Unimolecular Rate Constant and Threshold Energy for the HF

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Unimolecular Rate Constant and Threshold Energy for the HF Elimination from Chemically Activated CF3CHFCF3 Juliana R. Duncan, Michael S. Roach, Brooke Sibila Stiles, and Bert E. Holmes* Department of Chemistry, UniVersity of North Carolina at AsheVille, One UniVersity Heights, AsheVille, North Carolina 28804-8511 ReceiVed: January 8, 2010; ReVised Manuscript ReceiVed: May 18, 2010

Combination of CF3CHF and CF3 radicals at room temperature generated chemically activated CF3CHFCF3 molecules with 95 ( 3 kcal/mol of internal energy that decompose by loss of HF, initially attached to adjacent carbons, with an experimental unimolecular rate constant of (4.5 ( 1.1) × 102 s-1. Density functional theory was used to model the unimolecular rate constant for HF elimination, kHF, to determine a threshold energy of 75 ( 2 kcal/mol. 1. Introduction The reactions of CF3CHFCF3 in the gas phase are of great interest because CF3CHFCF3 is used as a fire suppressant in place of Halon 1301, CF3Br;1–6 as a working fluid in refrigeration and air conditioning applications;7–9 as a foam blowing agent with fire retardant capabilities;10 and as a propellant in medical sprays.11–13 Modeling studies of low-pressure and atmospheric pressure combustion rely upon accurate kinetic data for the unimolecular decomposition of CF3CHFCF3 and its bimolecular reactions with OH radicals and other reactive species. Experimental and computational studies14–26 of the product profile for combustion of CF3CHFCF3 and of the reactions between CF3CHFCF3 and OH radicals or atomic species (F, Cl, H, O, etc) have appeared. A shock tube pyrolysis26 of CF3CHFCF3 over the temperature range 1200-1500 K concluded that thermal decomposition dominated the removal processes of CF3CHFCF3 and that HF elimination predominates over C-C bond fission. They modeled the combustion profile using an assumed Arrhenius activation energy, Ea, for 1,2-HF loss of 69.6 kcal/mol. The Ea was estimated by adding 38.8 kcal/mol to the enthalpy change for the HF elimination reaction and corresponds to a threshold energy, E0(HF), of 67.4 kcal/mol; the A-factor was assumed to be 7.9 × 1012 s-1. A modeling study1 using laser-induced fluorescence detection of radical species in the CF3CHFCF3 inhibited CH4 + O2 flame agreed that unimolecular HF decomposition was dominant, but concluded that C-C bond rupture was increasingly important as the flame temperature increased, and it appeared that the same Arrhenius parameters were used as the earlier26 work. A very recent thermal decomposition investigation19b using UV photoelectron detection also found that 1,2-HF elimination was favored but suggested that formation of HCF3 + CF2dCF2, rather than C-C bond rupture, became more important at higher temperatures. A modeling study of the product profile from the reaction between CF3CHFCF3 and either atomic hydrogen or O(3P) used Ea ) 69.5 kcal/mol23 for HF elimination, but a similar approach27 for the inhibition by CF3CHFCF3 on shock heated ethaneoxygen-argon mixtures used Ea ) 75.6 kcal/mol. * To whom correspondence should be addressed. E-mail: bholmes@ unca.edu.

