J. Phys. Chem. 1994, 98, 11924-11930
11924
Temperature Dependence of the Product Branching Ratios of the C10 Self-Reaction in Oxygen A. Horowitz,**tJ. N. Crowley, and G. K. Moortgat' Max-Planck-lnstitut fur Chemie, Division of Atmospheric Chemistry, 0-6500, Mainz, Germany Received: March IO, 1994; In Final Form: July 26, 1994@
The Clz-sensitized continuous photolysis of 0 3 - O 2 mixtures was investigated in the temperature range 285331 K using time-resolved diode m a y spectroscopy to monitor the decay of 0 3 and the formation of OC10. The branching ratio was derived at each temperature from the measured quantum yield of ozone consumption (a-03) and the initial rate of OClO formation. At 298 K a-03 was found to be 4.04 f 0.35 and the following branching ratios into the three bimolecular disproportionation channels of the C10 self-reaction were determined: k3a/k3 = 0.39 f 0.06, kdk3 = 0.41 f 0.06, and k3Jk3 = 0.20 f 0.03, where C10 C10 C h 0 2 (3a), C10 C10 C1 ClOO (3b), and C10 C10 C1 OClO (3c). The contribution of the radical channels 3b and 3c was found to increase with temperature at the expense of the molecular channel 3a. The temperature dependence of k31Jk3~ can be described by the following apparent Arrhenius parameters, A3JA3b = 0.27 f 0.10 and E3c - E 3 b = 1.79 f 0.78 kJ, while k3a/k3cdid not exhibit Arrhenius type temperature dependence. The validity of the methods used was verified by the determination of the equilibrium constant K4, where C10 C10 M C1202 M (4), which was found to equal (2.24 f 0.35) x cm3 molecule-' at 285 K, in excellent agreement with the value derived from recommended kinetic data.
-
+
+
+
+
-
+
+
The bimolecular and termolecular reactions of C10 radicals have been the subject of extensive studies1-" mainly because of the important role that these radicals play in the chemistry of the stratosphere, in particular in the ozone destruction m e c h a n i ~ m . ' ~At .~~ room temperature the bimolecular reaction proceeds along three different channels,
c10
+ c 1 0 - C12 + 0,
+ c 1 0 - c 1 + ClOO 22 c 1 + 0, c 1 0 + c 1 0 - c 1 + OClO
while at lower temperatures, as found in the stratosphere, the termolecular reaction leading to the formation of the dimer C1202 predominates. C10
+ C10 + M
-
Cl20,
+
+
-
+
Introduction
c10
-
+M
Because of the key role of the C10 dimer in the foxmation of the "ozone hole"?s8 most of the recent kinetic studies related to C10 chemistry concentrated on the determination of lowtemperature rate data for C1202 formation. In the laboratory, C10 radicals are most conveniently generated mainly by reacting C1 atoms with ozone or C120. The distinct UV absorption spectrum of C10 is then utilized for monitoring of concentration, necessary for the evaluation of absolute rate constants of the self-reactions in flash photolysis as well as in modulated and continuous photolysis. For the determination of the branching ratio it is necessary to supplement this information by concurrent product analysis and determination of the overall mechanism of O3 or C120 consumption. While there seems to be a fairly good agreement regarding the Arrhenius parameters of the overall bimolecular reaction, t Permanent address: Division of Advanced Materials, Soreq Research Centre, Yavne 70600, Israel. Abstract published in Advance ACS Abstracts, October 1, 1994. @
0022-365419412098-11924$04.5010
this is not the case for the product branching ratio, the temperature dependence of which has not been determined so far. At 298 K the accepted values of this ratio are based on the values determined by Cox and Derwen6 in a modulated photolysis study of Cl2-03-02 mixtures at atmospheric pressure. However, a similar study of the C12-C120-02 system by Simon et a1.I' gave branching ratios that differ considerably from those obtained by Cox and Derwent. The accepted view expressed in the most recent CODATA14 and NASA15 reviews is that the branching ratio and its temperature dependence are not known with sufficient accuracy. Occurrence of secondary reactions appears to have been the main difficulty encountered in previous studies aimed at the determination of the branching ratio in the bimolecular selfreaction of C10. The extraction of these ratios from experimental data required numerical fitting to complex chemical schemes, which is reflected in the accuracy of the estimated rate constants. In an attempt to overcome these problems, we have recently carried out a study at 298 K in which the branching ratio was determined by using time-resolved singlewavelength and diode array spectroscopy to monitor 0 3 decay and initial OClO formation rate in the continuous photolysis of c12-03-02 mixtures under steady-state conditions.16 In that study we were able to demonstrate the applicability of the method used to generate accurate branching ratio data without resorting to complex numerical simulation of the overall reaction. The present investigation was carried out using similar experimental procedures over an extended temperature range to determine the temperature dependence of the branching ratio in the bimolecular self-reaction of C10 radicals. Experimental Section
The photolysis of mixtures of Cl2 (1% in N2). 0 2 (99.999%), and O3 (produced by an electric discharge) was carried out in an uncoated double-jacketed quartz cell 50 mm in diameter and 132 cm in optical length. In order to reduce the rate of direct photolysis of OC10, the light from the six photolytic lamps (Philips, TL12, 40 W) was attenuated by BrZ introduced into
0 1994 American Chemical Society
C10 Self-Reaction in Oxygen 15
J. Phys. Chem., Vol. 98, No. 46, 1994 11925
cc
I
As demonstrated in the previous room-temperature study16 of the continuous chlorine-sensitized photolysis of Cl2-03 mixtures in the presence of a large excess of oxygen and under steady-state conditions, the initial rates of ozone consumption and OClO formation are governed by the following reactions.
