Kinetics of Phenyl Radical Reactions with Ethane and Neopentane: Reactivity of C6H5 Toward the Primary C-H Bond of Alkanes

JCK(Wiley) LEFT INTERACTIVE

J. PARK, S. GHEYAS1, M. C. LIN Department of Chemistry, Emory University, Atlanta, GA 30322 Received 28 February 2000; accepted 7 August 2000

ABSTRACT: The kinetics of C6H5 reactions with C2H6 (1) and neo-C5H12 (2) have been studied

by the pulsed laser photolysis/mass spectrometric method using C6H5COCH3 as the phenyl precursor at temperatures between 565 and 1000 K. The rate constants were determined by

kinetic modeling of the absolute yields of C6H6 at each temperature. Another major product,

C6H5CH3, formed by the recombination of C6H5 and CH3, could also be quantitatively modeled using the known rate constant for the reaction. A weighted least-squares analysis of the two ϭ 11.32Ϯ0.05 Ϫ Ϯ 3 Ϫ1 Ϫ1 ϭ 11.37Ϯ0.03 sets of data gave k1 10 exp[ (2236 91)/T]cm mol s and k2 10 exp[Ϫ(1925 Ϯ 48)/T]cm3 molϪ1 sϪ1 for the temperature range studied. The result of our sen-

sitivity analysis clearly supports that the yields of C6H6 and C6H5CH3 depend primarily on the ϩ abstraction reactions and C6H5 CH3, respectively. From the absolute rate constants for the ϭ two reactions we obtained the value for the H-abstraction from a primary C-H bond, kp-CH 1010.40Ϯ0.06 exp(Ϫ1790 Ϯ 102/T)cm3 molϪ1 sϪ1. This result is utilized for analysis of other kinetic ᭧ data measured for C6H5 reactions with alkanes in solution as well as in the gas phase. 2000 John Wiley & Sons, Inc. Int J Chem Kinet 33: 64–69, 2001

INTRODUCTION for phenyl reactions in solution by Bridger and Russell ϩ using C6H5 CCl4 as a reference standard [2]. From In general, phenyl radical is more reactive than alkyl a series of studies carried out at 333 K, they deter- radicals [1], but unlike the alkyl, there has been very mined the relative reactivities of C6H5 toward the pri- little information available on the reactivity of C6H5 mary, secondary, and tertiary C-H bonds (0.12 Ϯ toward a speciﬁc type of C-H bonds of alkanes in the 0.01):1.01:4.8 for aliphatic hydrocarbons larger than gas phase; namely, the primary, secondary, and terti- C4. Further discussion on this and other relative rate ary CH bonds. data will be made later on the basis of our new results There had been many relative rate measurements for the primary C-H reaction and those for secondary and tertiary C-H reactions reported previously [3,4]. Correspondence to: M. C. Lin ([email protected]) This study is a continuation of our investigation on Contract grant sponsor: Basic Energy Sciences, Department of Energy the kinetics of C6H5 radical reactions [3–9] employing Contract grant number: DE-FG02-97-ER14784 the cavity ringdown spectrometry (CRDS) [10] and/or 1Current address: Chemistry Department, Temple University, Philadelphia, PA 19122 the pulsed laser photolysis/mass spectrometry (PLP/ short ᭧ 2000 John Wiley & Sons, Inc. MS) [11]. For several systems investigated, additional standard long JCK(Wiley) RIGHT INTERACTIVE

KINETICS OF PHENYL RADICAL REACTIONS WITH ETHANE AND NEOPENTANE 65

ϩ : measurements by pyrolysis/FTIR spectrometry (P/ CH65CH 3CHCH 65 3 (3) FTIRS) have been made to complement as well as to extend the range of reaction temperature [12,13]. On The significance of the toluene data will be discussed later. account of the slowness of the reactions of interest, The radical source, molecular reactants, and products were purchased fromAldrich; they were purified ϩ : ϩ by trap-to-trap distillation using appropriate cold CH65CH 26CH 66C 25 H (1) baths. He (Specialty Gases, 99.999% purity) was used ϩ : ϩ without further purification. CH65neo-C 512 H CH 66neo-C 511 H , (2) both rate constants were measured with the PLP/MS RESULTS AND DISCUSSION method. Rate Constant Determination