A theoretical investigation at the QCISD(T) level recommended28 E0 ) 79.2 kcal/mol, but five different levels of theory predicted an E0 in the range 82.3-89.1 kcal/mol and B3LYP with 6-31G(d) gave a barrier of 75.4 kcal/mol. The E0 is typically two or three kcal/mol lower than Ea at high temperature; thus, the theoretical work suggested an activation energy between 75 and 90 kcal/mol. The flame profile modeling studies1,26 agreed that unimolecular elimination of HF from CF3CHFCF3 is an important step in the complex reaction chemistry of inhibited flames and, because a precise threshold energy is essential to accurately model the combustion system, an experimental investigation of the 1,2-HF elimination reaction from CF3CHFCF3 seems warranted. We will measure the unimolecular rate constant for HF loss from CF3CHFCF3 chemically activated by the combination of CF3 and CHFCF3 radicals. The average energy, 〈E〉, of the chemically activated CF3CHFCF3 is estimated as 95 kcal/mol from the CF3CHF-CF3 bond dissociation energy, D0(CF3CHFCF3), plus the average thermal energy of the combining radicals. The RRKM theory29 will be used to calculate the rate constant for HF elimination from CF3CHFCF3, with an energy equal to 〈E〉, and the threshold energy, E0, will be varied until the computed unimolecular rate constant matches the experimental result. Input parameters needed for the RRKM computation of the rate constant (vibrational frequencies and moments of inertia) will be calculated with density functional theory (DFT) using the Gaussian03 suite30 of programs. A systematic study31 of DFT and ab initio methods for the 1,2-HF (DF) elimination from CF3CH3 (CF3CD3) determined that B3LYP or B3PW91 together with either a 6-31G(d′,p′) or a cc-PVDZ basis set gave the best agreement between computed and experimental rate constants and the kinetic isotope effect. In our recent work,32–34 DFT using the B3PW91 method with a 6-31G(d′,p′) or a 6-311+G(2d,p) basis set was found to give close agreement between the computed and experimental assigned E0(HF) for nine halopropanes and one halobutane. There are three main sources of uncertainty in matching the computed rate constant to the experimental measurement to determine the E0 for HF elimination: (1) The enthalpy of formation for CF3CHFCF3, the CF3CHF radical, and the CF3 radical are used to determine D0(CF3CHF-CF3). The experimental uncertainty in thermochemistry for these fluorocarbon species is often (1-2 kcal/mol leading to an uncertainty of

10.1021/jp100195e  2010 American Chemical Society Published on Web 06/10/2010

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(2-4 kcal/mol for the 〈E〉. This uncertainty will be represented as the horizontal edges of a box in Figure 2. (2) There is some error in measuring the experimental rate constant, but this is frequently less than the uncertainty associated with the collisional deactivation mechanism. This uncertainty will be represented by the height of a box in Figure 2. (3) The electronic structure calculations give vibrational frequencies and moments of inertia for the molecule and the transition state that are needed to evaluate the rate constant, kE, at a specific energy E according to the RRKM formulation. In Section 3.3 we will demonstrate that different DFT methods and basis sets, for a common E0, give nearly identical dependence of kE versus E. However, the two CF3 torsional frequencies can be treated as a vibration, hindered internal rotor or as a free rotor. The sums and densities of states can be sensitive to the specific model used to describe the torsional motion, and we will test different models for the CF3 torsional motion for the effect on kE. The best calculated rate constants are subject to the assumption inherent in transition state theory with harmonic counting of states. Any kE curve in Figure 2 that touches the box illustrating the uncertainty in 〈E〉 and in the experimental rate constant will be criteria for an acceptable E0. Agreement between the computed and the experimental rate constants should reduce the wide variation in the currently published E0 value (67-89 kcal/mol)23,26–28 to (2 kcal/mol. The chemically activated CF3CHFCF3, denoted with an asterisk (*), was formed by the combination of CF3CHF and CF3 radicals, eq 1 and the other radical combination reactions are 2 and 3. kc

CF3CHF + CF3 98 CF3CHFCF3*

kc

2CF3CHF 98 meso- and d, l-CF3CHFCHFCF3*

kc

2CF3 98 CF3CF3*

(1)

(2)

(3)

Photolysis of CF3CHFI and CF3I in pyrex vessels containing small amounts of mercury(I) iodide (to scavenge atomic iodine)35 produced the radicals shown in eqs 1-3. Equation 5 shows that chemically activated CF3CHFCF3* may be stabilized by collision with bath gas molecules, M, mainly the iodide precursors, or at sufficiently low pressures it may decompose via 1,2-HF elimination, eq 4. The hexafluoroethane, reaction 3, and meso- and d,l-CF3CHFCHFCF3, reaction 2, are stabilized at the pressures of these experiments. k1,2-HF

CF3CHFCF3* 98 CF2dCFCF3 + HF kM[M] 98 CF3CHFCF3

(4) (5)

The rate ratio for eqs 4 and 5 equals the product ratio so we can write eq 6.

