12278
J. Phys. Chem. 1994, 98, 12278-12283
Thermal Decomposition of CF3CI J. H. Kiefer* and R. Sathyanarayana Department of Chemical Engineering, University of Illinois at Chicago, Chicago, Illinois 60680
K. P. Lim and J. V. Michael* Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 Received: June 10, 1994; In Final Form: August 10, I994@
+
-
+ +
The unimolecular decomposition CF3C1 Kr CF3 C1 Kr has been studied using two different techniques, atomic resonance absorption spectrometry (ARAS) and laser schlieren (LS) density gradients, in two laboratories. As in our previous joint investigation of C C 4 dissociation, the ARAS and LS techniques give completely consistent results over the overlapping temperature range, 1800-2200 K. The title reaction is found to be fairly close to the low-pressure limit. The ARAS measurements between 1521 and 2173 K give k2nd = 1.73 x IO-' exp(-33837K/T) cm3 molecule-' s-l ( f 2 7 % at lo). This is in good agreement with the earlier ARAS measurements of b g e r and Wagner. k2nd = 1.15 x exp(-28330K/T) cm3 molecule-' s-' ( f 2 0 % at l o ) is obtained from the LS results between 1800 and 3000 K. The good agreement between methods verifies both the C-C1 fission path for the CFX1 dissociation and the curve-of-growth used in the C1 atom ARAS analysis. RRKM analysis of these rate data indicated a larger than usual magnitude for hEdown,in agreement with our previous findings on CC4, but here it was necessary that it increase with T. The best fit was with = 270 cm-'. The RRKM fit to the data is given by the three-parameter exp(-48133K/7') cm3 molecule-' s-l for a pressure of 300 Torr. This expression k2nd = 2.95 x 1024T8.50 final expression agrees with both the ARAS and LS results to within f 2 5 % and can be used in modeling applications between 1500 and 3000 K.
Introduction In earlier investigations from our laboratories the thermal decompositions of CH3C1,' CC4,2 C O C ~ Zand , ~ CH2C1z4 have been studied. The present work on the thermal decomposition of C S C I may be viewed as a continuing investigation on the chloromethane class of molecules. There are several reasons for continuing work on the chloromethanes. The f i s t motivation is practical. The incineration of chlorocarbon type molecules has presented potential air pollution problems that can only be properly assessed by understanding the chemical mechanisms for The first reactions that have to be considered in any such description are the thermal decompositions: (a) simple bond scission to C1 atoms and a radical and/or (b) molecular elimination to a diatomic molecule and a carbene radical. The subsequent chemistry would then be largely dictated by the reactions of the product radicals with 0 2 and other combustion species, e.g. 0, OH, and H. The second motivation is experimental. One of the analytical methods used in all of these studies has been C1 atom atomic resonance absorption spectrometry (ARAS). In the CH3Cl investigation,' the curve-of-growth for C1 atoms was determined from the long time steady-state formation yield. In this case, the secondary reaction, C1 CH3C1, became more important as [CH3Cl]o was increased, giving stoichiometry coefficients that were less than unity. Since such complications do not exist with CF3C1, the previously determined curve-ofgrowth can be unambiguously checked because the only possible decomposition reaction,
+
CF,Cl+ M
-
CF,
+ C1+ M
(1)
gives unit stoichiometry Over the entire usable concentration range. This decomposition has already been investigated by @Abstractpublished in Advance ACS Abstracts, September 15, 1994. 0022-365419412098-12278$04.50/0
C1 atom ARAS,8 and we can also compare with these results. The final motivation is theoretical. The A R A S has already been theoretically analyzed9 with a semiempirical version of Troe's modification of RRKM theory,1° and, in all cases, the experimental results can be explained by several mutual combinations of the threshold energy, EO, and the collisional energy transfer parameter, AEdown. Clearly, the best way to narrow the range of choice is to greatly extend the temperature range, and this can only be done by combining results from different techniques. As shown in the CC4 case? the ARAS and the laser schlieren (LS) density gradient techniques are quite complementary since the former is limited to lower temperatures, whereas the latter can best be used at higher temperatures. Lastly, the RRKM analyses for many of these cases give values for hEdownthat are higher than usual. As discussed earlier,2this may suggest the importance of "mass matching" between AI or Kr with peripheral C1 atoms in the energized molecules. In the present work two different detection techniques from two laboratories have been used to measure the rate of reaction 1: (i) ARAS detection of product C1 atoms in incident shock waves and (ii) LS density gradients in incident shock waves. With these joint studies, the kinetics experiments can be performed over a larger temperature range than is possible with either single technique. This combined effort gives a direct determination over large variations of density and temperature and allows a direct comparison of measured rates, thereby justifying both techniques.
