction will
be trapped by reaction with Cl2 to form C2H5Cl via reaction 5
Figure 3. Plot of the product yields (corrected for secondary
consumption) calculated using the sum of the products to represent
the mole fraction of ethyl formate consumed to reduce the data scatter
(see text) . The yield of the CH3CH2OC(O) radical is obtained
from the sum of the molar product yields, CH3CH2OC(O)Cl +
C2H5Cl, because the radical can decompose in addition to reacting
with Cl2 (see text). Dashed lines represent the ab initio calculations of
Balaganesh et al.1 (see text).
forcing the total carbon recovery to be 100%. This is equivalent
to dividing each raw product yield (corrected for secondary
consumption) presented in Table 2 by the total fractional
carbon recovery for that individual experiment. As seen in
Figure 3, this reduces the data scatter of the product yields, by
eliminating the uncertainty in the initial mole fraction of ethyl
formate, which will affect the calculated yields. Figures 2 and 3
both show that the major chlorinated product is 1-chloroethyl
formate followed by ethyl chloroformate and 2-chloroethyl
formate, which has the lowest yield. In Figure 3, the yield of
CH3CH2OC(O) + Cl2 → CH3CH2OC(O)Cl + Cl (3a)
CH3CH2OC(O) → CH3CH2 + CO2 (4)
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CH3CH2 + Cl2 → CH3CH2Cl + Cl (5)
Equations 3a, 4, and 5 show that in the decomposition
experiments the CH3CH2OC(O) radical can form two final
chlorinated organic products, CH3CH2OC(O)Cl and
CH3CH2Cl. The ethyl chloride product is the sole hydrocarbon
product formed from the decomposition reaction after the
C2H5 radical is trapped by Cl2 via reaction 5. By analyzing
kinetic eqs 3a, 4, and 5, an expression for k4/k3a is obtained.
This rate constant ratio for the two reaction channels of the
CH3CH2OC(O) radical can be calculated from the
measured final chlorinated product yields (in mole percent),
Y[C2H5Cl] and Y[C2H5OC(O)Cl] presented for each data
point in Table 2.
k4/k3a = Y[C2H5Cl][Cl2]av /Y[C2H5OC(O)Cl]
= (A4/A3a)e−[(Ea(4)−Ea(3a))/RT]
Figure 4. Molar yields of the products C2H5OC(O)Cl (open
circles) and C2H5Cl (red circles) plotted as a function of reciprocal
temperature. Also included in the figure is the sum of the two products
(blue triangles). All yields have been corrected to 100% carbon
recovery as described in section 3.2.
In this equation, a new expression, [Cl2]av, appears. Because Cl2
is consumed during reactions 1, 3, and 5, the average Cl2,
defined as [Cl2]av = {[Cl2]0 + [Cl2]t}/2, is used in the
calculation of this rate constant ratio and is also presented in
Table 2. Examining kinetic eqs 1, 3, 4, and 5, it can be seen that
one Cl2 molecule is consumed for each ethyl formate molecule
that reacts. The removal of chlorine during the secondary
consumption of products discussed earlier will be smaller and is
not included in [Cl2]av. One fact must be emphasized in these
decomposition experiments. Both ethyl chloride and ethyl
chloroformate are calibrated from pure samples. Therefore,
there are no assumptions made concerning the FID response
for these species that could contribute to uncertainty in the
expression for k4 /k3a. Also, since the ratio of the yields of these
two species is used in this expression, it will not be affected by
uncertainty in the initial ethyl formate mole fraction used in the
calculation of the yields, which was discussed in the Experiment
section. Table 2 presents all of the data points generated for
measuring the rate constant ratio k4/k3a as a function of
temperature. The thermal stabilities of C2H5Cl and
CH3CH2OC(O)Cl were checked in the high temperature
reactor. No measurable decomposition (<2%) was observed for
either species at temperatures up to 432 K for reaction times
encountered in these experiments. This agrees with shock tube
experiments on CH3CH2OC(O)Cl by Saito et al.16
the temperature increases to 435 K with a constant sum of 27
3%.
The slope of a plot of ln[k4/k3a] versus 1/T equals (Ea4 −
Ea3a)/R, where Ea4 represents the activation energy of reaction
4 and Ea3a is the activation energy of reaction 3a. R is the gas
constant (= 1.987 cal K−1 mol−1). Thus, the data in Table 2 can
be used to determine an approximate value for the activation
energy of reaction 4. The value is approximate because
obtaining Ea4 from the slope requires knowledge of the
activation energy of reaction 3a, which has not been measured.
