4048
J. Phys. Chem. 1996, 100, 4048-4054
Absolute Rate Measurements of the Reaction of OH Radicals with HCFC-21 (CHFCl2) and HCFC-22 (CHF2Cl) over an Extended Temperature Range Tunchen D. Fang, Philip H. Taylor,* and Barry Dellinger EnVironmental Sciences and Engineering and Center for Electro-Optics, UniVersity of Dayton Research Institute, Dayton, Ohio 45469-0132 ReceiVed: September 12, 1995; In Final Form: NoVember 9, 1995X
Rate coefficients of the reaction of hydroxyl (OH) radicals with CHFCl2 (k1) and CHF2Cl (k2) over an extended temperature range are reported. Measurements were performed using a laser photolysis-laser-induced fluorescence (LP/LIF) technique under slow flow conditions at a total pressure of 740 ( 10 Torr. Arrhenius plots of the data exhibited significant curvature and were fitted in the form of k(T) ) ATB exp(-C/T). A semiempirical fitting approach was used in which A and B were obtained from a transition state theory (TST) calculation and C was determined from a nonlinear least squares fit to the experimental data. The resulting modified Arrhenius expressions were k1(T) ) (3.13 ( 0.2) × 10-18 T1.93(0.01 exp[(-552 ( 18)/T] cm3 molecule-1 s-1 and k2(T) ) (3.10 ( 0.2) × 10-18 T1.94(0.01 exp[(-1112 ( 26)/T)] cm3 molecule-1 s-1. This semiempirical fit is shown to be superior to a purely empirical fit to the data. The expressions for k1 and k2 are in good agreement with the previous studies between temperatures of 240 and 480 K. Above 480 K, our extended temperature measurements verify previous TST predictions. The experimental results indicate that k1 is about 5 times as fast as k2 at 295 K. The difference in room temperature reactivity is consistent with recent BAC-MP4 calculations indicating a nearly 5 kcal/mol difference in C-H bond dissociation energies (BDE).
Introduction
k1
CFCl2H + OH 98 CFCl2 + H-OH
Knowledge of the high-temperature reactivity of hydroxyl radicals (OH) with hydrogen-containing chlorofluorocarbons (HCFCs) such as HCFC-21 (CHFCl2) and HCFC-22 (CHF2Cl) is important for several reasons. CHFCl2 and CHF2Cl have greater than a factor of 20 lower ozone depletion potentials (ODPs) compared with CFCs and were initially selected to be suitable replacements for a variety of industrial applications. However, their relatively slow reaction rates (particularly CHF2Cl) with OH and the resulting finite, albeit small, ODPs have led to concern about their long-term effects on stratospheric ozone depletion and has led to the further development of hydrofluorocarbon (HFC) substitutes with near-zero ODPs.1,2 Knowledge of oxidation rates for CHFCl2 and CHF2Cl at elevated temperatures is now needed because incineration has been selected as the primary means of disposal of major stockpiles of these chemicals.2 For the successful modeling of their combustion, accurate semiempirical Arrhenius parameters describing the rate behavior over extended temperature ranges are required. Previous measurements have only been reported over a limited temperature range encompassing tropospheric and stratospheric conditions.3-12 At temperatures above 480 K, the prediction of rate constants has been based solely on semiempirical transition state theory (TST)13,14 and structure-active relationship (SAR) calculations.15 Rate coefficient measurements over an extended temperature range are needed to verify and/or refine previously published TST and SAR models. In this paper, we report high-precision rate coefficients for the following exothermic hydrogen abstraction reactions over an extended range of temperature: * Author to whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, February 15, 1996.
