Kinetics and Thermochemistry of the Cl(2PJ) + C2Cl4 Association Reaction

Article abstract of DOI:10.1021/jp952396k

A laser flash photolysis-resonance fluorescence technique has been employed to study the kinetics of the Cl(²P_J) + C2Cl4 association reaction as a function of temperature (231-390 K) and pressure (3-700 Torr) in nitrogen buffer gas.The reaction is found to be in the falloff regime between third and second order over the range of conditions investigated, although the second-order limit is approached at the highest pressures and lowest temperatures.At temperatures below 300 K, the association reaction is found to be irreversible on the experimental time scale of ca. 20 ms.The kinetic data at T < 300 K have been employed to obtain falloff parameters in a convenient format for atmospheric modeling.At temperatures above 330 K, reversible addition is observed, thus allowing equilibrium constants for C2Cl5 formation and dissociation to be determined.Second- and third-law analyses of the equilibrium data lead to the following thermochemical parameters for the association reaction: ΔH⁰₂₉₈ = -18.1 +/- 1.3 kcal mol^-1, ΔH⁰₀ = -17.6 +/- 1.3 kcal mol^-1, and ΔS⁰₂₉₈ = -27.7 +/- 3.0 cal mol^-1 K^-1.In conjunction with the well-known heats of formation of Cl(²P_J) and C2Cl4, the above ΔH values lead to the following heats of formation for C2Cl5 at 298 and 0 K: ΔH⁰_f,298 = 8.0 +/- 1.3 kcal mol^-1 and ΔH⁰_f,0 = 8.1 +/- 1.5 kcal mol^-1.The kinetic and thermochemical parameters reported above are compared with other reported values, and the significance of reported association rate coefficients for understanding tropospheric chlorine chemistry is discussed.

Full text of DOI:10.1021/jp952396k

680
J. Phys. Chem. 1996, 100, 680-688
Kinetics and Thermochemistry of the Cl(2PJ) + C2Cl4 Association Reaction
J. M. Nicovich and S. Wang†
Georgia Tech Research Institute, Georgia Institute of Technology, Atlanta, Georgia 30332
M. L. McKee
Department of Chemistry, Auburn UniVersity, Auburn, Alabama 36849
P. H. Wine*
School of Chemistry and Biochemistry, School of Earth and Atmospheric Sciences,
and Georgia Tech Research Institute, Georgia Institute of Technology, Atlanta, Georgia 30332
ReceiVed: August 15, 1995; In Final Form: October 12, 1995X
A laser flash photolysis-resonance fluorescence technique has been employed to study the kinetics of the
Cl(2PJ) + C2Cl4 association reaction as a function of temperature (231-390 K) and pressure (3-700 Torr)
in nitrogen buffer gas. The reaction is found to be in the falloff regime between third and second order over
the range of conditions investigated, although the second-order limit is approached at the highest pressures
and lowest temperatures. At temperatures below 300 K, the association reaction is found to be irreversible
on the experimental time scale of ∼20 ms. The kinetic data at T < 300 K have been employed to obtain
falloff parameters in a convenient format for atmospheric modeling. At temperatures above 330 K, reversible
addition is observed, thus allowing equilibrium constants for C2Cl5 formation and dissociation to be determined.
Second- and third-law analyses of the equilibrium data lead to the following thermochemical parameters for
the association reaction: ∆H°298 ) -18.1 ( 1.3 kcal mol-1, ∆H°0 ) -17.6 ( 1.3 kcal mol-1, and ∆S°298
)
-27.7 ( 3.0 cal mol-1 K-1. In conjunction with the well-known heats of formation of Cl(2PJ) and C2Cl4, the
above ∆H values lead to the following heats of formation for C2Cl5 at 298 and 0 K: ∆H°f,298 ) 8.0 ( 1.3
kcal mol-1 and ∆H°f,0 ) 8.1 ( 1.5 kcal mol-1. The kinetic and thermochemical parameters reported above
are compared with other reported values, and the significance of reported association rate coefficients for
understanding tropospheric chlorine chemistry is discussed.
Introduction
atom source probably being photochemically labile chlorine
species such as Cl2 and ClNO2 produced via heterogeneous
Tetrachloroethylene (C2Cl4) is used widely for dry cleaning,
for metal degreasing, and as an industrial solvent.1,2 Global
production of C2Cl4 over the decade from the early 1980s to
the early 1990s averaged around 600 ktons yr-1, and a majority
of this production has found its way into the atmosphere.1 Field
observations of the global distribution of atmospheric C2Cl4 have
been employed in conjunction with spatially resolved emissions
data to deduce an average tropospheric lifetime of about 0.4
yr.1,3,4 This lifetime is consistent with the notion that C2Cl4
removal from the troposphere is dominated by reaction with
the OH radical, although uncertainties in the OH + C2Cl4 rate
coefficient and in tropospheric OH concentrations are such that
the lifetime for C2Cl4 toward reaction with OH could be
anywhere in the range 0.20-0.65 yr.2
Comparison of available kinetic data for the OH + C2Cl4
reaction5-8 with available data for the Cl(2PJ) + C2Cl4 reaction9-16
suggests that the Cl(2PJ) + C2Cl4 rate coefficient is several
hundred times faster than the OH + C2Cl4 rate coefficient at
tropospheric temperatures and pressures. Until recently, it has
been thought that chlorine atom levels in the troposphere were
so low that Cl(2PJ) could not be an important tropospheric
reactant. However, evidence is now mounting which suggests
that chlorine atom levels in the marine boundary layer may be
as much as one-tenth as high as OH levels,17,18 with the chlorine
reactions on the surfaces of moist sea salt particles.19 Hence,
it appears that in certain regions of the troposphere reaction
with Cl(2PJ) is an important removal mechanism for C2Cl4.
Reaction 1 must proceed via an addition mechanism, i.e., for
N2 buffer gas,
Cl(2PJ) + C2Cl4 + N2 f C2Cl5 + N2
(1)
The current state of knowledge concerning the atmospheric
oxidation mechanism for C2Cl5 has recently been reviewed by
Franklin.2 Phosgene (Cl2CO) is the major end product, but
significant yields of carbon tetrachloride, a compound with a
large ozone depletion potential, have been reported.20 While
CCl4 can be produced via the gas phase photolysis of the
intermediate photooxidation product CCl3CClO, it is now
thought that most CCl4 observed in laboratory photooxidation
studies is formed by heterogeneous photochemical processes.2
Hence, yields of CCl4 observed in laboratory “smog chamber”
studies may be larger than those which would actually be
produced in the atmosphere.