However, rate constant expressions for four organic radical
abstraction reactions with Cl2 have been measured, and these
rate constants can assist in estimating a value for Ea3a. The rate
expressions for these four reactions are presented in Table 3
along with the rate constants derived from them at two
temperatures (297 and 400 K), which span the range used in
the current experiments. The examples include the reactions of
Cl2 with the acetyl and formyl radicals, which are directly
related to the C2H5OC(O) radical by the free radical site
present on the carbon atom of the carbonyl group. The
activation energies of these two radical reactions are zero to
within experimental error. Ethyl and methoxy methyl radicals
are also included in the table and have activation energies of 0
and −700 cal mol−1, respectively. Of these four examples, the
closest analogue to the ethoxy carbonyl radical is the acetyl (or
methyl carbonyl) radical. For this radical, Ea = −140 210 cal
mol−1 based on the data of Maricq and Szente17 (212−357 K)
and Gierczak et al.18 (253−384 K). Taking into account the
activation energies of the other organic free radicals included in
Table 3 and their errors, the best estimate available for Ea3a is
−140 500 cal mol−1. The pre-exponential factor A3a can be
estimated to be 1.6 × 10−11 s−1 based on the average of the A
factors for the four chlorination reactions. Again taking into
account the other reactions in Table 3, a reasonable estimate
for the error in A3a is a factor of 2, yielding A3a = 1.6 (+1.6,
−0.8) × 10−11 s−1.
Assuming a positive activation energy for the decomposition
reaction 4 and near zero activation energy for reaction 3a as
discussed below, the yield of C2H5Cl should increase and that
of CH3CH2OC(O)Cl should decrease as the temperature of
the reactor increases while the sum of the two yields remains
constant. Table 2 and Figure 4 show that this is the case. At
ambient temperature, the raw (corrected for secondary
consumption but not corrected to 100% carbon recovery)
C2H5Cl yield, formed from decarboxylation reaction 4, is
∼0.2%, while the raw yield of CH3CH2OC(O)Cl is ∼20%.
At 435 K, C2H5Cl has risen to ∼20%, and CH3CH2OC(O)
Cl is below the GC/FID detection limit of ∼0.1%. The sum of
these two product yields remains constant at ∼20% over the
297−434 K temperature range, as required if these two species
are the sole products formed from the CH3CH2OC(O)
radical. Figure 4 plots the yields of CH3CH2OC(O)Cl and
C2H5Cl (now corrected to 100% total carbon recovery as
described above). This plot shows that there is a smooth
transition from CH3CH2OC(O)Cl at ambient to C2H5Cl as
Figure 5 presents a plot of log10[k4 /k3a] versus 1/T from 297
to 404 K. Values of k4 /k3a could not be determined at higher
temperature under the experimental conditions studied
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Table 3. Rate Constants for Four Reactions of Organic Free Radicals with Cl2
a
a
reaction
rate constant
297 K
400 K
citation
b
180)/RT
1. CH3C(O) + Cl2
2.8 × 10−11 e−(93
2.2 × 10−11 e+(190
6.3 × 10−12 e−(0
2.4 × 10−11
3.0 × 10−11
6.3 × 10−12
7.6 × 10−12
6.0 × 10−11
2.5 × 10−11
2.8 × 10−11
6.3 × 10−12
-
4.4 × 10−11
1.6 × 10−11
17
c
240)/RT
500)/RT
18
19
20
21
22
2. HCO + Cl2
7.6 ( 0.7) × 10−12
240)/RT
3. CH3OCH2 + Cl2
4. C2H5 + Cl2
1.8 × 10−11 e+(715
50)/RT
1.26 × 10−11 e+(131
1.5 × 10−11
a
b
c
Rate expression evaluated at stated temperature. Estimated error 25% (297−400 K). Estimated error 20% (297−400 K).
The data points at 297 K were not used in the fit because the
ethyl chloride signal was barely above the noise level for most
data and will have larger error limits than the measurements at
elevated temperature. The best ambient temperature data point
is that colored red (and labeled 2b in Table 2), in which over
70% of the ethyl formate was consumed, thereby forming more
product and producing a larger GC/FID signal. Even though
they were not used in the fit, the ambient temperature data
points fall on the least-squares fit to the higher temperature
data.