EXPERIMENTAL PROCEDURE The rate constants for reactions (1) and (2) have been determined by kinetic modeling of C6H6 yields, sum- The PLP/MS technique has been described in detail in marized in Table II, using the mechanism presented in a recent review [11]; the technique has been success- Table I. In the present measurements, both the radical fully employed for measurement of the rate constants source and molecular reactant concentrations were of C H reactions with H [12], CH [13], CH O [14], kept more or less constant to ensure reproducible sam- 6 5 2 4 2 pling. Product yields were measured near the plateaus and iso-C4H10 [3]. For the H2 and CH4 reactions, the PLP/MS results agree closely with those obtained by of individual concentration-time curves without early P/FTIRS and shock-tube studies [15], whereas for the time resolution because of the slow reaction and needed signal amplification. All calibration measure- CH2O and i-C4H10 reactions, PLP/MS rate constants agree quantitatively with the values determined by ments were carried out with the same amplifier setting CRDS. to ensure reproducibility. In PLP/MS experiments, we employed acetophen- By fitting the measured yields of C6H6 we could one as the phenyl radical source. The pulsed photolysis reproducibly obtain the rate constants k1 and k2 throughout the temperature range measured. The mod- of C6H5COCH3 at 193 nmwith an ArF excimerlaser (Lambda Physik, Compex 205) led to about 40% de- eled values are summarized in Table II and also graph- composition of acetophenone with an average of 60– ically presented in Figure 1.

70% efﬁciency yielding C6H5 radicals, according to the result of NO titration. This result is consistent with the amounts of ethane and toluene measured [13]. In present rate constant measurements, a constant amount of C6H5COCH3 carried by He was mixed with a molecular reactant before the reactor using a corru- gated ﬂexible stainless steel tube. Both C6H6 and C6H5CH3 were measured at 15 msec after photolysis near the plateaus of both product yields (because of the slowness of the reactions), with and without the molecular reactant. The absolute yields of C6H6 and

C6H5CH3 were determined by calibration using mixtures of the compounds of known compositions before and after the photolysis experiments, employing the same total pressure so as to ensure the same sampling efﬁciency. The measured absolute yields of the two products were kinetically modeled with the mechanism presented in Table I to obtain the corresponding rate constants for the primary processes giv- ing rise to the these products: Figure 1 Arrhenius plot of the rate constants for the C6H5 ϩ C H (᭺) and neo-C H (᭞) reactions. Inset: Arrhenius ϩ : ϩ 2 6 5 12 CH65RH CH 66 R plot of the rate constant per p-CH bond obtained by the C2H6 short ϭ ᭺ ᭞ (R CH,25neo-C 511 H ) (1,2) ( ) and neo-C5H12 ( ) rate constants. standard long JCK(Wiley) LEFT INTERACTIVE

66 PARK ET AL.

a ϩ Table I Reactions and Rate Constants Used in the Modeling of theCH65CH/ 26neo-CH 512 Reactions in the PLP/MS Experiment

c Reactions AnEa Ref.

ϩ !: ϩ ϩ b 1. C65 H CH 26CH 66CH 25 2.07E 11 0.0 4443 this work ϩ !: ϩ ϩ 2. C65 H CH 512CH 66CH 511 2.32E 11 0.0 3825 this work ϩ !: ϩ 3. C65 H CH 3CHCH 65 3 1.38E 13 0.0 46 ϩ !: ϩ 4. C6 H 5CH 6 5CH 12 10 1.39E 13 0.0 111 ϩ !: ϩ 5. C25 H CH 25CH 410 1.08E 13 0.0 0 17 ϩ !: ϩ ϩ 6. C25 H CH 25CH 24CH 26 1.45E 12 0.0 0 17 ϩ !: ϩ d 7. C65 H CH 25CH 810 1.38E 13 0.0 46 ϩ !: ϩ d 8. C65 H CH 511CH 1116 1.00E 13 0.0 0 ϩ !: ϩ d 9. C511 H CH 3CH 614 2.00E 13 0.0 0 !: ϩ ϩ 10. C511 H CH 48CH 3 1.07E 13 0.0 29800 18 ϩ !: ϩ 11. C5 H 11CH 5 11CH 10 22 1.26E 13 0.0 0 19 ϩ ϩ !: ϩ ϩ Ϫ 12. CH33CH ( M) CH( 26M) 2.12E 16 1.0 620 LOW / 1.770E ϩ 50 Ϫ9.670 6220.00/ TROE / .5325 151.00 1038.00 4970.00/

CH4/2.0/ CO/1.5/ C2H6/3.0/ C5H12/3.0/ He/ .7/ C6H6/3.0

a ϭ n Ϫ 3 Ϫ1 Ϫ1 Rate constants are deﬁned byk AT exp( Ea/RT) and in units cm , mol , and s ; Ea is given in units of cal/mol; additional reactions involving C6H6,C6H5CH3, and C6H5COCH3 can be found in ref. [3]. b11Read as 2.07 ϫ 10 . c Ref. [13] otherwise noted. d Assumed.

