7970
J. Phys. Chem. 1993,97, 7970-7977
A Diode Laser Study of the C1 + CzHs Reaction M. Matti Maricq,' Joseph J. Szente, and E. W. Kaiser Research Laboratory, Ford Motor Company, P.O. Box 2053, Drop 3083/SRL, Dearborn, Michigan 481 21 Received: March 22, 1993; In Final Form: May 14, 1993
Real time I R absorption measurements of the formation of C2H4 and HCl following the C1 initiated chain reaction between chlorine and ethane are presented. The ethylene molecules, formed by the reaction between chlorine atoms and ethyl radicals, are born highly vibrationally excited and are only slowly relaxed in a Nz bath gas. The addition of CZF6 provides efficient vibrational relaxation and reveals a very fast rise in the ethylene concentration. The measured C1+ CzH5 rare constant is k3(295 K) = (2.9 f 0.6) X 1&l0 cm3 s-l and resolves a discrepancy of a factor of 20 in previous reports of this rate constant. Measurements of the HCl concentration reveal a relatively short chain length under conditions for which the steady-state C1 and CzHs concentrations are comparable. Fits of the [HCl] time dependence yield a value of k3 = (3.4 f 0.6) X 10-lO cm3 s-1 for the C1 CzH5 rate constant, in agreement with the value derived from the formation of CzH4. We have also measured the rate constant for the addition of chlorine atoms to ethylene and find that k6 = (1.4 f 0.2) X l & l l and (3.5 f 0.7) X 10-11 cm3 s-l respectively at 30 and 120 Torr total pressure and 295 K, in good agreement with literature values.
+
I. Introduction The importance of chain reactions, particularly those involving chlorine, is made abundantly clear by the catalytic destruction of stratospheric ozone and the formation of the antarctic ozone hole.' The combustion of organic molecules in the presence of chlorine, during incineration for example, is another application in which chain reactions likely play an important role. An apparently simple, but very general, chain reaction involves the chlorination of alkanes; that is, C1+ R H -,R
R + C1,
-
+ HC1
C1+ RCl
Unstopped, these reactions would continue until the supply of available hydrocarbonsor chlorine is exhausted. However, there are numerous chain termination reactions such as C1 R products and R R' products which limit chain propagation. The present paper examines one such termination reaction and the effect that it has on the chain reaction, namely, when R is C2H5. While the chain propagation steps,
+
-
+
+
C1+ C2H6-,C2H5 HCl CZH5
+ C1,
-
AH = -19.7 kJ/mol (1)
AH = -99.6 kJ/mol
C1+ C,H,Cl
-
(2)
have been studied previously by many groups,2-9 only two measurements of the reaction rate constant for
+ HCl
AH = -269 kJ/mol (3) have been reported,'^^ and these differ by a factor of 20. The present measurements, based on the rate of ethylene formation, indicate that the reaction proceeds rapidly and is an effective inhibitor of the chain reaction. Reaction 3 is also interesting from a different perspective. It can proceed via one of two pathways: direct abstraction of a hydrogen atom by C1 or addition/elimination through an ethyl chloride intermediate. A considerable effort has been made to resolve this question in the analogous "light atom" situation of C1+ C2H5 -,C,H,
+
-+
H 'RF R HF with R representing, for example, CF2 or C2H4. The HF(v) infrared emission measurements of Arunan et a1.10 reveal a 0022-3654/93/2097-7970$04.00/0
monotonic decreasein population with increasing vibrationallevel, indicative of an addition/elimination reaction. Abstraction reactions, in contrast, lead to inverted vibrational distributions.11 Tsai and McFadden,'2 while pointing out that direct fluorine atom abstractionis often accompanied by large activationbarriers, suggest based on their kinetic data that this is the preferred pathway for H atom reactions with CF3, CF2, and C F radicals. Leone and co-workers13J4have extendedthe question of addition/ elimination versus the abstraction pathway to heavy atom reactions. For the C1+ C ~ Hreaction S they have measured timeresolved FTIR emission spectra of HCl(u) formed in vibrationally excited states with u = 1-4. As with the H F measurements of Arunan et a1.,*0they find the excited-state population to decrease monotonically with increasing vibrational quantum number, suggestingthat addition/elimination is the preferred mechanism. In this paper, we measure the rate constant for the C1+ C2Hs reaction by transient infrared absorption of the ethylene and hydrogen chloride produced via reactions 1-3. Both measurements support the value for ko reported previously by Kaiser et al.9 The C2H4 measurements reveal that, like HCl, the ethylene is formed with a large amount of vibrational excitation. The rate constant is nearly temperature independent between 218 and 295 K, indicating a very small activation energy. When combined with the data of ref 9, the reaction also appears to be independent of pressure over a range of 30-760 Torr. The paper is divided as follows. Section I1 describes the apparatus used for the transient IR measurements and the procedure used to determine the transient changes in C2H4 and HCl concentrations. Section I11 presents the experimentalresults for reaction 3 and for the addition of chlorine atoms to ethylene. A discussion of the kinetic measurements is presented in section IV.