[CF2dCFCF3]/[CF3CHFCF3] ) k1,2-HF/kM[M]

(6)

which is of the form y ) mx + b (y ) [CF2dCFCF3]/[CF3CHFCF3], m ) k1,2-HF/kM, x ) 1/[M], and b ) 0). The concentration of the collision partner, [M], equals the pressure, P; thus, a plot of [CF2dCFCF3]/[CF3CHFCF3] versus 1/P would be linear with a slope of k1,2-HF/kM and an intercept of zero. 2. Experimental Section Pyrex vessels with volumes ranging from 552 to 4900 mL containing normally 0.182 µmol of 1-iodo-1,2,2,2-tetrafluoroethane and 0.547 µmol trifluoromethyl iodide, and small amounts of mercury(I) iodide, were photolyzed with a highpressure Oriel 68811 arc lamp operating with a 500 W mercury lamp. The reaction vessel was placed at least 25 cm from the Hg lamp to reduce local heating during the photolysis. The presence of mercury(I) iodide in the vessels during photolysis aids in formation of the trifluoromethyl and 1,2,2,2-tetrafluoroethyl radicals.35 Photolysis times were between 10 and 20 min, at room temperature, resulting in the conversion of 12-22% of the reactants. For sample preparation, a pressure of either 1.00 or 3.00 Torr of an iodide was measured in a small, calibrated vessel with a MKS 270 electronic manometer and then transferred to the much larger reaction vessel. The total pressure in the reaction vessel was determined by adding together the residual pressure prior to addition of the iodides, typically between (2 and 4) × 10-4 Torr, and the pressure due to the iodides that had been transferred from the calibrated vessel. Following addition of the CF3CHFI and CF3I samples to the reaction vessel the total pressure was between (0.22 and 3.0) × 10-2 Torr. Product identification was based on comparison of mass spectral fragmentation patterns and retention times with authentic samples. A Shimadzu QP 5000 GC/MS with a 0.25 mm by 105 m Rtx-200 column was used for mass analysis, a GC/ MS trace is in Supporting Information. Analytical data were collected using a 0.53 mm by 210 m Rtx-200 combination column in a Shimadzu GC-14A with flame ionization detector and a Shimadzu CR501 Chromatopac Integrator for integration of peak areas. For an isothermal GC analysis at 35 °C the typical retention times were as follows: C2F6, 19.4 min; CF2dCFCF3, 20.4 min.; CF3CHFCF3, 21.2 min.; CF3I, 22.1 min, meso- and d,l-CF3CHFCHFCF3, 26 min and 29 min.; and CF3CHFI, 33 min. Kinetic data were collected using a 210 m GC column to ensure baseline separation of C2F6, CF2dCFCF3, CF3CHFCF3, and CF3I. Authentic samples of all products were available except CF3CHFCHFCF3. The flame ionization detector calibration factor was [CF2dCFCF3]/[CF3CHFCF3] ) 0.685 ( 0.007 based on four replicates from five different mixtures of authentic samples. 3. Results and Discussions 3.1. Experimental Chemical Activation Rate Constant. This chemical activation study using CF3CHFI and CF3I to produce the CF3CHF and CF3 radicals is a clean chemical activation system with no evidence for secondary unimolecular reactions and no evidence for disproportionation reactions of the radicals. A typical GC/MS trace of a photolyzed sample used to identify products, which is presented in Supporting Information, shows only products from eq 1-5 were observed. A plot of [CF2dCFCF3]/[CF3CHFCF3] versus inverse pressure, see eq 6, is in Figure 1 for 29 data points. The pressure range is smaller than desirable, but we wanted the pressure in the reaction vessels to be an order of magnitude larger than the residual pressure; thus, our vacuum system restrictioned the low pressure limit to 2 × 10-3 Torr which is 1/P ) 500 Torr-1. As

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Figure 1. The ratio of [CF2dCFCF3]/[CF3CHFCF3] vs reciprocal pressure for the 1,2-elimination of HF from chemically activated CF3CHFCF3, see eq 6 in the text. The slope is (3.4 ( 0.2) × 10-5 Torr, the intercept is -(2.9 ( 4.8) × 10-4, and the correlation coefficient is 0.96.