Experimental Section C1 Atom ARAS Technique. The thermal decomposition of CF3C1 was carried out in the incident shock wave mode with a c1 atom resonance lamp for observing the Product, c1. The apparatus used in this study has been previously described in detail." Hence, only a brief account of the experimental 0 1994 American Chemical Society
Thermal Decomposition of CF3C1 1o
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J. Phys. Chem., Vol. 98, No. 47, 1994 12279 ,
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Figure 1. Semilog plots of density gradient from two LS experiments: 2% CF3CyKr, 2373 K and 328 Torr (left); 2509 K and 200 Torr (right). The initial group of rapidly falling points during t < 1 ,us shows beam-shock front interaction. The solid lines represent the result of modeling with the mechanism of Table 2.
techniques pertaining to those aspects of the apparatus and procedures which are specific to this work is presented below. Gases. The high purity He (99.995%) used as the driver gas was obtained from Air Products & Chemicals, Inc. Scientific grade Kr (99.997%) used as the diluent was obtained from MG Industries. The ultrahigh purity grade He (99.999%) used in the resonance lamp was from Airco Industrial Gases. CF3Cl (99.5%) was obtained from AGA Specialty Gas, and research grade CL (99.999%) came from MG Industries. The C12 and CF3Cl were purified by bulb-to-bulb distillation, retaining only the middle third for use. The CF3Cl sample was further subjected to mass spectrometric assay to verify its purity. Apparatus. The shock tube consisted of two sections, a 7 m 304 stainless steel tube (id. 9.74 cm) and a driver chamber, separated by a thin aluminum diaphragm (4 mil, unscored 1100H18). The tube was routinely pumped to Torr between experiments by an Edwards Vacuum Products, Model CRlOOP, packaged pumping system. Eight pressure transducers (PCB Piezotronics, Inc., Model 1132A), placed at fixed intervals, measured the incident shock velocity. The photometer system was radially located 67 cm from the endplate and had an optical path length of 9.94 cm. Transmittances from the resonance lamps were measured with an EMR G14 solar blind photomultiplier tube. The signal was then recorded by a Nicolet 4094C digital oscilloscope. Mixture compositions and reactant pressures were measured with an MKS Baratron capacitance manometer. Temperatures and densities for each of the incident wave experiments were determined from the incident velocity and initial thermodynamic conditions. A complete Mirels’ calculation was applied to compensate for wall boundary layer formation.”J2 Laboratory times of each experiment were converted to the particle times from which the rate constants were determined. CI Atom ARAS Detection. The C1 atom resonance lamp has recently been de~cribedl-~ and has the same configuration as discussed by Whytock et al.13 and Clyne and Nip.14 Operating at 50 W microwave power and with a flowing pressure of 2.0 Torr of Xc12 = 1 x lop3 in He, the lamp gives a multiplet structure that is somewhat reversed. The resonance radiation
was measured through a BaF2 filter without further wavelength resolution. The thermal decomposition of large concentrations of CC4 at high temperatures was used to obtain the fraction of light that is C1 atom resonance radiation. It was determined that the current lamp configuration produced 86(&2)% resonance radiation. With this knowledge, the transmittance, T = Z/Zo,by product C1 atoms from the decomposition of CF3Cl can then be determined. Laser Schlieren Technique. Gases. Experiments were performed in a 2% C F 3 C M mixture. CF3Cl was obtained from Aldrich (99+% CF3C1) and Kr from Spectra-Gases (UHP).Both were used without purification. Mixtures were prepared manometrically with MKS capacitance manometers having a stated accuracy of 0.5%. Mixing and storage were in a 50 L glass bulb fitted with a Teflon-coated magnetic stirrer. Apparatus. The shock tube and associated laser schlieren (LS) equipment have been described in detail.15 Incident shock waves were generated by spontaneous bursts of Mylar diaphragms with helium. Velocities were determined from arrival intervals established by five piezoelectric detectors feeding a four-channel, 10 MHz clock. The uncertainty in velocity was estimated as 10.3%, based on the consistency of interval measurements, corresponding to a AT of about f 1 0 K at 2000 K. Examples of density gradient measurements are shown in the semilog plots of Figure 1 and 2. Each of these shows a positive gradient arising primarily from the endothermic dissociation of CF3C1. No exothermic gradients were seen at any time. These examples typify the results of 32 experiments covering postshock conditions, 1800-3000 K and 140-410 Torr in 2% CF3Cl/Kr.