+ hv -.C1+ C1 C l + O3-ClO + 0, c 1 0 + c 1 0 c1, + 0, C1,
"'
1ooxocIo I
0
l
l
l
l
l
l
l
l
l
50
l
l
100
l
l
(2)
-
v
0
(1)
l
l
l
l
150
Time [sec]
Figure 1. Typical ozone decay and OClO buildup profiles at 306 K (Clz = 1.12 x 10l6and 0 3 = 1.40 x 10l6molecule ~ m - P ~ ,= 520
Torr. the outer jacket (about 200 Torr at 298 K). Water from a temperature-controlled bath was circulated in the inner jacket. During an experiment the temperature was stable within izO.1 K. The analytical light from a Dz lamp was dispersed in a 0.5 m monochromator equipped with a grating blazed with 300 lines mm-' at 300 nm and detected by a diode array camera which recorded the spectra in the 203-370 nm region at a 0.2 nm resolution. Initially, only N2 and 0 2 at a preset pressure were flowed into the cell, the 0 2 flow being split so that part entered the cell directly and another part was diverted through the ozone generator. Once the spectrum at these conditions was taken, the ozone generator was activated and Cl2 was introduced into the cell. When again a steady flow and mixing of the gases were achieved, the cell was closed and allowed to stand for 10 min to ensure that the gaseous mixture was thermally equilibrated with the walls of the cell. Prior to the activation of the photolytic lamps the absorption spectrum was recorded again and then, for the first 16 s of photolysis, at 1.6 s intervals (4 x 0.4 s scans). The photolysis was continued for an additional 132 s, during which the spectrum was recorded at 26 s intervals. O3 was monitored at 215 nm and C12 at 350 nm, and the OClO concentration was determined from its differential absorption in the a(14) band (peak at 329.22 nm). This procedure was adopted after a number of preliminary experiments in which OClO concentrations were derived from its differential absorption at several other bands and found to agree within 23%. The absorption of OClO shows a strong temperature dependence, and therefore the differential absorption in the a( 14) band at each temperature was derived from the data of Wahner et al.17 C ~ Z - C ~ H ~ - O ~mixtures -N~ were used for actinometry,18taking @ - a 2 = 1. a-03 was determined from the slope between 15.2 and 148 s of the linear decay curves (see Figure 1). Results and Discussion General Features and Reaction Scheme. The characteristic features of OClO production and 0 3 consumption are depicted in a typical reaction profile shown in Figure 1. It can be seen that 0 3 decreases linearly with time, while a more complex behavior is observed for OC10, the growth of which slows down until a maximum concentration is reached when the rate of formation equals the rate of removal. Subsequently, secondary removal reactions take over, as evidenced by the decrease in OClO concentration at longer reaction times.
C10
+ C10
-.C1+
ClOO
(34
2C1+ 0,
+ ClO -c 1 + OClO CIO + C10 + M +.. C1,0, + M c10
(3b) (3c)
(4)
In the absence of secondary reactions and once the equilibrium concentration of the dimer C1202 has been reached, this mechanism leads to the following expressions. = 4/(2k',,
k'3a
+ kr3, + k'3c = 1
+ k'3c)
(A)
(C)
where k'sa, kf3t,, and k'3c stand for k3Jk3, k3dk3, and k3Jk3, respectively. Notice that a-03 refers to the quantum yield of the C12photosensitized ozone destruction in the presence of oxygen as the bath gas. In early studies by Nomsh and Nevillelg it has been shown that, when N2 is used as the bath gas, a-03 at about 298 K is considerably lower than in the presence of N2 (a-03 4 in 0 2 vs a-03 6 in N2). Hence, in terms of the mechanism proposed, these fmdings, which were later confiied by both Lin et and Wongdontri-Stuper et al.? indicate a priori that the branching ratios in these two gases can be expected to be different. Expressions A-C can be utilized for the determination of the product branching ratios provided that a sufficiently wide time interval can be found within which the rates of 0 3 destruction and OClO formation are constant. Since ozone depletion was found to satisfy this requirement, the applicability of expressions A-C depends on the possibility of determining the initial rate of OClO formation once the steady-state conditions were reached. Although we have shown in the earlier 298 K study16 that the time necessary to reach steady-state conditions was below 4 s and that between 5.6 and 15.2 s deviation of OClO formation from linearity with time was negligible, this need not necessarily be the case at higher temperatures. Turning now to Figure 2, in which OClO formation profiles at 285 and 328 K are compared, it appears at first glance that the linear approximation indeed can be applied to the 328 K results. A more careful examination indicates that this is not the case. Notice that at 285 K all the points at t < 5 s lie above the line and that, until the steadystate conditions are reached, the rate of OClO formation increases as expected. On the other hand, the rate of OClO formation at 328 K decreases almost from the onset of photolysis. As already mentioned, the nonlinearity of OClO growth profiles can be attributed to the occurrence of secondary
Horowitz et al.
