J. Phys. Chem. 1996, 100, 7533-7540
7533
Thermal Decomposition of CFCl3 S. S. Kumaran, M.-C. Su,† K. P. Lim, J. V. Michael,* and A. F. Wagner* Chemistry DiVision, Argonne National Laboratory, Argonne, Illinois 60439 ReceiVed: January 3, 1996X
The thermal decomposition of CFCl3 (CFC-11) has been studied in reflected shock waves using the Cl-atom atomic resonance absorption spectroscopy (ARAS) detection technique. The first thermal rate measurements for CFCl3 (+M) f CFCl2 + Cl (+M) are reported. The experimental Cl-atom concentration profiles show two distinct rates of formation. The initial fast process gives a Cl-atom yield of 2, and this is followed by slow secondary processes that are density and temperature dependent. The final Cl-atom yield is greater than 2[CFCl3]0. This behavior confirms that C-Cl bond scission is the dominant dissociation pathway for both CFCl3 and the product radical, CFCl2, as observed in an earlier study from this laboratory on the related CF2Cl2 decomposition. Profile fits require the fast subsequent dissociation of CFCl2, and therefore, the shorttime kinetics can be best explained as being due to C-Cl bond breaking in the parent, CFCl3. The temperature and density dependences of the later time Cl-atom profiles suggest that the slow secondary rate can be ascribed to reactions involving the carbene diradical, CFCl. The Cl-atom data were analyzed with detailed kinetics modeling calculations. Experiments were performed with varying [CFCl3]0 (15.23, 7.877, 5.159, and 2.496 ppm) in Kr diluent at three (3.1 × 1018, 2.1 × 1018, and 1.2 × 1018 cm-3) post-shock densities. An Arrhenius fit to the experimental CFCl3 dissociation rates over the T-range 1279-1950 K gives k ) (2.82 ( 1.22) × 10-8 exp(-26420 ( 674 K/T) cm3 molecule-1 s-1, with (36% error at the one standard deviation level. Comparing this expression to earlier results from this laboratory on CF3Cl, CF2Cl2, and CCl4 suggests that the C-Cl bond strength in CFCl3 should be between those for CF2Cl2 and CCl4. The temperature and pressure dependence of the rate constants, i.e., the falloff from the low-pressure limit, have been characterized with Rice-Ramsperger-Kassel-Marcus (RRKM) calculations using E0 ) (76.5 ( 0.5) kcal mol-1 with 〈∆E〉down ) (800 ( 215) cm-1. This E0 implies ∆fH°0,CFCl2 ) -20.3 kcal mol-1, and subsequently ∆H°0 ) (58 ( 2) kcal mol-1 for CFCl2 f CFCl + Cl. CFCl3 (+M) f CFCl + Cl2 (+M)
Introduction The chlorofluoromethanes have been extensively used as propellants, solvents, and refrigerants because they are so chemically inert. However, it has clearly been shown that these compounds constitute one of the major anthropogenic sources of atmospheric chlorine which eventually can deplete stratospheric ozone. In fact, production will cease in developed countries except for special needs beginning in 1996.1 The destruction of excess amounts of such compounds then presents another serious environmental problem. If incineration is to be considered, then a complete engineering design with accurate predictions of organic emissions2-5 requires a full knowledge of the elementary chemical decomposition and oxidation mechanisms for these molecules. Studies on the thermal dissociations of CH3Cl,6 CCl4,7 CH2Cl2,8 COCl2,9 CF3Cl,10 and CF2Cl2,11 as well as bimolecular reactions of O-atoms with CH3Cl, CH2Cl2, and CHCl3,12,13 are already complete. In all previous work from this laboratory, the studies have been carried out with a shock tube apparatus utilizing Cl- or O-atom atomic resonance absorption spectrometry (ARAS) as the detection technique. In this work, results on the thermal decomposition of CFCl3 (CFC11) are presented. The lowest available energy pathways for thermal decomposition of CFCl3 are C-Cl fission
CFCl3 (+M) f CFCl2 + Cl (+M)
(1a)
and three-center Cl2-elimination † X
On sabbatical leave from Butler University, Indianapolis, IN 46208. Abstract published in AdVance ACS Abstracts, April 1, 1996.