II. Experimental Section The transient IR absorption measurements of C2H4 and HCl described in this paper were made using the apparatus shown in Figure 1. A C12/C2Hs/C2Fs/N2 gas mixture is flowed through a jacketed and foam-insulated fused-silica cell measuring 3.2 cm in diameter by 51 cm in length. The unfocused output from a Lambda Physik LPX-300excimer laser operating at 351 nm is directed longitudinally through the cell. The ensuing flash photolysis of chlorinemolecules initiates a chain reaction involving chlorine and ethane which produces, among other products, HCl 0 1993 American Chemical Society
Study of the C1
+ C2H5 Reaction 2 . 5 ,
.
.
~
.
.
‘
.
r
.
’
.
*
.
’
.
”
’
’
“
,
0.34 t o r r .
C,H,
#ii=949.52
Wavenumber (cm
Figure 1. Schematic diagram of the UV photolysis/transient IR
absorption apparatus. and C2H4. A 30-ns, 400-mJ, photolysis pulse, having a cross section of approximately 2 cm X 1.2 cm, produces approximately 8 X lOI4 ~ m of- chlorine ~ atoms in a gas mixture containing 0.5 Torr of Cl2. The formation of C2H4 and HCl was monitored in real time by recording the transient change in light intensity of the infrared diode laser beam which counterpropagates through the cell. The infrared radiation is obtained from lead salt diodes using a Laser Analytics diode laser systemconsisting of a coldhead, temperature and current controllers, and optical chassis. The light passes through the reaction cell and a monochromator before impinging upon a HgCdTe detector, the output of which is amplified and recorded by a Data Precision 6000 transient recorder. The monochromator provides mode selection and reduces stray light, such as fluorescencefrom various optical elements in the excimer laser beam path. Apertures in front of and after the cell constrain the probe beam to lie within the volume traced by the photolysis beam. The specified response time of the HgCdTe detector is 200 ns. This was verified in two ways: by examining the rise time of the response to scattered light from a 10-ns Nd:YAG laser pulse at 1.06 pm and by observing the [HCl] rise time followingphotolysis of a mixture of C12/C&/02/N2 containing 2.5 Torr of C2H6, which is predicted to have a half-life of 150 ns. The detector also has a low-frequency cutoff whereby, following a step function change in light intensity, the output of the HgCdTe detector decays to zero with a rate constant of kdct = 600 s-l. This decay is taken into acount when modeling the transient C2H4 or HC1 concentration change. Frequency drift is prevented during signal averaging (typically 10&256 transients at a repetition rate of -0.6 s-l) by frequency locking the laser radiation to the vibration-rotation absorption line being monitored. The laser output is frequency modulated at approximately 8 kHz about the center frequency of the absorption line, ideally with a modulation depth small compared to the line width. A portion of the beam is split off and directed through the reference gas cell. The output of the lock-in detected signal, operating in first derivative mode, is then fed back into the laser diode injection current to lock the output frequency to the particular absorption feature. Mechanically induced laser frequency jitter, associated with the compressor piston of the closed cycle refrigerator, is reduced by the method of Sams and Fried.Is A piezoelectric transducer is used to detect the shocks which occur at the maximum and minimum extents of travel of the piston, which occur at 6 Hz. A counter selects one of N (typically N = 10) of these shock pulses. A delay from this point is set to allow the vibrations to subside, and the photolysis laser is then triggered. A photodiode detects the scattered excimer radiation and triggers the transient digitizer.