11926 J. Phys. Chem., Vol. 98, No. 46, 1994 c
I
L
5 3
3
E,
"O 0.9
4 \
I\
I
3 m 3
2 -
2
L
Y
2 u 0
1 0
50
0 -
100
150
200
250
300
Time [sec]
Figure 3. Dark decay of OClO at 298 K. 03 concentrations: 0.55 x 10l6(squares), 0.77 x 10l6(triangles), and 1.15 x 10l6molecule cm-3
-1
(circles). 10 15 time [sec] Figure 2. OClO formation profiles at 285 and 328 K. 0
5
reactions. The nature of these reactions and in particular their potential effect on the initial rates of OClO formation and the rate of ozone depletion should warrant a detailed examination. Direct photolysis of both ozone and OClO cannot be completely suppressed even when the light from the TL 12 lamps is attenuated by Br2. Ozone photolysis leads to the formation of O(lD) and O(3P) oxygen atoms, O3
+ hv - 0, + O('D and 3P)
0, (5)
both of which can then react with an additional ozone molecule and destroy it.
+ 0, - 0, + 0, o(,P) + 0, - 0, + 0,
O('D)
(6) (7)
While reaction 7 is very slow (k7 = 8 x 1 0 - l ~cm3 molecule-' s-l), reaction 6 is fast (k6 = 2.4 x cm3 molecule-' s-l, both at 298 K);14 however, its occurrence can be prevented by the addition of a sufficient amount of oxygen, which ensures the regeneration of the photolyzed ozone via 0
+ 0, + o,-oo, + 0, + hv
-
0
+c10
(9)
can be expected to have a negligible effect on the rate of ozone consumption. At the same time it can have a significant contribution to the reduction in the rate of OClO formation. In addition to direct photolysis, OClO can also be destroyed by reaction with C1 atoms
c1+ OClO
-
c10
+c10
+ OClO - products
(1 1)
for which an activation energy of 9.4 kcal mol-' has been estimated by Wongdontri-Stuper et al.* The preceding discussion of the secondary reactions clearly shows that, particularly at high temperatures, the observed initial rates of OClO formation, Rmlo(obs), cannot be used for the derivation of the branching ratios according to expressions A-C. The necessary true Roclo values can however be obtained by assigning the deviation from linearity at the initial stages of reaction to the fist-order disappearance of OClO so that
or
(8)
Because of the occurrence of this reaction on one hand and the ozone destroying sequence (reactions 3b and 3c followed by reaction 2) on the other, direct photolysis of OC10, OClO
photolysis proceeds and ozone is depleted, reaction 10 becomes the main route of OClO removal. The dark reaction was studied by us at 298 K by observing the dark decay of OClO generated in situ upon photolysis of Cl2-03-02 mixtures. Although no attempt has been made to examine the details of this reaction, we were able to establish its pseudo-first-order kinetics (see Figure 3). In addition the first-order decay rate constants extracted from these experiments increased with ozone concentration. This behavior is consistent with the occurrence of the following dark reaction,
(10)
which competes with reaction 2. Since the reaction of C1 with OClO is considerably faster than the reaction with 0 3 (k2 = 1.2 x IO-" and klo = 5.8 x IO-" cm3 molecule-' s-l at 298 K),14 it gains in importance as ozone is consumed during the course of photolysis. It appears however that, with the increase of temperature at which photolysis is carried out, dark decomposition of OClO becomes the main cause for the departure from linearity at the initial stages of reaction, while as the
where k is an effective rate constant representing mainly the sum of k9 and k11[03] and a small contribution of the term klo[CI]. Since, during the first 16 s of photolysis, the decrease in [03] and the increase in [Clz] amount to a few percent only, the last two terms remain practically constant during this time interval. The value of Roclo, which is a constant at a given Clz concentration, can thus be derived together with k by numerical fitting of the experimental data to expression E. In the present work we have used the FACSIMILE numerical simulation program21 for this purpose. Temperature Dependence of the Branching Ratio. The experiments aimed at the derivation of the temperature dependence of the product branching rate constants K3a, K3b, and K3c were carried out in two stages. First a series of isothermal roomtemperature experiments summarized in Table 1 were carried out, and these were followed by a second series summarized in Table 2 in which the temperature dependence of a-03and Roclo was determined. For these experiments Cl2 = (1- 1.2) x 10l6, 0 3 = (0.9-1.7) x 10l6 molecule cmP3, and total pressure is 503-576 TOIT.