anticipated for a unimolecular reaction in an efficient bath gas, the plot is linear and the intercept, -(2.9 ( 4.8) × 10-4, is zero within the experimental uncertainty ((1 standard deviation). The slope is (3.4 ( 0.2) × 10-5 Torr and equals k1,2-HF/ kM. The use of the strong collision model is defended in Section 3.5. The rate constant in pressure units is converted to units of s-1 by multiplication by the collision rate constant kM ) πd2A,M(8kT/πµA,M)1/2Ω2,2(T*). Using collision theory with collision diameters, d, and
/k values (in parentheses) of 5.1 Å (288 K), 5.2 Å (300 K), and 6.1 Å (200 K) for CF3I, CF3CFHI, and CF3CHFCF3, respectively, kM ) 1.32 × 107 (torr-s)-1. The slope is converted to a rate constant for HF elimination from CF3CHFCF3, k1,2-HF ) (4.5 ( 1.1) × 102 s-1. The collision diameters and the
/k values used for CF3CHFI and CF3CHFCF3 are estimates based on values employed for the CF3CHFCH3 system.32 The 6% uncertainty in the slope of the plot Figure 1 was increased to (25% to account for the uncertainty in converting the rate constant from pressure units to s-1 units. 3.2. Thermochemistry. Calculation of nonequilibrium rate constants for comparison with the experimental chemical activation results requires the average energy, 〈E〉, deposited in the CF3CHFCF3 from eq 1. The mean energy of the chemically activated CF3CHFCF3 is given by eq 7, where D0(CF3CHFCF3) is the bond dissociation energy for the C-C bond formed by radical combination, and it equals -∆H°rxn,0 for eq 1. The mean vibrational energy of the radicals is determined from their vibrational frequencies 〈Evib(CF3)〉 ) 0.4 kcal/mol and 〈Evib(CHFCF3)〉 ) 1.7 kcal/mol, and 3RT is the rotational energy of the radicals. 〈E〉

) D0(CF3CHF-CF3) + 3RT + 〈Evib(CF3)〉 + 〈Evib(CHFCF3)〉

(7)

The ∆H°f,0 (CF3) ) -111.7 kcal/mol is established.36 We adopt ∆H°f,298(CF3CHF) ) -166.7 kcal/mol, which is an average of four recent values (-168,37 -167.4,38 -166.7,39 and -164.5 kcal/mol26) and correction to 0 K gives ∆H°f,0 (CF3CHF) ) -165 kcal/mol. Five reports (-371.1,40 -374.2,41 - 374.5,38 -370.6,2 and -365.626b) for ∆H°f,298(CF3CHFCF3) were averaged to give

-371.2 kcal/mol and corrected to 0 K to give ∆H°f,0(CF3CHFCF3) ) -368.0 kcal/mol. The ∆H°rxn,0 for reaction 1 is -91.3 kcal/mol with a combined uncertainty of (3 kcal/mol. Peterson and Francisco28 calculated D0(CF3CHF-CF3) ) 92.3, in good agreement with our 91.3 ( 3 kcal/mol. Inserting these values into eq 7 gives 95.2 ( 3 kcal/mol, and we will use 〈E〉 ) 95 ( 3 kcal/mol. An alternative method to compute 〈E〉 will be given in Section 3.4. 3.3. Computed Chemical Activation Rate Constant. The vibrational frequencies and moments of inertia for the molecule and the transition state, used in the statistical rate constant calculations, were determined by DFT using Gaussian 03,30 see Table 1. The two CF3 torsional motions were treated as either torsion vibrations (TOR), hindered-internal rotors (HIR) or as free rotors for calculations42 of the harmonic density or sum of vibrational states. The reaction path degenercies were 4 for the TOR and 6 for the HIR or free-rotor models. Pitzer’s method was used to calculate the reduced moments of inertia, shown in Table 1, for the CF3 group for the molecule and for the transition state structure; the torsional potential energy barrier for rotation of a CF3 group, V(CF3), was calculated, using B3PW91 or B3LYP with the five basis sets listed in Table 2, to be 3 kcal/mol for the CF3CHFCF3, independent of method and basis set, and it was assumed the V(CF3) did not change in the transition state. At 〈E〉 ) 100 kcal/mol with an E0(HF) ) 74 kcal/mol, the HIR rate constant was just 6.8% lower than the rate constant calculated using a free-rotor model; thus, Figure 2 will only show the energy dependence of rate constants calculated using the HIR or TOR models. Two DFT methods (B3PW91 and B3LYP) and the five basis sets shown in Table 2 were used to illustrate that the calculate E0(HF) can decrease by more than 6 kcal/mol from the smallest to the largest basis set. However, the two DFT methods give very similar threshold energies for a common basis set. To explore whether rate constants computed using different methods or basis sets exhibited different magnitude and energy dependence the B3LYP/6-31G(d), B3PW91/6-31G(d′,p′), and B3PW91/ 6-311+G(2d, p) DFT methods were used to compute kE versus E, see Figure 2. The HIR method was used for all calculations. The rate constants at E0(HF) ) 74 kcal/mol with B3LYP/631G(d) were indistinguishable from the rate constants calculated using frequency and moments of inertia data computed using B3PW91/6-31G(d′,p′), see Figure 2. The same result was found at E0(HF) )76 kcal/mol when rate constants were compared for the B3PW91/6-31G(d′,p′), and B3PW91/6-311+G(2d, p) methods. Even though the E0(HF) values varied significantly for different DFT methods, the computed rate constants for a common threshold energy were nearly identical. Thus, we can compute kE at specific energies, E, using just one DFT method with confidence that other basis sets would give similar results. The remaining calculations will use B3PW91/6-31G(d′,p′), which has been very successful in our previous work.32–34 By contrast, use of TOR versus HIR models gave calculated rate constants differing by about a factor of 2, depending on the specific 〈E〉, see Figure 2. The two CF3 torsional motions appear to be strongly coupled because the frequencies are significantly different: one in the 10-25 cm-1 range and the other near 85 cm-1, see Table 1. Thus, the HIR model is preferred and just the HIR model based on B3PW91/631G(d′,p′) will be consided. Rate constant calculations were done for a range of E0(HF) values for the HIR model to determine which threshold energies produced computed rate constants that encompassed the uncertainties in both the experimental rate constant and the 〈E〉 shown as the box in