Table II Experimental Conditions,ab Product Yields and Modeled Rate Constants c in the PLP/MS Experiment at the Temperatures Studied

[C6H6]t [C6H5CH3]t

10 Temp(K) P(Torr) [C6H5COCH3]0 [C6H5]0 [C2H6]0 Exp Model k/10 Exp Predicted 583 3.07 2.77 0.93 533.4 0.14 0.14 0.48 0.30 0.31 667 3.06 2.62 1.08 535.6 0.18 0.18 0.68 0.34 0.38 765 3.06 2.85 0.86 533.9 0.22 0.22 1.09 0.28 0.28 795 3.06 2.67 1.03 533.8 0.25 0.25 1.14 0.33 0.35 865 3.07 2.76 0.94 536.8 0.29 0.29 1.60 0.29 0.29 900 3.03 2.83 0.87 529.7 0.29 0.29 1.71 0.27 0.26 955 3.04 2.85 0.85 531.2 0.33 0.33 2.03 0.23 0.23 1000 3.10 2.90 0.81 542.1 0.34 0.33 2.33 0.21 0.20

[C6H6]t [C6H5CH3]t

10 Temp(K) P(Torr) [C6H5COCH3]0 [C6H5]0 [C5H12]0 Exp Model k/10 Exp Predicted 565 3.08 2.87 0.83 200.2 0.09 0.09 0.75 0.30 0.31 616 3.09 2.90 0.80 200.7 0.11 0.11 1.02 679 3.06 3.03 0.67 198.9 0.12 0.12 1.32 709 3.07 3.11 0.59 199.9 0.13 0.13 1.66 0.21 0.21 761 3.08 2.96 0.74 199.6 0.15 0.16 1.82 0.29 0.29 785 3.04 2.84 0.86 196.9 0.16 0.16 1.94 0.36 0.34 861 3.06 2.95 0.75 199.1 0.18 0.18 2.48 0.28 0.29 927 3.07 2.56 0.84 196.8 0.21 0.22 3.00 0.28 0.33 968 3.05 2.37 0.83 196.4 0.22 0.22 3.12 0.30 0.31 991 3.09 2.35 0.85 201.3 0.23 0.22 3.23 0.31 0.32

a All concentrations are given in mTorr. b Product yields were measured att ϭ 15 msec at their plateaus. Typically, 2–3 runs were carried out for each temperature. short c In units of cm3 molϪ1 sϪ1 . standard long JCK(Wiley) RIGHT INTERACTIVE

KINETICS OF PHENYL RADICAL REACTIONS WITH ETHANE AND NEOPENTANE 67

Signiﬁcantly, as shown in Table II, the absolute yields of toluene can be quantitatively predicted with ϭ ϫ 13 Ϫ 3 the rate constant k3 1.38 10 exp( 23/T)cm molϪ1 sϪ1 determined previously from three indepen- ϩ dent sets of experiments on C6H5 H2 [12], CH4 [13], and i-C4H10 [3]. This is reassuring and important because the concentration of C6H5CH3 depends strongly on those of CH3 and C6H5. Our ability in predicting the toluene yields in this and other systems, including ϩ the recently completed C6H5 CH2O study [14], sug- gests that the concentration of C6H5, generated by the pulsed photolysis of acetophenone and measured by NO titration, is quite reliable. In addition, in our pre- ϩ vious study on the C6H5 CH4 reaction [13], we simultaneously measured the yields of C2H6 and

C6H5CH3 for several temperatures; both yields could be quantitatively modeled also. The results presented Figure 2 Comparison of various C6H5 abstraction rate in Figure 1 give rise to constants.

ϭ 11.32Ϯ0.05 k1 10 exp[Ϫ(2236 Ϯ 91)/T] cmmol3 sϪ1 Ϫ1 (I)

ϭ 11.37Ϯ0.03 k2 10 exp[Ϫ(1925 Ϯ 48)/T] cmmol3 sϪ1 Ϫ1 (II) based on a weighted least-squares analysis. The acti- vation energies thus determined, 4.43 Ϯ 0.18 and 3.83 Ϯ 0.09 kcal/mol, respectively, for C2H6 and C5H12 are considerably higher than the corresponding values for ϩ Ϯ the abstraction reactions, C6H5 toluene, 2.04 0.07 kcal/mol, and xylenes, 1.05 Ϯ 0.05 kcal/mol. The large difference between these two classes of reactions is fully expected because of the much weaker primary

C-H bonds in the CH3-substituted benzenes. Compar- ison of the present results with other C-H abstraction reactions involving alkanes will be made later. Figure 2 compares the absolute rate constants for the present C2H6 and neo-C5H12 reactions with those for H2,CH4, and i-C4H10 referred to earlier. It should be stressed that both H2 and CH4 data include the shock-tube results of Troe and co-workers [15] above 1000 K.