0022-3654/96/20100-4048$12.00/0
(∆H°298 ) -22.0 kcal mol-1; ∆S°298 ) 2.6 eu) k2
CF2ClH + OH 98 CF2Cl + H-OH (∆H°298 ) -17.6 kcal mol-1; ∆S°298 ) 2.6 eu) Significant curvature was evident from Arrhenius plots of extended temperature data sets for both k1 and k2. To provide a more accurate description of the experimental results, a modified Arrhenius expression was developed in the form
k(T) ) ATB exp(-C/T)
(1)
where both A and B were calculated using TST and C was determined from a nonlinear least squares fit to the experimental data. This semiempirical fit is shown to be superior to a purely empirical fit to the data. The modified Arrhenius expressions for k1 and k2 are then compared to previous TST and SAR predictions. Experimental Approach and Data Reduction The experimental procedures were very similar to our previous studies of OH reactions with chlorinated hydrocarbons.16-22 The following paragraphs briefly summarize these procedures and discuss recent modifications to the experimental approach designed to improve our measurements. A schematic drawing of the optical analysis system is shown in Figure 1. OH radicals were produced by 193.3 nm photodissociation of HCFC/N2O/H2O/He gas mixtures with a ArF excimer laser (Questek Model 2860). Initial OH concentrations, [OH]0, ranged from 2 × 1011 to 5 × 1011 molecules cm-3 and were determined from published values of the N2O absorption coefficient (8.95 × 10-20 cm2 molecule-1 at 298 K),23 a © 1996 American Chemical Society
Reaction of OH Radicals with HCFCs
J. Phys. Chem., Vol. 100, No. 10, 1996 4049
Figure 1. Schematic drawing of the optical analysis system.
Figure 3. Pseudo-first-order rate constant, k′, as a function of [CHF2Cl] at various reaction temperatures.
Figure 2. Two-dimensional schematic drawing of the optical reactor. The optical path of the Nd:YAG pumped dye laser is perpendicular to the plane of the figure and intersects the excimer laser beam in the center of the reactor.
photodissociation quantum yield for O(1D) production of unity,24 and the rapid reaction of O(1D) with H2O (95% conversion in 1000[OH] in all reactive experiments, exponential OH radical decays, of pseudo-first-order decay constant k′ ) k[HCFC] + kd, were observed. kd is the first-order rate constant for OH radical disappearance from the probe volume due to diffusion and reaction with impurities in the carrier gas. The bimolecular rate constant, k, was obtained from the slope of the least squares straight line through the graph of k′ versus [HCFC] as illustrated for CHF2Cl in Figure 3. Values of k′ ranged from about 79 to 985 s-1 and 47 to 1705 s-1 for CHFCl2 and CHF2Cl, respectively. kd varied from 79 to 193 s-1 in the absence of CHFCl2 and from 47 to 127 s-1 in the absence of CHF2Cl and was dependent on the incident photolysis laser intensity, background impurities, and the gas temperature. Gas chromatography-mass spectrometry (GC/MS) analyses indicated that CHF2Cl was free of contaminants (>99.9% pure) and that CHFCl2 contained CHF2Cl (2%), C2F4Cl2 (0.8%), CF3Cl (0.2%), and C2F3Cl3 (0.2%) as contaminants. However, these contaminants react several orders of magnitude slower with OH than CHFCl2 and, as such, did not contribute significantly to the OH decay rates. The remaining chemicals used in our gas delivery system had the following stated minimum purities: He (99.999+%), N2O (99.9%), and H2O (HPLC organic-free reagent grade). Absorption cross sections for CHF2Cl and CHFCl2 are very small (on the order of 10-22 cm2 molecule-1)25 in comparison with those for N2O at 193 nm. Thus, laser photolysis of HCFC reactants was expected to
4050 J. Phys. Chem., Vol. 100, No. 10, 1996 TABLE 1: Absolute Rate Coefficients for Reaction 1 (CFCl2H-OH) temp (K)
1014k1a (cm3 molecule-1 s-1)
temp (K)
1014k1a (cm3 molecule-1 s-1)
295 316 345 362 383 414 441 460
2.48 ( 0.67 2.85 ( 1.00 4.19 ( 0.60 5.38 ( 1.80 6.82 ( 2.10 9.19 ( 0.53 12.54 ( 2.51 13.31 ( 2.19
485 515 550 585 631 679 743 810
16.33 ( 1.00 18.73 ( 0.82 24.96 ( 2.96 29.48 ( 3.72 37.90 ( 3.92 44.18 ( 5.20 51.38 ( 7.74 68.40 ( 3.02
a
Errors represent (2σ.