-1
)
Figure 2. A portion of the v7 Q-branch of ethylene at 949 cm-l. Arrows mark the transitions used to monitor the ethylene concentration.
TABLE I line
Ethylene v7 Cross Section PT [C&] no.of (Torr) (Torr) meas
temp
no.
(K)
i i i i i i i i i ii ii ii
295 295 295 295 295 253 253 218 218 295 295 295
30 35 30 128 326 30 29 30 30 30 125 324
0 0 30 0 0 0 29 0 14-30 0 0 0
6 5 1 5 2 1 1 3
3 4 4 2
0.099 0.104 0.096 0.045 0.026 0.108 0.096 0.096 0.086 0.083 0.030 0.018
Approximate H W I R(2) Cross Section PT (Torr)
temp (K) 29 5 295
31 127
SD
u(#)
0.0059 0.0092 0.0019 0.0021 0.0106 0.0030 0.0065 0.0042 0.0021
u (A21
0.i 1 0.04
The transient decrease in IR light intensity observed following Cl2 photolysis often shows a small “spike” over the first few microseconds arising fromscattered light and/or electrical pickup. This is usually very reproducible and can readily be subtracted out. The result is converted to a C2H4, or HCl, concentration vs time profile using Beer’s law,
Because the output of the HgCdTe detector is AC coupled, the infrared light intensity through the gas mixture prior to the photolysis pulse, Ib, must be added to the transient intensity change before ratioing it with the reference probe laser intensity, IO. Absolute values for both I b and IOwere determined by amplitude modulating the laser radiation at 400 Hz by a mechanicalchopper and measuring the response of the HgCdTe detector. Both were measured using the same optical path and cell as used for the transient measurements. Because of their temperature and pressure dependence,the IR cross sections needed in eq 4 were measured as a part of this study. Ethylenewas monitored by one of two lines in the Q-branch of the v7(blu)out-of-plane bending vibration16J7centered at 949 cm-1. A portion of the spectrum is shown in Figure 2, and the two lines used to monitor C2H4 are indicated. Their IR cross sections, measured by modulating the light source and using the same optical path as for the transient measurements, but with a staticethylenegas mixture, arelisted in Table I. Thesubstitution of moderate amounts of CzF6 for N2 did not have a significant effect on the absorption intensity at a given total pressure.
7972 The Journal of Physical Chemistry, Vol. 97, No. 30, 1993
M a r i q et al.
TABLE Ik Chlorine plus Ethane Chain Reaction Mechanism reaction 1. C1+ C2H6 C2H5 + HC1 2. C2H5 + C12 C1+ CzH5C1 3. C1+ C2H5 C2H4 + HCl
kl k2 k3
+
+
+
6. CI + C2H4 + M
7.C2H4Cl+ C12 8. C2Hs + CzHs
+
C2H4C1+ M
C1+ CzH4C12 C2H4 + C2H6 9. C2H5 + C2H5 + M C4Hlo + M a Measured in this work. +
+
-
rate constant at 295 K = 5.7 X 10-l1 cm3 s-1 20 = 1.8 X 1W103113 s-l = (2.9 & 0.6)X 10-10
6
.
.
-
.
.
C,F,=18
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
10" om-S
torr
(1
0
+ 0, + M
.