Analysis and Results ARAS. In earlier work from this laboratory, the curve-ofgrowth for C1 atoms was obtained from the thermal decomposition of CH3C1 by observing long time steady-state absorption values.’ The results of these experiments were expressed in a modified Beer’s law form, T, = I d l o = exp(-~I[Cl]:), where [Cl], has units of atoms cmP3. With (ABS), E -ln(Zdlo), the values of KI and a were deduced from the data, giving
Kiefer et al.
12280 J. Phys. Chem., Vol. 98, No. 47, 1994 Io4 x
X
X
10'
10.6
1
3
2
t
4
1
(PSI
2
3
t
(PS)
4
Figure 2. Semilog plots of density gradient from two LS experiments: 2% C F Q K r , 2148 K and 335 Torr (left); 1821 K and 407 Torr (right). The solid lines represent the result of modeling with the mechanism of Table 2. 0.6
(ABS), = 4.41 x 10-9[C1]L581 These CH3C1 results were checked in this work by decomposing CF3C1 at sufficiently high temperatures so that steady-state absorptions, (ABS),, by product C1 were attained. These experiments were carried out with varying initial reactant concentrations, and the curve-of-growth for C1 atoms was determined by plotting the absorbance values against the initial reactant concentrations. The results are displayed in Figure 3, where the curve-of-growth obtained from the CH3Cl study, eq 2, is also shown as the dashed line. Within experimental error there is no significant difference in the two sets of results, confirming the adequacy of eq 2. Sixty-one kinetics experiments were performed at three loading pressures and different [CF3Cl]o by monitoring the temporal behavior of the C1 atom formation from reaction 1. For a given experiment, the measured (ABS), can be converted to its equivalent [Cl], using eq 2. In these ARAS experiments, significant secondary reactions are negligible with the presently used initial concentrations, densities, and temperatures. Hence, the kinetics are simple, and the rate law is given by (3) where [Cl], = [CF3Cl]o. When the right-hand side of eq 3 is plotted against particle time, the negative slopes, obtained by linear least-squares methods, yielded the first-order decomposition rate constants, kd. Table 1 lists the experimental conditions. Anticipating that the reaction is near the low-pressure limit, the derived second-order rate constants, k2nd, are also given in Table 1, and an Arrhenius plot of these values is shown in Figure 4. Linear least-squares analysis was applied to the 61 data points, giving the Arrhenius expression
ktnd = 1.73 x
exp(-33837K/T) cm3 molecule-' s-l
(4) for the temperature range 1521-2173 K. The data agree with eq 4 to within f 2 7 % at the one standard deviation level, indicating that strong pressure effects do not exist and that the reaction is near to the low-pressure limit.
0.5
0.4 0)
2a
.fi 0.3
s:
P
0.2
0.1
I 0
2xlO'j
4~10'~ 6~10'~ 8~10'~
[ C ~/I atom cmm3 Figure 3. [Cl], results from the complete decomposition of CF3Cl. The solid line is a least-squares fit to the data and is compared to the dashed line determined previously.'
