J. Phys. Chem. 1991, 95, 9890-9896
9890
Klnetlcs of the Reactions of Alkyl Radicals wlth HBr and DBr J. M. Nicovich, C. A. van Dijk, K. D.Kreutter, and P.H. Wine* Physical Sciences Laboratory, Georgia Tech Research Institute, Georgia Institute of Technology, Atlanta, Georgia 30332 (Received: June 10, 1991; In Final Form: July 23, 1991)
Time-resolved resonance fluorescence detection of Br atom appearance following laser flash photolysis of RI (R = CH,, CD3, C2H5,t-C4H9)or C12/RH (R = CH3, C2HS)has been employed to study the kinetics of the reactions CH3 HBr (I), CD3 + HBr (2), CH3 + DBr (3), C2H5+ HBr (4), C2H5+ DBr (9,t-C4Hg+ HBr (6), and t-C4H9 DBr (7) as a function of temperature (257-430 K) and pressure (10-300 Torr of N2).The rates of all reactions are found to increase with decreasing temperature; Le., activation energies are negative, and 298 K rate coefficients for reactions 1 and 3-7 are found to be significantly faster than previously thought. Arrhenius expressions for reactions 1, 3, 4, and 6 in units of cm3 molecule-' s-' are kl = (1.36 f 0.10) exp[(233 f 2 3 ) / q , k3 = (1.07 f 0.17) exp[(l30 k 5 9 / 7 7 , k4 = (1.33 f 0.33) exp[(539 f 78)/a1,and k6 = (1.07 f 0.34) exp[(963 f I52)/q; errors are 2a and represent precision only. Normal kinetic isotope effects are observed ( ~ H B ,> ~ D B , ) ,although the ratio kHBr/kDBf decreases in magnitude with decreasing activation is largest for R = CH3and smallest for R = t-C4H9. Combining our results with the best available energy; i.e., kHBr/kDBr kinetic data for the reverse reactions (Br + RH) yields the following 298 K alkyl radical heats of formation in units of kcal mol-': CH3, 35.3 f 0.6; C2H5,29.1 f 0.6; t-C4Hg,12.1 f 0.8; errors are 2a and represent estimates of absolute accuracy.
+
Introduction The thermochemistry and kinetics of alkyl radicals are subjects of considerable importance in many fields of chemistry. Accurate evaluation of alkyl radical heats of formation is required for determination of primary, secondary, and tertiary bond dissociation energies in hydrocarbons, for establishing rates of heat release in combustion, and for relating unknown "reverse" rate coefficients to known Yforwardwvalues. Kinetic data for numerous alkyl radical reactions are needed for modeling hydrocarbon combustion. Despite the importance of alkyl radical kinetics and thermochemistry, and an extensive literature which dates back several decades, important discrepancies in the data base have persisted. For example, results from iodination and bromination studies have consistently yielded heats of formation for alkyl radicals that are 2-4 kcal mol-' lower than those obtained from studies of bond scission and recombination rates of simple alkanes and Recent direct kinetic primarily by Gutman and coworkers,&' strongly suggest that alkyl + HX reactions have negative activation energies; while this finding seems counterintuitive for apparently simple hydrogen-transfer reactions, it can resolve the above-mentioned discrepancy in alkyl radical heats of formation since all earlier iodination and bromination studies were analyzed under the assumption that alkyl + HX reactions have small, positive activation energies. However, it should be noted that one recent direct study l o reports much slower rate coefficients (compared to other direct s t ~ d i e s ~ *and ~ J *positive ~) activation energies for the reactions of t-C4H9with DBr and DI. Motivated initially by the desire to obtain improved thermochemical data for sulfur-containing radicals of atmospheric interest, we developed a method for studying radical + HBr(DBr) reactions by observing the appearance kinetics of product bromine atoms." In this paper we report the results of a series of experiments where time-resolved monitoring of bromine atom appearance was employed to investigate the kinetics of the following reactions: CH3 + HBr Br + CHI (1) CD3 + HBr Br + CD3H (2) CH3 + DBr Br + CH3D (3) C2H5 + HBr Br + C2H6 (4) C2HS+ DBr Br + C2H5D (5) t-C4Hg + HBr Br + (CH3)$H (6) t-C4H9 + DBr Br + (CH3),CD (7)
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'Author to whom correspondence should be addressed.