J. Phys. Chem., Vol. 98, No. 46, 1994 11927
C10 Self-Reaction in Oxygen TABLE 1: Summary of Experiments in Which k;, and a-03 Were Determined
~
~~
529 460 471 578 399 461 381 292 532 538 549
t
-
v
~
1.07 0.976 1.28 1.89 1.03 0.949 0.737 0.452 1.283 1.16 1.29
1.15 0.945 1.27 1.66 1.15 1.03 0.848 0.666 1.41 1.41 1.41
1.60 1.39 1.40 1.71 1.18 1.39 1.15 0.879 1.58 1.60 1.64
0.182f0.012 0.185 f 0.006 0.193 f 0.005 0.198 f 0.009 0.187f0.005 0.177 f 0 . 0 0 3 0.176f0.004 0.160 f 0.005 0.183 f 0 . 0 0 3 0.196 f 0.005 0.184 f 0.006
0.265f0.011 0.224 f 0 . 0 1 4 0.212f0.016 0.215 f 0 . 0 0 7 0.219f0.010 0.193 fO.O1O 0.174f0.004 0.175 f 0.020 0.192 fO.O1l 0.195 f 0.002 0.198 f 0 . 0 0 2
4.11 4.34 3.85 4.05 4.01 3.91 3.91 3.86 3.93 4.17 3.89
? t
/
e
9 This work
1
0 CoxandDenvent
290
300
310
320
330
TEMPERATURE [K] Figure 4. Temperature dependence of ozone formation.
a Pressure in Torr, concentrationsin molecule ~ m - ~k. ' ~ (average) ~ = 0.184 f 0.020. k'3c = k3Jk3 average = 0.199 f O.O20(2u). k'3,(f) from FACSIMILE numerical fitting (see text), average value 0.204 f 0.032, first point not included. a-03 = 4.04 ic 0.35.
TABLE 2: Summary of Temperature Dependence Experiments T,K N Q-03 k'3a k'3b k'3c k, s-l 285 287 288 292 298" 306 315 324 328 33 1
5 2 1 2 15 2 2 3 4 3
3.05 3.19 3.55 3.58 4.05 4.18 4.19 4.34 4.20 4.39
0.575 0.538 0.473 0.464 0.392 0.369 0.365 0.347 0.362 0.347
0.263 0.284 0.347 0.346 0.404 0.412 0.410 0.425 0.410 0.436
0.162 0.178 0.180 0.190 0.204 0.219 0.225 0.228 0.228 0.217
0.0 (linear) 0.005 f 0.015 0.010 f 0.030 0.008 f 0.060 0.021 f 0.013 0.029 f 0.007 0.040 f 0.010 0.048 f 0.013 0.047 f 0.010 0.076 f 0.010
Total of 11 experiments carried out in the first series and 4 in the second series. The first series was carried out mainly in order to assess the effect of the BrZ filter which was not used in the previous work and in order to make a detailed comparison between the results obtained for Roclo by linear approximation and those derived by numerical fitting of the experimental data according to expression E. It turns out that the present results (see Table 1) are in a very good agreement with those obtained in the earlier work16 and yield the following average values (20 error limits): 0 - 0 3 = 4.00 f 0.29 and k'3c, derived by linear approximation, equals 0.184 f 0.20. The earlier results were 4.1 f 0.1 and 0.18 f 0.2, respectively. At the same time inspection of the results presented in Table 1 clearly indicates that the k'3c values derived by numerical fitting are consistently higher than those obtained by linear approximation. Neglecting the apparently high first point of 0.265, the average k'3c value obtained using the former method turns out to be 0.199 f 0.032. When the experiments canied out in the second series are added to those in Table 1 the results are @ - 0 3 = 4.04 f 0.32 and k'3c = 0.204 f 0.032, from which we find that K 3 a = 0.39 f 0.06 and k'3b = 0.41 f 0.06 at 298 K. The error for k ' f c is 20, while for the other two ratios it was estimated from the error in k'3c and 0 - 0 3 . The present 298 K results are in reasonable agreement with those obtained in the modulated photolysis study by Cox and D e r ~ e n twhose , ~ estimates at these temperature are 0.49 f 0.1 1, 0.34 f 0.09, and 0.17 f 0.05 for K 3 a , k'3b, and k'3c, respectively. It is however rather difficult to reconcile our results with those of Simon et al." They found k'3a = 0.33 f 0.08, k'3b = 0.33 f 0.07, and K 3 c = 0.34 f 0.12. The reason for the discrepancy, particularly insofar as K 3 c is concerned, is not clear since one would expect the behavior in the C12-03-02 system used by Cox and Denvent4 and by us to be similar to that in the ClzC120-02 system used by Simon et al." The fact that Simon
u
0.4 n
ufl 0
0
0
0.3 U
290
300
310
320
330
Temp. [K]
Figure 5. Temperature dependence of the branching ratio.