Laser Schlieren. All 32 experiments were analyzed for the rate of reaction 1 by the usual method.16 Semilog plots like those of Figures 1 and 2 were extrapolated to t = 0, and rate constants for (1) were then derived from the resulting zerotime gradients, assuming vibrationally relaxed, chemically frozen conditions. The resulting rate constants are nearly proportional to the AH!& = 85.7 kcal mol-' for (l), as determined from the JANAF compilation." Since these experiments were canied out at higher initial concentrations and temperatures than the ARAS set, allowance had to be made for secondary chemistry. Hence, in all experiments, the t = 0 extrapolations were made in accord with the predictions of a full modeling of each experiment using the eight-step model of Table 2. Here the rate constants of reactions 2, 3, and 8 are taken from our own RRKM modeling of the data given in refs 18, 19, and 20, respectively. This mechanism has been tested against not only the present results but also data on CF3Br and CF31decomposi-
Thermal Decomposition of CF3Cl
J. Phys. Chem., Vol. 98, No. 47, 1994 12281
TABLE 1: Rate Data for Reaction 1 (ARAS) P/Torr mach # Q/x1OIs cm-3
15.85 15.79 15.97 15.99 15.87 15.87 15.99 15.98 15.96 15.89
4.207 4.436 3.996 3.718 4.023 3.925 3.997 4.063 4.081 4.200
15.90 15.88 16.01 15.91 15.91 15.93 15.97 15.93 15.96 10.91 10.95 10.99 10.98 10.96 10.94 10.88 10.99
3.937 4.069 3.940 3.948 3.652 3.776 3.868 4.070 3.998 3.950 4.370 4.245 4.219 4.144 3.647 3.737 3.733
15.91 15.97 10.92 10.92 10.96 10.91 10.91 10.99 10.92 5.95 5.96 5.96 5.97 5.97 5.96 5.94 5.98 5.96 5.96 5.96
4.198 3.940 4.131 4.179 4.318 4.245 3.978 3.925 3.761 4.521 4.006 3.912 3.386 3.981 4.245 4.020 3.602 3.976 4.122 4.547
15.95 15.92 10.92 10.96 5.97 5.94 5.96 5.95 5.96 5.94 5.93 5.94 5.94 5.95
3.984 4.050 4.348 4.065 4.286 4.316 4.280 4.047 3.926 4.238 4.172 4.448 4.297 4.153
kdls-l
Mole Fraction = 7.259 x 1.796 3223 1.809 13493 1.775 1169 1.762 225 1.777 1135 1.763 577 1.781 953 1.782 1886 1.774 2188 1'773 5732 Mole Fraction = 1.452 x 1.754 593 1.763 2140 1.769 695 1.758 835 1.743 107 1.753 201 1.757 590 1.768 2163 1141 1.766 1.218 467 1.247 11949 1.244 5795 1.246 5063 1.239 3082 1.218 34 1.211 102 1.233 73.1 Mole Fraction = 2.181 x 1.796 6313 1.779 728 1.231 2726 1.229 4905 1.243 9796 1.233 6103 1.219 731 1.228 465 1.216 106 6.876 12820 6.797 639 6.810 215 6.787 284 6.819 392 6.820 2506 6.759 499 6.733 87 6.775 1187 6.779 2127 6.870 16365 Mole Fraction = 2.879 x 1.771 1031 1.774 1906 1.241 10959 1.225 1488 6.792 4004 6.773 6053 4232 6.780 6.620 1009 6.777 254 6.779 2559 6.784 1530 11313 6.830 6.786 4195 6.770 1944
T/K
10-6 1891 2070 1756 1570 1782 1710 1760 1804 1823 1910 10-5 1708 1803 1713 1718 1525 1604 1662 1803 1752 1716 2015 1926 1902 1846 1521 1574 1579 10-5 1880 1693 1834 1874 1981 1924 1731 1696 1589 2144 1764 1703 1759 1748 1929 1780 1602 1833 1837 2173 1728 1775 2005 1788 1963 1987 1958 1788 1707 1922 1868 2082 1964 1858
