Reaction of Ethylene Oxide with O(3P) Atoms
The Journal of Physical Chemistry, Vol. 82, No. 19, 1978 2067
Absolute Rate Constant, Kinetic Isotope Effect, and Mechanism of the Reaction of Ethylene Oxide with O ~ y g e n ( ~ PAtoms ) Denis J. Bogant and Clifford W. Hand" Department of Chemistty, University of Alabama, University, Alabama 35486 (Received January 20, 1978; Revised Manuscript Received May 15, 1978) Publication costs assisted by the University of Alabama
The kinetics of the reaction of ethylene oxide with O(3P)atoms has been investigated in detail using a discharge flow syEtem with mass spectrometric and photometric detection. Absolute measurements of the rate constant, kinetic isotope effect, and stoichiometry have been made. The overall stoichiometry is 3 f 1 oxygen atoms consumed per ethylene oxide molecule. Arrhenius parameters for the reaction of C2H4O with 0 are A = 10(9.28*0.08) L mol-l and E = 5250 f 150 cal mor1 over the temperature range 298-691 K, and Arrhenius parameters for the kinetic isotope effect are AH/AD = 0.9 f 0.20 and ED- EH = 1460 f 230 cal mol-', over the temperature range 482-691 K. The magnitude of the preexponential factor and the temperature dependence of the isotope effect establish that hydrogen abstraction,rather than insertion to form a dioxetane intermediate, is the sole reactive channel for ethylene oxide plus O(3P).The Arrhenius parameters are discussed and compared to other hydrogen abstraction reactions of O(3P). Comparison is also made to the reactions of O(3P)with other strained three-membered ring compounds. The final products H2,H20,HCHO, CO, and C02were identified, and a mechanism is proposed to account for their formation from the radical products of the initial step.
I. Introduction The bimolecular reactions of atoms with substrate molecules are of continuing interest because a knowledge of these processes is essential to the understanding of more complex kinetic ~ystems.l-~Oxygen atom reactions are particularly important because they are fundamental to combustion processes,1i2upper atmosphere chemistry: and the photochemical smog cycle.4 The reactions of ground state O(3P)atoms with alkanes and alkenes have been extensively studied and recently reviewed,'" and it is known that the reactions with alkanes proceed via hydrogen abstraction. By contrast, the reactions with alkenes,laS6p6alkynes,l&&aomatics,la and some other species (e.g., sulfide^^"^^ and nitrileslaP8) involve short-lived, energy-rich addition complexes which undergo unimolecular fragmentation, often by more than one pathway.lP* Reactions having multiple product channels present opportunities to study the principles which govern the selection of a reaction path.g The objective of the present investigation of the system atomic oxygen, O(3P), plus ethylene oxide (Etox) was to determine the mode of attack of the O(3P) atom upon the Etox molecule; Le., hydrogen abstraction or addition (insertion) at a C-0 bond. Marsh and HeicklenlO studied the competition for 0 atoms between Etox and perfluoropropene and obtained a rate constant of 107.2exp(-1800 cal mol-l/RT) L mol-l s-l for the reaction with Etox. Based upon this unusually low A factor they postulated that the reaction involved attack at a C-0 bond with ring opening rather than hydrogen abstraction. Insertion requires a more specific orientation of the reacting species and hence should have a lower A factor. Such a process would produce an energy-rich dioxetane-like intermediate. We report here the results of absolute rate constant measurements over the range 298-691 K and measurement of the deuterium kinetic isotope effect (KIE) over the range 482-691 K. The overall stoichiometry of the reaction has been determined and the major products have been Chemistry Division, Code 6180, Naval Research Laboratory, Washington, D.C. 20375. 0022-3654/78/2082-2067$01 .OO/O
identified. Hydrogen abstraction from Etox by O(3P) is the exclusive reaction path, and a multistep mechanism consistent with the observed final products is proposed and discussed.