TABLE 2: Absolute Rate Coefficients for Reaction 2 (CF2ClH-OH) temp (K)
1015k1a (cm3 molecule-1 s-1)
temp (K)
1015k1a (cm3 molecule-1 s-1)
294 305 317 329 344 359 376 391 409 432
4.65 ( 0.66 5.73 ( 0.08 6.99 ( 0.88 8.43 ( 1.24 9.43 ( 0.58 13.23 ( 1.00 14.60 ( 1.40 18.99 ( 1.00 23.75 ( 2.20 27.60 ( 2.20
455 481 512 544 582 625 676 735 807
30.66 ( 1.80 43.58 ( 3.20 49.02 ( 3.60 60.23 ( 4.80 73.59 ( 3.60 116.70 ( 6.00 163.70 ( 14.00 224.80 ( 26.00 450.70 ( 30.00
a
Errors represent (2σ.
Figure 4. Arrhenius plot of kinetic data for k1. Also shown are the results of previous studies, the recent NASA evaluation, an empirical best fit expression, and two semiempirical, TST-based, modified Arrhenius expressions to the extended temperature data.
be insignificant. This was verified by numerous experiments where variation of the excimer laser intensity had no observable effect on OH decays. Experimental Results Absolute rate constants for reactions 1 (CFCl2H-OH) and 2 (CF2ClH-OH) are listed in Tables 1 and 2, respectively. Random error limits ((2σ), derived from a propagation of error analysis, ranged from 4% to 34% for reaction 1 and from 2% to 15% for reaction 2. To our knowledge, this is the first report of experimental measurements for these reactions above temperatures of 480 K. Arrhenius plots of the data for reactions 1 and 2 indicated significant curvature as illustrated in Figures 4 and 5, respectively. Also shown are previous measurements reported using different techniques. The various techniques include (1)
Fang et al. discharge flow-laser magnetic resonance spectroscopy (DFLMR),3 (2) flash photolysis-resonance fluorescence spectroscopy (FP-RF),4,5 (3) flash photolysis-resonance absorption spectroscopy (FP-RA),6,7 (4) discharge flow-resonance fluorescence spectroscopy (DF-RF),8-11 and (5) pulse radiolysisresonance absorption spectroscopy (PR-RA).12 With the exception of Clyne and Holt,9 our overlapping rate measurements are in reasonably good agreement with previous measurements. Our measurement for reaction 1 at 295 K (2.48 × 10-14 cm3 molecule-1 s-1) is 8% lower than that reported in the work of Atkinson et al.4 at 298 K (2.7 × 10-14 cm3 molecule-1 s-1). The measurements from 316 to 345 K are 25% lower than those given in the work of Jeong et al.10,11 At 362 K, our data is 8% lower than those listed in the work of Jeong.10,11 From 383 to 485 K, our data are in good agreement with previous measurements.4,5,8,10,11 Similarly, our measurement for reaction 2 at 294 K (4.65 × 10-15 cm3 molecule-1 s-1) is only 2% lower than that reported in the work of Atkinson et al.4 at 297 K (4.75 × 10-15 cm3 molecule-1 s-1). From 294 to 481 K, our data are in excellent agreement with previous measurements.4,5,7,8,10,11 Rate measurements were observed to rapidly increase above 810 K for both samples (k1 ) 1.71 × 10-12 cm3 molecule-1 s-1 at 896 K and k2 ) 1.49 × 10-12 cm3 molecule-1 s-1 at 891 K). This was attributed to the rapid reaction of OH with HCl26 which is known to be a stable reaction product of the unimolecular decomposition of CHFCl2 and CHF2Cl.27 The only available reaction mechanism for reactions 1 and 2 is H-atom abstraction. Our experimental results indicate that reaction 2 is a factor of 5 slower than reaction 1 at 295 K. This result can best be rationalized in terms of differences in C-H bond dissociation energies (BDE). Experimental measurements yield D°(CF2Cl-H) of 101.6 ( 1.0 kcal/mol.28 Experimental measurements for CFCl2-H are not available. However, recent BAC-MP4 estimates29 for D°(CF2Cl-H) and D°(CFCl2-H) were 101.3 and 96.8 kcal/mol, respectively. This substantial reduction in the C-H BDE with increasing Cl substitution is consistent with the factor of 5 difference in room temperature reactivity. A nonlinear least squares fit of our data (weighted as ωk ) 1/σk2) to the modified Arrhenius equation produced the following expressions (error limits represent 2σ) depicted as the best fit in Figures 4 and 5:
k1(295-810 K) ) (1.53 ( 5.36) × 10-15T1.11(0.48 × exp(-1078 ( 262/T) (3) k2(294-807 K) ) (1.31 ( 12.56) × 10-22T3.28(1.36 × exp(-361 ( 564/T) (4) As indicated in eqs 3 and 4, the parameters comprising the modified Arrhenius equation are strongly coupled and to assign a meaningful estimate of uncertainty to the biomolecular rate constants obtained from it requires the inclusion of covariance terms. Covariance terms obtained from a weighted LevenbergMarquardt algorithm for k1 and k2 are, for k1, COVAB ) -6.38 × 10-16, COVAC ) -3.50 × 10-13, and COVBC ) 31.00; and for k2, COVAB ) -4.27 × 10-22, COVAC ) -1.77 × 10-19, and COVBC ) 190.94. These values translate into an uncertainty (2σ) in k1 and k2 at 1000 K of (30% and (39%, respectively. The value of B (i.e., 1.11 and 3.28) in eqs 3 and 4 is indicative of the degree of curvature in the Arrhenius plot for k1 and k2, respectively. For reaction 1, the best fit expression is consistent with available data (excluding Clyne and Holt9) between 345 and 810 K but underestimates previous measurements at 241 and 245 K by an average of ∼30%. For reaction 2, the best fit
Reaction of OH Radicals with HCFCs
J. Phys. Chem., Vol. 100, No. 10, 1996 4051
expression is consistent with available data (excluding Clyne and Holt9) from 295 to 807 K but overestimates previous measurements at 250 and 263 K by an average of ∼30%. The recommended expression for reaction 1 from a recent NASA evaluation is also shown in Figure 4.30 A simple Arrhenius expression was chosen as being representative of the previous low-temperature data. Above 485 K, our data deviates substantially from the NASA recommendation. Similarly, for reaction 2, our data also deviate from the NASA recommendation above 582 K (cf. Figure 5). The significance here is the error that results from the use of the simple Arrhenius expression (developed for use in atmospheric models) as compared to nonArrhenius expressions for predicting the rate of these reactions at combustion temperatures. For example, for both k1 and k2, use of the NASA evaluation30 predictions compared to the recommended three-parameter expression derived from this study results in an underestimation of the reaction rate at 1000 K by about a factor of 3. This error increases to nearly a factor of 10 at 2000 K. Development of Semiempirical Arrhenius Parameters Although the purely empirical fit is the best representation of the data, the difference in values of A, B, and C is not theoretically justifiable considering the structural and electronic similarities between reactions 1 and 2. Consequently, a semiempirical fitting approach was explored that might provide more physical insight into the thermodynamic properties of the respective transition states. Our approach was to calculate A and B using the thermochemical version of transition-state theory (TST) and then determine C by an empirical fit to the three-parameter expression that has been now reduced to one variable. This approach is justified because A and B can be shown to be expressed in terms of the thermodynamic quantities ∆Cq and ∆Sq which are relatively accurately calculable using TST (whereas C is related to ∆Hq which is not accurately calculable using TST).31 Following Shaw,32 we can show