While numerous kinetics studies of reaction 1 have been
reported,9-16 the temperature and pressure dependences of the
rate coefficient have not been systematically investigated. In
this paper we report the results of experiments where laser flash
photolysis of Cl2/C2Cl4/N2 mixtures has been coupled with Cl-
(2PJ) detection by time-resolved atomic resonance fluorescence
spectroscopy to investigate the kinetics of reaction 1 over the
temperature range 231-298 K and the pressure range 3-700
† Present address: Dalian Institute of Chemical Physics, Chinese
Academy of Sciences, P.O. Box 110, Dalian, People’s Republic of China.
* To whom correspondence should be addressed.
X Abstract published in AdVance ACS Abstracts, December 15, 1995.
0022-3654/96/20100-0680$12.00/0 © 1996 American Chemical Society

Kinetics of the Cl(2PJ) + C2Cl4 Association Reaction
J. Phys. Chem., Vol. 100, No. 2, 1996 681
TABLE 1: Summary of Kinetic Data for the Reaction
Cl(2PJ) + C2Cl4 + N2 f C2Cl5 + N2 Obtained under
Experimental Conditions (T < 300 K) Where the Reaction
Was Irreversible on the Time Scale for Cl(2PJ) Decaya
Torr; over this range of experimental conditions the reaction is
found to be in the falloff regime between third and second order,
although the high-pressure second-order limit is approached at
the low-temperature and high-pressure limits of the range of
conditions investigated. We also report experiments at higher
temperatures (332-390 K) where Cl(2PJ) regeneration is
observed on the experimental time scale (10-5-10-2 s), thus
indicating the occurrence of the reverse dissociation reaction:
no. of
T
P
[Cl2]
[Cl]t)0 [C2Cl4]max exptsb k′max
k1 ( 2σc
231 3.1 77
6.2 69
1.9
0.8
0.6
0.6
0.6
1.4
6000
2750
2490
2320
1870
2500
7330
2330
2130
2070
1630
2070
6750
2590
2120
3370
3230
1790
1620
2360
1700
1760
6
5
6
6
6
6
9
6
6
17500 28.1 ( 0.8
9300 33.1 ( 1.1
10700 43.0 ( 2.5
12200 50.3 ( 3.1
9770 51.6 ( 0.9
12200 48.0 ( 2.4
11900 15.6 ( 0.3
5080 20.3 ( 1.8
7290 33.6 ( 1.2
8630 41.5 ( 3.2
7150 42.8 ( 3.1
9740 46.5 ( 2.3
5700 7.9 ( 0.3
3020 11.1 ( 0.8
3140 14.4 ( 0.9
6490 18.7 ( 0.7
6150 18.6 ( 1.1d
4110 22.6 ( 0.8
4370 26.9 ( 0.8
7830 32.5 ( 2.1
6560 37.8 ( 3.2
7600 38.7 ( 2.5
26 63
101 60
401 61
702 99
C2Cl5 + N2 f Cl(2PJ) + C2Cl4 + N2
(-1)
260 3.1 22-76 1.6
Analysis of equilibration kinetics as a function of temperature
provides information about the thermochemistry of reaction 1.
6.2 62
26 61
101 54
402 57
702 85
0.7
0.6
0.6
0.7
0.9
1.9
5
5
5
Experimental Technique
297 3.1 70
10
20
10
21
10
5
7
12
8
The laser flash photolysis-resonance fluorescence apparatus
employed in this study was similar to those employed in our
laboratory in several previous studies of chlorine atom kinet-
ics.21,22 Important features of the apparatus and experimental
techniques which are specific to this study are described below.
6.1 27-240 0.2-1.5
13 10-56 0.1-0.7
26 10-79 0.1-1.8
26 43
52 35
101 54
201 32-93 0.3-1.0
401 64
701 10
0.8
0.6
0.9
Chlorine atoms were produced by 355 nm laser flash
photolysis of Cl2. Third harmonic radiation from a Quanta Ray
Model DCR-2 Nd:YAG laser provided the photolytic light
source. The photolysis laser could deliver up to 1 × 1017
photons per pulse at a repetition rate of up to 10 Hz; the pulse
width was 6 ns. Fluences employed in this study ranged from
1.3
1.3
14
a Units: T (K); P (Torr); concentrations (1011 molecules cm-3); k′max
(s-1); k1 (10-12 cm3 molecule-1 s-1). b Expt ≡ determination of one
pseudo-first-order decay rate. c Errors represent precision only. d 1.0
× 1015 CF2Cl2 per cm3 added to reaction mixture.
5 to 50 mJ cm-2 pulse-1
.
In order to avoid accumulation of photochemically generated
reactive species, all experiments were carried out under “slow
flow” conditions. The linear flow rate through the reactor was
typically 3 cm s-1 while the laser repetition rate was varied
over the range 2-10 Hz. (It was 2 Hz in most experiments at
T < 300 K and 10 Hz in most experiments at T > 330 K.)
Since the direction of flow was perpendicular to the photolysis
laser beam, no volume element of the reaction mixture was
subjected to more than a few laser shots. Molecular chlorine
(Cl2) and C2Cl4 were flowed into the reaction cell from 12 L
Pyrex bulbs containing dilute mixtures in nitrogen buffer gas,
while N2 flowed directly from its high-pressure storage tank.
The Cl2/N2 mixture, C2Cl4/N2 mixture, and additional N2 were
premixed before entering the reaction cell. Concentrations of
each component in the reaction mixture were determined from
measurements of the appropriate mass flow rates and the total
pressure. The C2Cl4 concentration was also measured in situ
in the slow flow system by UV photometry at 228.8 nm using
a cadmium penray lamp as the light source. The C2Cl4
absorption cross section at 228.8 nm was measured during the
course of this study and was found to be 8.36 × 10-18 cm2.
Kinetics results were found to be independent of whether the
60.3-201 cm long absorption cell was positioned upstream or
downstream from the reaction cell. In the lowest pressure
experiments a small correction was required for the pressure
differential between the absorption cell and the reaction cell;
the pressure differential never exceeded 1%. In all photometric
measurements (including the absorption cross section measure-
ments) the absorption cell temperature was 297 ( 2 K.