S0022-3654(96)00023-8 CCC: $12.00
(1b)
The existing experimental14-17 values for the endothermicity of reaction 1a range from 68.0 to 75.7 kcal mol-1. The theoretical calculations of Gutsev18 however suggest that a value as low as 67.1 kcal mol-1 may be possible. The threshold energy for reaction 1b, where CFCl is in its singlet state, is also ambiguous. However, the endothermicity can be estimated. For the overall reaction CFCl3 ) CFCl + 2Cl, Ibuki et al.19 report 133.0 kcal mol-1, which yields ∆H°0(1b) ) 75.8 kcal mol-1. Also, if the C-F bond energy in CF2Cl, reported by Dispert and Lackman,20 is combined with ∆fH°0,CF2Cl ) 63.0 kcal mol-1, as suggested from our recent study,11 then 76.2 kcal mol-1 is obtained in agreement with Ibuki et al.19 A barrier of >8.0 kcal mol- 1 has been reported for CF2 insertion into Cl2.21 If a barrier of similar magnitude exists for CFCl insertion into Cl2, then the reaction threshold for reaction 1b would be ∼84.0 kcal mol-1. The dominant thermal dissociation pathway for CFCl3 should then be the entropically favored lowest energy C-Cl fission route, 1a. Additional experimental evidence for the dominance of reaction 1a comes from other sources. Morrison et al. observed 100% conversion through C-Cl fission in a multiphoton IR photochemical study on CFCl3.22 In a recent experimental study from this laboratory,11 the C-Cl bond fission processes in CF2Cl2 and CF2Cl were observed to be the only thermal dissociation pathways. It should be noted that the C-Cl bond energy should decrease with increasing Cl-atom substitution (∼85 in CF3Cl to 67.7 kcal mol-1 in CCl4), suggesting that the bond strength in CFCl3 should be greater than that in CCl4 but less than that in CF2Cl2 (84.5 kcal mol-1). Hence, by analogy, © 1996 American Chemical Society
7534 J. Phys. Chem., Vol. 100, No. 18, 1996 rapid C-Cl bond cleavage should start to occur at a relatively low temperature of ∼1200-1300 K.7,11 Because the interfering secondary reaction, Cl + CFCl3 f CFCl2 + Cl2, is highly endothermic (∼15 kcal mol-1), it will be negligible for the dilute experimental mixtures used here. Hence, absolute determinations of [Cl]t can yield good values for the relative rates of reactions 1a and 1b. This measurement can also give information on the stability of the CFCl2-radical. Analogous with CF2Cl2,11 the subsequent C-Cl fission in CFCl2 may be the dominant depletion process. As noted above, ∆H°0 for CFCl3 ) CFCl + 2Cl has been reported to be 133.0 kcal mol-1.19 From ∆fH°0,CFCl3 ) -68.2 kcal mol-1,23 a value for ∆fH°0,CFCl ) ∼9.5 kcal mol-1 can be derived, which is consistent with the 298 K value of (7 ( 6) kcal mol-1 reported in the 1994 NASA Tables.24 Considering the range of experimental values for ∆H°0(1a) noted above, the ∆H°0 for CFCl2 f CFCl + Cl ranges from 57 to 65 kcal mol-1. Assuming ∆H°0 ) E0, this reaction has a higher E0 than that for the analogous process in CF2Cl;11 however comparisons of the respective molecular properties25 suggest that CFCl2 should have a larger threshold state density than CF2Cl, and, therefore, the rates of dissociation of these two radicals should be similar at the low-pressure limit. In any case, the range of threshold energies is ∼8 kcal mol-1 lower than that for reaction 1a, and therefore, this subsequent process should be at least an order of magnitude faster than reaction 1a in the temperature range of our experiments. Experimental Section The experimental apparatus, technique, and the associated electronics used in the present study have been completely described elsewhere.26,27 Therefore only a few comments are necessary that are pertinent to the present study. Apparatus. The shock tube equipment used here is comprised of a driver chamber and a 7-m 304 stainless steel tube (9.74 cm i.d.) section, the inside surface of which has been polished to be quite passive. These two sections are separated by a thin aluminum diaphragm (4 mil, unscored 1100-H18). This is mounted between vacuum flanges that are attached to the ends of the driver and driven sections. The tube was routinely pumped by an Edwards Vacuum Products Model CR100 P fore-pump diffusion-pump combination to 0.1 and is best represented by a modified Beer’s law expression,