rcli--13.6 -v
01133 s-1 a k6 = 1.2 X cm3s-l at 30 TorPS2l k6 = 3.3 X 10-11 cm3 s-1 at 120 TorPS2l k7 = 3.0 X 10-12 cm3 s-122 k8 7.0 X cm3S-I 23 ks = 1.8 X 10-11 cm3 s-123
HCl(u-0) was monitored via the R(2) transition18 of H3SCl at 2944.916 cm-1 and H3'Cl at 2942.723 cm-'. These lines are extremely narrow. Particularly at 30 Torr total pressure, the modulation depth was not small compared to the HCl line width, and stabilization of the diode laser frequency at the absorption maximum became difficult. As a result, attempts to measure HCl IR cross sections yielded unacceptably largevariations from one measurement to the next. Instead, the following alternative procedure was used to convert the transient IR absorption into a transient HCl concentration change. For each measurement of the HCl generated in the chlorine/ethane chain reaction, two correspondingexperimentswere conducted on a gas mixture with 0 2 substituted for N2 (or Ar) and the ethane concentration increased to about 2 Torr. One. recorded the formation of ethylperoxy radicals and provided a measure of the initial chlorine atom concentration (vide infra). The other recorded the rise in [HCl], which except for a 5-10% correction for residual effects of the chain reaction is equal to [ C ~ H S O ~This ] . provides an "effective" absorption coefficient for HCl with which to deduce the amount generated by the chain reaction measured in the accompanying experiment. Initial chlorine atom concentrations were measured as follows. Immediately before and/or after a transient IR measurement, the positions of kinematically mountedmirrors,at the twolocations marked by dashes in Figure 1, would be switched in order to allow UV light from a D2 lamp to probe the reaction cell. The UV light is dispersed using an Instruments SA HR320 0.32-m monochromator,with a 147 groove/" grating, and detected by a gated, intensified, diode array (Princeton Instruments IPDA700SB detector and STlOOO controller) at a specified time delay (typically 10ps) from the photolysis laser pulse. The gas mixture was altered to increase the ethane partial pressure to 2 2 Torr and to substitute approximately 10 Torr of 0 2 for an equal amount of N2 in the gas mixture. These changes to the gas mixture ensure termination of the chain reaction and rapid formation of C ~ H S via O ~reaction 1 followed by C,H,
.
+
C2HS02 M
(5) Care is taken not to alter the Cl2 and total gas pressures. The Cl2 flow is remeasured in order to account for any variation from its flow in the accompanying transient IR experiment. The ethylperoxy, and thereby initial chlorine atom, concentration is determined using the known UV absorption cross section19 of C2HsO2. In practice, a correction ( 6 % ) is applied to this measurement of [Clloin order to adjust for residual effects of the chain reaction, as determined by the kinetic model in Table 11, and for a minor loss of radicals via the reaction between C1 and C2H502. (Our preliminary results show this reaction to proceed with a rate constant of (0.5-1) X 10-10 cm3 s-1,) The majority of experimentswere run at 30 Torr total pressure, although some were performed at 120 and 300 Torr. Attempts at PT 233; however, a large part, approximately half, of the fitting error in Figure 4 arises from the systematic residual delay in the initial appearance of C2H4. As a more reasonable error estimate, one might choose values of k3 for which x2 > 233 x2dn;thus, the error estimate for the example of Figure 5 is f 0 . 5 X 10-10cm3 s-l. The same procedure was used to compute error bounds for the other entries in Table 111. In some cases, the Xzvalue exceeded the minimum for a 95% confidence; however, this was primarily becauseof the systematic deviation at short times owing to incomplete vibrationalrelaxation of the C2H4, and the fit was considered as acceptable. Also presented in Table I11 are average values and standard deviations ( u ) for k3 at each temperature. The error in the average value is the root mean average of the individual experimental 95% confidenceintervals. This error, based on the quality of the data, is consistent with the scatter of the data; namely, *0.22 versus 2 u / d n = 0.33 in units of 10-10 cm3 s-1. The procedure discussed atove and illustrated by Figure 5 addresses the random errors incurred in the determination of k3 which originatefrom the effects of diode laser fluctuations,excimer laser power fluctuations, detector noise, etc, on the transient IR absorption. There are three additional sources of errors: (1) the IR absorption cross section used to calculate C2H4 concentration, (2) initial gas composition, and (3) other parameters in the kinetic model. The IR cross sectionsused in these experiments are listed in Table I along with the standard deviations (SD)in their measurement. The (2u) error in the mean, which is given by 2SD/(no. measured)lI2,ranges from 2.5 to 8%. For the majority
+
/
k,-0
"'SJ' ,.
{
HCI born vibrationally excited
.
and relaxed by N,; k;=4.S
Expt. I1 k, unit# In 10-Locm8m-1
3
20
40
60
80
100
120
140
160
180
200
time (ps) Fipure6. Comparison of the HCl generatedby the chlorine/ethanechain reaction with model predictions. The full model consists of the reactions in Table I1 augmented by the sequential vibrational relaxation of HCl(ue1-4) by energy transfer to N2.
