J . Phys. Chem. 1990, 94, 3313-3317
3313
Chemical Activation Analysis of the Reaction of C2H, with O2 Joseph W. Bozzelli*it and Anthony M. Dean* Corporate Research Labs, Exxon Research and Engineering Company, Annandale, New Jersey 08801 (Received: October 17, 1989; In Final Form: January 31, 1990)
The addition reactions of ethyl radical with molecular oxygen to form the energized adduct C2HS02*and the reactions of the adduct to varied products have been analyzed by using the bimolecular version of the quantum Rice-Ramsperger-Kassel (QRRK) theory for temperatures from 200 to 1800 K and pressures between 0.001 and 10 atm in helium and nitrogen bath gases. The calculations satisfactorily explain the observed low-pressure(0.5-13 Torr) rate constants of Slagle et al. for loss of ethyl and production of ethylene over their temperature range (300-900 K) in addition to the room-temperature data for C2H4 production of Kaiser et al. over a pressure range of 1-6000 Torr. We present a complete description of the complex pressure and temperature dependence of the reaction system in the analysis; the adduct undergoes a H atom shift through a cyclic (five-member ring) intermediate to an alkyl-hydroperoxy radical which then undergoes j3 scission to products. There is no need to invoke a direct hydrogen-transfer pathway to explain the observed data. Apparent rate constants are presented for stabilization and reaction to C2H4 + H 0 2 over the above temperature and pressure ranges; in addition, rate constants for the C 2 H S 0+ 0 and CH3CH0 OH reaction channels are given.
+
Introduction The initial products from pyrolysis, oxidation, combustion, or photochemical reaction of saturated hydrocarbons are alkyl radicals, which are often produced by O H abstraction. While these abstraction reactions are relatively well understood, the subsequent elementary reactions of the alkyl radicals with molecular oxygen are more complex and present a source of some controversy. These reactions, furthermore, represent the principal pathways of the alkyl radical reactions in most hydrocarbon oxidation and combustion processesls2 in addition to photochemical smog formation and stratospheric chemistry of hydrocarbons. There have been several recent studies which show that the reactions of ethyl radicals, at pressures from 1 to 6000 Torr and temperatures from 300 to 900 K, exhibit a significant negative pressure dependence for production of C2H4 + H02.3-7 Walker has also reported a similar pressure dependence for reactions of isopropyl radicals with 02.8The rate of ethyl radical loss decreases significantly with temperature3 and increases with pressure as expected for the commonly accepted reversible formation of an adduct at r c " temperatures. The adduct, CzHsOO (CCOO) radical, is readily stabilized at low temperatures and dissociates back to reactants more rapidly at higher temperature^.^^^ The observed pressure and temperature dependence for the olefin formation is not, however, consistent with a direct hydrogentransfer mechanism, which has often been invoked in combustion modelir~g.~,~~ The C2H5 O2 reaction has been analyzed by Wagner et using variational RRKM theory for ethylene production and ethyl radical loss at pressures and temperatures relevant to the experimental data of Slagle et al.)q7 This analysis" assumes formation of a chemically activated adduct, which can react directly through a cyclic (five-member ring) intermediate to a primary hydroperoxy-alkyl radical and then to C2H4+ HOz or be stabilized to CCOO. Subsequent reaction of the stabilized peroxy back to reactants and forward, over the isomerization barrier, to ethylene H 0 2 is accounted for with an analytical solution to a four-reaction mechanism, which assumes the kinetics depend only on the reactions leading to and including formation of the cyclic intermediate (excludes stabilization of the alkyl-hydroperoxy intermediate). One emphasis in the approach of Wagner et a1.I' is the use of variational RRKM theory to calculate elementary reaction rate constants. These calculations are relatively complex and still require adjustments in certain parameters. It is our intent in this paper to show that one can interpret the observed data on reactions of alkyl radicals with oxygen using a more straightforward cal-