k~~dcm-~ molecule-' S-I 1.795 x 7.459 x 10-15 6.586 x 1.277 x 10-l6 6.387 x lowL6 3.273 x 5.351 x 1.058 x 1.233 x 3.233 x 3.381 x 1.214 x 3.929 x 4.750 x 6.139 x 1.147 x 3.358 x 1.223 x 6.461 x 3.834 x 9.582 x 4.658 x 4.063 x 2.487 x 2.791 x 8.423 x 5.929 x 3.515 x 4.092 x 2.214 x 3.991 x 7.881 x 4.950 x 5.997 x 10-16 3.787 x 8.717 x 1.864 x 9.401 x 3.157 x 4.184 x 5.749 x 10-16 3.674 x 7.383 x 1.292 x 1.752 x 3.138 x 2.382 x lo-'" 5.822 x 1.074 x 10-15 8.831 x 1.215 x 5.895 x 10-15 8.937 x 6.242 x 1.524 x 3.748 x 3.775 x 10-15 2.255 x 1.656 x 6.182 x 2.871 x
tion.21 The resulting rate constants are tabulated in Table 3 and exhibited in the Arrhenius plot of Figure 5. Density gradients generated by the above numerical simulations are also exhibited in Figures 1 and 2. In general, the agreement is quite satisfactory throughout, with small, but discernible, deviations at extreme conditions. The slight excess of late gradient in the first example of Figure 1 is a consistent
Figure 4. Arrheniusplot of second-orderrate constants for reaction 1 derived from the ARAS experiments at three loading pressures. The solid line, eq 4 in the text, shows a least-squares fit of the data of Table 1.
1
,
2 -
4.0
,
1
5.0
10000/T
Figure 5. Arrhenius plot of second-orderrate constants for reaction 1 derived from LS density profiles of experiments over 140-410 Torr. The solid line, eq 5 in the text, shows a least-squares fit of the data of Table 3. problem, and some deviations (not shown) are also seen for a very few high-temperature, low-pressure examples, where the calculated late gradient is too low. The latter deviations may indicate the presence of a small incubation period, i.e., a breakdown of the vibrationally relaxed assumption for t = 0. However, all of these deviations are small and have little effect in the extrapolated gradients or rate constants. In particular, the second-order rate constants at both low and high temperatures change but little over the full range of pressure, showing that neither incubation nor secondary reactions much affect the result. Considering data scatter and the cited model problems, we suggest second-order rate constants which are effectively pressure-independent over the 140-410 Torr range, with
kZnd= 1.15 x IO-* exp(-2833OK/T) cm3 molecule-'
s-l
(5)
Kiefer et al.
12282 J. Phys. Chem., Vol. 98, No. 47, 1994 TABLE 2: Reaction Mechanism for the Pyrolysis of CF&l reaction" log Ab (cm3molecule-I (la) CF3Cl+ Kr CF3 + C1+ Kr 24.27' C1+ KI 24.51d (lb) CF3Cl-k Kr-CF3 (2) CF3 KI CF2 + F + KI 21.62 (3)CF4+Kr-CF3+F+Kr 37.62 (4) CF3 C2F6 CF4 CzFs -11.78 35.87 (5) C2F5 + Kr-CzF4 + F + Kr -11.78 (6) CF3 + CzF5 CF4 + C2F4 -12.48 (7) 2CF3 +.CF4 + CF2 (8) C2F6 + KI 2CF3 + Kr 54.02
+ +
-
-
-
SKI)
+
+
+
E (kcal mol-')
n -8.50
-8.50 -7.80 -11.80 0.00 -11.94
95.64 97.78 97.68 147.56 0.00 92.34
0.00 0.00
0.00 0.00
- 16.50
119.15
source present work present work see text see text estimated see text estimated estimated see text
a The reverse of each reaction is included through detailed balance. Rate expressions are of the form log k (cm3molecule-' s-') = log A 4- n log T - H2.303RT (kcal mol-'). Rate expression for the mean pressure of 300 Torr. Rate expression for the mean pressure of 1318 Torr.