0022-3654/91/2095-9890$02.50/0
+
The isotope effect studies have been motivated by a recent theoretical study of the t-C4Hg HI, DI reactions,12which suggests that negative activation energies for alkyl + HX reactions should be accompanied by inverse kinetic isotope effects, Le., k H x / k o x < 1.
+
Experimental Technique The experimental approach involved coupling alkyl radical production by laser flash photolysis of suitable precursors with time-resolved detection of bromine atom appearance by resonance fluorescence spectroscopy. A schematic diagram of the apparatus, as configured for bromine atom detection, can be found elsewhere.', A description of the experimental methodology is given below. A Pyrex, jacketed reaction cell with an internal volume of 150 cm3 was used in all experiments. The cell was maintained at a constant temperature by circulating ethylene glycol ( T > 298 K) or methanol ( T < 298 K) from a thermostatically controlled bath through the outer jacket. A copper-constantan thermocouple with a stainless steel jacket was injected into the reaction zone through a vacuum seal, thus allowing measurement of the gas temperature under the precise pressure and flow rate conditions of the experiment. Alkyl radicals were produced by 266-nm pulsed laser photolysis of RI/HBr/N, mixtures (R = CH,, CD,, C2H5, t-C4H9)or by 355-nm pulsed laser photolysis of CI2/RH/HBr/N2 mixtures (R = CH3,C2H5). Third or fourth harmonic radiation from a Quanta Ray Model DCR-2Nd:YAG laser provided the photolytic ra~~
(1) Tsang, W. In?. J . Chem. Kinet. 1978, 10, 821. (2) Tsang, W. J . Am. Chem. SOC.1985, 107, 2872. (3) McMillen, D. F.; Golden, D. M. Annu. Reu. Phys. Chem. 1982, 33, 493. (4) Russell, J. J.; Seetula, J . A.; Timonen, R. S.; Gutman, D.; Nava, D. F. J . Am. Chem. Soc. 1988, 110, 3084. (5) Russell, J. J.; Seetula, J. A.; Gutman, D. J . Am. Chem. Soc. 1988,110, 3092. (6) Seetula, J . A.; Russell, J. J.; Gutman, D. J . Am. Chem. Soc. 1990, 112, 1347. (7) Seetula, J. A.; Gutman, D. J . Phys. Chem. 1990, 94, 7529. (8) Richards, P. D.; Ryther, R. R.; Weitz, E. J . Phys. Chem. 1990, 94, 3663. (9) Seakins, P. W.; Pilling, M. J. J . Phys. Chem. 1991, 95, 9874. ( I O ) Miiller-Markgraf, W.; Rossi, M. J.; Golden, D. M. J . Am. Chem. Soc. 1989, 111, 956. ( 1 1) Nicovich, J. M.; Kreutter, K. D.; van Dijk, C. A.; Wine, P. H. J . Phys. Chem., submitted for publication. (12) McEwen, A. B.; Golden, D. M. J . Mol. Sfrucr. 1990, 224, 357. (13) Nicovich, J . M.; Shackelford, C. J.; Wine, P. H. J . Phofochem. Phorobiol. A: Chem. 1990, 5 1 , 141.