Results and Discussion
In all experiments, chlorine atoms were generated by laser
flash photolysis of Cl2:
Cl2 + hν (355 nm) f nCl(2P3/2) + (2 - n)Cl(2P1/2) (2)
The fraction of chlorine atoms generated in the excited spin-
orbit state, Cl(2P1/2), is thought to be very small, i.e., less than
0.01.24,25 Recently, it has been reported that the rate coefficient
for Cl(2P1/2) quenching by N2 is considerably slower than
previously thought, i.e., 5.0 × 10-15 cm3 molecule-1 s-1 26
.
However, on the basis of reported rate coefficients for Cl(2P1/2
)
deactivation by saturated halocarbons (all gas kinetic except,
possibly, CF4),26-29 we expect that the rate coefficient for
Cl(2P1/2) deactivation by C2Cl4 is very fast, i.e., (2 ( 1) × 10-10
cm3 molecule-1 s-1. Hence, it seems safe to assume that all
Cl(2PJ) + C2Cl4 kinetic data are representative of an equilibrium
mixture of Cl(2P1/2) and Cl(2P3/2). As a further check on the
assumption of spin state equilibration, the rate coefficient at T
) 297 K and P ) 26 Torr was measured with and without
CF2Cl2, a very efficient Cl(2P1/2) quencher,26,28,29 added to the
reaction mixture; as expected, this variation in experimental
conditions had no effect on the observed reaction rate (see Table
1). The equilibrium fraction of chlorine atoms in the 2P1/2 state
ranges from 0.0021 at 231 K to 0.019 at 390 K. It is worth
noting that, given the small fraction of chlorine atoms in the
2P1/2 state and the fast values for k1 which are measured (Tables
1 and 2), it must be the case that observed reactivity is
2
dominated by chlorine atoms in the P3/2 state.
The gases used in this study had the following stated
minimum purities: N2, 99.999%; Cl2, 99.9%.23 Nitrogen was
used as supplied while Cl2 was degassed at 77 K before being
used to prepare mixtures with N2. The liquid C2Cl4 sample
had a stated purity of 99+%. It was transferred under nitrogen
atmosphere into a vial fitted with a high vacuum stopcock and
then degassed repeatedly at 77 K before being used to prepare
mixtures with N2.
All experiments were carried out under pseudo-first-order
conditions with C2Cl4 in large excess over Cl(2PJ). Hence, in
the absence of side reactions that remove or produce chlorine
atoms, the Cl(2PJ) temporal profile following the laser flash
would be described by the relationship
ln{[Cl(2PJ)]0/[Cl(2PJ)]t} ) (k1[C2Cl4] + k3)t ) k′t (I)

682 J. Phys. Chem., Vol. 100, No. 2, 1996
Nicovich et al.
Figure 2. Plots of k′, the Cl(2PJ) pseudo-first-order decay rate, versus
C2Cl4 concentration, as a function of temperature for data obtained at
P ) 26 Torr of N2 with no added CF2Cl2. The solid lines are obtained
from linear least-squares analyses and the resulting rate coefficients,
i.e., the slopes of the plots, are listed in Table 1.
Figure 1. Typical Cl(2PJ) temporal profiles observed at T < 300 K.
Experimental conditions: T ) 259 K; P ) 100 Torr; M ) N2; [Cl2] )
5.4 × 1012 molecules cm-3; [Cl]0 ) 5.6 × 1010 atoms cm-3; [C2Cl4] in
units of 1014 molecules cm-3 (A) 0, (B) 0.724, (C) 1.07, and (D) 2.07;
number of laser shots averaged (A) 400, (B) 2000, (C) 2000, and (D)
3000. Solid lines are obtained from least-squares analyses and give
the following pseudo-first-order decay rates in units of s-1: (A) 245,
(B) 3250, (C) 4560, and (D) 8630. For the sake of clarity, traces A
and D are scaled by factors of 0.9 and 1.5, respectively.
where k3 is the rate coefficient for the process
Cl f first-order loss by diffusion from the detector field
of of view and/or reaction with background impurities (3)
The bimolecular rate coefficients of interest, k1([N2],T), are
determined from the slopes of k′ versus [C2Cl4] plots for data
obtained at constant [N2] and T and under conditions where N2
is the dominant third body collider with the energized C2Cl5
complex. Observation of Cl(2PJ) temporal profiles that are
exponential, i.e., obey eq I, a linear dependence of k′ on [C2-
Cl4], and invariance of k′ to variation in laser photon fluence
and photolyte concentration strongly suggests that reactions 1
and 3 are, indeed, the only processes that significantly affect
the Cl(2PJ) time history.
Kinetics at T < 300 K. For all experiments carried out at
temperatures below 300 K, well-behaved pseudo-first-order
kinetics were observed; i.e., Cl(2PJ) temporal profiles obeyed
eq I, and k′ increased linearly with increasing [C2Cl4] but was
independent of laser photon fluence and photolyte concentration.
Typical data are shown in Figures 1-3. Measured bimolecular
rate coefficients, k1([N2],T) are summarized in Table 1. As
expected for an association reaction in the non-high-pressure-
limit regime, k1([N2],T) is found to increase with increasing
pressure and with decreasing temperature.
Parametrization of k1([N2],T) for Atmospheric Modeling.
For purposes of atmospheric modeling, it is convenient to
generate a mathematical expression that can be used to compute
k1([N2],T) over the range of relevant temperatures and pressures.
(The efficiency of O2 as a third body collider is generally very
similar to that of N2.) The expression generally used for this
purpose is30
Figure 3. Plots of k′, the Cl(2PJ) pseudo-first-order decay rate, versus
C2Cl4 concentration as a function of pressure for data obtained at T )
297 K. The solid lines are obtained from linear least-squares analyses,
and the resulting rate coefficients, i.e., the slopes of the plots, are listed
in Table 1.
where
A ) k1,0(T)[N2] ) k1,0(300 K)(T/300)-n[N2]
(III)
B ) k1,∞(T) ) k1,∞(300 K)(T/300)-m
Fc ) 0.6
(IV)
(V)
In the above expression, k1,0 and k1,∞ are approximations to the
low- and high-pressure limit rate coefficients for reaction 1, and
Fc is the “broadening parameter”. The value Fc ) 0.6 is found
to fit data for a wide variety of atmospheric reactions reasonably
2
-1
k1([N2],T) ) {A/[1 + (A/B)]}Fc{1+[log(A/B)] }
(II)

Kinetics of the Cl(2PJ) + C2Cl4 Association Reaction
J. Phys. Chem., Vol. 100, No. 2, 1996 683
Figure 4. Falloff curves for the reaction Cl(2PJ) + C2Cl4 + N2 f
C2Cl5 + N2 at T ) 231, 260, and 297 K. Solid lines are best fits of the
complete data set to eq II.