A ) (R′k/h)298(-∆Cp T/R) exp[(∆Spq298 K - ∆CpqT)/R] q
(5)
B ) 2 + (∆CpqT)/R
(6)
C ) (∆Hpq298 K - 298∆CpqT)R
(7)
where ∆Spq298 K is the entropy of the transition state at 298 K in pressure standard state, ∆CpqT is the heat capacity of the transition state at a specified temperature, ∆Hpq298 K is the enthalpy of the transition state at 298 K in pressure standard state, R is the ideal gas constant in cal/(mol K) units, R′ is the ideal gas constant in L atm/(mol K) units, k is the Boltzmann constant, and h is Planck’s constant. The units of A are the same as k(T), i.e., L/(mol s). ∆Spq298 K for reactions 1 and 2 has been previously reported by Jeong and Kaufman13 using halogenated alcohols as the reference compounds. Jeong and Kaufman then developed a simple Arrhenius expression over a limited range of temperature. In contrast, Cohen and Benson14 calculated values of ∆Spq298 K using the reagents as the reference compounds. Cohen and Benson then developed a modified Arrhenius expression over a wider range of temperature by combining thermochemical TST calculations and curve fitting schemes to available data over a limited range of temperature. The geometry of the transition states for both reactions 1 and 2 were not explicitly given by either Jeong and Kaufman13 or Cohen and Benson.14
Figure 5. Arrhenius plot of kinetic data for k2. Also shown are the results of previous studies, the recent NASA evaluation, an empirical best fit expression, and two semiempirical, TST-based, modified Arrhenius expressions to the extended temperature data.
Figure 6. Geometric representation of the transition states for k1 and k2.
We have utilized the general approach of Jeong and Kaufman13 based on their bond energy-bond order (BEBO) calculation for the reaction of OH with CH4. Modifications to the TS included corrections in C-H and O-H bond lengths (taken from stable molecules in the JANAF tables33) and the O-H-C bond angle (based on the recommendations of Cohen34). This TS geometry will be further tested and modified as additional data are gathered on the reaction of OH with other HCFCs. The procedure used to calculate ∆Spq298 K thus involved the following: (1) choice of appropriate reference compounds, i.e., CCl2FOH for reaction 1 and CClF2OH for reaction 2, (2) specification of a plausible geometry, and (3) application of the following five correction terms: (i) the translation correction, ∆Strans, (ii) the spin correction due to the contribution of an unpaired electron from OH, ∆Sspin, (iii) vibrational frequency corrections, ∆Svib, (iv) external rotation corrections, ∆Ser, and (v) internal rotation corrections, ∆Sir. Of these corrections, ∆Sir is the largest and most difficult to estimate. Two internal rotation axes along the C‚‚‚H and H‚‚‚O bonds were considered in this calculation. However, in contrast to Jeong and Kaufman, a finite barrier to rotation about the C‚‚‚H and H‚‚‚O bonds of 1.0 and 2.0 kcal/mol, respectively, was used, as reported by Cohen and Benson.14 The geometries used to calculate ∆Ser and ∆Sir are specified in Figure 6. As OH abstracts the H from CF2ClH (k2), the C‚‚‚H bond length was stretched by 0.07 Å over the normal bond length. The newly forming H‚‚‚O bond was stretched by 0.42 Å over the normal OH bond length. The asymmetric extensions of the C‚‚‚H and H‚‚‚O bond lengths were based on the BEBO calculations discussed by Jeong and Kaufman.13 The O‚‚‚H‚‚‚C
4052 J. Phys. Chem., Vol. 100, No. 10, 1996
Fang et al.