culational technique with literature rate constants for the bimolecular reactions, transition-state theory for the isomerization, thermodynamics to calculate reverse reactions, and bimolecular QRRK theoryi2to calculate reaction probabilities of the initially formed chemically activated complex. We feel that these techniques readily lead to a fundamentally correct interpretation with the added advantage of a straightforward treatment of the complex reaction process. Our treatment of the energized complex reactions allows decomposition back to reactants, intramolecular transfer of primary and secondary hydrogen atoms to form hydroperoxy radicals which further decompose to C2H4 + H 0 2 and C H 3 C H 0 OH, respectively. Stabilization to ground-state peroxy or hydroperoxy radicals as well as alkoxy formation is included. Further reactions of the stabilized peroxy and hydroperoxy radicals to reactants or to hydroperoxy via H shift and then /3 scission to final products, in addition to several other important reactions, are accounted for, using a small elementary reaction mechanism. This is useful when comparison to data at relatively long experimental reaction times is required. Reaction to epoxides is also briefly discussed. The results for loss of ethyl and production of ethylene show good agreement with recent experimental data of Slagle and G ~ t m a n , ~Walker ?' et al.,4 and Kaiser.6 Sensitivity analysis on loss of parent ethyl at lower temperatures indicates that the ratio of forward to reverse A factors for the initial radical addition and the well depth are important. The isomerization A factor (tight transition state) is much lower than that for decomposition of the complex to reactants, but the isomerization barrier height is also lower and temperature controls the relative rates of energized complex reaction through each of these channels. The lower barrier to isomerization, 27.2 kcal/mol, versus decomposition to reactants, 32 kcal/mol, always allows a fraction of the complex
Permanent address: Chemistry Division, New Jersey Institute of Technology, Newark, NJ 07 102.
Chem., in press. (12) Dean, A. M. J . Phys. Chem. 1985, 89, 4600.
+
+
0022-3654/90/2094-33 13$02.50/0
+
(1) Benson, S. W. Thermochemical Kinetics; Wiley: New York, 1976; p 237. (2) Slagle, 1. R.; Ratajczak, E.; Gutman, D. J . fhys. Chem. 1986,90,402. (3) Slagle, I . R.; Feng, Q.;Gutman, D. J . fhys. Chem. 1984. 88, 3648-3653. (4) McAdam, G. K.; Walker, R. W. J . Chem. Soc., Faraday Trans. 2
1987,83, 1509. ( 5 ) Plumb, 1. C.; Ryan, K. R. Int. J . Chem. Kinet. 1981, 23, 1011-1028. (6) Kaiser, E. W.; Rimai, L.; Wallington, T. J. J . Phys. Chem. 1989, 93, 4094-4098; J . Phys. Chem., this issue. (7) Gutman, D. J . Chim. fhys. 1987, 84, 409-414. (8) Gulati, S. K.; Walker, R. W. J . Chem. Soc., Faraday Trans. 2 1988, 84, 401. (9) Pitz, W. J.; Westbrook, C. K. Combust. Name 1986, 63, 113. (IO) Cox, R. A.; Cole, J . A. Combust. Flame 1985, 60, 109. ( I I ) Wagner, A. F.; Slagle, 1. R.; Sarzynski, D.; Gutman, D. J . fhys.
0 1990 American Chemical Society
Bozzelli and Dean
The Journal of Physical Chemistry, Vol. 94, No. 8,1990
3314
TABLE I: Input Parameters for QRRK
Analysis of CzHS
+ Oz
Products'
k 1
-I
2 3 -3 4
E,'
A'
3.OE12 1.9E15 1.4El5 2.55E12 1.45E11 7.5812
5
5.5812
6
2.7814
0.0
32.0 59.6 27.2 15.2 39.5 15.6 1 .o
1081 cm-' LJ parameters: u = 4936 A, c / k = 450 K
(u) =
-
E (kcal/mole)
\
source a b c
d
20
e
f
g
CCOOH
$H,+HO,
iks
;
0
i, m
+--/
\
CCOOH
CCOO'
I
n
*This study, E, from microscopic reversibility. *From Monk et cFrom A-2 = 3.5 X lo", which was taken as 0 + CHI X 0.55 (Benson2') and microscopic reversibility. "Transition-state theory (this study): loss of two rotors, symmetry, C-H stretch; gain of bends CH-0, H-0-0, three equivalent H's. E, = 6.3 + 12 + 9 (ring strain + H,,,+ E, abstraction). Microscopic reversibility. /Transition-state theory (this study): loss of one rotor. E, = 27 + 5.5 + 7 (ring strain + H,,, + E, abstraction). k4 microscopic reversibility. gFrom A-s = 5.6 X IO" (average value reported for H 0 2 + olefins, Kerr and Moss2s) and microscopic reversibility. E,, this study. From A+, = 8 X 10l2which was taken from OH + CHICH=CH2, Kerr and Moss?s and microscopic reversibility. 'CalculatedI6 (0) for CCOO is 1094 cm-I; CCOOH, 990 cm-I. /He: u = 2.58 A, e l k 10.2 K, A E = 431 cal. N,: u = 3.62 A, c / k 97.5 K, AE = 830 cal. 'Units are cm3/(mol s) for bimolecular reactions and s-I for unimolecular reactions. 'In kcal/mol. Reference 1 I . "Reference 18.