Sensitivity Analysis We have carried out sensitivity analysis for the two key products, C6H6 and C6H5CH3, using the SENKIN program[16]. The results are presented in Figures 3 and 4 for C2H6 and C5H12, respectively. Those reactions that have mole fraction (Xi) sensitivity coeffi- Figure 3 Sensitivity analyses for C6H6 (a) and C6H5CH3 cients, defined by S ϭ (␦X /␦k )(k /X ), less than 0.1 ϩ ij i j j i (b) in the C6H5 C2H6 reaction at 900 K. Reaction condi- are not included in the figures. As is evident fromthe tions are given in Table II and the sensitivity coefficients results, only three reactions in each of the systems evaluated in terms of mole fractions are as defined in the short have a significant effect on the measured concentra- text. standard long JCK(Wiley) LEFT INTERACTIVE

68 PARK ET AL.

analysis convoluting all errors fromindividual measurements gives the following expression with rela- tively small standard deviations:

ϭ 10.40Ϯ0.06 kp-CH 10 exp[(Ϫ1790 Ϯ 102)/T] cmmol3 sϪ1 Ϫ1 (III)

for the temperature range 565–1000 K. Equation (III) allows us to estimate the rate con-

stants for the C6H5 attack on a secondary and a tertiary

C-H bond, ks-CH and kt-CH, respectively, with Bridger and Russell’s relative rates obtained at 333 K in solution for aliphatic reactions, 0.12:1.01:4.8 [2], as cited in the Introduction,

ϭ ϫ 93Ϫ1 Ϫ1 ks-CH 1.0 10 (aliphatic) cmmol s

ϭ ϫ 93Ϫ1 Ϫ1 kt-CH 4.7 10 (aliphatic) cmmol s

This result may be compared with other speciﬁc examples that have also been measured by Bridger and ϩ Russell [2] at 333 K in solution using the C6H5 CCl4 reaction as the reference standard. Combining with our

Figure 4 Sensitivity analyses for C6H6 (a) and C6H5CH3 absolute rate constant for the CCl4 reaction measured ϩ (b) in the C6H5 neo-C5H12 reaction at 927 K. Reaction in the temperature range 298–523 K [4], their relative conditions are given in Table II and the sensitivity coeffi- rate constants can be converted to kp-CH, ks-H and kt-CH cients evaluated in terms of mole fractions are as defined in for comparison with our absolute rate constants mea- the text. sured in the gas phase, typically over a range of temperatures overlapping 333 K. Table III summarized these specific examples. As is evident fromthese results, the agreementbe- tions of C6H6 and C6H5CH3; they are tween the relative rate data measured in solution and CH ϩ RH : CH ϩ R (1,2) our more elaborate direct measurements of absolute 65 66 rate constants in the gas phase is reasonable, except the reactions with cyclopentane and 2,3,4-trimethyl CH ϩ CH : CHCH (3) 65 3 65 3 pentane. The reason for the deviation in these two cases is not clear and should be examined further. In CH ϩ CH : C H (4) 6 5 6 5 12 10 addition, we notice a significant molecular-size dependence among in the three tertiary C-H abstraction re- The rate constants for these reactions except (1) and actions in the gas phase fromisobutane to 2,3,4-tri- (2) have been reliably determined [11–13]. Accord- methyl pentane. Such dependence was, however, not ingly, k1 and k2 can be individually determined with observed in solution for the two larger molecules stud- reliability on account of the larger Sij values as shown. ied, as shown in Table III.

Relative Reactivities of C H Toward p-, s-, 6 5 CONCLUSION and t-CH Bonds

The absolute rate constants for the C2H6 and neo- The kinetics of the C6H5 reactions with ethane and

C5H12 reactions given by Eqs. (I) and (II) can be used neopentane have been measured by the pulsed laser to calculate the rate constant per primary C-H bond, photolysis/mass spectrometry method employing ace- kp-CH, by dividing the values of k1 and k2 by 6 and 12, tophenone as the radical source. Kinetic modeling of respectively. The result is presented in the inset of Fig- the benzene formed in these systems over the temper- ure 1. The two sets of the data agree within the com- ature range 565–1000 K yielded the following rate short bined errors as indicated. A weighted least-squares constants, given in units of cm3 molϪ1 sϪ1, for the re- standard long JCK(Wiley) RIGHT INTERACTIVE