et al. did not monitor OClO formation and determined the branching ratio only by numerical fitting of the C10 profiles can be conceived as a potential source of error in their modulated photolysis study. Even though this is not necessarily the actual source of error, we believe that the present results should be preferred over those of Simon et al." Turning now to the results in Table 2, it is worth noting first that k increases with temperature. This observation lends further support to the assumption that this rate constant is correlated primarily with the dark reaction between OClO and 0 3 . Also, since C1 atoms are titrated by ozone, a qualitative estimate of the relative importance of the C1-generating reactions 3b and 3c can be obtained from the variation of @-03 with temperature. As can be seen from Figure 4, the quantum yield of ozone consumption initially rises sharply and then starts to level off. Since the activation energy of the reaction of C1 with 0 3 is close to ~ e r o , ' ~this , ' ~ observation indicates that the total amount of C1 atoms formed via channels 2b and 2c must also level off. The effect of temperature on the branching ratio is best seen from Figure 5, which clearly reveals that, with increasing temperature, the channels leading to C1 gain in importance, while a reverse trend is shown by the channel leading to Clz. Qualitatively, this behavior can be correlated with the thermochemistry of the different product ~hanne1s.l~
+ c 1 0 - c1, + 0, C~O + C ~ O- CI + C ~ O O C10 + C10 - C1+ OClO
c10
AZP = -204 kJ mol-' AZP = 12 k~ mol-' M = 18 kJ mol-'
The two endothermic radical channels can be expected to have
11928 J. Phys. Chem., Vol. 98, No. 46, 1994
Horowitz et al. 1
1
TABLE 3: Summary of Experimental Data Used in the Derivation of Kd at 285 Ka (10-16)- (10-16)P, (10-13)(-10-12)(1014)Cb 1.27 1.21 1.22 1.18 1.20
I
1,
3.0
3.1
3.2
3.3
3.4
Torr 539 528 527 504 508
k'jc
3.54 3.34 3.37 3.01 3.28
0.160 0.166 0.160 0.167 0.157
interceut
KA
9.56 10.4 8.86 8.60 9.15
2.19 2.53 2.07 2.09 2.33
a All concentrations in units of molecule ~ m - R-03 ~ , in units of molecule cm-3 s-l, and K4 in units of cm3 molecule-'.
3.5
lOOOlT [K.']
Figure 6. Arrhenius plots of k3alk3c and k3Jk3b.
a higher activation energy than the exothermic molecular channel. If it is assumed that the transition states of the radical pathways have a linear head to tail and tail to tail configuration, Le. ClOClO and ClOOCl, then the ability of the radical reactions to compete with the energetically more favorable molecular decomposition route can be attributed to the simplicity of the bond-breaking product-generating step in the linear complexes. One can envisage the molecular reaction as proceeding by a four-center transition state in which more complex bond breaking and forming is necessary to form the products. Variation of the rate constants k3a, k3b, and k3c with temperature can be expected to be described by an Arrhenius expression provided that the reaction along each of the channels proceeds by a simple mechanism. In this case, since k'3Jk'3b = k3Jk3b and k'3alkf3c = k3a/k3c,the temperature dependence of these rate constant ratios should be adequately described by Arrhenius plots. These plots are shown in Figure 6. A reasonable linearity is shown by the plot for k'3 Jk'3b, for which the linear leastsquares fitted Arrhenius parameters turn out to be A3c/A3b = 0.27 f 0.10 and E3b - E3c = 1.79 2Z 0.78 kJ. Apparently, the two endothermic channels require essentially the same activation energy. It is quite obvious however that in the case of the k3$ k3c ratio the Arrhenius temperature dependence is not observed. The line for this rate constant ratio shown in Figure 6 thus does not fully reflect the true behavior. The Arrhenius parameters derived for this line, A3alA3c = (-1.8 f 1.0) x lo-* and E3c E3a = 12 f 4 kJ, can serve only as a rough approximation of the temperature dependence expected between 285 and 331 K. To the extent that the Arrhenius type temperature dependence is observed for the other two channels, the non-Arrhenius behavior of the ksalk3, ratio has to be associated with the molecular channel 3a. The accepted Arrhenius expression for the temperature dependence of the overall reaction k314J5 is largely based on the discharge flow studies of Clyne and Coxon (294-495 K)22 and of Clyne and White (273-730 K).23 The present work shows that the different channels of the bimolecular C10 selfreaction have different activation energies and that deviations of the temperature dependence of the overall reaction rate from Arrhenius behavior can be expected. That this was not observed in the studies of Clyne and co-workers probably reflects the fact that the temperature range covered was not extended sufficiently to show departures from linearity when channel 3c is important. It should be mentioned that, in the course of their molecular modulation study of the C10 dimer forming reaction in C12 0 2 mixtures at 268-338 K, Hayman et have estimated an E3a value of 11.2 f 3.3 kJ. According to the present work, the radical channels have very close activation energies which are considerably higher than the activation energy of the molecular channel. We have found that already at 331 K, about 65% of the C10 radicals react along the radical
+
O3 1.63 1.70 1.55 1.38 1.45