TABLE 3: Chemically Frozen Postshock Conditions and Derived Rate Constants for Reaction 1 (Laser Schlieren) 2292.0 2254.9 2177.0 2206.9 2047.7 2097.5 2373.3 2094.5 1940.5 2015.7 2147.9 2136.8 2509.0 2599.2 2651.1 2760.0
5.50 x 4.07 x 2.54 x 2.92 x 1.07 x 1.46 x 7.19 x 1.43 x 4.66 x 8.58 x 2.13 x 2.24 x 1.59 x 2.16 3.35 x 4.23 x
307 322 330 356 374 357 328 381 383 375 335 257 200 189 175 164
10-14 10-14 10-14 10-14 10-14 10-14 10-14 10-14 10-15 10-15 10-14 10-14 10-13 10-13 10-13 lo-"
3058.9 2984.9 2409.6 2352.6 2183.7 2217.1 2799.3 2861.1 1876.6 1916.7 1890.6 1824.4 1846.5 1820.9 1810.0
146 143 240 223 236 229 206 234 398 384 381 398 397 407 410
1.12 x 1.01 x 6.44 8.91 x 3.19 3.90 x 3.24 x 4.37 x 3.25 x 4.78 3.70 x 2.02 2.69 2.09 x 1.79
10-12 10-12 10-14 10-14 10-14 10-14 lo-'.' 10-13 10-15 10-15 10-15
10-15 10-15 10-15 10-15
methodologies but also the presumption that reaction 1 is the sole channel in CF3C1 dissociation.
4.0
5.0
6.0
10000/T
Figure 6. Comparison plot of all rate constants for reaction 1: (0) LS, 140-410 Torr; (0)ARAS, 120-147 Torr; and ( x ) 287-388 Torr. The solid lines show RRKM calculations using the model of Table 4: upper, 300 Torr; lower, 1318 Torr. The 0-0 line shows the fit for the [MI = 8.4 x loL8molecules cm-3 (-1500 Torr) ARAS data given by Kruger and Wagner.8 between 1800 and 3000 K, carrying an uncertainty of 2 ~ 2 0 % over 2000-2500 K, and somewhat more outside this range. It is useful to compare eqs 4 and 5 over the common range of temperature overlap, 1800-2200 K. The predictions from the two equations are within --f25% of one another, and this is well within the combined one standard deviation error limits of the sets. Hence, the results from the two quite different types of experiments are in remarkably good agreement and are plotted together in the Arrhenius form in Figure 6. The separate anlayses (eqs 4 and 5) cross at the center of this range. As in our previous study of C C 4 dissociation,2 we find that these two very different techniques provide completely consistent results for C1 atom fission reactions. This not only supports the
Discussion There have been two previous studies of the CF3C1 dissociation.8,22 A summary result, given by Kruger and Wagner* for [Ar] = 8.4 x 10l8molecules cm3 (-1500 Torr), is also shown in Figure 6. Although the apparent activation energy of these ARAS experiments is lower (cf. 57.36 to 67.23 kcallmol), the rate constant magnitude is quite close to our ARAS results. They also confirm the very weak pressure dependence of the secondorder rate constants. Hidaka et a1.22derived a rate for (1) from HCl IR emission in shock waves of CF3Cl/H2 mixtures covering 1400-1600 K. In this experiment, the onset and subsequent growth in magnitude of emission should result from the initial formation of C1 atoms through reaction 1. However, their rate constant at 1500 K is nearly an order of magnitude lower than either the present value or that of Kruger and Wagner,8 implying that some nonlinear effect must be present that substantially decreases the apparent bimolecular rate constant. We have applied unimolecular reaction rate theory to reaction 1. Some results of a corrected23 strong-collision RRKM calculation are also displayed in Figure 6 for two pressures, 300 and 1318 Torr. The model parameters are given in Table 4. Here we adopt the barrier height from JANAF," A@ = EO = 84.83 kcal mol-', and only the parameter (mallwas adjusted to fit the data. The transition state is a loose restricted rotor G ~ r i nmodel ~ ~ that has often been used for bond fission reactions. In this, the restriction parameter 7,which effectively determines the high-pressure A-factor, was estimated from a fit of high-pressure dissociation data on CF3Br and CF31.25 However, given experimental rate constants which are very close to second order, there is no way to check this assumption. The RRKM model with this transition state does agree with the observed small deviation from second-order behavior; this is seen in Figure 6, where the 300 and 1318 Torr calculations are only slightly different.