KINETICS OF PHENYL RADICAL REACTIONS WITH ETHANE AND NEOPENTANE 69

Table III Comparison of the Rate Constants per C-H bond, kp-CH, ks-CH, andkt-CH for Reactions Studied in the Gas Phase and in Solution at 333 Ka

kp-CH ks-CH kt-CH Reactant Gas Soln Gas Soln Gas Soln neopentane 0.12b 0.22c tetramethyl butane 0.22c cyclopentane 0.55d 1.9c cyclohexane 1.4d 1.7c cycloheptane 3.5d 3.1c cyclooctane 3.4d 3.5c isobutane 3.0e 2,3-dimethyl butane 13e 11c 2,3,4-trimethyl pentane 62e 6.2c

a 9 3 Ϫ1 Ϫ1 kx is given in units of 10 cm mol s . b This work. c Ref. [2]. d Ref. [4]. e Ref. [3].

actions with C2H6 and neo-C5H12, respectively: 7. Yu, T.; Lin, M. C.; Melius, C. F. Int J ChemKinet 1994, 26, 1096. k ϭ 1011.32Ϯ0.05 exp[Ϫ(2236 Ϯ 91)/T] 8. Park, J.; Lin, M. C. J Phys ChemA 1997, 101, 14. 1 9. Park, J.; Chakraborty, D.; Bhusari, D. M.; Lin, M. C. J Phys ChemA 1999, 103, 4002. ϭ 11.37Ϯ0.03 Ϫ Ϯ k2 10 exp[ (1925 48)/T] 10. Park, J.; Lin, M. C. Cavity-Ring-Down Spectrometry- A New Technique for Trace Absorption Measurements; These results provide for the ﬁrst time the absolute rate ACS Symposium Series 720: Am. Chem. Soc., Wash- constant for the reaction of the phenyl radical with a ington, D.C., 1999; Chapter 13, p 196. single primary C-H bond in the 560–1000 K range, 11. Park, J.; Lin, M. C. Recent Research Development in ϭ 10.40Ϯ0.06 Ϫ Ϯ 3 Ϫ1 kp-CH 10 exp[( 1790 102)/T]cm mol Physical Chemistry; Transworld Research Network: In- sϪ1. The data can be used to extract rate constants for dia, 1998; Chapter 2, p 965. 12. Park, J.; Dyakov, I. V.; Lin, M. C. J Phys ChemA 1997, C6H5 attacks on secondary and tertiary C-H bonds fromavailable total rate constants. 101, 8839. 13. Tokmakov, I. V.; Park, J.; Gheyas, S. I.; Lin, M. C. J Phys ChemA 1999, 103, 3636. 14. Choi, Y. M.; Xia, Wensheng; Park, J.; Lin, M. C. J Phys The authors are grateful for the support of this work from ChemA 2000, 104, 7030. the Basic Energy Sciences, Department of Energy, under 15. Heckmann, E.; Hippler, H.; Troe, J. 26th Symp (Int) on contract no. DE-FG02-97-ER14784. Combustion; The Combustion Institute: Pittsburgh, PA, 1996; p 543. 16. Lutz, A. E.; Lee, R. K.; Miller, J. A. SENKIN: A FOR- TRAN Programfor Predicting HomogeneousGas- BIBLIOGRAPHY Phase Chemical Kinetics with Sensitivity Analysis; Sandia National Laboratories Report No. SANDIA 89- 1. Yu, T.; Lin, M. C. Combust Flame 1995, 100, 169. 8009, 1989. 2. Bridger, R. F.; Russell, G. A. J AmChemSoc 1963, 17. Baulch, D. L.; Cobos, C. J.; Cox, R. A.; Esser, C.; 85, 3754. Frank, P.; Just, Th.; Kerr, J. A.; Pilling, M. J.; Troe, J.; 3. Park, J.; Gheyas, S. I.; Lin, M. C. Int J ChemKinet Walker, R. W.; Warnatz, J. J Phys ChemRef Data 21, 1999, 31, 645. 1992, 411. 4. Yu, T.; Lin, M. C. J Phys Chem1995, 99, 8599. 18. Tsang, W. J AmChemSoc 1985, 107, 2872. 5. Yu, T.; Lin, M. C. J AmChemSoc 1993, 115, 4371. 19. Nielsen, O. J.; Ellermann, T.; Wallington, T. J. Chem 6. Yu, T.; Lin, M. C. J AmChemSoc 1994, 116, 9571. Phys Lett 1993, 203, 302.

short standard long