of experiments, which employ laser line i and PT = 30 Torr, the estimated error is 2.5%. Unfortunately, the effect of this uncertainty on k3 is amplified by about a factor of 3. Perhaps the largest uncertainty in k3 arises from the initial gas composition. Stable gas concentrations, which are reproducibly measured to within a few percent, do not present a problem. However, the best fit determination of k3 is very sensitive to [Cllo; a 5% change in its level translates to a 15% change in k3. Futhermore, the gas composition must be altered in order to measure [Cl]o using the ethylperoxy method described in section 11, and this introduces a small change in concentration of Clz and, therefore, [Cllo. Although we take thesechangesintoaccount when fitting theethylenedatafor k3, thescatterin therateconstant reported in Table I11 is likely due to residual errors in our assessment of [Cl],. In addition to this scatter, a systematic error of 15%is introduced into k3 from the 5% uncertainty in the C2H5O2 UV absorption cross section. Under the low [C2H6]/[Cl2] ratios used in these experiments, the predominant potential uncertainty in the model arises from the secondary consumption of ethylene via reaction 6. As will be discussed in section IIId, we have remeasured the rate constant under conditions essentially identical to those used in the determination of k3 and found good agreement with previously reported values.21 Varying k6 within its error bounds has less than a 10% effect on the best fit value for k3. The total error is found by combining the random error listed in Table I11 with the three uncertainties described above (15% for uUv(C2H~O~), 10% for ub(CzH4), and 10% for the model). Assuming that these are statistically independent, the total variance is the sum of the component variances; thus, the rate constant is ks(295) = (2.9 f 0.6) X cm3s-I, k3(253) = (2.4 0.7) X cm3 s-l, and k3(218) = (2.0 0.6) X 10-10 cm3 s-l, The values of k3 at 300 Torr total pressure were not used in computing k3(295) owing to the poorer signal- to noise inherent in these measurements. b. The Formation of HCI. The rate of HCl formation affords a different perspective from which to examine the C1 CzH5 reaction rate constant. In Figure 6, the data are compared to three different predictionsof the HCl concentration as a function of time. The dashed curve shows the predicted HCl formation with k3 = 0 in the model of Table 11. (The decay due to ac coupling of the detector is, however, included.) Clearly, in the absence of the chain termination due to reaction 3, the predicted HCI concentration grossly overestimates the observed levels. When k3 is set to a value slightly higher than that obtained from the ethylene formation experiments (k3 = 4.3 X 10-10cm3 s-l in the example of Figure 6), the predicted HCl levels fall dramatically (dot-dash curve), but they still overestimate the
*
*
+
Study of the C1
+ C2H5 Reaction
The Journal of Physical Chemistry, Vol. 97, No. 30, 1993 7975
data. If k3 is treated as an adjustable parameter, then values approximately 1.5-2 times larger than the ethylene determination of k3 are needed to fit the experimental HCl concentrations at long times (a value of 6.4 X 10-locm3 s-l for Figure 6). However, then the predicted rate of HC1 rise at short times is too fast. An examination of Table I1 reveals two sources of HCl: the reactionsof atomicchlorine with either ethane or the ethyl radical. The energeticsof HC1 productionvia reactions 1 and 3,however, are quite different. Reaction 1 has an exothermicity28 of A H 1 = -20 kJ/mol; thus, only the formation of vibrationally groundstate HCl is energetically allowed. In contrast, M l 3 = -270 kJ/mo1,*8 permitting the formation of HCl(u=0-7). In fact, Leone and co-workers13J4 have observed extensive HCl vibrational excitation from reaction 3, with relative populations of 1.O,
0.74,0.57,andO.25forHCl(u)withu=1,2,3,and4,respectively. The diode laser probe beam, tuned to the R(2) line of the u = 0-7 transition, monitors the population difference between the u = 0 and u = 1 levels. HCl(u>l) is transparent to the probe beam. While the relative population of HCl(u=l) has been previously reported, the population of u = 0 is unknown. An estimate can be made from a comparison to the H F vibrational distributions reported by Arunan et a1.10 for H F elimination from CH3CH2F. They observed infrared chemiluminescence from HF(u= 1-4), with relative intensities which are very close to those reportedby Seakinset al.13for HCl, and determinedthe population in u = 0 from laser gain experiments, with the result that the relative populationsof HF(u=O) and HF(u= 1) are 37.2 and 25.6, respectively. Let us assume that the HCl born from reaction 3 has the vibrational distribution reported by Seakins and Leone and that the (u= l)/(u=O) ratio is the same as observed for H F by Arunan et al.; then, in reaction 3, the probabilities for the formation of u = 0-4are 0.36,0.26,0.18,0.14, and 0.06, respectively. Because our experiments are carried out in a collision-dominated environment, the vibrational relaxation processes HCl(u)