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TABLE 1: Calculated Frequencies, Moments of Inertia, and Reduced Moments of Inertia for CF3CHFCF3 and the HF Elimination Transition State at B3PW91/6-31G(d′,p′), B3LYP/6-31G(d), and B3PW91/6-311+G(2d, p) CF3CHFCF3 6-31G(d′,p′) -1

frequencies (cm )

amu (Å2)

Ired (amu Å2) a

Ix Iy Iz

9.389 83.56a 149.6 213.5 234.5 288.8 322.3 342.1 454.9 519.3 537.4 552.8 608.1 688.0 743.4 868.7 917.0 1145.2 1156.8 1212.3 1246.0 1273.6 1297.1 1330.0 1394.5 1407.9 3106.4 242.1 479.5 544.1 60.9

a

6-31G(d) a

16.66 87.52a 153.6 215.3 233.6 288.5 322.1 341.1 450.5 512.0 530.1 546.3 606.9 683.7 742.3 875.9 923.4 1158.5 1166.8 1224.1 1257.8 1286.3 1310.1 1341.1 1410.8 1426.6 3121.2 242.4 478.5 543.0

transition 6-311+G(2d,p)

6-31G(d′,p′)

6-31G(d)

6-311+G(2d,p)

52.44a 77.56 156.2 200.9 240.7 268.9 287.1 346.0 374.7 420.5 504.0 547.9 599.4 621.7 716.1 777.0 812.0 1029.9 1146.1 1207.9 1226.6 1245.4 1363.0 1455.6 1575.2 1736.3 263.8 510.9 558.2

54.13a 79.12 159.1 199.7 238.3 263.9 279.6 344.6 371.9 419.3 498.5 544.6 596.7 618.7 718.1 775.8 813.4 1033.2 1142.3 1217.1 1232.8 1257.3 1368.9 1468.7 1580.8 1733.2 265.0 510.8 556.9

51.09a 80.38 153.1 204.9 235.7 260.4 271.1 344.7 368.9 403.0 499.6 532.7 595.2 612.3 694.7 763.5 787.7 1025.0 1141.7 1181.0 1198.7 1237.5 1347.3 1446.9 1554.5 1738.7 265.8 513.6 556.5

62.3

62.1

a

24.06 85.12a 149.7 214.9 239.2 288.4 319.7 341.2 449.9 512.4 531.6 547.5 602.5 684.9 739.8 859.6 910.1 1114.8 1141.7 1168.9 1212.5 1225.0 1273.0 1305.1 1377.3 1394.3 3097.6 241.5 481.8 545.9

Reduced Moment of Inertia of the CF3 Group (Ired) 61.1 60.6 62.1

Frequency replaced with Ired in hindered internal rotor and free rotor rate calculations.