TABLE 3: TST Calculations of ∆Spq298 K for k1 and k2
a
reaction
∆Sqpq298 K (eu)
θOHC (deg)
rC‚H (Å)
rH‚O (Å)
ref
2 2 2 2 1 1 1 1 1
-28.1 -28.0 -27.9 -29.4 -28.2 -25.0 -28.1 -28.5 -30.0
165 160 150 180 145 165 160 150 180
1.396 1.3a normal + 0.07 normal + 0.07 1.416 1.396 1.3a b b
1.256 1.2a normal + 0.42 normal + 0.42 1.316 1.256 1.2a b b
this work Cohen and Benson14 Jeong and Kaufman13 Jeong and Kaufman13 this work this work Cohen and Benson14 Jeong and Kaufman13 Jeong and Kaufman13
General assumption according to the more recent work of Cohen.34 b Values were not specified.
bond angle was set at 165° as the midpoint of the previous calculations of Jeong and Kaufman. This resulted in a ∆Spq298 K for reaction 2 of -28.1 entropy units (eu). A comparison of ∆Spq298 K for reaction 2 with previous studies is shown in Table 3. ∆Spq298 K was in excellent agreement with previous calculations, except for the calculations of Jeong and Kaufman for a O‚‚‚H‚‚‚C bond angle of 180°. Because of the substitution of a F atom with the slightly less electronegative Cl atom, the geometry of the TS structure for k1 was adjusted for the reaction coordinates of bond length and bond angle. This effect is shown by a slight expansion in the C‚‚‚H and O‚‚‚H bond lengths at the transition state (cf. Figure 6). The C‚‚‚H bond is thus stretched by 0.09 Å, and the new forming H‚‚‚O bond is 0.48 Å larger than a normal OH bond. Reaction coordinates unchanged from k2 yielded ∆Spq298 K ) -25.0 eu. This result was ∼3-5 eu lower than that of previous calculations. The aforementioned expansion of C‚‚‚H and O‚‚‚H bond lengths and a reduction in the O‚‚‚H‚‚‚C bond angle to 145° yielded ∆Spq298 K ) -28.2 eu, demonstrating the sensitivity of ∆Spq298 K to the O‚‚‚H‚‚‚C bond angle. This result was in much better agreement with previous calculations, except once again for the calculations of Jeong and Kaufman for a O‚‚‚H‚‚‚C bond angle for 180°. In contrast to the indirect curve fitting approach used by Cohen and Benson14 for estimating B, we have directly calculated ∆CpqT from 298 to 1000 K using the harmonic oscillator-rigid free rotor approximation with a correction for hindered internal rotation in the TS. Calculation of ∆CpqT involves the following considerations: (i) changes in vibrations between the transition state and the reference state, ∆Cpqvib, (ii) changes in the external rotor, ∆Cpqer, by assuming a 1-D rotor for OH, CHFCl2, and CHF2Cl and a 3-D rotor for the transition states, (iii) changes in internal rotors along the C‚‚‚H and O‚‚‚H axes due to barrier differences, ∆Cpqir, with respect to the reference state (free rotor), (iv) electronic contributions arising from low-lying electronic states of species with odd numbers of electrons, ∆Cpqelec, and (v) translational contributions, ∆Cpqtrans. Of these considerations, ∆Cpqelec, and ∆Cpqtrans are negligibly small and ignored here.31 We thus consider the contribution of the first three terms to calculate the mean of ∆CpqT between 298 to 1000 K. Above 1000 K, ∆CpqT is relatively small and can be safely ignored.32 The changes in vibrational frequencies for reactions 1 and 2 between the transition state and the reference state were based on the frequencies listed by Jeong and Kaufman.13 The changes of two vibrational modes were considered. For CHFCl2, the reference model frequencies were Cl-C-O (240 cm-1) and F-C-O (340 cm-1) and the estimated TS frequencies were Cl-C‚‚‚H‚‚‚O (170 cm-1) and F-C‚‚‚H‚‚‚O (240 cm-1). For CHF2Cl, the reference model frequencies were Cl-C-O (275 cm-1) and F-C-O (340 cm-1) and the estimated TS frequencies were Cl-C‚‚‚H‚‚‚O (195 cm-1) and F-C‚‚‚H‚‚‚O (240 cm-1). ∆Cpqvib is temperature dependent and is defined as
TABLE 4: Thermochemical Data for the Transition States of Reactions 1 and 2 transition state