+ N,(u=O)
-
HCl(u-1)
+ N,(u=l)
must be added to the reaction model of Table 11. The relevant energy-transfer rate constants have been measured29and tabulated.3O Upon accounting for the generation and relaxation of vibrationally excited HCl in this way and fitting the value of k3 to the experimental data, the dotted curve in Figure 6 is obtained. This fit provides an accurate representation of both the early HCl concentration rise and the eventual level that it reaches using a rate constant of 4.3 X 10-10 cm3 s-1 for reaction 3. It is interesting to note that, although at 30 Torr the half-life for HCl(u= 1) relaxation is about 50 ps and those for HCl(u> 1) are even shorter, the HCl concentration (actually [HCl(u=O)][HCl(u= l)]) lags the "thermal" counterpart (dot-dash curve) even after 200 ps. There are two reasons for this. First, the ethylene generation itself is distributed over this time range, although most of it is formed by about 50 MS. Second, while HCl(u= 1) is relaxed to the ground state, thereby increasing the difference in population between the u = 0 and u = 1 states, cascading from u > 1 offsets this increase and prolongs the rise in the "apparent" HCl concentration. The values of k~ obtained in the above manner from five experiments are presented in Table IV. The error analysis for the determinations of k3 from the HCl measurements was performed in essentially the same way as described in section IIIa. The errors accompanying the entries in Table IV originate from fitting the HCl transient concentrationchange to the reacion model and are due to noise, laser intensity fluctuations, etc. The scatter in the entries reflects errors in resetability, such as gas composition and calibration of the initial chlorine atom concentration. These lead to a standard deviation of the mean of 0.27 X 10-10 cm3 s-I, or an approximately 10% error. Uncertainties of 5% in a,(C2Hs02) and 5% in ui,(HCl) would
TABLE rV: CI + C a s Reaction Rate Constant at 297 K As Determined from the Formation of HCI conditions expt [CZH~]" [Clz]" [Ar]" [totalIb I 11 111 IV V
0.073 0.055 0.19 0.19 0.05
0.41 0.41 0.68 0.74 0.28
29 30 128 128 125
0 0 23 23 20
[c1]oc 8.1 6.0 11.1 12.2 4.5
results hd 3.2 f 0.6 4.3 f 0.7 2.6 f 0.3 4.2 f 0.6 2.7 f 0.7 av 3.4 h 0.27 SD 0.72
Units are Torr. In nitrogen. Units are lOI"r3. Units are cm3s-l. Indicated errors are those arising from the fitting procedure and do not include systematic errors. @
ordinarily be amplified to 15-20% systematic errors in k3. However, these largely cancel because [Cl]o and ui,(HCl) are both determined from the formation of ethylperoxy radicals in the presence of oxygen (see section 11); a residual change of 8% in the best fit value of k3 remains when [Cllo is increased and uh(HC1) is simultaneously decreased by 5%. When this error is statistically combined with the random error and a 10% error owing to uncertainties in the model, the estimated error is 0.5 X 10-10 cm3 s-1. Not included in the error analysis is the effect of initial vibrational distribution assumed for the HCl from reaction 3. The major uncertainty arises from using the data of Arunan et al. to estimate the relative (u=O)/(u=l) populations. If we double (halve) this ratio, but retain the reltive populations in u = 1-4, then an increase of approximately 15% (decrease of 5%) is required in k3 to fit the HCl formation at 30 Torr. However, at 125 Torr only a * 5 % change in k3 is necessary to account for doubling (halving) the [HCl(u=O)]/[HCl(u=l)] ratio, because of the increased efficiency of HCl vibrational relaxation at the higher N2 pressure. Upon including the uncertainty in the HCl nascent vibrational distribution in the error analysis, the HCl measurements yield k3 = (3.4f 0.6) X 10-lOcm3s-I. This value agrees well with that determined from the CzH4 formation data. c. C a * . The contrast in Figure 3 between the ethylene profiles in the