11. Experimental Section A schematic diagram of the flow reactor and mass spectrometer is shown in Figure 1. The flow reactor was constructed of Pyrex glass and included one fixed and one movable reactant inlet, a thermocouple inlet (not shown in Figure l ) , and a 50-cm reaction zone, 42 cm of which could be heated by nine independently adjustable sections of nichrome wire wrapping. The flow reactor was fitted to the ion source of the mass spectrometer with an O-ring seal and flange, and gases were sampled into the ion source via a Pyrex pinhole of diameter ca. 0.05 mm. Kinetic experiments were performed when the reactants were present to the extent of a few percent in a flow of inert carrier gas, helium, argon, or nitrogen. All experiments were done under pseudo-first-order conditions, where the validity of the pseudo-first-order assumption was verified by computer modeling (see Discussion). Carrier gas flows in the range lo4 to mol s-l were controlled by needle valves and measured by capillary flow meters with interchangeable capillaries. Two such systems were available so that independent measurements of the flows of inert gas and O2could be made when necessary. Reactant (Etox) and titrant (NO and NO2) gas flows in the were measured by metering range to lo4 mol systems utilizing differential pressure transducers.ll For most of the rate constant determinations O(3P) atoms were produced via the titration, with nitric oxide, of N(4S)atoms generated by a microwave discharge in pure nitrogen. In practice, NO was always added t o slightly beyond the end point of the titration; under these conditions N(4S) was absent from the reaction zone and this in turn ensured the absence of excited states of N and NPl2 For the remaining experiments, 0 atoms were produced by a microwave discharge in mixtures of 5-2070 O2in rare gas (either Ar or He). Measurement of the 0 atom concentration in the reaction zone was accomplished by the chemiluminescent 0 1978 Amerlcan Chemical Society
2068
The Journal of Physical Chemistry, Vol. 82, No. 19, 1978
f
A
FlgMre 1. Flow reactor and mass spectrometer (not to scale): A, atom inlet for introduction of discharged gas; P, reactant probe for introduction of stable reactant; T, titrant inlet for introduction of NO; F, flushing line for introduction of undischarged carrier gas; ST, standard taper joint, the outer joint containing ten electrical leads for heating wires; G, glass pinhole: X, distance between reactant probe tip and glass pinhole; P,, flow system pump: P,, ion source differential pump: PB,flight tube pump.
titration with NOz as described by Kaufman.lb The 0 atom concentration at the point of introduction of NOz was calculated from the metered flow of NOz and a suitable correction factor for the equilibrium existing between NOz and NzO4 in the flow system re~erv0ir.l~ Nitrogen, oxygen, and argon were Matheson prepurified grade, of 99.997% purity, and helium was of 99.8% purity. Nitrogen and oxygen were used in most experiments without further purification; however for product searches they were passed through a -196 "C trap placed upstream of the discharge. The concentration of Etox during kinetic runs was followed by mass spectrometric observation of the total m/e 44 ion current, with the ionizing voltage set at 13 eV. Operation at such a low voltage was necessary in order to eliminate the m/e 44 ion current due to COz, which was a major product (see below). Separation of the CzH40+ and COz+ion currents was not difficult since the ionization potential of Etox (10.56 eV) is significantly lower than that of COz (13.76 eV). At 13 V, in our instrument, equal concentrations of Etox and COZ produced relative m/e 44 ion currents of 165 and 1, respectively. Thus the total current at m/e 44 was almost exclusively due to Etox, and no correction for COz was required. The kinetic isotope effect was determined in a competitive experiment using mixtures of Etox-h4 and Etox-d4.11 These runs followed the same general procedure as outlined above, and they too were under pseudofirst-order conditions with [O]>> [Etox]. In order to minimize systematic errors in the KIE determinations, alternate measurements were taken at m/e 48 (CzD40+) and m/e 44 (CZH,O+), and the order of points, with respect to contact time, was randomly selected at the start of each run. Several attempts were made to follow the 0 atom concentration in the presence of excess Etox by mass spectrometric observation of the m/e 16 peak. However no satisfactory procedure could be devised for quantitative measurement because Etox has a major fragment ion (CH4+)of m/e 16 which has an appearance potential of 12.3 eV;14since this is less than the first ionization potential of O(3P),it was impossible to isolate the ion current due to O+. An alternative procedure was therefore needed to monitor the relative concentration of O(3P)in the presence of excess Etox. The technique wed15was the measurement of the relative intensity of the 0 + NO chemiluminescent reaction in the presence of a constant concentration of NO, in excess of that needed to quantitatively convert N(4S) to O(3P). We found that the most reproduceable results were obtained when [O] N [NO] in the reaction zone.
D. J. Bogan and C. W. Hand
7
.?