0 1991 American Chemical Society
-Keaction Kinetics .,. .. ot,.AIKYI .,. , t .-,. ,-.. , ntrrtutrrj *
,
diation. The laser could deliver up to 3 X 10I6photons per pulse at 266 nm and up to 1 X IO1’ photons per pulse at 355 nm; the maximum repetition rate was IO Hz, and the pulse width was approximately 6 ns. A bromine resonance lamp, situated perpendicular to the photolysis laser, excited resonance fluorescence in the photolytically produced atoms. The resonance lamp consisted of an electrodeless microwave discharge through about 1 Torr of a flowing mixture containing a trace of Br2 in helium. The flows of a 0.2% Br, in helium mixture and pure helium into the lamp were controlled by separate needle valves, thus allowing the total pressure and Br2 concentration to be adjusted for optimum signal-to-noise ratio. Radiation was coupled out of the lamp through a magnesium fluoride window and into the reaction cell through a magnesium fluoride lens. Before entering the reaction cell, the lamp output passed through a flowing gas filter containing 50 Torpcm of methane in nitrogen. The methane filter prevented radiation at wavelengths shorter than 140 nm (including impurity emissions from excited oxygen, hydrogen, and nitrogen atoms) from entering the reaction cell but transmitted the strong bromine lines in the 140-160-nm region. Fluorescence was collected by a magnesium fluoride lens on an axis orthogonal to both the photolysis laser beam and resonance lamp beam and was imaged onto the photocathode of a solar blind photomultiplier. Signals were processed by using photon counting techniques in conjunction with multichannel scaling. A large number of laser shots were typically averaged to obtain a bromine atom temporal profile with signal-to-noise ratio sufficient for quantitative kinetic analysis. It is worth noting that the resonance fluorescence detection scheme is sensitive to both ground state bromine atoms. (,P3/2) and spin-orbit excited state To avoid accumulation of photolysis or reaction products, all experiments were carried out under “slow flow” conditions. The linear flow rate through the reactor was in the range 2-10 cm s-I, and the laser repetition rate was varied over the range 5-10 Hz ( 5 Hz typical). Hence, no volume element of the reaction mixture was subjected to more than a few laser shots. The alkyl iodides, ethane, CI,, HBr, and DBr flowed into the reaction cell from bulbs (1 2-L volume) containing dilute mixtures in nitrogen while methane, hydrogen, and additional nitrogen were flowed directly from their storage cylinders. All gases except C12 (see below) were premixed before entering the reactor. The concentrations of each component in the reaction mixture were determined from measurements of the appropriate mass flow rates and the total pressure. The concentrations of HBr and DBr were also determined by in situ UV photometry at 202.6 nm (Zn+ line). A zinc hollow cathode lamp was employed as the light source for the photometric measurement, and a quarter meter monochromator was used to isolate the 202.6-nm line. The absorption cross sections needed to convert measured absorbances into concentrations were determined during the course of this investigation and were found to be 1.02 X cm2 for HBr and 9.7 X cm2 for DBr. The measured HBr cross section agrees well with values reported by Goodeve and Taylor14 and by Huebert and Martints but is -20% higher than the value reported by Romand16 and -20% lower than the value of Nee et al.” Experimental results were found to be independent of whether the 2 m long absorption cell was positioned upstream or downstream relative to the reaction cell. The gases used in this study had the following stated minimum purities: N,, 99.999%; HZ, 99.999%; C12, 99.99%;18 CH4, 99.9995%; C2H6.99.99%; HBr, 99.8%;18 DBr, unstated chemical purity and 99 atom % D.I8 Nitrogen, hydrogen, methane, and ethane were used as supplied, while C12, HBr, and DBr were purified by repeated freeze (77 K)-pump-thaw cycles. It is worth noting that the HBr and DBr gas samples taken directly from their storage cylinders contained significant (25-50%) levels of a (14) Goodeve,
C. F.; Taylor, A. W. C. Proc. R. Soc. 1935,AI52, 221.
(IS) Huebert, B. J.; Martin, R. M. J . Phys. Chem. 1968, 72, 3046. (16) Romand, F. Ann. Phys. (Paris) 1948,4, 527. (17) Nee, J. B.i Suto, M.; Lee, L. C. J . Chem. Phys. 1986,85, 4919. (1 8) Stated purity of liquid phase in cylinder.