A least-squares fit to the data in Figure 5 yields the
expression below. The error limits are 2 σ:
375)/RT
k4/k3a = 1023.56 0.22e−(12700
molecules cm−3
Figure 5. Plot of the expression log10[k4/k3a] versus 1/T, where k4/k3a
= Y[C2H5Cl][Cl2]av/Y[C2H5OC(O)Cl]. The red filled circle is the
best data point at 297 K. The 297 K data points are not included in the
fit as discussed in the text.
Note that the error limits are correlated in this expression.
When used to calculate the error in the ratio k4/k3a, a plus [or
minus] sign in the A factor error must be used with the
corresponding plus [or minus] sign in the activation energy
error to match the observed data scatter. Based on the earlier
discussion of an estimate for the activation energy of reaction
because, as shown in both Table 2 and Figure 4 and discussed
above, at a temperature of 434 K, no measurable ethyl
chloroformate remains, precluding calculations of k4/k3a at and
above this temperature. This indicates that essentially all of the
C2H5OC(O) radicals decompose to C2H5 + CO2 during the
experiment to within experimental error at 434 K. Initial
composition ranges for ethyl formate and Cl2 are (103−237
ppm) and (388−790 ppm), respectively, and the ethyl formate
consumption varies from 12% to 80%. All data points lie within
15% from the least-squares fit shown by the solid line, while
the value of k4/k3a changes by approximately a factor of ∼300.
3a (Ea3a = −140
500 cal mol−1), the activation energy of
reaction 4 (CH3CH2OC(O) → CO2 + C2H5) is calculated
to be Ea4 = 12560 875 cal mol−1 over the range T = 297−404
K. The pre-exponential factor in the relative rate constant ratio
is equal to the ratio of the A factors, A4/A3a:
0.22
A4/A3a = 1023.56
= 3.6(+2.5, −1.5) × 1023 molecules cm−3
Table 4. Non-Arrhenius Ab Initio Rate Constant Expressions for Reaction 9 and the Rate Constants Calculated from Them at
Two Temperatures Compared to the Measured Arrhenius Rate Constant for k4
a
b
rate constant (s−1
)
Arrhenius expression
297 K
400 K
ref.
conditions
c
5.8 × 1012e−12700/RT
2.6 × 103
7.8 × 102
1.0 × 103
9.1 × 102
7.7 × 102
1.9 × 102
5.1 × 102
5.4 × 103
2.0 × 104
1.7 × 103
2.4 × 103
2.6 × 103
6.7 × 105
9.4 × 104
2.1 × 105
3.1 × 105
3.4 × 105
1.7 × 105
2.3 × 105
1.8 × 105
8.2 × 105
1.4 × 105
3.5 × 105
5.9 × 105
∼1 atm, N2
1 atm, N2
10 atm
7.20 × 1015T−1.65 e−12071/RT
2.06 × 1017 T−1.79 e−13439/RT
8.59 × 1017 T−1.72 e−14572/RT
5.92 × 1010 T0.78 e−13340/RT
1.55 × 1012 T0.514 e−15182/RT
2.33 × 1011 T0.546 e−13600/RT
1.89 × 1009 T0.13 e−7974/RT
1.06 × 1010 T0.18 e−8378/RT
1.25 × 1016 T−1.83 e−11341/RT
1.04 × 1018 T−2.1 e−12827/RT
8.69 × 1017 T−1.81 e−13657/RT
8.81 × 1010 e−10932/RT
9.66 × 1011 e−12204/RT
6.46 × 1012 e−13385/RT
1.24 × 1013 e−13880/RT
5.25 × 1013 e−15536/RT
9.81 × 1012 e−13976/RT
4.60 x109 e−8062/RT
6
6
6
100 atm
6
k∞
d
3
d
24
23
23
25
25
25
1 atm
10 atm
1 atm
3.63 × 1010 e−8500/RT
4.45 × 1010 e−10080/RT
5.82 × 1011 e−11380/RT
3.55 × 1012 e−12410/RT
10 atm
100 atm
a
b
Ab initio expressions derived for k9. Arrhenius expressions calculated from the non-Arrhenius ab initio rate constants in column 1 over the range
c
297−404 K. First line is k4 for CH3CH2OC(O) decarboxylation derived from this work Experimental k4 for CH3CH2OC(O) decarboxylation
derived from this work. Estimated error in the rate constant is a factor of 2 over the 297−404 K range studied (see text). Error in Ea4 is estimated to
d
be 850 cal mol−1 (see text). Pressure for ab initio calculation not stated.