6.0
t I
1
I
I
I
20
- J
3.0 1000/ T
FlgMre 2. Temperature dependence of k,. Abcissa is l€JOO/T(K), ordinate is log k 2 (L mol-' s-').
When [NO] < [O], scatter was encountered which became increasingly serious with decreasing [NO],11 111. Results A. Rate Data and Arrhenius Parameters. The results of the rate measurements with 0 in excess, with Etox in excess, and of the competition between Etox-h4 and Etox-d4 are presented in Table I. It is shown in the discussion that secondary reactions (reactions of Etox with species other than 0 ) cannot account for significant consumption of Etox when [O] >> [Etox]; thus the results in Table I, with 0 in excess, are to be interpreted, within the accuracy of the measurements, as being the absolute rate constant for the elementary reaction
0 + CzH4O
-
OH + CzH30
(2)
The least-squares estimate of the Arrhenius parameters is obtained from 57 experiments with 0 in excess over the temperature range 298-691 K and is kz = (1.91 f 0.31) x lo9 exp(d250 f 150/RT) L mol-l s-l, where the error limits represent one standard deviation of the least-squares parameters. These data are plotted in Arrhenius form in Figure 2. B. Kinetic Isotope Effect. The primary KIE for a H or D transfer reaction is expected to be larger than the secondary isotope effect for the 0 atom attack at the C-0 bond with ring opening. In addition a primary KIE decreases markedly with increasing temperature, whereas a secondary isotope effect is less sensitive to temperature. Measurements of the KIE could not be obtained below 480 , K because of the smallness of the rate constant k ~ and conclusive identification of the KIE as primary or secondary could only be obtained from a determination of KIE as a function of temperature. Sets of four measurements were obtained at three different temperatures. The results, shown in Table I and Figure 3, are kH/kD = (0.9 f 0.2) exp(1460 h 230/RT) C. Stoichiometry. The overall stoichiometry of the reaction of 0 with Etox can be expressed in the form nO
+ Etox
k2
products
Since the stoichiometric coefficient of Etox is unity, n is given by - n=-= d[Ol d[Etox]
d/dt 101 d/dt [Etox]
The rates [8tox] and [O] at a given temperature are given
Reaction of Ethylene Oxide with O(3P) Atoms
The Journal of Physical Chemistry, Vol. 82, No. 19, 1978 2069
TABLE I: Exaerimental Rate Constants and Conditions k , (lo5L mol-' s- ) Tk3,K P, Torr ( v ) , cm/s 300 2.40 99 2.55 300 2.54 95 4.55 300 2.15 98 3.05 300 2.44 86 3.42 300 8.55 125 3.87 300 8.88 121 3.37 300 1.60 147 3.87 300 1.72 137 3.31 300 2.28 118 3.67 300 2.11 123 4.00 300 2.37 135 4.46 300 9.15 115 4.43 300 7.96 121 5.66 300 2.97 106 2.76 3.78 f 0.81 (mean of above 1 4 values at 300 K, 0 in excess) 300 0.93 323 10.2 300 0.97 309 9.58 300 0.77 335 10.4 300 0.70 310 10.1 300 0.88 36 5 12.2 300 0.81 363 12.1 300 0.65 398 12.9 9.76 300 0.79 330 12.1 300 0.84 310 11.0 f 1.3 (mean of above 9 values at 300 K, Etox in excess) 1.03 318 2 15 490 1.03 328 131 506 53.2 (H) 482 2.50 140 14.8 (D) 482 2.50 140 48 2 2.52 140 54.5 (H) 13.3 (D) 482 2.52 140 52.6 (H) 482 2.45 144 12.7 (D) 482 2.45 144 50.3 (H) 482 2.47 143 482 2.47 143 11.9 (D) 240 (H) 583 2.98 182 583 2.98 182 62.1 (D) 246 (H) 583 2.99 181 583 2.99 181 68.7 (D) 227 (H) 583 3.02 180 70.5 (D) 583 3.02 180 583 2.85 192 222 (H) 75.3 (D) 583 2.85 192 958 (H) 691 1.57 308 416 (D) 691 1.57 308 691 1.59 304 885 (H) 373 (D) 691 1.59 304 946 (H) 691 1.61 303 335 (D) 691 1.61 303 807 (H) 691 1.62 297 314 (D) 691 1.62 297 129 501 2.22 145 99,4 509 2.31 116 5.58 355 2.51 122 6.41 355 2.52 120 6.38 353 1.89 165 6.29 353 1.89 164