hOOH
I
'
h
!
y6
I' II
i-20
II
I
,
I
------.
I
C Y H O + OH 1-40
Figure 1. Potential energy diagram for addition of C2H5 to O1.The solid line indicates the dominant route in which the intramolecular H transfer occurs via a five-member cyclic intermediate. The dashed line indicates a less favorable path via a four-member cyclic intermediate. The highenergy dissociation channel of C2H5O2 to 0 + C2HsO is not shown. 0
21 oBc3
-
3
Y
+
to isomerize and then dissociate to C2H4 H02. At higher temperatures, increased isomerization relative to stabilization of the activated complex leads to higher C2H4 H 0 2 formation rates. Apparent rate constants for reaction of O2with ethyl radicals are presented for temperatures from 200 to 1800 K and pressures of 0.001-1 atm with helium and nitrogen bath gases along with comparisons of calculated product concentrations to experimental data.
+
,
I
Calculations Energized complex/QRRK theory as described by Dean'* was used to model radical addition reactions to 02.The theory utilizes the quantum RRK reaction theory of Kassel,I3 which treats the storage of excess energy as quantized vibrational energy. Further details on specifics of the calculation are presented in ref 14. Preexponential factors ( A factors) and activation energies ( E , ) for the bimolecular addition reaction at the high-pressure limit are obtained from the literature and the methods of Benson.Is A and E, values for the unimolecular isomerization and dissociation come from thermodynamic heats of formation and entropies for the species involved and by analogy to similar reactions. Kinetic parameters for dissociation to reactants and products are obtained from application of microscopic reversibility. The geometric mean frequency was calculated from the data of Wagner" and from heat capacity data,I6 and Lennard-Jones parameters were obtained from tabulations1' and a calculational method based on molar volumes and compressibility.l8 Our objective is to show that a straightforward chemical activation methodf2can be utilized to analyze these complex addition reactions. We do not wish to indicate that the parameters we present for the varied reactions are the only ones which will fit the data, but that we feel they are quite reasonable. Perhaps more ~~~
(13) Kassel, L. S.J . Phys. Chem. 1928, 32, 225, 1065. (14) Bozzelli, J. W.; Dean, A. M. J . Phys. Chem. 1989, 93, 1058. ( I 5 ) Benson, S. W . Reference I , Chapters 2-4. (16) Ritter. E. R. Ph.D. Thesis, New Jersey Institute of Technology, May
1989.
( I 7) Reid, R. C.; Prausnitz, J. M.; S h e r w d , T. K. Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977. (18) Ben Amotz, D.; Herschbach, D. R. Group Additivity and Compressibility to Calculate Molecular Volume and LJ Parameters. Personal communication
\ I
50
I
100
I
I
150
200
I
I
250
300
1/T
350
w4
Figure 2. Arrhenius plot showing the various channels for C2H5+ O2 at 0.76 Torr in a bath gas of N2:0 , high-pressure addition rate constant; 0,rate constant for stabilization; 0, rate constant for production of C2H, + HO,; +, rate constant for the CH,CHO + OH channel; X, rate constant for stabilization to CCOOH (after isomerization).
important, the parameters are based upon literature data and transition-state theory; adjustments are kept to a minimum.
Results The energy level diagram and input parameters for the chemical activation calculations of the reaction of C2HS O2are shown in Figure 1 and Table I, respectively. The parameters in Table 1 are referenced to the ground (stabilized) level of the complex because this is the formalism used in QRRK theory. The calculations incorporate the specific fraction of the energized complex (adduct) in each level of excitation above the threshold (critical energy) for determination of the specific rate constants at a given temperature and pressure. Heats of formation are those obtained by using a bond dissociation energy for ROO-H of 88 kcal/mol, with a primary C-H bond energy of 100.6 kcal/mol.'g-2' The ethyl radical combines with O2to form the chemically activated CCOO* adduct.