∆Spq298 K (eu)
∆Cp,Tqave
∆Hpq298 K (cal/mol)
CCl2F-H‚‚‚OH (hindered rotor) CCl2F-H‚‚‚OH (free rotor) CClF2-H‚‚‚OH (hindered rotor) CClF2-H‚‚‚OH (free rotor)
-28.2 -26.8 -28.1 -26.9
-0.07R -0.44R -0.06R -0.43R
1057 1912 2173 2820
TABLE 5: Comparison of the Modified Arrhenius Parameters in the Form of k(T) ) ATB exp(-C/T) for k1 and k2 to Previous TST and SAR Models k (cm3/ molecule‚s)
A (cm3/ molecule‚s)
B
C
ref
k1 k1 k1 k2 k2 k2
3.13 × 10-18 1.5 × 10-17 1.89 × 10-18 3.10 × 10-18 8.14 × 10-18 1.89 × 10-18
1.93 1.7 2 1.94 1.8 2
552 610 554 1112 1180 955
this work, TST calc TST calc14 SAR calc15 this work, TST calc TST calc14 SAR calc15
Cp,vibq(TST) - Cp,vibq(ref). The resulting mean ∆CpqT for reactions 1 and 2 was -0.07R and -0.06R, respectively. After establishing values for A and B on the basis of TST calculations using eqs 5 and 6, our extended temperature measurements were fitted to the modified Arrhenius expression and the best value for C was determined by minimization of nonlinear least squares error. The thermochemical properties of the TS that resulted in the best fits to the experimental data are summarized in Table 4. The experimental results for reactions 1 and 2 were most consistent with nearly identical entropies of activation at 298 K and slightly different O‚‚‚H‚‚‚C bond angles. However, additional theoretical work is required to better characterize the transition state. The TST-based modified Arrhenius expressions for reactions 1 and 2 were
k1(T)TST ) (3.13 ( 0.2) × 10-18T1.93(0.01 exp(-552 ( 18/T) (8) k2(T)TST ) (3.10 ( 0.2) × 10-18T1.94(0.01 exp(-1112 ( 26/T) (9) The uncertainity in the modified Arrhenius parameters is based on a (10% uncertainty in the vibrational frequencies. It is worthwhile to consider further the errors involved in calculating the semiempirical parameters A and B (eqs 5 and 6) and the resulting error in C. Given a reasonable approximation of the transition state geometry, the only significant source of error in determining ∆Spq298 K and ∆CpqT is the characterization of the two new internal rotations created in the transition state. In the aforementioned calculation, we assumed a finite barrier to rotation about the C‚‚‚H and H‚‚‚O bonds of 1.0 and 2.0 kcal/ mol, respectively. It is difficult to rationalize that these barriers could be any larger. However, it is conceivable that both of
Reaction of OH Radicals with HCFCs
Figure 7. Comparison of TST-based modified Arrhenius expression for k1 with experimental results and previous TST and SAR predictions.
these rotations are free, especially at elevated temperatures. This uncertainty has a measurable impact on both ∆Spq298 K and ∆CpqT. For reaction 1, ∆Spq298 K increased by 1.36 eu and ∆CpqT decreased by 0.74 cal mol-1 K-1, respectively. Similarly, for reaction 2, ∆Spq298 K increased by 1.23 eu and ∆CpqT decreased by 0.74 cal mol-1 K-1. This translates into roughly a factor of 20 increase in A and a 20% decrease in B for both reactions. Fitting these parameters to the experimental data resulted in an increase in C for both reactions 1 and 2 of a factor of 1.3 and 1.8, respectively. The transition state parameters for the free rotor case are summarized in Table 5. The free rotor case resulted in an acceptable fit to all of the available experimental data, i.e., within a factor of 2 (cf. Figures 4 and 5). However, the hindered free rotor calculations clearly resulted in the best overall fit, particularly at lower temperatures. A comparison of the empirical best fit expression and the TST-based expression (cf. Figures 4 and 5) indicates that the TST-based expression is in better agreement with all of the available literature data, with significant improvement over the empirical best fit most evident at subambient temperatures (