(ABS)Cl ) 4.41 × 10-9[Cl]0.582
(2)
where [Cl] is expressed in atoms cm-3.30 Gases. The He driver gas (99.995%) was obtained from Air Products and Chemicals, Inc. Diluent Kr used in the reaction mixture was Scientific grade (99.997%) from MG Industries. Electronic grade Cl2 (99.999%) from MG Industries, diluted in Scientific grade He (99.9999%) from MG Industries, was used in the Cl-atom resonance lamp. CFCl3 and CF3Cl (both at 99.8%) were obtained from AGA Specialty Gases and were purified by bulb-to-bulb distillation. The middle thirds were retained for mixture preparation. Results CFCl3 dissociation experiments were performed between 1279 and 1950 K at three different loading pressures by observing the temporal behavior of Cl-atom formation behind reflected shock waves. The top panel of Figure 1 shows a typical experimental Cl-atom ARAS transmittance signal. The signal decreases as product Cl-atoms are formed. During the course of the study, a method for performing running calibrations was adopted for determining the overall Cl-atom yield. There are day-to-day fluctuations in the operation of the photometer system due to changes in lamp pressure, cooling air, mixture composition, microwave power, and window transmission. Therefore, corrections were made by using thermal decomposition results on CF3Cl interspersed with those on CFCl3. We showed earlier with CF3Cl10 that [Cl]∞ ) [CF3Cl]0 gave the curve of growth summarized by eq 2. In a similar way as in CF2Cl2,11 10 CF3Cl experiments were performed under nearly identical conditions as those with CFCl3. The ratio of [CF3Cl]0 to that of [Cl]∞, calculated from eq 2, then provided a scale factor for deriving the final [Cl]t profile for the CFCl3 experiments done on the same day. All of the experimental conditions in the present study are given in Table 1. In all of the present experiments, the ARAS profiles show two distinct Cl-atom formation rates. This is shown explicitly in Figure 1 (top panel) by the initial steep drop in the transmittance signal, but slow secondary formation clearly continues at longer times with a much slower rate. Thus, there are two separate time scales associated with formation. The ARAS signal was converted to [Cl]t using eq 2, giving the profile displayed in the bottom panel of Figure 1. The inset shows the first 200 µs of the profile. The thin horizontal lines correspond to the yield, [Cl]fast/[CFCl3]0 ) 2.0, following the fast buildup. For all of the experiments, these yields were nearly 2, unambiguously indicating that the CFCl3 decomposition initially produces 2 Cl-atoms. Hence, reaction 1a and
Thermal Decomposition of CFCl3
J. Phys. Chem., Vol. 100, No. 18, 1996 7535
Figure 2. A [Cl]t profile showing the secondary formation following the rapid conversion of CFCl3 to CFCl and 2Cl. The post-shock conditions are [CFCl3]0 ) 2.496 ppm in diluent Kr, T5 ) 1885 K, P5 ) 648 Torr, and F5 ) 2.771 × 1018 cm-3. Note that the late Cl-atom formation rate is lower for this experiment than that in Figure 1 where [CFCl3]0 is 2 times higher. This concentration dependence of the secondary kinetics is characterized by the reactions of CFCl included in the Table 2 mechanism. The thin horizontal and smooth solid lines are as identified in Figure 1.
Figure 1. A typical experimental record (top) showing decreasing ARAS signal as Cl atoms are formed from the thermal dissociation of CFCl3. The composition and post-reflected-shock conditions are [CFCl3]0 ) 7.878 ppm in diluent Kr, T5 ) 1748 K, P5 ) 405 Torr, and F5 ) 2.236 × 1018 cm-3. The transmittance shows two distinct consecutive Cl-atom formation rates. A fast process, exemplified by the initial steep drop in the signal, is followed by a slow secondary formation rate. The bottom panel shows the experimental [Cl]t profile derived from the curve of growth with the inset showing the initial formation for 200 µs. This initial rate follows single exponential growth corresponding to the CFCl3 dissociation rate. The thin horizontal lines represent a stoichiometric yield, [Cl]fast/[CFCl3]0 ) 2.0. The smooth solid lines are the Table 2 model calculated fit (see text).