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 9891 noncondensible impurity which was determined by weighing to be Hz(D2). The liquids used in this study had the following stated minimum purities: CH31, 99.5%; CD31, unstated chemical purity and 99.5+ atom 7% D; C2HSI,99%; t-C4H91, 95%. All liquid samples were transferred under nitrogen into vials fitted with high-vacuum stopcocks and were subjected to repeated freeze (77 K)-pumpthaw cycles before being used to prepare gaseous RI/N2 mixtures. When not in use, the vials were stored in the dark at 278 K.
Results and Discussion In most experiments, alkyl radicals were generated by 266-nm laser flash photolysis of the appropriate alkyl iodide ([RI] in the range 1-12 x i O I 3 molecules ~ m - ~ ) : RI
+ hv(266 nm)
-
R
+ I,
R = CH3, CD3, C2H5, t-C4H9 (8)
Reactions 1 and 4 were also studied using the following alternate alkyl production scheme: C12
C1 + R H
-
-
+ hu(355 nm) 2 CI R + HCI, R = CH3, C2H5
-
(9)
(IO)
When the alternate production scheme was applied, CI, (concentration 1 x I O l 3 molecules ~ m - was ~ ) injected into the gas flow just upstream from the reaction zone to suppress the heterogeneous dark reaction between C12and HBr.I9 Also, R H was added to the reaction mixture in sufficient quantity that (a) production of alkyl radicals was essentially instantaneous on the time scale for the alkyl HBr reaction and (b) nearly all CI (>95%) reacted with R H rather than with HBr. Observed kinetics were found to be independent of the choice of alkyl radical production scheme. As will be discussed in more detail below, the invariance of observed kinetics to the alkyl radical source rules out some potential sources of systematic error. Reactions 1-5 are sufficiently exothermic that the bromine atom product could be formed in the spin-orbit excited state, Br(2Pl/2). To ensure that relaxation of Br(*P,/,) was not rate-limiting in defining observed Br appearance rates, all experiments were carried out with 0.2-2 Torr of H2 added to the reaction mixtures. The reaction
+
Br(ZPl/2)+ H2(v = 0)
-
-
Br(,P3/,)
+ H2(u ’1)
(11)
is known to be fast, with k l l 6 X cm3 molecule-l s-I.,O All experiments were carried out under pseudo-first-order conditions with HBr in large excess (typically a factor of IO4) over the alkyl radical. Concentrations of photolytically generated radicals were typically in the range 5-10 X IOI0/cm3, although this experimental parameter was varied over a wide range (factor of 20). Observed kinetics were found to be independent of both the alkyl iodide concentration and the concentration of photolytically generated radicals. In the absence of side reactions that remove or produce Br, the observed temporal profile following the flash would be described by the relationship
In eq I, S, is the fluorescence signal level at time t (proportional to [Br],), ka and kd are the pseudo-first-order rate coefficients for Br appearance (k,) and disappearance (kd), and the parameters CI and C, are defined as follows: CI = 4 R l d
(11)
C, = a[BrIo In the above equations [RIo and [Brio are the alkyl and Br concentrations after photolysis and reaction 10 have gone to com(19)Nicovich, J. M.;Wine, P. H. Inr. J . Chem. Kiner. 1990, 22, 379. (20)Nesbitt, D.J.; Leone, S.R. J . Chem. Phys. 1980,73,6182.
Nicovich et al.
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
9892
/
-
I
I
(
/
I
r
,
I
t
(a)
1
lot
c
J
K
0
0
'1
[HBr] ( ~ o ~ ~ m o ~ e ccii3) u~es Figure 2. Typical plots of k, vs [HBr]. Reaction: C2H5 HBr. C2H5
+
-4 0
10
5
I
I
I
0
5
10
time ( 1 6 ~ 8 ) Figure 1. Typical Br atom temporal profiles. Reaction: C2H5 + HBr.