TABLE 2: Computed Threshold Energies using DFT for HF Elimination from CF3CHFCF3 threshold energy (kcal/mol) basis Set

B3PW91

B3LYP

6-31G(d) 6-31G(d′,p′) cc-PVDZ 6-311+G(2df, 2p) 6-311+G(2d, p)

75.2 71.7 69.7 69.7 69.0

75.4 71.7 69.7 69.7 69.0

Figure 2. At 〈E〉 ) 95 kcal/mol, the k〈E〉 ) 170 s-1 for an E0 ) 76 kcal/mol and k〈E〉 ) 660 s-1 for an E0 ) 74 kcal/mol. The experimental value is in the range 340-560 s-1. Using the HIR model an E0(HF) from 73 to 77 kcal/mol would just touch the box, see Figure 2; thus, we are confident in assigning E0(HF) ) 75 ( 2 kcal/mol. 3.4. Comparing the Specific Rate Constant, k〈E〉, at an Average Energy 〈E〉 to the Average Rate Constant, 〈kE〉. The previous section used the specific rate constant, k〈E〉 at 〈E〉 to determine acceptable values for the threshold energy for the HF elimination reaction. This is an approximation because the radical combination reaction, eq 1, produces CF3CHFCF3 with a distribution of energies, f(E), and the average rate constant, 〈kE〉 can be calculated once f(E) is determined. Given the large uncertainty in 〈E〉, it is not reasonable to attempt a further refinement of E0, but it would be of interest to know how k〈E〉 compares to 〈kE〉. The f(E) can be calculated29 once a model for the association complex for eq 1 is constructed. The association complex consists of the vibrational frequencies for the two

radicals, four bending frequencies (two at 50 cm-1 and two at 100 cm-1), and one free rotation. The torsional motion about the C-C bond for the CF3CHF radical was treated as a free rotor. The calculated energy distribution function is shown in the Supporting Information. Using the f(E) and the kE values for HIR at E0 ) 74 kcal/mol the 〈kE〉 ) 1470 s-1. This is a factor of 2.2 larger than k〈E〉 ) 660 s-1 for 〈E〉 ) 95 kcal/mol. The E0 for the 〈kE〉 calculation would need to be raised by about 1 kcal/mol to give agreement with the k〈E〉. 3.5. Strong Collision Assumption. The experimental rate constant was evaluated with the assumption that each collision between the bath gas and CF3CHFCF3* (see eq 5) removed sufficient energy such that further reaction was negligible relative to deactivation by subsequent collisions. However, in cases where the difference between 〈E〉 and E0 is large and/or the collision partner is inefficient, a multistep deactivation scheme could be more appropriate. In order to calculate a rate constant for multistep deactivation the average energy removed per collision and the model (stepladder, exponential, or some other model) for the energy removal mechanism must be known or assumed. None of this information is available for CF3CHFCF3* colliding with a bath gas that is a mixture of CF3I and CF3CHFI. Experimental evidence of multistep deactivation would be the upward curvature of a D/S vs 1/P plot at lower pressures where D/S > 1.0. Our data, see Figure 1, does not extend beyond D/S ) 0.02, and no evidence for multistep deactivation is observed. In addition, we have studied32,33 several chemically activated hydrohalocarbons with CF3I and other

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Figure 2. Plots of log kE vs E for hindered internal rotor (HIR) and torsional (TOR) models for various E0 using results from the B3PW91/ 6-31G(d′,p′) calculations unless specified as G(d) or G(2d,p) for the B3LYP/6-31G(d) or the B3PW91/6-311+G(2d,p) calculations, respectively. [HIR, E0 ) 74 kcal/mol with two different basis sets: O B3PW91/6-31G(d′,p′) and b - B3LYP/6-31G(d)]; [0 - TOR, E0 ) 74 kcal/mol using B3PW91/6-31G(d′,p′)]; [HIR, E0 ) 76 kcal/mol using two different methods and basis sets: [[ - B3PW91/6-31G(d′,p′) and 4 - B3LYP/6-31G(d)] and [2 - HIR, E0 ) 77 kcal/mol using B3PW91/ 6-31G(d′, p′)].