Figure 5. Typical Cl(2PJ) temporal profiles observed at T > 330 K.
Experimental conditions: T ) 360 K; P ) 100 Torr; M ) N2; [Cl2] )
7.3 × 1012 molecules cm-3; [Cl]0 ) 1.3 × 1011 atoms cm-3; [C2Cl4] in
units of 1014 molecules cm-3 ) (A) 1.89, (B) 3.90, and (C) 11.2; number
of laser shots averaged ) (A) 30 000, (B) 30 000, and (C) 40 000.
Solid lines are obtained from nonlinear least-squares fits to eq VI. Best
fit parameters, i.e., λ1, λ2, and Q, are summarized in Table 2. For the
sake of clarity, traces B and C are scaled by factors of 1.1 and 1.5,
respectively.
well,30 although in principle Fc may vary with temperature and
may be different for different reactions.31-33 Fitting our
measured values for k1([N2],T) to eq II gives the following
parameters:
k1,0(T) ) 1.40 × 10-28(T/300)-8.5 cm6 molecule-2 s-1
k1,∞(T) ) 3.97 × 10-11(T/300)-1.2 cm3 molecule-1 s-1
Observed Cl(2PJ) temporal profiles were fit to the double-
exponential eq VI using a nonlinear least-squares method to
obtain values for λ1, λ2, Q, and So. The background Cl(2PJ)
loss rate in the absence of C2Cl4, i.e., k3, was directly measured
at each temperature and pressure (see Table 2). Rearrangement
Experimental falloff data are compared with curves calculated
using the above parameters in Figure 4. The parametrization
represents the experimental data reasonably well. Variation of
the parameter Fc does not significantly improve the quality of
the fits.
of the above equations shows that the rate coefficients k1, k-1
,
and k4 can be obtained from the fit parameters and the measured
k3 using the following equations:
Kinetics at T > 330 K. At temperatures above 330 K,
chlorine atom regeneration via a secondary reaction became
evident. Under these experimental conditions, observed Cl-
(2PJ) temporal profiles were independent of laser fluence and
Cl2 concentration but varied as a function of [C2Cl4], pressure,
and temperature in the manner expected if unimolecular
decomposition of C2Cl5 was the source of regenerated Cl(2PJ).
Assuming that C2Cl5 decomposition is the source of regenerated
Cl(2PJ), the relevant kinetic scheme controlling the Cl(2PJ)
temporal profile includes not only reactions 1 and 3 but also
reactions -1 and 4:
k1 ) -(Q + k3 + λ1 + λ2)/[C2Cl4]
k4 ) (λ1λ2 - k3Q)/k1[C2Cl4]
k-1 ) Q - k4
(X)
(XI)
(XII)
Typical Cl(2PJ) temporal profiles observed in the high-
temperature experiments are shown in Figure 5 along with best
fits of each temporal profile to eq VI. The results for all high-
temperature experiments are summarized in Table 2. It is worth
noting that values for k1([N2],T) obtained from analysis of the
high-temperature data are consistent with those expected based
on extrapolation of the results from T < 300 K. We believe
that reported values for k1, even at high temperature where Cl-
(2PJ) regeneration is fast, are accurate to within (20%. Absolute
uncertainties in reported values for k-1 are somewhat more
difficult to assess. Inspection of Table 2 shows that the precision
of multiple determinations of k-1 at a particular temperature
and pressure (for varying [C2Cl4]) is quite good. An inherent
assumption in our analysis is that the only significant C2Cl5
loss process that results in chlorine atom production is reaction
-1; as long as this assumption is correct (it almost certainly
is), we believe the absolute accuracy of our reported k-1 values
is (30% over the full range of temperature and pressure
investigated.
C2Cl5 f first-order loss by processes
that do not regenerate Cl(2PJ) (4)
Assuming that all processes affecting the temporal evolution
of Cl(2PJ) and C2Cl5 are first-order or pseudo-first-order, the
rate equations for reactions 1, -1, 3, and 4 can be solved
analytically:
St/S0 ) {(Q + λ1) exp(λ1t) - (Q + λ2) ×
exp(λ2t)}/(λ1 - λ2) (VI)
where St and So are the resonance fluorescence signal levels at
times t and 0, and
Q ) k-1 + k4
(VII)
(VIII)
(IX)
Possible Secondary Chemistry Complications. The pho-
tochemical system used to study the kinetics of reactions 1 and
-1 appears to be relatively free of complications from unwanted
side reactions. The only potential secondary reactions we are
aware of which could destroy or regenerate chlorine atoms (other
Q + k3 + k1[C2Cl4] ) -(λ1 + λ2)
k3Q + k4k1[C2Cl4] ) λ1λ2

684 J. Phys. Chem., Vol. 100, No. 2, 1996
Nicovich et al.