+
(19) Tsang, W. J. Am. Chem. Soc. 1985, 107.2872. (20) Slagle, 1.; Gutman, D. J . Am. Chem. Soc. 1988. 110, 3084. 3092. (21) Brouard, M.; Lightfoot, P. D.; Pilling, M. J. J . Phys. Chem. 1986,
90, 445.
(22) Baldwin, R. R.; Pickering, 1. A. S.;Walker, R. W. J . Chem. Soc., Faraday Trans. I 1980. 76, 2374. ( 2 3 ) Baldwin, R. W.; Dean, C. E.; Walker, R. W. J . Chem. Soc.,Faraday Trans. 2 1986, 82, 1445.
Chemical Activation Analysis of C2H5
9.49 -57.80 2.50 12.54 28.30 -20.24 -4.22 -4.70 7.30 3.92 -40.80 -39.69
OH H20 H02 CZH, C2H5 C2H6 C2H50
C2H5O.2 CH2CH200H C HZCH200H C2HsOOH CHSCHO
" Units:
+ O2
The Journal of Physical Chemistry, Vol. 94, No. 8, 1990 3315
7.16 8.02 8.37 10.28 12.13 12.58 14.16 18.28 19.87 19.86 20.28 13.22
43.88 45.10 54.73 52.39 59.27 54.85 65.10 74.03 77.50 76.87 76.65 63.20
7.05 8.41 9.48 14.92 17.19 18.68 20.76 25.50 26.62 26.67 28.50 18.16
7.15 9.24 10.78 20.03 22.93 25.80 27.68 32.89 32.89 32.81 36.65 24.17
7.33 9.85 I 1.43 22.45 25.73 29.33 31.04 36.80 35.54 35.40 40.40 27.01
7.87 11.23 12.47 26.21 30.23 34.92 37.06 41.72 40.37 40.36 45.81 30.60
8.27 12.20 13.23 28.35 33.30 38.37 39.72 45.43 45.03 45.03 49.85 34.20
HI in kcal/mol; S in cal/(mol K); Cpin cal/(mol K).
-
TABLE 111: Apparent Rate Constants for C,H, + 0, Products" products A n E,b press., atm
Rate Constants cc/mole-sec
1.000€*13
1
k,",
1.000E*12 CZ
1.000E*ll
Y
t
1.000E*08L 0.1
w*
' '
'
' ' "'""
I
1
'
1 1 1 ' ' ' '
10
I
100
' ' ' 1 ' ' '
1000
Pressure (Torr) Figure 3. Predicted effect of temperature and pressure on branching ratios in the C2H5 O2reaction. kinris the high-pressure addition rate constant. Rate constants for production of stabilized C2H5O2: A, 300 K; +, 1200 K. Rate constants for production of C2H4 + H02: *, 300 K; 0,I200 K. X represents rate constants for production of CH,CHO + OH at I200 K.