CFCl2 (+M) f CFCl + Cl (+M)
(3)
are adequate for modeling the profiles. This is exactly the same behavior as observed in the dissociation of CF2Cl2;11 i.e., the radical product decomposes much faster than CFCl3. RRKM calculations on CFCl2 using previously published molecular parameters25,33 were then carried out, confirming that reaction 3 is at least 20 times faster than reaction 1a. Because of this behavior, first-order rate constants for reaction 1a could then be derived by simple kinetics analyses of the short-time [Cl]t profiles using a closed expression. However, in this study the more extensive mechanism given in Table 2 was used for full modeling of [Cl]t over the entire time range. With this model, the smooth solid lines in the bottom panel of Figure 1 were calculated, illustrating the quality of fits particularly for the short-time regime (i.e., the inset). These results strongly argue against any contribution from molecular dissociation, reaction 1b. We therefore conclude that reaction 1a is rate controlling with reaction 3 instantaneously contributing a second Cl-atom. The rate constants for reaction 1a thereby derived are given in Table 1. The subsequent long-time chemistry requires additional consideration. Figure 1 (bottom panel) shows a [Cl]t profile obtained at low temperature and relatively high [CFCl3]0, and this can be contrasted to the experiment shown in Figure 2 where lower [CFCl3]0 is used but at higher temperature. These two experiments illustrate the behavior of long-time Cl-atom formation. Note that [Cl]t increases to >2[CFCl3]0 in both experiments. However, the secondary rate is larger for higher
[CFCl3]0. It is clear, following C-Cl bond cleavage in CFCl3 and subsequent loss of Cl from CFCl2, that the additional [Cl] must arise solely from the reactions of CFCl. To explain these results, we considered two additional reactions:
CFCl (+M) f CF + Cl (+M)
(4)
and dissociative recombination
CFCl + CFCl f C2F2Cl + Cl
(5)
where the produced vinyl radical would undoubtedly decompose rapidly to Cl + C2F2; i.e., giving an overall process, 2CFCl ) C2F2 + 2Cl. Reaction 4 may be inconsequential at low T considering the high C-Cl bond energy; however, it may contribute to [Cl]t under high-T/low-concentration conditions. There are no literature data for reaction 4. With a known reaction threshold23 of ∼81 kcal mol-1 and an assumed energy transfer parameter, RRKM low-pressure limit rate constants for the reaction were calculated using the molecular properties of Karolczak et al.33 The low-pressure values were assigned to the reaction since falloff does not exist in triatomics at these densities and temperatures. In the Table 2 mechanism, the rate constant for reaction 4 was iteratively adjusted by varying 〈∆E〉down to best fit the late behavior of the [Cl]t profiles for the high-T/lowconcentration experiments. Of course, k1a determines the fit to the initial portion as shown in the Figure 1 inset. The optimized k4 given in Table 2 results from 〈∆E〉down ) 1000 cm-1, and a typical model calculation is shown in Figure 2 where the fit is seen to be excellent. The larger rate seen at higher [CFCl3]0 and lower temperatures (Figure 1, bottom panel) cannot be rationalized by including only reaction 4. For these experiments it was necessary to postulate reaction 5. The recombination reactions of carbenes have not been extensively studied other than for CH2 + CH2. It is not clear if barriers are present or what the height of the barriers could be if they exist. For CFCl recombination, the lowest energy process after formation of the olefin should be the Cl-atom elimination process from the chemically activated intermediate; i.e., 2CFCl f C2F2Cl2* f C2F2Cl + Cl. The vinyl radical, C2F2Cl, could then easily undergo fast unimolecular dissociation, C2F2Cl (+M) f C2F2 + Cl (+M). We have accordingly included 2CFCl f C2F2 + 2Cl, at the reaction 5 rate, in the
7536 J. Phys. Chem., Vol. 100, No. 18, 1996
Kumaran et al.