TABLE 2: Results of the Cl(2PJ) + C2Cl4 T C2Cl5 + N2 Equilibration Kinetics Experimentsa
T
P
[Cl2]
[Cl]t)0
[C2Cl4]
Q
-λ1
-λ2
k3
k4
k1
k-1
Kp
332
25
83
83
83
83
87
87
87
87
61
61
61
61
61
61
61
57
57
57
57
48
48
74
48
48
48
48
48
74
57
210
210
57
110
57
70
70
70
90
73
73
90
73
68
68
68
83
83
83
83
73
73
75
75
75
75
210
210
89
89
89
89
1.6
1.6
1.6
1.6
1.7
1.7
1.7
1.7
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.7
0.7
0.7
0.7
0.7
0.7
1.3
0.7
0.7
0.7
0.7
0.7
1.3
0.9
0.7
3.2
0.9
0.7
0.9
1.0
1.0
1.0
1.7
1.3
1.3
1.7
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.0
1.0
1.2
1.2
1.2
1.2
3.6
0.9
1.0
1.0
1.0
1.0
1390
2650
4480
6950
1190
2500
3920
6770
496
469
484
83
86
2130
3670
5670
8910
3260
5370
8420
14100
802
1130
1240
1290
1960
2410
2490
829
187
187
187
187
85
57
11.2
11.6
11.3
12.0
20.2
18.5
19.3
19.5
411
411
60.3
62.4
60.7
62.9
58.1
62.7
56.7
53.9
29.6
33.0
34.5
33.4
36.4
34.3
32.8
27.4
30.2
29.2
33.2
34.3
34.8
31.7
34.6
34.0
34.9
36.7
35.7
32.9
14.5
14.7
14.3
15.9
15.5
14.1
73
122
124
100
38
534
127
127
96
412
544
420
334
340
100
864
764
689
44
85
651
869
116
217
109
170
175
162
185
187
245
93
85
85
119
225
-63
10
93
37
750
1020
327
795
6.5
319
444
319
444
444
444
319
188
188
188
188
88
5.34
390
682
424
6.33
6.61
5.93
5.73
5.42
5.50
8.32
9.00
9.06
414
890
984
506
414
420
383
2160
3080
3310
238
467
127
141
230
-188
-15
-25
90
340
482
341
592
362
340
340
25
536
655
648
628
83
39
1320
2200
5180
2050
2860
3210
3470
3350
3440
4340
4940
6720
2950
4640
4790
4750
4780
10700
3870
5930
10500
5460
6200
9280
13200
21500
6080
9350
11000
11100
13500
18700
30700
7760
13700
11800
14800
18700
21300
20300
21700
10700
19000
20000
22600
643
1550
4230
452
645
669
757
103
82
10.3
668
100
1220
1150
1270
1210
1150
1110
1120
1150
1220
2150
2130
2300
2070
2110
2550
2040
2020
2070
3780
3560
3570
4050
4120
3230
3270
3050
6800
6240
6490
7010
4340
5110
9820
9690
11500
10700
9630
10500
7860
8330
8260
8660
74
18.2
17.7
17.7
17.6
18.3
17.2
18.1
17.9
17.7
14.8
15.1
15.2
15.8
15.7
15.9
1150
1090
1200
1100
1160
1060
1070
1080
1160
2150
2150
2230
2080
2130
2370
1940
1950
1970
3870
3550
3550
4030
3860
3200
3220
3070
6780
6210
6380
6630
4370
4990
9730
9720
11300
10600
9630
10400
7710
8120
8170
8380
955
71
88
60
1070
1220
1240
1340
1760
2110
3040
529
83
116
88
63
64
55
66
88
52
61
88
49
62
88
53
72
88
67
73
116
61
64
350
100
44
1
1630
1640
1670
1670
5190
2120
4920
10700
1110
1890
3900
6290
11200
4010
8440
11200
2910
5780
8420
15100
6060
12700
2200
5060
6280
9920
10800
10900
6000
21400
24100
27000
17
61
-21
70
66
61
19
61
-13
-21
178
103
73
94
-89
2
15
61
152
126
98
61
360
360
25
148
148
148
166
92
8.53
7.84
7.88
8.96
8.20
8.13
7.71
7.92
8.34
7.31
8.25
4.29
4.37
4.53
4.30
3.99
4.53
4.76
2.42
2.60
1.79
2.01
1.96
1.95
1.99
1.91
1.14
1.15
1.12
1.16
104
88
100
14.6
53
13.8
14.5
14.5
15.6
43
92
166
92
14
23
265
30
54
67
233
129
111
50
370
370
25
217
217
217
87
6.92
7.08
7.01
-15
100
61
56
104
319
99
147
78
40
124
78
54
117
174
203
128
242
20
14.7
87
30
12.5
14.6
15.9
87
113
384
-28
117
90
87
380
380
25
199
199
75
5.48
6.72
9.04
10.1
11.5
10.7
9.91
10.3
4.68
4.97
4.85
5.18
100
75
101
75
75
75
184
184
184
184
-26
158
81
0
156
146
218
88
390
25
278
a Units: T (K); P (Torr); concentrations (1011 molecules cm-3); Q, λ1, λ2, k3, k4, k-1 (s-1); k1 (10-12 cm3 molecule-1 s-1); Kp (104 atm-1).
than reaction -1, of course) are the following:
Cl(2PJ) + C2Cl5 f Cl2 + C2Cl4
not be an important Cl(2PJ) removal process even if the rate
coefficient were gas kinetic. Experimentally, the fact that
observed kinetics were unaffected by significant variations in
[Cl]0 confirms that reaction 5 did not contribute significantly
to Cl(2PJ) removal. The only kinetics studies of reaction 6
reported in the literature involved competitive chlorination
studies where kinetic information was derived by fitting
observed product distributions to a complex chemical mecha-
nism;10,34 these studies, while indirect, suggest that k6 is much
too slow for reaction 6 to be a significant interference.
Experimentally, we found that observed kinetics were unaffected
(5a)
9
M8 C2Cl6
C2Cl5 + Cl2 f C2Cl6 + Cl(2PJ)
(5b)
(6)
The concentrations of photochemically generated radicals
employed in this study, i.e., e3 × 1011 cm-3, were sufficiently
small that a radical-radical interaction such as reaction 5 could

Kinetics of the Cl(2PJ) + C2Cl4 Association Reaction
J. Phys. Chem., Vol. 100, No. 2, 1996 685
Figure 7. Structure for C2Cl4 and C2Cl5 derived from ab initio
calculations at the Becke3LYP/6-31+G(d) level as discussed in the
text. Bond lengths and bond angles shown in parentheses are at the
MP2/6-31+G(d) level of theory and values for C2Cl4 in square brackets
are recommendations from the JANAF tables (ref 46).
Since experimental data concerning the structure of C2Cl5
are not available, ab initio calculations have been carried out
for this species. The calculations employed density functional
theory35-37 as implemented in the GAUSSIAN 92/DFT program
system.38 With an appropriate choice of gradient correction and
a modest basis set, DFT has been shown to frequently give
results of near chemical quality.39-44 In addition, spin con-
tamination does not seem to be as serious for DFT compared
to Hartree-Fock (HF) theory.45 Becke3LYP, which seems to
be a good choice of exchange and correlational functional, has
been used with the 6-31+G(d) basis set to optimize geometries
for C2Cl5. Vibrational frequencies have been calculated with
the same method. The results for C2Cl4 can be compared with
experiment to lend credibility to the approach while the results
for C2Cl5 can be employed to compute its absolute entropy as
well as heat capacity corrections. As a check on the DFT
results, MP2/6-31+G(d) optimizations were also carried out for
C2Cl4 and C2Cl5. Only small differences in the geometries were
noted. Since the DFT results were closer to experiment for
C2Cl4, the DFT geometries and frequencies for C2Cl5 were used
in the third-law analysis.