relative'-c [ 0 ] :[ Etox ] 5:l 5:l 4:l 4:l 2.5: 1 2.5:l 8:1
carrier gas NZ NZ
NZ NZ Nl
NZ
NZ
8:l 6:l 6:l 8: 1 2:l 3: 1 5:l
N2
1:2.8(30) 3 :1.1(3 0) 1:1.9(27) 1:3.3( 25) 1:5.4( 25) 1:4.3( 23) 1:14(35) 1:10(30) 1:8.1( 18)
NZ
1:0.5( 1 8 ) 1:0.5( 1 7 )
NZ
{;;;;I {19:1} 19:l
{;;;;I {19:1} 19:l {10:1} 1O:l
NZ Nl
NZ NZ NZ NZ NZ
NZ NZ NZ NZ
NZ NZ NZ
?}
3.60
}:
4.10
2N:}
14:l
{;;;;I 9:l 8:l 1O:l 1O:l 1O:l 1O:l
4.16
NZI
4.24
$1
3.87
NZ
{;;;;I {;;;;I {;;;;I {;;;;I {;;;;I {14:1)
k ~ / k ~
3.59
:;I
3.22
::I
2.94
NzI NzI N,
2.30
NZ
2.38
N
NZ,}
2.82
NzI
2.57
2
He NZ NZ NZ
NZ
All rate measurements reported here were done under effectively pseudo-first-order conditions established by computer modeling, see Discussion, Runs with Etox in excess had [O] = 1.0 (t1.0; - 0.5) x lox4atoms/cm3. The procedure involved variation of [Etox] with [O], and contact time fixed, see ref 11, 13, and 15. The smaller relative [Etox] is the minimum value used and the larger number in parentheses is the maximum value used. For the 300 K runs [O]/[O], > 0.8. Runs with 0 in excess had [Etox] = 1.0 0.7 x l O I 4 molecule/cm3. The procedure involved variation of contact time with [O], and [Etox], fixed. For the 300 K runs [Etox]/[Etox],= 0.9 even at the longest contact time. For the k H / k D determinations [Etox] refers to the sum of Etox-h, and Etox-d,.
by the rate constants k 2 (0 in excess) and k 2 (Etox in excess), respectively. Fourteen measurements of k2 (0 in excess) at room temperature yielded a value of (3.77 f 0.81) X lo5 L mol-' s-l and nine measurements of k2 (Etox in excess) yielded a value of (11.0 f 1.3) X lo6 L mol-' s-l, where the errors are the standard deviations of the samples. From these values the stoichiometric coefficient, n, is calculated to be 2.92 f 1.12 at 300 K. Three determinations of h2 with Etox in excess at ca. 500 K yielded
a stoichiometric coefficient of 1.6 f 1.0. D. Product and Intermediate Searches. The technique used for product identification was mass spectrometry. Product searches were conducted at both low and high ionizing voltage (Vi), and electron impact ionization potentials were obtained to confirm the product identifications. The presence of a product was clearly indicated at those mf e values which showed a decrease in ion current upon turning off the discharge (thus eliminating 0 atoms).
2070
D. J. Bogan and C. W. Hand
The Journal of Physical Chemistry, Vol. 82, No. 19, 1978
TABLE 11: Effect of Secondary Reactionsaib initial concn, M
T, K 300 450 700 700
0
final concn, M
Etox 8.31 X lo-" 2.67 x 5.81 x 5.81 x
4.15 x 2.16 X 8.31 x 8.31 x
time, s 0.50 0.25 0.10 0.30
0 1.91 X 9.12 X 4.35 X 1.23 X
lo-'
lo-'
fractional Etox consumption
p* 0.998 0.986 0.966 0.945
Etox 7.97 X 2.18 X 4.39 x 3.47 x
p4
0.002 0.008 0.016 0.020
p, 0.0002 0.006 0.018 0.035
The computed results are for the mechanism 1-7, see text.