+
The major reaction channels of CCOO* include dissociation back to reactants ( k - , ) , stabilization to C C O O (ks),and intramolecular isomerization (five-member cyclic intermediate) to CCOOH' ( k 3 ) . The CCOOH* can then p scission to C2H4 H 0 2 ( k 5 ) ,be stabilized to CCOOH (ks),or isomerize back to CCOO* ( k 3 )Minor . reaction channels of the CCOO* adduct are included for completeness: dissociation to CCO 0 (k2,not shown, only important above 1200 K); intramolecular isomerization, four-member cyclic intermediate, to CCOOH ( k 4 ) ,which is unstable with respect to dissociation to CH'CHO O H (k6). The thermodynamic parameters for most species important to the potential energy level diagram and those used in the mechanism to follow the reaction progress with time are listed in Table 11. Standard thermodynamic parameters were used for all other species. Arrhenius plots for the various apparent rate constants at 0.76 Torr are shown in Figure 2 (N2 bath gas). The data illustrate that at the low pressure more of the complex reacts to C2H4 + H 0 2 radical than is stabilized at temperatures as low as 425 K. It is worthwhile to note that the high-pressure-limit rate constant, Le., the rate constant for formation of the energized adduct, is much faster than any of the 0.76-Torr apparent rate constants calculated. This is a manifestation of the activated complex's primary reaction channel-dissociation back to reactants. This very high reverse reaction rate is due to the high A factor and low pressure. The stabilization channel does not reach the high-pressure limit even at 250 K. We note that the apparent rate constant to the C2H4channel decreases slightly with increasing temperature. This small decrease is due to the higher probability for dissociation back to reactants at higher temperature (much higher A factor for dissociation). A plot of apparent rate constants versus pressure for two temperatures, 300 and I200 K, is shown in Figure 3. We again point out that dissociation of the complex to C2H5 02,the reverse
+
+
+
+
C2H5OO C2H50+ 0 C2H4 + HO2 CHSCHO + OH CZH5OO C2H5O + 0 C2H4 + H02 CH3CHO + OH C2H500 C2H50+ 0 C2Hd + H02 CHSCHO + OH CCOOH
N2 Bath Gas 6.7E41 -10.5 l.OE13 -0.20 6.83El8 -2.63 4.3El3 -1.03 2.0E42 -10.3 l.OE13 -0.20 2.56819 -2.77 4.55E13 -1.03 5.17835 -7.63 l.lE13 -0.21 3.OE20 -2.86 1.6E14 -1.17 1.3E40 -9.41
C2H500 C2H50+ 0 C2H4 + H02 CHSCHO + OH C2H500 C2H5O + 0 C2H4 + H02 CHSCHO + OH C2H5OO C2H50+ 0 C2H4 + H02 CHSCHO + OH CCOOH
Helium 7.8841 l.OE13 6.70818 4.3E13 5.15E42 l.OE13 3.OE19 4.5El3 3.2E37 l.lE13 6.07821 2.1E14 4.3E41
5729c 27902 1307 9649
0.001
6081c
0.01
27902 1978 9665 6033d 27937
1
6761d
10391 1 1 026d
Bath Gas -10.575 569W 27902 -0.20 1289 -2.63 9648 -1.025 -10.50 6092c 27902 -0.20 1937 -2.80 9663 -1.03 6344d -8.094 27933 -0.21 691 I d -3.27 -1.21 10373 -9.93 1 1200d
0.001
0.01
1
"Best-fit equation A7" exp(-E,/RT) cm3/(mol s). E, in cal/mol. Modified Arrhenius form of the rate constants, k , incorporate changes in concentration [MI with temperature. [MI should not be included in rate expressions. bValid from 200 to 1800 K except where noted. cValid from 250 to 1200 K. dValid from 300 to 1200 K. reaction, is the primary reaction channel of the energized adduct at low pressure. At 300 K stabilization to CCOO approaches the high-pressure limit at 1-atm pressure, but at 1200 K stabilization is still well into the falloff regime at 1 atm. Reaction to C2H4 at 300 K shows a maximum at low P and steadily decreases with increasing pressure. At 1200 K, however, ethylene yield is nearly constant, resulting from dissociation to ethyl being the dominant channel and stabilization not being important through the pressure range up to 1 atm. The acetaldehyde + O H product channel is only a very small fraction even at 1200 K, because of more favorable (lower energy) competing channels. Best-fit apparent rate constants (within f15%) in the modified Arrhenius form equation A T exp(-E,/RT) are listed in Table I l l for N2 and He bath gases, for reaction of ethyl + O2to the indicated products. In order to make comparisons of ethyl radical and ethylene concentrations with the data of Slagle et al.' and reproduce concentration versus time behavior, a small elementary reaction mechanism was assembled and used to generate reactant and product concentration profiles over time. The mechanism is listed
Bozzelli and Dean
3316 The Journal of Physical Chemistry, Vol. 94, No. 8, 1990 TABLE IV: C,H,
+ O2 Mechanism (N2Bath GasY
reactionsb C2H5+ O2 = C2H500 C2H5+ O2 = C2H50+ 0 C2H5 + 02 = C2H4 + HO2 C2HS + 02 = CH3CHO + OH C2H5+ 0, = CCOOH CCOOH = C2H4 + HO2 C2HsO0= CCOOH C2H5 + HO2 = C2HSO + OH C2H5 = C2H4 + H
A
k (1.OE-13 cc/molec-sec)
n
2.0842 -10.3 I.OE13 -0.20 2.56El9 -2.77 4.55813 -1.03 -9.37 I .35E37 1.87E26 -5.93 1 , I E48 -1 I .56 0.0 3.OE13 3.8E43 -9.54
Ea
608 1 27932 I978 9665 5066 15233 37565
3 904 K /--
51006
“ k = A 7 exp(-EJRT). Units: cm3/(mols). E , in cal/mol. Reverse rate constants calculated from thermodynamic properties. Reaction rate constants at 0.01 atm (7.6 Torr). bAccounting for further reactions o f stabilized products.