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Inserting the estimate for A3a presented above (A3a = 1.6[+1.6,
−0.8] × 10−11) into the expression for A4/A3a, the value of A4 is
calculated to be 5.8 (+7.0, −3.8) × 1012 s−1. The error limits for
A4 are obtained by propagating the individual errors for A4/A3a
and A3a using the quadrature formula for products. In this case
this is an approximation since the error in A3a is only an
educated guess rather that a statistical 2σ. However, it the best
estimate for the errors that can be obtained. This is a reasonable
A factor range for a first-order decomposition reaction. The
final best expression for the temperature-dependent rate
constant k4 is
private communication, Klippenstein25 also calculated k9 as a
function of temperature and pressure. Although Klippenstein
did not present a high-pressure limiting rate constant, stopping
instead at 100 atm, his results show a monotonic approach to
100 atm at both 297 and 400 K rather that the nonmonotonic
results of Tan et al. at 297 K. Finally, the ab initio potential
energy surface was also derived for k9 by McCunn et al.4 These
authors did not derive a rate constant. They did identify the cis
configuration of the methoxy carbonyl radical as by far the
more favorable transition state for reaction 9, and the calculated
energy above initial reactants of that transition state is 14.6 kcal
mol−1 (see Figure 18 of that reference).
k4 = 5.8(+7.0, −3.8) × 1012e−(12560
s−1
875)/RT
The experimental Arrhenius rate constant measured herein
for k4 and the five ab initio calculations of the non-Arrhenius
rate constant expression for k9 are compared in Table 4 over
the temperature range 297 to 400 K. I believe that it is
reasonable to assume that the decarboxylation of the two
carbonyl radicals should have similar rate constants and
transition state energies based on their structural similarity.
Table 4 also presents the Arrhenius expressions derived from
the non-Arrhenius ab initio rate constants over the temperature
range 297−404 K. This provides a clearer comparison of the
rate constants from the ab initio calculations with the measured
rate constant expression for the ethoxy carbonyl radical. The
rate constant k4 will be closer to its high pressure limit than is k9
at 1 atm throughout the measured temperature range because it
has significantly more vibrational degrees of freedom. For this
reason, I believe that the best comparison of the calculated rate
constants to this experiment can be obtained using the high
pressure limiting rate constants from the ab initio calculations
where available. Klippenstein25 presents a value for k9 at 100
atm, which must be at or very near the high pressure limit
within this temperature range as confirmed by the pressure-
dependent calculations of k9 and k9∞ by Tan et al.6 which are
presented in Table 4.
Figure 6 presents the rate constant curves generated by the
five ab initio calculations of the decarboxylation of the methoxy
carbonyl radical for comparison to the curve (red line)
measured in the current experiments for the ethoxy carbonyl
radical. The factor of 2 uncertainty estimated for the
experimental measurement of the decarboxylation of the ethoxy
carbonyl radical is indicated by the red vertical line. The
experimental result, while for a different but very similar radical,
provides the only data against which to compare the gas phase
ab initio calculations of the decarboxylation of the methoxy
carbonyl radical to my knowledge. All of the curves are linear
over the experimental temperature range. The 100 atm line of
Klippenstein’s calculation of k9 (line 2, blue) lies on the
experimental line for the ethoxy carbonyl radical. The k9∞ line
of Tan et al. (line 3, black) lies close to the experimental line,
nearly within the estimated factor of 2 error in k4. These two ab
initio calculations are the best choices for comparing to k4, since
both were derived at essentially the high-pressure limit. The
calculations of Glaude et al. (line 4, green) and Farooq et al.
(line 5, brown) are in reasonable agreement with k4 in light of
the fact that the experimental results were obtained for a
different albeit very similar alkoxy carbonyl radical and the
pressures used for these two calculations are unstated. The ab
initio rate constant of Zhao et al.23 is derived from their 10 atm
result. Based on the calculations of Tan et al. and Klippenstein,
the Zhao et al. rate constant is at its high pressure limit at 297 K
but in the falloff region at 400 K, resulting in an apparent value
of Ea9, which will be too low. Once again, however, this rate
In this expression, there is also some unknown degree of
correlation between the errors in the A and Ea expressions as
described above. This uncertainty in the error limits makes this
expression less accurate for comparing to the ab initio
calculations than the measured value of k4/k3a.