absence versus presence of c2F6 indicates that the ethylene is born with considerable vibrational excitation. Over the first 8 ps the transient absorption remains zero, which implies that the concentration of C2H4 v7(u=l) equals that of v,(u=O); however, it is likely that both populations are near zero. Subsequently, there is a slow rise in ethylene absorption, presumably from relaxation by collisions with N2 or C2Hs. A nascent vibrational state analysis of the ethylene is beyond the scope of this paper. More difficult yet would be a description of the vibrational relaxation pathways. However, a crude model for the relaxation can be formed as follows. We assume that reaction 3 produces C2H4* and add to the model in Table I1 the reaction
+
CzH4* M
-
C,H,
+M
which occurs with the rate k,. A fit of the ethylene formation in a N2 bath to this model yields the rate k, = (4.5f 0.7) X lo4 s-1 at 30 Torr and 297 K and provides the dotted curve in Figure 3. Albeit crude, the model produces a reasonable fit of the data. The rate implies that significant relaxation occurs after =SO00 collisions, a reasonable value for nonresonant vibrational energy transfer. Table V lists the relaxation rate at various temperatures and pressures. Interestingly, there appears to be relatively little variation in this overall relaxation rate with temperature or N2 pressure. In contrast, the relaxation rate changes dramatically with C2F6 pressure. It is possible that the vibrational relaxation rate of C2H4* with N2 is sufficiently low that radiative or intramolecular processes become competitive. d. CI C f i . Experiments to measure the rate constant for the addition of chlorine to ethylene were undertaken for two
+
7976 The Journal of Physical Chemistry, Vol. 97, No. 30, 1993
C2&* Relaxation Rate Constant conditions eXPt [C2H6IU [cl~]' [total]' T (K) [Cl]ob results krC 29 297 8.1 4.5 f 0.8 A 0.060 0.36 129 297 5.9 6 k 1.5 B 0.050 0.46 30 253 7.5 5.5 f 1.5 C 0.063 0.42 30 218 7.9 8.5 f 2 0.41 D 0.062 Units are Torr. Units are lOI4 ~ m - ~Units . are lo4s-*. Indicated errors are those arising from the fitting procedure and do not include systematic errors.
Maricq et al.
TABLE V
TABLE VI: C1+ C f i Reaction Rate Constant conditions expt [Cl]oU [C2H4]oU PT,,~(Torr) T (K) results ksb 30 297 1.4 k 0.3 i 12.5 49.3 1.3 k 0.3 30 297 ii 4.4 38.1 129 297 3.5 f 0.7 iii 10.1 50.4 253 2.0k 0.3 30 iv 6.5 37.1 218 2.2f0.5 30 V 7.3 42.3 02 concentration is 11-17 Concentrations are in units of lOI4 Torr. b Units are 10-1l cm3 S-I. Errors represent the quality of fit but do not include systematic errors. reasons: first, this reaction is the most important of the secondary reactions needed to model the C2H4 (and HCl) formed in the C12/C& chain reaction and, second, it affords the opportunity to verify the accuracy of the laser photolysis/transient IR spectroscopy method for determining reaction rate constants.The reactions were performed under conditions similar to those described above. The only differences lay in the composition of the gas mixture which typically consisted of 0.12 Torr of C2H4, 0.5 Torr of C12, 10 Torr of 02,and 20 Torr of N2, with the oxygen added to suppress the chain reaction between ethylene and chlorine. In these experiments the IR probe beam revealed a transient increase in transmission caused by the consumption of ethylene. Because the disappearance of a reactant is monitored, only the ground vibrational state is significantly populated, and questions of vibrational relaxation do not arise. The transient increase in IR transmission is converted via eq 4 to a change in C2H4 concentration, examples of which are displayed in Figure 7. The data are fit to a model consisting of the reactions
+M C,H4C1 + 0, + M C1+ CZH4
-
C1+ C2H4CL0,
C,H,Cl+ M
C2H4C10, products
+M
(6) (10) (11)
Because large amounts of 02 are used, reaction 10 is taken to be instantaneous. The transient decrease in ethylene then depends on [Cllo, [ C Z H ~ ]k6, ~ , and kll. The initial chlorine atom concentration can be determined either by calibration against ethylperoxy radicals, as described in section 11,or from the amount of ethylene consumed. Except in cases where [ello was comparable to [ C Z H ~ the ] ~ ,two methods gave consistent results. The initial ethylene concentration was determined by its IR absorption prior to the photolysis laser pulse. Thus, only the two unknown rate constants require fitting by a comparison of the model predictions to the data. The results of the fit for k6 are provided in Table VI, and a comparison between the model predictions and the data is provided by the dotted lines in Figure 7. The best fit rate constants depend only weakly on the choice of k l l , which ranged from 0.3 to 2 X 10-11 cm3 s-1. Little is known about the kinetics of chlorine atom reactions with peroxy radicals. The reaction between C1 and CFzClOz has been reported3l to be very fast, in the range of (1-3) X 10-10 cm3 s-1, while preliminary experiments in our laboratory yield a rate constant of (0.5-1) X