hydrofluoroalkyl iodides as bath gases and have not found evidence for inefficient behavior in the D/S plots. Nonetheless, the use of the strong collision assumption for CF3CHFCF3* colliding with a bath gas comparable to our mixture of CF3I and CF3CHFI can be examined. The question of multistep deactivation has been investigated for two chemically activated molecules, CF3CH343 and 1,1,2,2-tetrafluorocyclopropane,44 with a structure analogous to CF3CHFCF3. For cyclo-CF2CF2CH2* colliding with CF2dCF2 the average energy removed per collision was 9 kcal/mol.44 The more exhaustive study43 of CF3CH3* with numerous collision partners showed that for molecules similar to our bath gas the average energy removed per collision would be 6-10 kcal/mol. The HIR kE vs E curve with E0 ) 74 kcal/mol in Figure 2 will be used to examine whether the strong collision assumption is valid for our system, and we will assume that our bath gas mixture removes an average of 6 kcal/mol from CF3CHFCF3* per collision. We believe this is the worst-case scenario because the studies with CF3CH3* and cyclo-CF2CF2CH2* suggest that each collision will likely remove more than 6 kcal/mol of energy. At 〈E〉 ) 95 kcal/mol the kE ) 660 s-1, and if 6 kcal/ mol is removed by one collision the rate constant declines to 34 s-1 at 〈E〉 ) 89 kcal/mol. Following just one collision that removes 6 kcal/mol of energy, the rate constant is only 5% of the value at 〈E〉 ) 95 kcal/mol. This relatively large decline in kE is a consequence of the steep slope of the kE versus E curve in Figure 2. It is important to note that for the lowest pressures in Figure 1 the D/S < 0.02; thus, the collision rate is at least 50

Duncan et al. times larger than kE in these experiments. On the basis of this analysis, the strong collision assumption does not introduce any significant additional error in the assignment of the threshold energy. 3.6. Arrhenius Rate Constants. Studies modeling the product profile for combustion of CF3CHFCF3 use Arrhenius rate constant parameters. We computed k(T) for the HIR model with V(CF3) ) 3 kcal/mol and Ired ) 61 amu Å2. The Arrhenius parameters at 1000 K for the full reaction path degeneracy are 14.2 × 1013 s-1 and Ea ) 77.2 kcal/mol. The pre-exponential factor for V(CF3) ) 6 kcal/mol is 20.4 × 1013 s-1. This change arises because the HIR in the transition state is canceled by one in the molecule, and the partition function is smaller for the remaining HIR in the molecule with the higher barrier. If one removes a factor of 6 for reaction path degeneracy the preexponential factor is “normal” for a tight transition state.31–34 If the pre-exponential factor for dissociation of the C-C bond is 1016 s-1, then HF elimination is dominant at 1000 K but dissociation would become competitive with HF elimination at higher temperatures, consistent with the experimental findings.1,26 3.7. Computed Structures for the Reactant, Transition State, and Product. Figure 3 has the bond distance and bond angles for the structures computed using B3PW91/6-31G(d′,p′) for CF3CHFCF3, the transition state structure for HF loss and the CF2dCFCF3 product. For the following discussion the carbon losing the hydrogen is designated CH, and CF represents the carbon losing the F. The degree of sp2 character of the carbons in the four-centered ring of the transition state is illustrated by the 14.7° angle at CF (the angle defined by the triangular plane between the CF2 and an imaginary line extending along the CdC) and the corresponding angle at CH is 37.8°, see Figure 3. For reference, the angle is 55° for a sp3 carbon and 0° for a sp2 carbon. The degree of planarity differs at the two carbons in the transition state ring with the carbon losing the F being significantly more planar that the carbon losing the hydrogen. A similar trend34g has been observed for other transition states involving elimination of HF. It is interesting to note that the out-of-ring C-F bond distance at CF is shorter in the transition state (1.29 Å) than in either the reactant (1.34 Å) or the CF2dCFCF3 product (1.31 Å), suggesting that the fluorine substituents are donating electron density to CF. By contrast, the out-of-ring C-F bond distance (1.36 Å) at CH is nearly the same as in the CF3CHFCF3 molecule (1.37 Å). The C-C bond distance in the ring (1.43 Å) is exactly half way between the bond distance of the reactant (1.53 Å) and product (1.33 Å). 3.8. Comparison with Previous Studies Involving HF Elimination. Unimolecular rate constants for HF elimination from other chemically activated fluoropropanes32 (CF3CH2CF3, CF3CHFCH3, and CF3CH2CH3) have been reported. We have previously noted32 the good agreement between threshold energy values for these hydrofluoropropanes. A comparison would be useful between CF3CHFCF3 and CF3CH2CF3 because for both fluoropropanes an H on the central carbon is eliminated together with an F atom from either end CF3 group. For CF3CH2CF3 the 〈E〉 ) 104 kcal/mol, kHF ) 1.2 × 105 s-1, and E0 ) 73 kcal/ mol compared to 〈E〉 ) 95 kcal/mol, kHF ) 4.5 × 102 s-1, and E0 ) 75 kcal/mol for CF3CHFCF3.33 The experimental rate constant is a factor of 270 smaller for CF3CHFCF3 compared to CF3CH2CF3. A difference of 9 kcal/mol in 〈E〉 accounts for a factor of 30 in the rate constant, for example, for 〈E〉 ) 95 kcal/mol the calculated kHF ) 8.8 × 102 s-1 for CF3CHFCF3 and at 〈E〉 ) 104 kcal/mol the kHF ) 2.90 × 104 s-1, which is a difference of 33. A reaction path degeneracy of 6 for