Fortunately, the uncertainty in k4 within the temperature
range in which k4/k3a was determined (297−404 K) can be
estimated more accurately as follows. The data scatter in Figure
4 shows that k4/k3a is known to within 15% throughout this
temperature range. The uncertainty in k3a was estimated
previously to be plus or minus a factor of 2, and this will
dominate the error in k4 over the measured temperature range.
Thus, k4 (297−404 K) can be represented by the following
expression to within a factor of 2.
k4 = k3a(k4/k3a) = 1.6 × 10−11k4/k3a
= 1.6 × 10−11 × 1023.56e−(12700)/RT
= 5.8 × 1012e−(12700)/RT s−1
(C)
Results from this experimental expression for k4 can be
compared to the rate constants calculated from ab initio
expressions derived in five determinations of the rate constant
for decarboxylation reaction 9, which is a reaction very similar
to reaction 4, at temperatures from 297 to 404 K.
CH3OCO) → CH3 + CO2
(9)
The recommended rate constant expressions from these five ab
initio calculations and the rate constants calculated from them
at 297 and 400 K are presented in Table 4. The most complete
published ab initio calculation of k9 is that of Tan et al.,6 who
calculated not only the temperature dependence but also the
effect of pressure on k9. As shown in Table 4, k9 from this
reference is predicted to be near its high-pressure limit at
ambient temperature and 1 atm total pressure, although the
predicted rate rises 20% at 10 atm and then falls off slightly as
the pressure increases further at ambient temperature. At 400
K, the predicted rate constant increases monotonically with
pressure until the high pressure limit is reached at a factor of
∼3 times that at 1 atm. Zhao et al.23 presents an ab initio
calculation for k9 at several pressures up to and including 10
atm. Farooq et al.3 derived an expression for k9 by ab initio
calculation and tested it using shock tube measurements of
CO2 generation from the thermal decomposition of three
methyl esters over the temperature range 1260 to 1653 K and
1.4 to 1.7 atm in the shock tube. The pressure used in the ab
initio calculation is not stated by Farooq et al. Glaude et al.24
performed an ab initio calculation of k9 for use in modeling
atmospheric-pressure dimethyl carbonate flames. No pressure
was stated for this ab initio calculation. In an unpublished
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fact that their calculations were performed at a maximum
pressure of 10 atm. This is below the high pressure limit at 404
K as seen from the results of Klippenstein and of Tan et al. in
Table 4, and will result in a reduced apparent activation energy.
However, the value of Ea9 determined by Zhao et al. is
considerably lower than that determined by Klippenstein25 and
by Tan et al.6 at 10 atm as shown in Table 4.
4.0. SUMMARY
Results from three separate kinetic and mechanistic studies on
ethyl formate and the ethoxy carbonyl radical formed from
ethyl formate are reported herein. The measurements are
summarized below:
(1) The ratio of the rate constant for reaction of ethyl
formate with atomic chlorine (reaction 1) was measured
relative to that of ethyl chloride with atomic chlorine
(reaction 2) at 297 K and 1 atm, yielding k1/k2 = 1.09
0.05. This agrees with two previous measurements of this
rate constant ratio to within the combined error limits.1,2
Reaction 1 represents the sum of the hydrogen
abstraction reactions from the three possible hydrogen
atom sites in ethyl formate to form the free radicals
CH3CH2OC(O) [reaction 1a], CH3CHOC(O)H
[reaction 1b], and CH2CH2OC(O)H [reaction 1c].
This experiment was carried out in mixtures of ethyl
formate, Cl2, and N2 using UV light to dissociate Cl2 into
Cl atoms.
(2) The yields of the three product radicals formed after H
atom abstraction by Cl from ethyl formate were
determined by measuring the yields of the stable
chlorinated products CH3 CH2 O(CO)Cl,
CH3CHClO(CO)H, and CH2ClCH2O(CO)H.
These species are generated by the quantitative reactions
of the free radical products with Cl2 in the initial mixture.
The product radical yields from channels 1a, 1b, and 1c
are 25 3%, 67 5%, and 8 2%, respectively at 297 K.