Thermal Decomposition of CF3C1
J. Phys. Chem., Vol. 98, No. 47, 1994 12283
+
TABLE 4: Gorin Model RRKM Parameters for CF&I Kr- CFj C 1 f Kr frequencies (cm-I) CSC1 1106.0,782.0,474.0, 1217.0 (2), ref 17 560.0 (2), 350.0 (2) CS 1090.0, 701.0, 1259.0, 500.0 (2) ref 17 IAI& (gm3cm6) CSCl 9.44 x 10-114 ref 17 ref 17 CS 9.61 x 10-115 1.0 - (0.37T"3) present work v EO(kcal mol-') 84.83 ref 17 present work -(A&, (cm-') 270
+
Unfortunately, the RRKM calculations find these rates are also some distance (a factor of 2-5) from the low-pressure limit: this dissociation is in the falloff regime. Thus, the calculated rates are not independent of the chosen k,, and the magnitude and temperature dependence of the optimum pc (or (AE)) is affected by the selected restricted-Gorin parameters (see below). We have considered three popular choices for the temperature dependence of pc (or (AE)); a fixed AEdown,a fixed (AE)atl, and AEdownaT. These three cover a range of temperature dependences for &om from constant to linear in T. The choice of a fixed (A@,, corresponds to a &?down which increases somewhat less than linearly.23 These choices have been respectively advocated at various times by Tardy and Rabinovitch,26 T~oe,*',*~ and Gutman's arising from their extensive study of small radical dissociations. With all three tied to a single appropriate AEdown = 770 cm-' for T ' = 6.5 x and 1318 Torr, they respectively generate rate constants P = for the highest temperatures herein (T' = 3.25 x 300 Torr) of 5.77 x 1.08 x and 1.54 x cm3 molecule-' s-'. The data give k = 1.1 x cm3 molecule-' s-' for these conditions, and we therefore have selected the intermediate method of fixed (mall= -270 cm-'. With this choice, &?down increases from 770 cm-' at 1538.5 K to 1188 cm-' at 3077 K with corresponding pc changes of 0.13 to 0.06. Although these results and calculations are somewhat ambiguous for the reasons discussed above, it is clear that some increase of AEdownwith temperature is necessary. The selected RRKM model is compared to all the data in Figure 6. The Kruger and Wagner8 results were obtained at -1500 & 200 Torr and should be compared to the 1318 Torr calculation. The final theoretical results at the two pressures have been fitted to three parameter expressions, and these are given in Table 2 following reactions l a and lb. The one for 300 Torr can be directly compared to the experiments. This threeparameter expression gives values that are well within f 2 5 % of eqs 4 and 5 over the entire temperature ranges of applicability. Hence, we suggest that the three-parameter expressions be used by chemical modelers in practical applications. It is instructive to compare the present full RRKM calculations to those obtained using only the ARAS results along with Troe's semiempirical method for fitting RRKM calculation^.^ As mentioned in the Introduction, several mutual values of EO and could be used over the narrow temperature range of the ARAS data to explain the results. The calculation with EO= 84.83 kcal mol-' implied m d o w n = 700 cm-'. This is very close to the full RRKM analysis for the same conditions. Despite this consistency, it is important to recognize that even though AEdownhas a physical meaning, it really must be considered to be an empirically adjusted parameter that makes theory fit experiment. It is still true that there is no first principles theory for a priori calculation of these quantities for molecules near threshold.30 Therefore, if there is to be further progress in the theory of unimolecular reactions, it will only