TABLE 1: Kinetics Data for the Thermal Decomposition of CFCl3 k1ac/(10-17 cm3/ (molecules‚s))
k5c/(10-11 cm3/ (molecules‚s))
2086 108.7 453.6 58.46 11.83 460.0 1235 270.3
1.75 0.90 1.30
P1/Torr
Msa
F5b/1018 cm-3
5.91 5.88 5.98 5.96 5.90 5.97 5.96 5.94
2.716 2.450 2.551 2.373 2.335 2.568 2.670 2.520
1.222 1.104 1.168 1.086 1.057 1.174 1.215 1.147
XCFCl3 ) 15.23 × 10-6 25500 1823 1200 1508 5300 1625 635 1418 125 1377 5400 1645 15000 1767 3100 1588
10.98 10.93 10.92 10.94 10.88 10.92 11.00 10.99 10.90 10.98
2.659 2.641 2.501 2.414 2.637 2.459 2.532 2.429 2.356 2.317
2.236 2.205 2.093 2.023 2.192 2.058 2.133 2.045 1.965 1.943
XCFCl3 ) 7.877 × 10-6 20000 1748 19500 1732 3000 1567 870 1468 16500 1727 2200 1519 3800 1602 900 1485 367 1405 175 1363
5.92 5.90 5.99 5.92 5.92 5.90 5.95 5.96 5.95
2.664 2.378 2.513 2.776 2.816 2.642 2.516 2.405 2.402
1.204 1.074 1.153 1.247 1.262 1.191 1.147 1.098 1.095
10.94 10.98 10.93 10.90 10.86 10.93 10.93
2.687 2.603 2.506 2.343 2.403 2.445 2.589
2.234 2.179 2.092 1.946 1.992 2.041 2.158
5.96 5.84 5.95 5.93
2.236 2.790 2.648 2.608
1.008 1.231 1.199 1.179
45.00 37000 10700 7000
1279 1923 1746 1698
4.464 3005 892.2 593.8
15.89 15.96 15.99 15.90 15.99 15.92 15.89 15.94 15.90
2.360 2.691 2.661 2.642 2.552 2.568 2.471 2.440 2.367
2.858 3.235 3.211 3.173 3.097 3.101 2.989 2.963 2.868
350 36000 23000 18000 6900 6900 2200 1250 475
1413 1789 1753 1729 1625 1644 1535 1500 1421
12.25 1113 716.3 567.2 222.8 222.5 73.60 42.19 16.56
10.93 10.89 10.91 10.97 10.96
2.398 2.792 2.665 2.599 2.608
2.000 2.298 2.212 2.173 2.186
XCFCl3 ) 2.496 × 10-6 850 1455 40000 1926 16000 1767 7450 1687 8450 1692
42.50 1741 723.4 342.8 386.6
15.90 16.00 15.88 15.84 15.96 15.98 15.91 15.93
2.594 2.771 2.664 2.639 2.553 2.448 2.453 2.715
3.125 3.319 3.192 3.159 3.093 2.979 2.972 3.252
15.92 15.78 15.93
2.653 2.649 2.888
3.189 3.157 3.408
k1st/s-1
13000 350 3000 26000 43000 10500 3000 450 275
T5b/K
1760 1429 1580 1899 1950 1733 1584 1458 1455
XCFCl3 ) 5.159 × 10-6 21000 1794 15000 1692 2900 1578 170 1395 525 1461 1400 1508 9500 1675
8550 47500 21000 19000 7200 2000 1275 39000
1674 1885 1757 1726 1626 1508 1515 1817
XCFCl3 ) 7.877 × 10-6 29000 1743 25000 1738 2032
894.3 884.2 143.3 43.00 752.7 106.9 178.1 44.01 18.68 9.005 1080 32.58 260.1 2085 3407 881.7 261.5 40.99 25.12 940.1 688.3 138.6 8.736 26.36 68.59 440.3
1.30 1.00 1.50 1.00 0.80 1.20 0.90 1.00
1.00 1.00 1.75 2.00
1.20 0.80 0.80 0.70 0.90 2.00 1.20 1.20 1.00 0.70 0.70 0.70 0.70
1.00 0.90 0.80 0.80
273.6 1431 657.9 601.5 232.8 67.14 42.90 1199
0.80 1.00 1.00 0.90 0.70
909.5 791.9
0.70 0.80 0.80
1.00
a The error in measuring the Mach number, M , is typically 0.5-1.0% at the one standard deviation level. b Quantities with the subscript 5 refer s to the thermodynamic state of the gas in the reflected shock region. c The rate constants are derived as described in the text.
Thermal Decomposition of CFCl3
J. Phys. Chem., Vol. 100, No. 18, 1996 7537
Figure 3. Arrhenius plot of optimized rate constants for the CFCl radical dissociative recombination process, reaction 5. Over the complete temperature range, the data can be represented by the thin solid line, corresponding to k5 ) (1.03 ( 0.34) × 10-11 cm3 molecule-1 s-1, eq 6.