Rate constants and their sources are as follows: (1)k , = s-', this work; (3) k , = 1010*36 L mol-' s-l, ref 26; ( 4 ) h , = 1010*82 exp{-3600/RT} L mol-' s-l, ref 27, the value for ethane was used; ( 5 ) k , = 1010-8z exp{-92OO/RT} L mol-' s-l, ref 28, the value for ethane was used; ( 6 ) k , = 20{1 t ( T - 300)/133} s-', assigned from observation.
k, = 1.5{1 t ( T - 300)/133} s-l, assigned from observation; (2) k , = 109*28 exp{-5250/RT} L mol-'
molecules lead to highly reactive radical species which undergo fast secondary reactions. A computer modeling study was performed in order to estimate the extent to which Etox was depleted by the secondary species H and OH and, hence, the correction factors, if any, which would have to be applied to the rate constants calculated under the assumption of straightforward bimolecular kinetics. The following mechanism was modeled: 0 + wall products (1)
0.25 i
0
+ + + + + + Etox
0
I .6
1.8
2.0
1000/ T Flgure 3. Kinetic isotope effect. The logarithm of the ratio of rate constants for protiated and deuterated Etox is plotted against reciprocal temperature. Abcissa is 1000/T (K), ordinate is log ( k , / k d ) : 0, experimental points, error bars extend to one standard error unit (the plotted points are means of subgroups, each comprising four measurements); ( 0 )simulated points using Arrhenius parameters reported in Table 111 for a hypothetical parallel-channel mechanism. The experimentally measured effect of deuterium substitution on the activation energy, ED - E,,, is 1460 f 230 cal mol-'; this value is obtained by multiplying the (upper) slope by 2.30R.
In some cases such changes of the ion current could be clearly perceived only at low Vi, since fragment ions derived from Etox contributed to the ion current at higher Vi. In order to deal with this problem, several replications of mass spectra were obtained and peak height (discharge on/discharge off) ratios of suspected products were compared to the corresponding ratio for the Etox+ parent peak. An analysis for statistical significance (at 95% confidence) was performed before products were considered confirmed. Product searches were run in both N2 and rare-gas/Oz mixtures and with Etox-h4 and Etox-d4. The principal products were found to be H, Hz, H20, CO, and COz. Minor products were HCHO, HCO, and OH. Repeated efforts were made under various conditions of pressure, temperature, and flow velocity to observe the adduct of 0 plus Etox, products containing two or more carbons, and the species CH3, CH2, and HCOOH. No evidence was found for any of these species. In addition, we did not observe visible chemiluminescence (using a 1P28 photomultiplier without filter or dispersive optics), chemiionization, or polymer deposits on the walls of the flow reactor. A product search conducted in an equimolar mixture of Etox-h4 and Etox-d4showed that HCDO was not formed. Some HDO was found even when pure Etox-d4only was present in the reactor, and this can be attributed to wall reactions. IV. Discussion A. Effect of Secondary Reactions on Measured Rate Constants. The reactions of atoms with hydrocarbon
OH H
OH H
C2H3O + OH
Etox
+H C2H30 + HzO
Etox
C2H30
OH 4 0
wall
wall
2
+ Hz
products
products
(2) (3) (4)
(5) (6)
(7)
The numerical integration of the corresponding set of coupled differential equations was accomplished using the Treanor modification of the fourth-order Runge-Kutta procedure.16 Input quantities for these calculations were temperature, initial concentrations for the reactants 0 and Etox (all others were set at zero for time zero), maximum run time, Arrhenius parameters for the bimolecular reactions (2, 3, 4, and 5), and temperature dependent expressions for the wall recombination reactions (1,6, and 7) which were assigned empirically from our observations of the system behavior. Calculations were performed for conditions which typified our experiments at the temperatures 300, 450, and 700 K. Using the results of these integrations we have expressed the probabilities for consumption of Etox via the bimolecular paths 2, 4, and 5 (under 0 in excess conditions); these are shown in Table 11. The probabilities for following the respective paths, Pj, are given by [product by path j ] Pj = C [product by path i] i=2,4,5
The resultant Pj can be used to approximate the differential rate expression for the loss of Etox by path j as, -Pi (d [Etoxlldt). From this it follows that the experimentally measured rate constants for depletion of Etox (which necessarily include all paths) are related to the true rate constant by, kz,true= P ~ k 2 , ~ ~ ~ ~ . Inspection of Table I1 shows that the fractional probabilities P4 and P5are negligibly small under all of our experimental conditions, hence we have assumed Pz = 1.00 and used uncorrected rate data throughout. Comparison of initial and final Etox concentrations in Table I1 shows that neglect of the consumption of 0 by C2H30radical is justified.