,
0.1 0
2
4
6
8
10
12
14
Pressure (Torr) Figure 5 . Comparison of the predicted rate constants for loss of C2H5 as a function of temperature and pressure to those observed by Slagle et al.3.7 Predictions are shown as connected by solid lines. Data are shown as discrete points. 0.296 K; X, 383 K; 0 , 4 6 7 K; 0, 580 K;0. 904 K .
r
05
Ethylene Yield (%)
573K
\
04C
100
1 .
r -
I\. ,
.
03
\
-
0 -~
1 . . . . 1
. .‘ . -... .-
--1 473K . .
1 .
02-
0
1:
0.0
1 .
l . . .
1 _ _ -
2
4
6
8
10
12
14
16
Pressure (torr) Figure 4. Comparison of predicted C2H4yields as a function of temperature and pressure that observed by Slagle et al.).’ Predictions are shown as solid lines. Data are shown at discrete points. 0,373 K; A, 413 K; 0, 573 K.
‘
0.01
in Table IV and includes the apparent rate constants calculated above, as well as subsequent isomerization and dissociation of the thermally stabilized adducts. The code reproduced reagent loss curves with time (10-50 ms, depending on temperature) similar to those shown as inserts in the figures of Slagle et aL2s33’ Figure 4 shows a comparison of the ethylene yield versus pressure at three different temperatures with the data of Slagle et al. The agreement of the chemical activation treatment with the experimental data is quite good. A comparison of rate constants for loss of ethyl radical versus pressure with data obtained by Slagle et aL3 is illustrated in Figure 5 for five temperatures between 296 and 904 K in helium bath gas. Again the agreement is quite good, and both the data and chemical activation treatment show significant increases in rate constant with increasing pressure, consistent with stabilization of the adduct. The calculations from our theoretical treatment include the sum o f the rate constants for reaction to CCOO, CCOOH (both stabilized), and C2H4 + H 0 2 . We chose a value of 33.0 kcal/mol as the well depth ( L W ~ , ~ ~ ~ ( C CofO -4.7 O ) kcal/mol). This well depth is between the value of 34 kcal/mol reported by Wagner“ as calculated from earlier data of Slagle et al.2 using a revised determination of entropy and values in the literature around 30 kcal/mol.’ We made small adjustments in several parameters from the initial values we estimated using transition-state theory and the thermodynamic properties to obtain agreement of the calculated values with experimental data of Slagle et aL3s7 This included adjustment of A_, up from our initial estimate of 1.6 X I O l 5 (s-I) to I .9 X 10’’. This adjustment of A - , , without a corresponding change in A , , effectively reduces the entropy of CCOO by 0.3 eu. Ea, was increased from 26.0 to 27.2 kcal/mol, and A , was adjusted from 2.2 X 10l2to 2.55 X 10l2 (s-I). These changes are well within the uncertainty of the estimation techniques employed. The agreement of the calculations to the 296 K data of Slagle et al.3,7could be improved by a small decrease (10-204) in A _ ,
1
100
10
1000
Pressure (torr) Figure 6 . Comparison of the effect of pressure on the predicted C2H, yield to that observed by Kaiser et al.? dashed lines, observed, with the
upper line for He and the lower line for N2; A, He (predicted); 0,N, (predicted). while also decreasing A, or .E3 to offset the effect of the change in A _ , on ethylene production. While improving the agreement at low temperatures, this detracts from agreement a t higher temperatures, where the QRRK calculations would be expected to be more accurate. E , was adjusted slightly downward from the initial estimate of 16.6 kcal/mol (AHrxn 9),24in order to improve our match to the higher pressure data of Kaiser et a1.6 (see below). A comparison of ethylene product for reaction in helium and in air or mixed nitrogen/oxygen systems with room-temperature data of Kaiser et aL6 is illustrated in Figure 6. The calculations for both helium and nitrogen bath gases are in reasonable agreement with the experiment considering the broad pressure range. There is a slightly stronger pressure dependence for the QRRK calculated values, and the differences between our helium and nitrogen predictions appear to be less than observed in the experiments. This difference in N, versus He is possibly due to our energy-transfer parameters (see Table I). Analysis of these experiments requires the use of the mechanism in Table IV. This allows us to include reactions ~o and from both the stabilized alkyl-hydroperoxide radical (CCOOH) and the C2H4 + HOz channels, which were omitted in the analytical solution of Wagner
+
(24) Page, M. Naval Research Labs, Washington, D.C., personal communication. ( 2 5 ) Gulati, S . K.; Mather, S.; Walker, R. W. J . Chem. SOC.,Faraday Trans. 2 1987. 83. 21 7 1 ( 2 6 ) Monk. J.; Pagsberg, P.; Tatajczak, E.; Sillesen, A. Chem. Phys. Leu. 1986. 132. 417.