There is a small decrease in the product yield from
channel 1b and a small increase in the product yield from
channel 1c with increasing temperature. The product
yield from reaction 1a remains constant to within
experimental error over the temperature range 297 to
434 K. These experimental yields are compared with a
recent ab initio calculation of the free radical yields from
reaction 1.1
Figure 6. Plots of k4 and k9 vs 1/T. Line 1 (red) = k4 from this work
(see Table 4); vertical red line indicates estimated error of a factor of 2
as described in the text. 2 (blue) = ab initio calculation of k9 at 100 atm
(ref 25). 2b (dashed blue) = ab initio calculation of k9 at 1 atm (ref
25). 3 (black) = ab initio calculation of k9∞ (ref 6). 3b (dashed black)
= ab initio calculation of k9 at 1 atm (ref 6). 4 (green) = ab initio
calculation of k9 at an unstated pressure (ref 24). 5 (brown) = ab initio
calculation of k9 at an unstated pressure (ref 3). 6 (black dotted) = ab
initio calculation of k9 at 10 atm (ref 23).
constant is in decent agreement with the experimental data for
k4 in the 297−404 K range.
The ethoxy carbonyl radical has a measured activation energy
of 12560 875 cal mol−1 as described earlier in this section
over the temperature range 297−404 K, in which the error limit
includes the data scatter in k4/k3a and the error estimated for
Ea3a. This value can be compared to the activation energies of
the Arrhenius expressions derived over the same temperature
range for reaction 9 from the ab initio non-Arrhenius
expressions presented in Table 4. Because reactions 4 and 9
might be expected to have similar activation energies, this
comparison can provide a test of the ab initio calculations of
Ea9 over this temperature range. Unfortunately, the effect of
pressure on the rate constant ratio k4/k3a was not measured
during these experiments because the laboratory space was
taken out of service during a building renovation. However, as
mentioned earlier, k4 must be closer to its high-pressure limit
than k9 is throughout this temperature range because of the
larger number of vibrational modes in the ethoxy carbonyl
radical. The pressure dependent ab initio calculations of k9
predict that k9 is at its high pressure limit at 1 atm and 297 K,
and only a factor of 3 below it at 1 atm and 400 K. It seems
reasonable to assume that k4 will be very near to its high-
pressure limit from 297 to 400 K at the experimental pressure
of ∼1 atm. Thus, it is appropriate to compare the Arrhenius
activation energy of k4 to the ab initio high-pressure Arrhenius
activation energy values in Table 4 which were determined by
Klippenstein25 (12410 cal mol−1) and by Tan et al.6 (13880 cal
mol−1) for k9. Ea4 agrees with the high-pressure values of Ea9
calculated by both of these authors to nearly within the
experimental error estimated for Ea4. As expected, as the
pressure is lowered, the ab initio apparent activation energy of
k9 decreases (see curves 2b and 3b in Figure 6) because, as the
temperature increases, k9 at 400 K falls off to a greater extent
than at 297 K. The value of Ea9 calculated by Zhao et al.23 is the
smallest of all the ab initio determinations as seen in Table 4
and Figure 6. Some of this difference can be attributed to the
(3) Finally, the rate constant for decarboxylation of the
ethoxy carbonyl radical [CH3CH2OC(O) → CH3CH2
+ CO2, reaction 4] was measured relative to the rate
constant of its reaction with Cl2 [CH3CH2OC(O) +
Cl2 → CH3CH2OC(O)Cl + Cl, reaction 3a] over the
temperature range 297 to 404 K. The rate constant ratio
determined at ∼1 atm can be expressed as k4/k3a
=
0.22
375)/RT
1023.56
e−(12700
molecules cm−3 in which the
error limits are 2σ but correlated. By estimating the value
of k3a, which has not been measured, based on similar
reactions, the expression k4 = 5.8 × 1012 e−(12700)/RT s−1 is
obtained. This expression has an estimated error of
a
factor of 2 over the stated temperature range. These
results are compared to recent ab initio calculations of
the rate constant of the decarboxylation of methoxy
carbonyl [CH3OC(O)], which is very similar
structurally to the ethoxy carbonyl radical.
I
DOI: 10.1021/acs.jpca.6b02767
J. Phys. Chem. A XXXX, XXX, XXX−XXX

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AUTHOR INFORMATION
Corresponding Author
*E-mail: ewkaiser@comcast.net; Mailing address: 7 Windham
Lane, Dearborn, MI 48120, United States.
Notes
■
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
I thank Prof. Craig J. Donahue (University of Michigan-
Dearborn) for his assistance during this research. I also thank
Dr. William Pitz and Dr. Charles Westbrook of Lawrence
Livermore National Laboratory for helpful discussions during
the preparation of this manuscript.
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J. Phys. Chem. A XXXX, XXX, XXX−XXX