result from a detailed theoretical understanding of the fundamental quantity &??down. Conclusions. As in our previous joint investigation of CC4 dissociation, the LS and ARAS techniques are found to give completely consistent results over a significant temperature range of common measurement. The present ARAS measurements are in excellent agreement with the earlier ARAS measurements of Kruger and Wagner.8 These points of agreement verify both the C-Cl fission path for the CF3C1 dissociation and the curve-of-growth used in the C1 atom ARAS analysis. RRKM analysis of these rate data indicated a large magnitude for smaller but similar to our findings on cc4. However, here it was necessary that mdom increase with T. A possible rationale for such larger AEdownvalues in halocarbons is discussed in the CC4 paper.2
Acknowledgment. This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, under Contract No. DE-FGO285ER13384 (J.H.K. and R.S.), and W-31-109-Eng-38 (K.P.L. and J.V.M.). References and Notes (1) Lim, K. P.; Michael, J. V. J . Chem. Phys. 1993, 98, 3919. (2) Michael, J. V.; Lim, K. P.; Kumaran, S. S.; Kiefer, J. H.J. Phys. Chem. 1993, 97, 1914. (3) Lim, K. P.; Michael, J. V. J . Phys. Chem. 1994, 98, 211. (4) Lim, K. P.; Michael, J. V. Twenty-Fifth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, submitted. ( 5 ) Graham, J. L.; Hall, D. L.; Dellinger, B. Environ. Sci. Technol. 1986, 20, 703. (6) Senkan, S. M. Environ. Sei. Technol. 1988, 22, 368. (7) Taylor, P. H.; Dellinger, B.; Tirey, D. A. Int. J. Chem. Kinet. 1991, 23, 1051. (8) Kruger, B. C.; Wagner, H. Gg. Proceedings of the 14th International Symposium on Shock Tubes and Waves; Sydney Shock Tube Symposium Publishers: Sydney, 1983; p 738. (9) Lim, K. P.; Michael, J. V. Preprint, 207th American Chemical Society, Symposium on Combustion Chemistry and Soot Formation, Fuel Chemistry Division 1994, 39, 131. (10) Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 161. (11) Michael, J. V. Prog. Energy Combust. Sci. 1992, 18, 327 and
references cited therein. (12) Michael, J. V.; Sutherland, J. W. Int. J . Chem. Kinet. 1986, 18, 409. (13) Whytock, D. A.; Lee, J. H.; Michael, J. V.; Payne, W. A,; Stief, L. J. J . Chem. Phys. 1977, 66, 2690. (14) Clyne, M. A. A.; Nip, W. S. J . Chem. Soc., Faraday Trans. 2 1976, 72, 838. (15) Kiefer, J. H.;Manson, A. C. Rev. Sei. Instrum. 1981, 52, 1392. (16) Kiefer, J. H.;Shah, J. N. J. Phys. Chem. 1987, 91, 3024. (17) Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Fnuip, D. J.; McDonald, R. A,; Syverud,A. N. J . Phys. Chem. Ref. Data 1985,14, Suppl. 1. (18) Schug, K. P. Untersuchung des Reaktionsverhaltens von FluorKohlenstofiadikalen bei hohen Temperaturen. Zur Aktivierungsenergie von Drei-Zentren-Eliminierung,Thesis, Gottingen, 1976. (19) Modica, A. P.; Sillers, S. J. J . Chem. Phys. 1968, 48, 3283. (20) Tschuikow-Roux, E. J. Chem. Phys. 1965, 43, 2251. (21) Kiefer, J. H.;Sathyanarayana, R. To be published. (22) Hidaka, Y.; Kawanami, K.; Kawano, H.;Suga, M. J . Chem. Phys. 1984, 103, 393.
(23) Gilbert, R. G.; Luther, K.; Troe, J. Ber. Bunsen-Ges. Phys. Chem. 169 and references therein. (24) Benson, S. W. Thermochemical Kinetics; Wiley: New York, 1974. (25) Tsang, W. J. Phys. Chem. 1986, 90, 414. Saito, K.; Yoneda, Y.; Kidoguchi, S.; Murakami, I. Bull. Chem. SOC.Jpn. 1984, 57, 2661. (26) Tardy, D.; Rabinovitch, B. S. Chem. Rev. 1977, 77, 369. (27) Troe, J. J. Chem. Phys. 1977, 66, 4745. (28) Troe, J. J. Phys. Chem. 1979, 83, 114. (29) Feng, Y.; Niiranen, J. T.; Bencsura, A.; Knayazev, V. D.; Gutman, D.; Tsang, W. J . Phys. Chem. 1993, 97, 871. (30) (a) Michael, J. V.; Lee, J. H. J . Phys. Chem. 1979, 83, 10. (b) Michael, J. V. Ibid. 1979, 83, 17. 1983, 87,