( 2 7 ) Benton. S W Can J Chem. 1983, 61. 881
Chemical Activation Analysis of C2H5
+ O2
The Journal of Physical Chemistry. Vol. 94, No. 8, 1990 3317
s-1
Discussion The reaction of C2H, + O2 forms a complex, and at low pressures, a significant fraction dissociates back to reactants. A small fraction of the complexes at low pressures undergoes isomerization and subsequent dissociation to C2H4 H 0 2 . Another small fraction undergoes stabilization to the CCOO adduct. With increasing pressure the fraction of energized complex that is stabilized approaches unity. The large fraction of complex that dissociates to reactants is controlled by the loose transition state-high Arrhenius A factor for this dissociation reaction. We do not need to explain part of the reaction path at any temperature by a direct hydrogen-transfer mechanism and do not feel the reaction proceeds by this route. We are in complete agreement with Wagner et al. and with Kaiser et a!. on this point. The energized hydroperoxy radical CCOOH*, if formed, dissociates to C2H4 H 0 2 almost completely at low pressures due again to the high P-scission A factor (compared to reverse isomerization), while at higher pressures larger fractions can be stabilized. This well is very shallow, however, and the stabilized radical dissociates, again almost completely to CzH4 H 0 2 . At temperatures above ca. 500 K the lowest energy adduct, CCOO', has a lifetime of less than 50 ms (high-pressure limit). Thus, over a several second experiment the isolated chemical O2 to C2H4 H 0 2 including the CCOO and system CC' CCOOH adducts is essentially at thermodynamic equilibrium. We conclude that the reaction of H 0 2 C2H4 to CCOOH has an activation energy of only ca. 8 kcal/mol. This is in agreement with Wagner et al.," but in significant disagreement with the value of 17.1 kcal/mol published by Baldwin et aLz3 and values of 12.7-14.1 of Gulati et aLz5for longer chain olefins, which are based on oxirane formation. Furthermore, as shown above, the data of Kaiser et al. are totally inconsistent with these high barriers. We think this oxirane formation process might be a complication from production and addition reactions of atomic oxygen. Our calculations show that significant amounts of H 0 2 are produced in the reaction (up to 5 ppm), and this readily reacts with the ethyl radical to form ethoxy + OH. Including this in the mechanism for the reactions of Slagle et aL2v7only decreased the H 0 2 levels by 5% for the short times indicated above. However, reactions of H 0 2 and other radicals at longer times relevant to experiments of Walker4,* and of B a l d ~ i are n ~ significant. ~ ~ ~ ~ One route to production of O H , in addition to the reaction above, is HO2 reacting with itself to form H 2 0 2 + 02.The H 2 0 2dissociates to two OH, and two O H react to H 2 0 0. The 0 atoms can build up and react with ethylene to form epoxides, a significant product in the Walker and Baldwin experiments. We are continuing to work on this system to try and understand this oxirane component. Our estimates of the transition-state energy for epoxide formation from the alkyl-hydroperoxy radical include ring strain E, (27 7 = 34 kcal/mol). This combined with an Arrhenius A factor of ca. 5 X 10l2 (tight transition state) makes this channel unlikely when the lower energy 0 scission to olefin or isomerization to peroxy are considered. We have shown that a chemical activation analysis using a QRRK formalism successfully accounts for the wide range of observables. Of particular interest is the successful application at relatively low temperatures where the use of a single vibrational frequency approximation would be most suspect. We attribute use of the gamma function representation, which avoids the necessity of rounding energy barriers to an integral number of quanta, as an important factor in this successful analysis. Another advantage of the QRRK approach is that it is readily extended to reactions of larger alkyl hydrocarbons with oxygen, and we shall present results on these systems in future publications. We caution that accurate thermodynamic parameters must be used in addition to correct bi- and unimolecular rate constants for the analysis to be meaningful.