pathways and therefore, as has been already suggested by Clyne and c o - w o r k e r ~the , ~ ~estimated activation energy of 10 f 4 kJ based on the determinations by Clyne and co-workers most probably represents the activation energy of the radical processes. Worth noting in this context is the fact that the CODATA14 estimate based on thermochemical calculations and the assumption that E-2 and E-3 equal 0 yields E2 and E3 values of 12 and 18 kJ, respectively. It should be mentioned that our estimate of E3c - E J = ~ 12 & 4 kJ compares quite well with the approximate value of E3b - E3a = 11.8 f 2 kJ obtained by Cox and Dement4 from the temperature dependence of a-03in the modulated study of the Cl2-03-02 system. While this agreement seems to support the conclusion that E 3 b and E3c are very close, attention should be drawn to the fact that, unlike in the present work, Cox and Dement4 observed an almost linear rather than curving increase of "-03. The agreement between the values obtained for a-03 at both ends of the temperature range is however quite good (see Figure 4). Considering the overall change in a-03 and the relatively large error of the 298 K a-03 determinations in both studies (2a = 0.5 in the Cox and Derwent study and 0.35 in this work), it seems that a clear-cut choice between the patterns of 0 - 0 3 growth with temperature cannot be made. Estimation of K4 at 285 K. Central to our method of the product branching ratio determinations is the assumption that following the initial induction period during which the steadystate concentration of C10 and the equilibrium concentration of its dimer are reached, the three bimolecular channels of the C10 self-reaction become the only route of C10 removal. This assumption can be tested when steady-state conditions have been established and the initial formation of OClO is linear with time. As can be seen from the data presented in Table 2, only the results at 285 K, for which the numerical simulation did not return any k value, satisfy this requirement. These results are presented in detail in Table 3. In terms of the mechanism proposed, the negative intercepts obtained for the plots of OClO vs time have to be proportional to the amount of C10 radicals that were not removed in the bimolecular reaction. In other words, the vertical displacement from the origin of the lines describing OClO formation under steady-state conditions reflects the "loss" of C10 radicals necessary to build up their steady-state concentration, CIOss, and to reach the equilibrium concentration of the C10 dimer, C1202Y Accordingly, the C10 material balance yields [CIOss]
+ 2[C1202q] = -2(intercept/k',,)
(F)
Since
R,,, = k2[C1][03] - 2k3[C10I2 and under steady-state conditions R-03 equals 2k3[C10ss]2,it follows that
J. Phys. Chem., Vol. 98, No. 46, 1994 11929
C10 Self-Reaction in Oxygen
where K4 is the equilibrium constant of reaction 4,in which the dimer is formed. In principle, expression H can be utilized for the determination of both k3 and K4 provided that experiments can be carried out over a sufficient range of R-03 values. Experimental considerations such as the OClO detection limit make this impractical in our system. However, expression H can be numerically solved for K4 by substituting for k3 its value at 285 K derived from the known Arrhenius parameters of this reaction. Taking A =8 x cm3 molecule-’ s-l and EIR = 1250 K,15 k3(285) turns out to be 1.0 x cm3 molecule-’ s-’. The K4 values listed in Table 3 were obtained using this k3 value and the results obtained separately in each experiment for R-03, the intercept, and k’3c. For consistency the K3c values used were those obtained from the linear plots of OClO vs time. It is worth noting that the estimated K4 values are independent of the actinometry. The average K4 value of (2.24 f 0.35) x cm3 molecule-’ obtained from the results of Table 3 compares extremely well with the value of 2.26 x cm3 molecule-’ derived from the van’t Hoff temperature dependence expression determined by Cox and Hayman.* Considering the errors in R-03, the intercept, and k’3c in the present study as well as the sizable error estimate of the error in the temperature dependence Of K4 (K4 = 3 x lo-,’ exp(8450 f 850)/7‘),15it is quite obvious that the excellent agreement is partially fortuitous. Nevertheless, it provides very strong evidence supporting the validity of the assumptions inherent in the method used in the present work for the estimation of the branching ratio. Critical Examination and Comparison with Branching Ratio in Nitrogen. Recently, during the course of the present investigation, Nickolaisen et aLZ5carried out an extensive study in which the Arrhenius parameters for the individual channels of the C10 C10 bimolecular and termolecular reaction were determined in nitrogen. Flash photolysis combined with timeresolved ultraviolet absorption spectroscopy was employed in this study in which C1 atoms formed in the photolysis of C12 were reacted with C120 to generate C10. The decay of these radicals and OClO formation were monitored under various experimental conditions. The k’3a, k’3br and k‘3c values at 298 K, derived from the Arrhenius parameters determined by Nickolaisen et al.,25are 0.30, 0.49, and 0.21, respectively. On the basis of these values and expression A the predicted quantum yield of O3 destruction in nitrogen equals 5.6, which compares well with the experimental value of a6. As expected, the difference between the latter value and @-03 x 4 in oxygen can be entirely accounted for by the observed difference between the branching ratios in these two gases. Worth noting in this context is the fact that the work of Nickolaisen et al.25and the present study yield practically identical 298 K values for k’3c, 0.21 and 0.20, respectively. Unless, contrary to the accepted vie^,'^^'^ not all directly and indirectly generated C1 atoms react with ozone irrespective of the buffer gas, these results indicate that the quantum yield increase in NZ reflects a change in the “internal distribution” between the channels leading to the radical products. Carrying this line of argument one step further and borrowing on the terminology used by Nickolaisen et al.,25 it can be said that in the C10 C10 reaction 0 2 is involved more actively than the simple purely bimolecular mechanism would suggest; that is, it does not simply play the role of a third body quencher. Thus, rather than representing elementary pathways, the branching ratios reflect final product distribution.