Figure 6. van’t Hoff plot for the reaction Cl + C2Cl4 T C2Cl5. The
solid line is obtained from a linear least-squares analysis and gives the
second-law thermochemical parameters for the reaction (see Table 4).
Different symbols indicate data obtained at different total pressures.
by significant variations in Cl2 concentration, thus confirming
that reaction 6 played no role in controlling observed Cl(2PJ)
temporal profiles.
C2Cl5 Thermochemistry: Second-Law Analysis. The
equilibrium constants, Kp, given in Table 2 are computed from
the relationship
Kp ) k1/k-1RT ) Kc/RT
(XIII)
Use of eq XIII involves making the assumption that reaction
-1 is truly the reverse of reaction 1, i.e., that the products of
reaction -1 do not contain substantial internal excitation. If,
for example, reaction -1 resulted in production of predomi-
nantly Cl(2P1/2), it would be inappropriate to use the ratio k1/
k-1 as a basis for evaluating the thermochemistry of reaction 1.
While it seems reasonable to assume that energy is distributed
statistically in the translational and internal degrees of freedom
of the C2Cl4 and Cl(2PJ) products of reaction -1, it should be
kept in mind that there presently exists no experimental
verification that this assumption is correct.
Two distinctly different Cl(2PJ)-C2Cl4 adducts are possible.
A chlorine atom could add symmetrically to Cl2CdCCl2 to form
a π-complex or a three-membered ring with unpaired spin
density on chlorine. Alternatively, a chlorine atom could add
unsymmetrically to form a σ-complex with unpaired spin density
on the â-carbon. Our calculations predict that the most stable
form for C2Cl5 is the haloalkyl radical CCl3CCl2, i.e., the
σ-complex. Calculated structures for C2Cl4 and C2Cl5 are shown
Assuming that Kp can be computed from the ratio of measured
values for k1 and k-1, a van’t Hoff plot, i.e., a plot of ln Kp
versus T-1, can be constructed; such a plot is shown in Figure
6. Since
in Figure 7. For comparison, experimental bond lengths and
46
bond angle for C2Cl4
are also shown in Figure 7; the
calculated structure of C2Cl4 is in good agreement with
experiment.
ln Kp ) (∆S/R) - (∆H/RT)
(XIV)
To carry out the third-law analysis, absolute entropies as a
function of temperature were obtained from the JANAF tables46
for Cl(2PJ), calculated using vibrational frequencies and mo-
ments of inertia taken from the JANAF tables for C2Cl4,47 and
calculated using the moments of inertia and vibrational frequen-
cies in Table 3 for C2Cl5. The moments of inertia in Table 3
were computed using the C2Cl5 structure shown in Figure 7.
The vibrational frequencies in Table 3 were calculated using
the approach described above. Because calculated vibrational
frequencies for C2Cl4 are very close to those given in the JANAF
tables,46 no scaling of the C2Cl5 frequencies is deemed neces-
sary. At 360 K, the third-law analysis gives the results ∆H )
the enthalpy change associated with reaction 1 is obtained from
the slope of the van’t Hoff plot while the entropy change is
obtained from the intercept. At 360 K, the midpoint of the
experimental T-1 range, this “second-law analysis” gives the
results ∆H ) -17.5 ( 0.6 kcal mol-1 and ∆S ) -26.1 ( 1.8
cal mol-1 K-1, where the errors are 2σ and represent precision
only.
C2Cl5 Thermochemistry: Third-Law Analysis. In addition
to the second-law analysis described above, we have also carried
out a third-law analysis, where the experimental value of Kp at
360 K (79 800 ( 8000 atm-1) has been employed in conjunction
with a calculated entropy change to determine ∆H.
-18.6 ( 0.5 kcal mol-1 and ∆S ) -29.3 ( 1.0 cal mol-1 K-1
;

686 J. Phys. Chem., Vol. 100, No. 2, 1996
Nicovich et al.
6-311+G(3df) (using the DFT geometry) and 20.3 kcal mol-1
at PMP2/6-311+G(3df) (using the MP2 geometry). While the
spin-projected PMP2 value is in reasonable agreement with
experiment, the DFT value is several kcal mo1-1 too small. It
appears that the DFT method calculates the relative strength of
the C-C π bond to be too strong relative to the Cl-C σ bond.
In a very recent assessment of computational methods for
calculating radical addition reactions to alkenes, Wong and
Radom found that addition enthalpies may be too positive by
DFT by as much as 10 kcal mol-1 when compared to QCISD
results.48 In light of their work, the underestimation of the Cl-C
bond energy by DFT is not unexpected.
TABLE 3: Summary of Parameters Used in Calculations of
Absolute Entropies and Heat Capacity Corrections
a
species ν (cm-1
)
σ
IABC (amu3Å6) g0 g1 ∆ꢀ (cm-1
)
Cl
C2Cl4
4
1
2
882.36
1571
1000
918
777
512
447
347
324
288
235
176
110
1124
942
782
721
624
447
406
342
327
264
233
231
173
129
39
4
7.50 × 107
Comparison with Previous Research. Although this study
represents the first systematic investigation of the temperature
and pressure dependence of k1, there are several published
measurements with which our results can be compared. Davis
et al.,14 in one of the pioneering applications of the flash
photolysis-resonance fluorescence technique, measured k1 at
298 K in helium buffer gas; they reported rate coefficients of
4.8 × 10-12 and 6.10 × 10-12 cm3 molecule-1 s-1 at pressures
of 15 and 100 Torr, respectively. The magnitude of Davis et
al.’s rate coefficients seems a little low compared to values one
might expect based on our measurements in N2 buffer gas, and
the ratio k1(100 Torr of He)/k1(15 Torr of He) ) 1.25 obtained
from Davis et al.’s results is smaller than one would predict
based on the 297 K falloff curve we have obtained using N2 as
the buffer gas (Figure 4). Breitbarth and Rottmayer have
employed a discharge flow system with an EPR detector to study
the kinetics of the O(3PJ) + C2Cl4 reaction at 298 K and 0.3
Torr total pressure in O2 buffer gas.15 They observed that Cl-
(2PJ) was produced as a reaction product and, by following the
temporal evolution of both O(3PJ) and Cl(2PJ), extracted a value
of 3 × 10-13 cm3 molecule-1 s-1 for k1; this value is slower
than one would predict from extrapolation of our 297 K falloff
curve down to P ) 0.3 Torr under the assumption that N2 and
O2 are equally efficient as third body colliders. In addition to
the two “direct” studies discussed above, there have been a
number of competitive kinetics studies of reaction 1, 9-13,16 two
of which 13,16 report results where meaningful comparisons can
be made with our results. Franklin et al. employed CW
photolysis of Cl2 in conjunction with gas chromatographic
detection of C2Cl4; they employed the reference reactants C2H6
and CH2ClCH2Cl to measure the ratios k7/k1 ) 0.0295 at 310
K and k8/k1 ) 1.66 at 348 K.