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1/T *lo-* Figure 7. Arrhenius plot showing the various channels for C2H, O2 at 760 Torr in a bath gas of N,: 0,high-pressure addition rate constant; 0, rate constant for stabilization; 0, rate constant for production of C2H, + HO,; +, rate constant for )he CH,CHO + OH channel; X, rate constant for stabilization to CCOOH (after isomerization); A, rate constant for the CCO + 0 channel.
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et aIsi1(One would not expect the analytical solution to be valid at conditions of high pressure and relatively long reaction time.) Stabilization is the dominant reaction below 1500 K at I-atm pressure, with the rate constant for the ethylene channel increasing and then decreasing as temperature increases-at higher temperatures reactions to CH,CHO O H and CCO 0 become competitive. Figure 7 shows an Arrhenius plot of the ethyl + O2 reaction at I-atm pressure. This figure clearly illustrates that the rate constant to hydroperoxy channel is favored over reaction to C2H4,. by ca. 1 order of magnitude at this pressure and 300 K. The CCOOH radical is in a very shallow well, only ca. 15 kcal/mol. This represents a half-life (high pressure) for reaction out of the well of ca. 0.02 s at 298 K ( & 5 ) . The ethylene concentration is quite small and is affected by reaction out of this well and to a smaller extent, by reaction out of the CCOO well. We can use the data of Kaiser to estimate the energy of activation of the CCOOH to C2H4 + H 0 2 . A barrier greater than 17 kcal/mol dramatically decreases the ethylene production at high pressures-more than a factor of 10 below that observed. We place a barrier to ethylene of 15.6 kcal/mol or AH 8. This is in reasonable agreement with calculations of who reports a value of 9 kcal/mol for the reverse reaction based on extensive quantum mechanical computations. The A and E, are also similar to addition of ethyl radical, which is isoelectronic with H 0 2 , to ethylene2*(E, = 7.3 kcal/mol). At higher pressures, a significant fraction of the stabilized hydroperoxy radical is formed and the reaction mechanism (which includes further reactions of the stabilized adducts) is utilized and needed to determine the final concentrations. Our calculations for pressures below 12 Torr essentially provide branching ratios controlled by entropy. The lower pressure reactions, where stabilization is less important, are therefore less sensitive to the relative barriers out of the well. In order to obtain agreement with the data of Slagle et al. using the well depth of Wagner et al.," 34 kcal/mol (AH1,298(CC00) = -5.7 kcal/mol), A_, needed to be adjusted upward to 2.65 X I O i 5 s-I (decrease entropy of CCOO by ca. 1 eu), and E,, then increased to 27.8 kcal/mol. This increase in well depth slows reaction out of the well for conditions of the higher pressure room-temperature experiments of Kaiser et aL6 and decreases our calculated ethylene yield. Our analysis indicates that at pressures of ca. 100 Torr and above stabilization to CCOO represents the significant component of the reaction with small but comparable apparent reaction rates to CCOOH and the ethylene channels. Here the bleed out of the CCOO well is very small, k = 5 X 10" s-I, but at long times it can account for some of the very small fraction of the ethylene observed. Use of the deeper CCOO well decreases the calculated ethylene from that shown in Figure 6 .
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(28) Kerr, J. A.; Moss, S . J . Handbook of Bimolecular and Termolecular Reacrions; CRC Press: Boca Raton, FL, 1981; Vols. 1-111.
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Acknowledgment. The authors acknowledge publication preprints of ref 1 1 by Dr. A. F. Wagner, ref 18 by Dr. D. Ben Amotz, and ref 24 by Dr. M. Page and Mr. Hsing-Hui Yu for help in performing the calculations.