C2H5 source: (a) C2H51+ hv(266 nm), (b) C12/C2H6+ hv(355 nm). Experimental conditions: T = 298 K; P (Torr) = (a) 100, (b) 50; photolyte concentrations in units of IOl3 molecules cm? (a) [C2H51]= 6.3, (b) [Cl,] = 1.3 and [C2H6]= 160; [C2H5I0( l o l o radicals cm-') = (a) 5, (b) 9; [HBr] (10" molecules cm") = (a) 5.45, (b) 5.64; number of laser shots averaged = (a) 5000, (b) 2000. Solid lines are obtained from nonlinear least-squares analyses which give the following best fit parameters: k , (s-I) = (a) 5470, (b) 6320; k, (s-I) = (a) 22, (b) 39: C, = (a) 5920, (b) 2950; C, = (a) 190, (b) 240. pletion but before significant removal of alkyl radical has occurred,
f is the fraction of alkyl radicals that are removed via a reaction which produces Br, and CY is the proportionality constant which relates S, to [Br],. For the reaction systems of interest, we expect that k, = ki[HBr(DBr)] + k I 2 ( i = 1-7) (IV)
f = ki[HBr(DBr)]/k,
( i = 1-7)
(VI
-
where k I 2is the rate coefficient for the following reaction(s): R first-order loss by processes that do not produce Br (12) A nonlinear least-squares analysis of each experimental temporal profile was employed to determine k,, kd, Cl, and C2. The bimolecular rate coefficients of interest, k,(P,T) were determined from the slopes of k, vs [HBr(DBr)] plots. Typical data are shown in Figures 1 and 2. It is worth pointing out that the accuracy with which k, could be determined via the nonlinear least-squares fitting technique was quite good because it was always the case that k , >> kd and CI>> C,. Observation of Br temporal profiles that are well described by eq I, a linear dependence of k , on [HBr(DBr)], and invariance of k , to variation in laser photon fluence and photolyte concentration suggest that the alkyl + HBr(DBr) reaction and reaction 13 (kl3 = kd) are the only Br first-order loss by diffusion from the detector field of view and reaction with background impurities (13)
-
processes that significantly affect the Br time history (once photolysis and CI reaction with R H and HBr are complete). One potential interference that is not ruled out by the above observations is reaction of alkyl radicals with impurities which are either present in the HBr sample or produced via dark reactions of HBr with other components in the reaction mixture; impurity reactions are considered below when potential systematic errors are discussed.
source: (0)C2HJ + hv(266 nm), (0)C12/C2H6+ hv(355 nm). Experimental conditions: T = 298 K; P (Torr) = ( 0 ) 100, (0)50. Solid and dashed lines are obtained from linear least-squares analyses of the solid and open circle data points, respectively, and give the following cm3molecule-' s-': (0)8.24 bimolecular rate coefficients in units of f 0.65, (0) 7.81 f 0.51. Arrows indicate the two points obtained from the data shown in Figure 1 . One interesting aspect of the data in Figure 2 is the relatively large value for kI2,Le., the relatively large intercept in the k, vs [HBr] plot. The observed values for k12were typically larger than expected if background removal of alkyl radicals was due only to reaction with their photolytic precursors and to diffusion out of the detector field of view. At low [HBr(DBr)], where k I 2> k,[HBr(DBr)] ( i = 1-7), fluorescence signal levels were considerably reduced; this indicates that the process responsible for background alkyl radical removal did not result in production of bromine atoms. The magnitude of kI2tended to increase with decreasing temperature and with increasing complexity of the alkyl radical, suggesting that a process responsible for significant background removal of alkyl radicals was reaction with 02: R 02 + N2 RO2 N2 (14)
+
+
+
The O2levels required to account for observed k12values are around 0.01 Torrsignificantly higher than expected O2impurity levels in the N2 buffer gas. Hence, a small leak in the slow flow system is the probable source of 02.The presence of a reactive impurity a t the levels encountered in our experiments is not expected to introduce systematic error into the kinetic measurements. However, when the condition k 1 2