C2Cl5
6
1.76 × 108
2
a ∆ꢀ ≡ assumed energy splitting between lowest two electronic states.
C2Cl4 has no low-lying excited electronic states, and C2Cl5 is assumed
to have none.
TABLE 4: Thermochemical Parameters for the Reaction
a
Cl(2PJ) + C2Cl4 f C2Cl5
T
method
-∆H
-∆S
∆H°f,T(C2Cl5)b
360
2nd law
3rd law
2nd law
3rd law
2nd law
3rd law
17.5 ( 0.6
18.6 ( 0.5
17.5 ( 0.7
18.7 ( 0.6
17.1 ( 0.8
18.2 ( 0.7
26.1 ( 1.8
29.3 ( 1.0
26.2 ( 1.9
29.4 ( 1.0
298
0
8.5 ( 0.8
7.4 ( 0.7
8.7 ( 0.9
7.5 ( 0.8
a Units: T (K); ∆H, ∆H°f,T(C2Cl5) (kcal mol-1); ∆S (cal mol-1 K-1).
b Calculated using values for ∆H°f,T(Cl) and ∆H°f,T(C2Cl4) taken from
ref 46.
the uncertainties we report reflect an estimate of the uncertainties
introduced by our imperfect knowledge of the input data needed
to calculate absolute entropies (the low frequency vibrations of
C2Cl5 are most significant) as well as our estimated uncertainty
in the experimental value for Kp(360 K).
Cl(2PJ) + CH2ClCH2Cl f HCl + CHClCH2Cl (7)
Cl(2PJ) + C2H6 f HCl + C2H5
(8)
Summary of Thermochemical Results. The thermochemi-
cal results of this study are summarized in Table 4. Appropriate
heat capacity corrections have been employed to obtain ∆H
values at 298 and 0 K. Using literature values46 for the heats
of formation of Cl(2PJ) and C2Cl4 at 298 and 0 K allows the
heat of formation of C2Cl5 to be evaluated. As can be seen
from Table 4, the agreement between the second- and third-
law results is not perfect. Since the uncertainties in the ∆Hf,T(C2-
Cl5) values obtained by the two methods are about the same, it
seems appropriate to report simple averages of the second- and
third-law values, while adjusting reported uncertainties to
encompass the 2σ error limits of both determinations. Using
this approach, we report ∆H°f,298(C2Cl5) ) 8.0 ( 1.3 kcal mol-1
and ∆H°f,0(C2Cl5) ) 8.1 ( 1.5 kcal mol-1. The Cl-C bond
energy can also be directly calculated from theory, where single-
point energies are determined with an expanded basis set and
zero-point corrections are made with DFT frequencies. The
predicted bond energy at 0 K is 14.2 kcal mol-1 at Becke3LYP/
Assuming k7(310 K) ) 1.7 × 10-12 cm3 molecule-1 s-1 49 and
k8(348 K) ) 5.9 × 10-11 cm3 molecule-1 s-1 30
,
Franklin et
al.’s data give k1(310 K) ) 5.8 × 10-11 cm3 molecule-1 s-1
and k1(348 K) ) 3.6 × 10-11 cm3 molecule-1 s-1; these rate
coefficients are not quantitatively consistent with each other but
are in approximate agreement with the values expected based
on our data, given the more efficient third-body colliders
employed in the Franklin et al. study.50 Atkinson and Aschmann
have also employed CW photolysis of Cl2 in conjunction with
gas chromatographic detection of C2Cl4 and ethylene to measure
k9/k1 ) 2.56 at 298 K in 735 Torr of air.
Cl(2PJ) + C2H5 + M f CH2ClCH2 + M
(9)
Assuming k9(298 K, 735 Torr of air) ) 1.040 × 10-10 cm3
30
molecule-1 s-1
,
the Atkinson and Aschmann16 data give k1-
(298 K, 735 Torr of air) ) 4.1 × 10-11 cm3 molecule-1 s-1
;

Kinetics of the Cl(2PJ) + C2Cl4 Association Reaction
J. Phys. Chem., Vol. 100, No. 2, 1996 687
Interestingly, Cl(2PJ) reacts much more rapidly with C2Cl4 than
with C2H4 in the low-pressure limit, but much more rapidly
with C2H4 than with C2Cl4 in the high-pressure limit. This
interesting reactivity pattern can be rationalized in terms of the
simple Lindemann-Hinshelwood mechanism,54,55 where reac-
tion 1, for example, proceeds via the following three-step
process:
Cl(2PJ) + C2Cl4 f C2Cl5*
(1a)
C2Cl5* f Cl(2PJ) + C2Cl4
C2Cl5* + M f C2Cl5 + M
(1b)
(1c)
If one makes the steady state approximation for the energized
adduct, C2Cl5*, the low- and high-pressure limit rate coefficients
are obtained as k1,0 ) k1ak1c/k1b and k1,∞ ) k1a. The fact that
k9,∞ > k1,∞ implies that Cl(2PJ) adds more rapidly to C2H4 than
to C2Cl4 to form the energized species C2H5-nCln*; this seems
reasonable since the four chlorine atoms in C2Cl4 would be
expected to sterically hinder approach of Cl(2PJ) to a carbon
atom. The fact that k9,0 < k1,0 also seems reasonable since
collisional deactivation of C2H5-nCln* would be expected to
be more efficient for C2Cl5* than for C2H4Cl* due to the much
higher density of states in C2Cl5*.