TABLE 2: Reaction Mechanism Used for the High-Temperature Pyrolysis of CFCl3a 1a 3 4
CFCl3 (+M) f CFCl2 + Cl (+M) CFCl2 (+M) f CFCl + Cl (+M) CFCl (+M) f CF + Cl (+M)
5
CFCl + CFCl f C2F2 + 2Cl
k1a ) to be fitted k3 g 20k1ab k4 ) F(3.55 × 10-9 exp(-36183 K/T)b k5 ) to be fitted
All rate constants are in molecular units. b RRKM estimated rate constant, see text.
Figure 4. Arrhenius plot of measured second-order rate constants for CFCl3 (+Kr) f CFCl2 + Cl (+Kr). The rate data are from Table 1 at F5 ) 1.16 × 1018 (O), 2.11 × 1018 (×), and 3.10 × 1018 cm-3 (9) (i.e., P1 ) 6, 11, and 16 Torr, respectively). The solid line is the linear least-squares fit to the three sets of data, eq 7.
TABLE 3: Molecular Parameters Used in the Theoretical Calculations for the Dissociation Reaction: CFCl3 (+M) f CFCl2 + Cl (+M) frequencies (cm-1)
a
Table 2 mechanism. The overall reaction is only 46.2 kcal mol-1 endothermic.23 Both reactions 4 and 5 are required to simultaneously model the results at both low and high concentrations and temperatures. Late [Cl]t predictions with reaction 5 alone gives poor fits for the high-T/low-concentration experiments since the rate is quadratic. We therefore conclude that both processes, reactions 4 and 5, must be included to explain the entire range of experimental conditions. k5 can then be determined by iterative adjustment with k4 being fixed at the value given in Table 2. The results are listed in Table 1 and are plotted in Figure 3. A T-independent value,
k5 ) (1.03 ( 0.34) × 10-11 cm3 molecule-1 s-1 (6) is the best representation of these data for 1508 e T e 2032 K. The second-order rate constants for reaction 1a given in Table 1 are shown as an Arrhenius plot in Figure 4. The experiments are distinguished from one another on the basis of loading pressures, 6, 11, and 16 Torr, corresponding to average ((5%) post-shock densities of 1.16 × 1018, 2.11 × 1018, and 3.10 × 1018 cm-3, respectively. The solid line is the linear least-squares fit to the three sets of data. For 1275 e T e 1950 K, the data can be represented by k1a ) (2.82 ( 1.22) × 10-8 exp(-26420 ( 674/T) cm3 molecule-1 s-1 (7) The points in the figure are within (36% of the line given by eq 7 at the one standard deviation level. The scatter is largely due to unimolecular falloff as can be seen by the small separation of the second-order rate constants at the different densities. Hence, we have attempted to characterize the rate data by using RRKM models, as discussed in the next section. Discussion To our knowledge there are no previous rate constant measurements for reaction 1a, nor are there any theoretical
species
moments of inertia (amu Å2)
ref
206.6, 206.6, 293.6 23 CFCl3 1085.0, 349.5, 535.3, 241.0, 241.0, 398.0, 398.0, 847.0, 847.0 218.7, 154.9, 66.7b 25 CFCl2 1172.7, 765.0, 516.6, 378.9, 319.5, 239.4a a These frequencies are taken from ab initio calculations presented in ref 25 and are, in accordance with usual practice, scaled by 0.9. b Calculated from the structure given in ref 25.