HF Elimination from Chemically Activated CF3CHFCF3

J. Phys. Chem. A, Vol. 114, No. 26, 2010 7001 found E0 > 95 kcal/mol for the 2,2-HF elimination reaction forming the CF3CCF3 carbene. We found no evidence for carbene formation consistent with their predictions. For the 1,2HF elimination reaction Peterson and Francisco predicted an E0 ranging from 75.4 [B3LYP/6-31G(d)] to 89.1 kcal/mol [QCISD(T)/6-31G(d)] and recommended 79.5 kcal/mol based upon QCISD(T)/6-311G(d,p). Our results using 〈E〉 ) 95 kcal/ mol are consistent only with the smallest E0 calculated by Peterson and Francisco. A comparison of the various E0 values can also be useful to examine the effect of different substituents. Assuming that CF3CH3 with E0 ) 69 kcal/mol is the selected for comparison32 then E0 ) 73 kcal/mol33 for CF3CH2CF3 suggests that replacement of one H of CF3CH3 with a CF3 group raises E0 by 4 kcal/mol. The present work with E0 ) 75 kcal/mol for CF3CHFCF3 suggested that replacement of a second H with atomic F may increase E0 by an additional 2 kcal/mol. 3.9. Conclusions The unimolecular rate constant for HF elimination from CF3CHFCF3 chemically activated at 95 kcal/mol was kHF ) 4.5 × 102 s-1. Matching computed rate constants to the experimental measurement for HF elimination from chemically activated CF3CHFCF3 at 〈E〉 ) 95 kcal/mol gives E0(HF) ) 75 ( 2 kcal/ mol. Threshold energies for 1,2-HF elimination from fluoropropanes span 20 kcal/mol from the simplest member of the series CH3CHFCH345,46 (E0 ) 55 kcal/mol)33a and CH3CH2CH2F46,47 (E0 ) 57 kcal/mol)33a to CF3CHFCF3, the most highly fluorinated propane for which HF loss is possible. In general,32,33a replacement of H by F on a carbon increases the E0 by 2-4 kcal/mol. Elimination of F from the central carbon has a lower E0 than loss of F from the end carbon if the total number of F substituents is constant. Methyl substituents generally decrease32,33a the E0, but the effect is more pronounced at CF than when attached to CH. Acknowledgment. Financial support from the National Science Foundation (CHE-0647582) is acknowledged. We are grateful to Professors George L. Heard and D. W. Setser for helpful discussions. Professor Setser kindly assisted in computing the Arrhenius A-factor and the energy distribution for the chemically activated CF3CHFCF3. Supporting Information Available: The energy distribution computed from an association complex for the chemically activated CF3CHFCF3 and a GC/MS trace of a photolyzed sample are included. This information is available free of charge via the Internet at http://pubs.acs.org. References and Notes

Figure 3. Calculated structures for CF3CHFCF3, the transition state for HF elimination, and CF2dCFCF3 at the B3PW91/6-31G(d′,p′) method.

CF3CHFCF3 versus 12 for CF3CH2CF3 accounts for an additional factor of 2.33 A two kcal/mol lower threshold energy will increase the unimolecular rate constant by about a factor of 4, see Figure 2. All three factors combined contribute a factor of over 240 to the difference in rate constants, showing that the RRKM models for the two molecules are actually quite consistent despite the large difference in the actual rate constants. Peterson and Francisco28 computationally investigated the possible decomposition pathways for CF3CHFCF3 using ab initio and DFT methods. For all methods and basis sets tested they

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