Conceivably, these products are formed by unimolecular decomposition of various short-lived (C10)2 intermediates, in which case the bath gas effect may not be limited to oxygen only. Whatever the case might be, for atmosphere purposes the effect of oxygen on the branching ratio cannot be neglected a priori. Turning now to the temperature dependence of the branching ratio and the Arrhenius parameters of the different routes of reaction, it is quite evident that, as has been already pointed o~t,’~ theJ ~simple bimolecular reaction mechanism does not seem to account fully for the observed behavior at temperatures below 298 K. This behavior is not limited to the case of C10 C10 reactions in 0 2 . Similar observation were made in earlier studies in which N2 was used as a bath gas. The recent and by far most detailed study by Nickolaisen et aLZ5 in which Arrhenius dependence for the three bimolecular channels was reported does not exclude this possibility. The Arrhenius expressions for k3b and k3c obtained in that work (k3b = 2.98 x lo-’’ exp -2450/T and ksC= 3.50 x exp -1370/T cm3 molecule-’ s-I) are based on results at temperatures exceeding 298 K, while in the case of the derivation of the Arrhenius expression for k3a (k3a = 1.01 x 10-l2 exp -1590/T cm3 molecule-’ s-’) the data used at 270, 280, and 290 K were determined with a rather low accuracy of about f100%. The departure of the bimolecular rate constants from Arrhenius type temperature dependence, as reflected also by the rapid decrease in @-03 at temperatures below 298 K, could be ascribed to the occurrence of a transition from the bimolecular reaction channels to the termolecular dimer forming channel. Conceivably, in this temperature range, the steady-state concentration of the dimer might be sufficiently high to allow it to compete with 0 3 in the reaction with C1 atoms. This, in turn, could lead to a net enhanced C10 termination via the following reaction sequence.
+
C10
+
+
+ C10 + M
c 1 + c1,0, ClOO net:
c10
-
-
c1,
C1,02
+M
+ ClOO
-c1+
0,
+ c 1 0 - c1, + 0,
In order to assess the possibility that this mechanism is responsible for the observed decrease in @ - 0 3 under our experimental conditions, a series of model calculations using the reaction mechanism summarized in Table 4 and the FACSIMILE simulation program were carried out at 285 and 298 K (see Table 5) using NASA-recommended K4 values15 as well as those derived from the results of Nickolaisen et al.25 Based on the Arrhenius parameters determine by Nickolaisen et al. and as a first approximation, we have assumed first that lowering of the temperature from 285 to 298 has a negligible effect on the branching ratio. Therefore, for the first pair of simulations at 285 K, k’3b, and k’3c were set as equal to the experimentally determined values at 298 K. For the second pair of 285 K simulations the experimental values at 285 K were used. Finally, the third pair of simulations, at 298 K, were carried out in order to verify the validity of the simulation procedure. According to the widely accepted view, at this temperature dimer formation does not interfere with the reactions that lead to ozone consumption, and therefore the simulation should return @-03 values equal to those determined experimentally. The 298 K @-03 data of Table 5 show that the mechanism and rate constant data used indeed correctly predict the quantum
11930 J. Phys. Chem., Vol. 98, No. 46, 1994 TABLE 4:
Horowitz et al.
Summary of Reactions Used in the Simulation of the Reaction Mechanism reaction
rate constant'
ref
Clz c 1 + c 1 c1 0 3 -c10 0 2 c 1 0 c 1 0 Clz 0 2 c10+c10-c1+02+c1 0 c 1 0 c 1 + OClO C10 C10 M C1202 M C1202 M C10 C10 c 1 + OClO c 1 0 c 1 0 c 1 + c1202 c 1 + 0 2 c 1 03 OClO products
kl = 1.00 x k2 = 2.9 x lo-" exp(-260/T) k3 = 8.0 x exp(-1250/nb
this work 15 15
k4 = 7.0 x 10-'2(T/300)-2.6 k-4 = kdK4' kg = 3.4 x lo-" exp(l60/T) klo = 1 x lo-'' kll = 2.1 x exp(-4700/T)
15
-
1 2 3a 3b 3c 4 -4 9 10 11
+ +
+
-
---
+ + +
+
In units of s-l, cm3 molecule-' branching ratio and K4,see Table 5.