descriptions of the unimolecular rate behavior. In this work, in a manner similar to that done in a previous study,11 the second-order dissociation rate constants for the reaction were theoretically modeled in three ways: a semiempirical Troe calculation and two distinct RRKM calculations.34-37 All three of these approaches include weak collision corrections through the efficiency factor βc, which in turn is determined by the average energy transfer parameter, 〈∆E〉down. The theory depends strongly on 〈∆E〉down and also on the threshold energy, E0. Since all three methods are sensitive to these two highly coupled quantities, all calculations were carried out iteratively for various mutual combinations of E0 and 〈∆E〉down until the best fit with the measured data was obtained. Since the measurements were taken at approximately three different total densities, a “best fit” was defined as that resulting in the lowest, approximately equal, root mean square errors for each of the three total densities. This ensures a balanced representation for all the measurements. The first method utilizes the semiempirical method of Troe34-37 to calculate the pressure and temperature behavior for reaction 1a. The molecular parameters necessary for this determination are given in Table 3. This type of calculation uses the Whitten-Rabinovitch method for calculating the density of states. The rate of collisions between CFCl3 and the buffer gas Kr is calculated from the standard expression38 for collisions under a Lennard-Jones interaction potential:
kLJ )
( )
( ) ()
gq 8πkT σ 2Ω(2,2) g1g2 12 µ
1/2
exp
12 kT
(8)
7538 J. Phys. Chem., Vol. 100, No. 18, 1996
Kumaran et al.
TABLE 4: Best Fit Values for the High- and Low-Pressure Limiting Rate Constants Used in the Theoretical Calculations for the Dissociation Reaction: CFCl3 (+M) f CFCl2 + Cl (+M)a k1a0 ) A0T-n0 e-T0/T calculation type Troel/Lennard-Jones RRKM/Gorin RRKM/ab initio
A0
/1032
cm3
molecule-1 s-1
0.01229 2.065 100.86
k1a∞ ) A∞ T-n∞ e-T∞/T
n0
T0/K
A∞/1016 s-1
10.27 10.85 11.50
42 444 42 463 42 950
2.18 0.220 3.86
n∞
T∞/K
0 0 0
37 184 37 179 37 938
a The derived values for k-1a∞ for each of the models are 5.7, 0.57, and (8.6 ( 0.4), respectively from top to bottom, all in units of 10-11 cm3 molecule-1 s-1.
where the ratio of electronic degeneracy factors g is unity.38 The interaction potential parameters σ and for both CFCl3 and Kr are derived from polarizabilities (by methods described in Hirschfelder, Curtis, and Bird38) as suggested by Cambi et al.39 and combined as in that reference to obtain σ12 and 12 for use in the above equation. This method in effect replaces the simple combining rules for determining σ12 and 12 that are commonly used.38 From the density of states and the above rate of collisions, the strong collision low-pressure rate constant can be determined. We have carried out the calculations with variations in E0 between 72 and 78 kcal mol-1. The best overall fit is with E0 ) 76.0 kcal mol-1 and 〈∆E〉down ) 700 cm-1. With these values, the predicted rate constants for 1250 e T e 2000 K range between 0.33 and 0.55 of the low-pressure limit, k1a0βcksc 1a0. Hence, there should be some sensitivity to pressure seen in Figure 4) and to the values used for the high-pressure limit in the calculation. As noted above, because the data are slightly in the falloff region, the Troe fit theoretical conclusions are influenced by the method for calculating k1a∞, the limiting high-pressure rate constant for reaction 1a. As in earlier work,6,8,9,11,30 highpressure values have been calculated between 1200 and 2000 K for the reverse reaction -1a assuming that the transition state is a Lennard-Jones complex. This model then presupposes that there is no barrier to reaction -1a and immediately identifies E0 as being identical to ∆H°0(1a). k-1a can then be calculated from eq 8 with gq ) 1, g1 ) gCFCl2 ) 2, and g2 ) gCl ) 2(2 + exp(-hc(882.36 cm-1)/kT)).23 Since the Lennard-Jones parameters are not known for CFCl2, they are again calculated from CFCl2 and Cl polarizabilities38 as described by Cambi et al.39 Equation 8 is then evaluated between 1200 and 2000 K giving a nearly constant value of k-1LJ ) 5.7 × 10-11 cm3 molecule-1 s-1. Equilibrium constants, K1a, have been directly calculated from the molecular constants in Table 3 for the best fit value, E0 ) ∆H°0(1a) ) 76.0 kcal mol-1. The resulting values then follow the van’t Hoff equation,
K1a ) 3.82 × 1026 exp(-37184 K/T) molecules cm-3 (9) to within (2.5% over the 1200-2000 K temperature range. The value for the high-pressure Cl-atom dissociation rate constant is then calculated as k1a∞ ) k-1LJK1a. The resulting k1a∞ and an analogous fit to the low-pressure limit, k1a0, are listed in Table 4. All fits listed in this table have a root mean square relative error over the 1200-2000 K of