C1
+
C,H,-
CH,CH,Cl
h
c)
I
E
2
0
40
3
0
20
40
60
80
100
time ( p s )
Figure 7. Decrease in ethylene concentration observed following the
photolysis of C12 in the presence of 02. The pseudo-first-orderdecay is essentiallydetermined by the rateof additionof chlorineatomstoethylene. The small spike in the upper trace is a result of incomplete subtraction of the optical/electronic interference discussed in section 11. 10-10cm3 s-1 for C1+ (CH3O2, C2H502, and CH3CHC102). The value of kll determined in the above fits is very sensitive to [Cllo. Increasing the initial C1 concentration by 10% provides good fits of the data with kll in the (0.5-1) X 10-locm3s-l range with little effect on k6. Because the initial chlorine atom and ethylene concentrations can be deduced from the IR absorption measurements, the only sources of error in k6 are from noise in the transient absorption measurement and from uncertainty in the IR absorption cross section. Depending on temperature and pressure, the latter ranges from 2.6 to lo%, whereas the fitting error bounds are approximately 20%. Clearly, noise contributes the major uncertainty; thus, our recommended errors are simply those listed in Table VI. The values of k6 reported here are in good agreement with the relative rate measurements of Wallington et alez1At 295 K and 30 Torr total pressure our value of k6 = 1.4 X cm3 s-I compares well with the previous determination of k6 = 1.1 X cm3 s-l. At 129 Torr the comparison is 3.5 X versus 3.2 X 10-11 cm3 s-I. An average of the present and previous measurements was used in the model of Table I1 when fitting either the CzH4 or HCl data to determine k3, as discussed in sections IIIa,b. IV. Discussion The transient IR absorption arising from ethylene formation provides a direct, real time measure of the rate constant for the C1 C2H5 reaction. Although somewhat less direct, the time dependence of the HCl formation gives an independent measure of the same constant. Both measurements lead to a value of k3 of the order 3 X l0-Io cm3 s-l, which is approximately a factor of 25 larger than the rate constant determined by Dobis and Benson3 using the very low-pressure reactor. The present value agrees within experimental error with the relative rate determination of k3 previously reported by Kaiser et al.9 Seakins et al.13 have fit their time-resolved FTIR emission spectra of HCl(u= 1-4) produced by reaction 3 and find the emission to be consistent with the value of k3 reported herein and by Kaiser et a1.9 It is important to address a few potential difficulties that may arise when using flash photolysis to study chain reactions. The reactions initiated by the photolysis can, in general, generate electronically, vibrationally, rotationally, and translationally excited fragments. The present experiments were conducted in a collision-dominated environment; thus, rotational and translational excitation should be rapidly thermalized and electronic
+
Study of the C1
+ C2H5 Reaction
excitation quenched. Indeed, no significant differences were encountered in the determination of k~ over the pressure range 30-300 Torr. The effect of vibrational excitation on the transient C2H4 and HCl measurements was discussed in section 111. Vibrationally excited ethylene was relaxed by adding C2F6 to the gas mixture, and HCl vibrational relaxation was included in the reaction model. Because laser photolysis initiates a chain reaction, there is the possibility that thegas mixtureis significantly heated. An increase in temperature would affect the kinetic measurements in two ways. First, reaction rate constants would change as a function of time following initiation of the chain reaction. Second, the effective C2H4 or HC1 IR absorption cross sections would also vary in time. Heating of the gas mixture was avoided by employing a reduced ethane concentration. From the measured HC1 production, and the correspondingmodeled ethane consumption, the temperature rise over 200 ms was calculated to be