Figure 8. Falloff curves (298 K) for reactions of Cl(2PJ) with C2Cl4
and C2H4. The C2Cl4 curve is calculated from falloff parameters
determined in this study while the C2H4 curve is calculated from the
falloff parameters recommended in ref 30.
this is slightly faster than the value we report but in agreement
within combined experimental uncertainties.
Franklin et al.13 in their competitive kinetics studies (described
above) derived the following relationship from their data: log-
(k-1/k1k6) ) 4.90-10650/4.576T mol2 L-2 s. They used their
determinations of k1 in conjunction with the measurements of
34
k6(T) reported by Dusdeil et al. to obtain values for k-1(T).
Implications for Atmospheric Chemistry. The results
reported in this paper confirm that C2Cl4 reacts with Cl(2PJ)
several hundred times faster than with OH under atmospheric
conditions. Hence, in selected atmospheric environments such
as the marine boundary layer, where Cl(2PJ) levels appear to
be particularly high,17-19 reaction with Cl(2PJ) will be the
dominant atmospheric removal mechanism for C2Cl4. In
addition, C2Cl4 is being employed as a “tracer” for analyzing
the potential importance of chlorine atoms as an oxidant in the
free troposphere;56 the temperature- and pressure-dependent
values for k1(T,P) reported in this study are useful for making
such an analysis as quantitative as possible.
Franklin et al.’s values, when corrected for updated information
about k7(T) and k8(T), give values for k-1(T) which are somewhat
faster than the values we report. A more quantitative compari-
son does not appear to be worthwhile because (a) the Arrhenius
expression for k6(T) is highly uncertain,10,34 (b) Franklin et al.
report k-1 to be pressure independent while we find k-1 to be
pressure dependent (Table 2), and (c) as mentioned above,
Franklin et al. employed more efficient third-body colliders (C2-
Cl4, Cl2, C2H6, CH2ClCH2Cl, CO2, and SF6) in their study than
we did in ours (N2). From their evaluations of k1 and k-1 at
two temperatures, Franklin et al. derived ∆H ) -16.9 ( 1.0
kcal mol-1, i.e., somewhat higher than the value we report but
in agreement within combined experimental uncertainties. (We
believe the uncertainty in the Franklin et al. determination of
∆H is actually considerably larger than their published estimate
Acknowledgment. The experimental component of this
research was supported by the National Aeronautics and Space
Administration, Upper Atmosphere Research Program, through
Grant NAGW-1001 to Georgia Institute of Technology. Com-
puter time for this study was made available by the Alabama
Supercomputer Network and the NSF-supported Pittsburgh
Supercomputer Center. We thank C. A. Piety for helping with
some of the experiments.
13
of (1.0 kcal mol-1.)
The best fit value for the parameter n (describing the
temperature dependence of k1,0) obtained in this study, i.e., n
) 8.5, is larger than is typically found for association reactions
of atmospheric interest.30 Recommended values of n for 62
atmospheric association reactions range from 0.0 to 6.7, with
the largest values found for the CF2ClO2 + NO2 and CCl3 +
O2 reactions.30 Interestingly, both CF2ClO2NO2 and CCl3O2
are relatively weakly bound species, with bond strengths only
a few kcal mol-1 stronger51,52 than that of C2Cl5. While the
results reported in this paper clearly demonstrate that k1 increases
significantly with decreasing temperature, the value of n is rather
uncertain because no data were obtained at pressures anywhere
near the low-pressure limit. As a result, extrapolation of our
results outside of the experimental temperature regime should
be carried out with caution.
References and Notes
(1) Wiedmann, T. O.; Guthner, B.; Class, T. J.; Ballschmiter, K.
EnViron. Sci. Technol. 1994, 28, 2321.
(2) Franklin, J. Toxicol. EnViron. Chem. 1994, 46, 169.
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1995, 22, 1097.
(4) Singh, H. B. In Composition, Chemistry, and Climate of the
Atmosphere; Singh, H. B., Ed.; Van Nostrand Reinhold: New York, 1995;
pp 216-250.
(5) Winer, A. M.; Lloyd, A. C.; Darnall, K. R.; Pitts, J. N., Jr. J. Phys.
Chem. 1976, 80, 1635.
(6) Howard, C. J. J. Chem. Phys. 1976, 65, 4771.
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(8) Kirchner, J.; Helf, D.; Ott, P.; Vogt, S. Ber. Bunsen-Ges. Phys.
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(9) Goldfinger, P.; Jeunehomme, M.; Martens, G. J. Chem. Phys. 1958,
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(10) Ayscough, P. B.; Cocker, A. J.; Dainton, F. S.; Hirst, S.; Weston,
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(11) Goldfinger, P.; Huybrechts, G.; Martens, G. Trans. Faraday Soc.
1961, 57, 2210.
The 298 K falloff curves for Cl(2PJ) reactions with C2H4 and
C2Cl4 over the pressure range 1-10 000 Torr of N2 are
compared in Figure 8. The C2Cl4 curve is based on the falloff
parameters determined in this study while the C2H4 curve is
calculated from the falloff parameters recommended by the
NASA panel for chemical kinetics and photochemical data
evaluation,30 which are based on the experimental data of
Wallington et al.53 over the pressure range 10-3000 Torr.
(12) Knox, J.; Waugh, K. C. Trans. Faraday Soc. 1969, 65, 1585.

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(13) Franklin, J. A.; Huybrechts, G.; Cillien, C. Trans. Faraday Soc.
1969, 65, 2094.
(14) Davis, D. D.; Braun, W.; Bass, A. M. Int. J. Chem. Kinet. 1970, 2,
101.
M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley,
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(15) Breitbarth, F.-W.; Rottmayer, S. Plasma Chem. Plasma Proc. 1986,
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(16) Atkinson, R.; Aschmann, S. M. Int. J. Chem. Kinet. 1987, 19, 1097.
(17) Jobson, B. T.; Niki, H.; Yokouchi, Y.; Bottenheim, J.; Hopper, F.;
Leaitch, R. J. Geophys. Res. 1994, 99, 25355.
(40) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
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Phys. Lett. 1992, 197, 499.
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