s-l,
+
+
-.+
+
+
+
15 14 15
and cm6 molecule-2 s-' for unimolecular, bimolecular, and termolecular reactions, respectively. For
TABLE 5: Summary of Simulation Resultsa
References and Notes
(1) Clyne, M. A. A,; McKenney, D. J.; Watson, R. T. J . Chem. Soc., Faraday Trans. 1 1975, 71, 322. (2) Wongdontri-Stuper, W.; Jayanty, R. K. M.; Simonaitis, R.; Heicklen, J. J . Photochem. 1979, 10, 163. (3) Basco, N.; Hunt, J. Int. J. Chem. Kinet. 1979, 11, 649. (4) Cox, R. A.; Dement, R. G. J . Chem. Soc., Faraday Trans. 1 1979, 75, 1635. (5) Burrows, J. P.; Cox, R. A. J . Chem. SOC.,Faraday Trans. I 1981, a In all simulations initial concentrations of 0 3 , Cl2, Nz, and 0 2 were 77, 2465. 1.0 x 10l6, 1.0 x 1.0 x and 1.54 x loL9molecule ~ m - ~ . (6) Hayman, G. D.; Davies, J. M.; Cox, R. A. Geophys. Res. Lefr. 1986, cm3 molecule-', lower values from ref 15, higher In units of 13, 1347. values from ref 25. In units of cm3 molecule-' s-I. Experi(7) Molina, L. T.; Molina, L. J. J . Phys. Chem. 1987, 91, 443. mental, this work. e From simulation at about 50% conversion of 03. (8) Cox, R. A.; Hayman, G. D. Nature 1988, 332, 796. f Experimental at the same conversion. (9) Sander, S. P.; Friedl, R.; Young, Y. L. Science 1989, 245, 1095. (10) Trolier, M.; Mauldin, R. L., III;Ravishankara,A. R. J . Phys. Chem. 1990, 94, 4896. yield of ozone consumption. The slight difference between the (11) Simon, F. G.; Schneider, W.; Moortgat, G. K.; Burrows, J. P. J . experimental and simulated values of 0.15 should be added also Photochem. Photobiol. A. Chem. 1990, 94, 4896. to the results at 285 K. Bearing this in mind, it can be seen (12) Stolarski, R. S.; Cicerone, R. J. Can. J . Chem. 1974, 52, 1610. from the fist pair at 285 K results that, if at all, dimer formation (13) Rowland, F. S.; Molina, M. J. Rev. Geophys. Space Phys. 1975, accounts only for a small fraction of the decrease in Q-03. At 78, 5341. (14) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F.; Kerr, J. the same time, for the second pair of 285 K results a good A.; Troe, J. J . Phys. Chem. Ref. Data 1989, 18, 881. agreement between the experimental and simulated quantum (15) DeMore, W. B.; Sander, S. P.; Golden, D. M.; Hampson, R. F.; yields is observed when the k3, K 3 b , and kf3c values determined Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R.; Kolb, C. E.; Molina, at 285 K are used. M. J. JPL Publication 92-20; Jet Propulsion Laboratory, California Institute According to the simulation results, the enhanced dimer of Technology, 1992. (16) Horowitz, A,; Bauer, D.; Crowley, J.; Moortgat, G. K. Geophys. formation does not appear to be responsible for the rapid Res. Left. 1993, 20, 1423. decrease of Q-03 at temperatures below 298 K. The observation (17) Wahner, A.; Tyndall, G. S.; Ravishankara, A. R. J . Phys. Chem. that the mechanism used correctly predicts Q-03 as well as K4 1987, 91, 2734. at 285 K indicates that, for practical purposes and within the (18) Bauer, D.; Crowley, J. N.; Moortgat, G. K. J . Phofochem.Photobiol. temperature range of the present study, the temperature depenA. Chem. 1992, 65, 329. (19) Nonish, R. G. W.; Neville, G. H. J. J . Chem. SOC.1934, 1864. dence of the branching ratio in oxygen is better described by (20) Lin, C. L.; Jaffe, S.; DeMore, W. B. Photochemistry of chlorinethe present results than by extrapolation of Arrhenius parameters ozone mixtures. American Chemical Society, 169th meeting, Philadelphia, determined at temperatures above 298 K. Thus, as long as the 1975. exact reaction mechanism operative at low temperatures is not (21) Chance, E. M.; Curtis, A. R.; Jones, I. P.; Kirby, C. R. FACSIMILE known and within the temperature range studied, the present Report, AERE-R 8775, AERE Hanvell, 1977. (22) Clyne, M. A. A.; Coxon, J. A. Proc. R. Soc. London, Ser. A 1968, results can be considered as yielding only the apparent, but still 303, 207. working, temperature dependence of the branching ratio in the (23) Clyne, M. A. A.; White, I. F. Trans. Faraday SOC.1971,67,2068. bimolecular C10 C10 reaction in oxygen. (24) Clyne, M. A. A.; McKenney, D. J.; Watson, R. T. J. Chem. Soc., Acknowledgment. We wish to thank Dr. Stanley P. Sander Faraday Trans. 1 1977, 73, 1169. from the Jet Propulsion Laboratory for kindly providing us with (25) Nickolaisen,S. L.; Friedl, R. R.; Sander, S. P. J . Phys. Chem. 1994, a preprint of his article. 98, 155. 285 285 285 285 298 298
2.25 3.40 2.25 3.40 0.62 0.89
1.0 1.0 1.0 1.0 1.2 1.2
0.392 0.392 0.575 0.575 0.392 0.392
+
0.404 0.404 0.263 0.263 0.404 0.404
0.204 0.204 0.162 0.162 0.204 0.204
3.7 3.6 2.9 2.8 3.9 3.9
3.05 3.05 3.05 3.05 4.05 4.05