Reaction of Ethylene Oxide with O(3P) Atoms
The modeling also showed the loss of 0 atoms by path 1 was more important than loss by path 2: Thus an independent check of the validity of the simple pseudofirst-order approximation was desired. Since we had available ComputerLgenerated data on the concentration of 0 and Etox as a function of time we tested the accuracy of eq I in extracting the input value of k2 from least-squares analysis of these data. In ([Eto~]~/[Etox]) = k,[OI,t (1) The subscript 0 denotes a measurement made in the absence of 0 atoms (discharge off) and the subscript m denotes the midpoint of the reaction zone. The results showed that h2 evaluated from eq I, that is, on the assumption of pseudo-first-order behavior, would be in error by no more than 10% provided that the amount of Etox consumed a t the longest reaction time was less than 5% of the oxygen atom concentration measured at the midpoint of the reactor. Errors approaching 10% were calculated a t the highest temperatures of measurement, however at 300 K the error was less than 5%. B. Mechanism of the Elementary Process. The Arrhenius parameters determined in this study indicate that hydrogen abstraction, rather than ring opening, is the elementary reactive process for O(3P)plus Etox. The A factor is on the low end of the range of values measured for abstraction of H from substituted alkanes,l" and the activation energy is likewise low but not unreasonably so compared to those of other alkane reactions (see section C). Huie and Herron have recently presented an updated Evans-Polanyi plot for H atom abstraction by O(3P).1a Using the Huie and Herron plot, and our energy of activation of 5250 cal mol-l, a bond dissociation energy of D0298(C-H)= 97.5 kcal mol-l can be estimated for Etox. Recent experiments by Smith et al. support a C-H bond energy for Etox equal to that of cyclopropane (100.5 kcal mol-l) .17 These Arrhenius parameters differ from those reported previously by Marsh and HeicklenlO (A, = L mol-l s-l, E 2 = 1800 cal molt1). Their rate constant measurements spanned a temperature range of 307-398 K and a pressure range of 470-530 Torr. Ground state oxygen atoms were generated by the mercury sensitized photolysis of NzO in the presence of perfluoropropene and mixtures of perfluoropropene with Etox. The measurements were done by a competitive technique based upon the known rate of production of CF3CF0 and CF20, the only products of the 0 plus perfluoropropene reaction. The Arrhenius parameters reported in the present work encompass a much larger temperature range and are obtained from absolute rate measurements, and for these reasons our data are preferred. The interpretation offered by Marsh and Heicklen, in order to explain their very low A value, was that O(3P) attack was upon the C-0 bond with ring expansion.1° Thus, owing to a more ordered transition state, the entropy of activation for such a process would be lower than that for hydrogen abstraction. The experimental rate constants, shown in Figure 2, have relatively large scatter and suggest a possible upward curvature. Upwardly curved Arrhenius plots can arise from competition between two elementary processes, where the steeper, higher temperature region is due to dominance by a process with a larger A factor and larger activation energy than the process which dominates at low temperature. The KIE experiments were undertaken in the hope of resolving the question of competition between reactive
The Journal of Physical Chemlstry, Vol. 82, No. 19, 1978 2071
TABLE 111: Model for Simulated Kinetic Isotope Effecta ~ t o xt 0
Etox t 0
- n+k2'
0-0
2
products
- v'
t OH,
\IH-'* 0
L mol-' s-' A,,H = A,,-, = A 2 f ,=~A,',-, = E,,H = 5250 cal mol-' E,,-, = 6450 E,',H = Eat9-,= 1800
-_kH - ki,H t kz',H kD
kz,D
ka',D
a Sources of Arrhenius parameters are as follows: A 2 , ~ , A,,-,, E Z p ,E,,-, taken from this work;A,',H,A,',-,, E 2 ) , ~E,!,-, , taken from ref 10.
channels beyond any doubt. The quantity ED -E! = 1460 f 230 cal mol-l obtained from the KIE Arrhenius plot (Figure 3, experimental points) is, within experimental error, equal to the value of 1200 cal mol-l expected for a hydrogen transfer process.18 For attack of O(3P)at the C-0 bond, with ring opening, ED - E H , would be zero. It was considered necessary to determine the KIE, as a function of temperature, which would be obtained in the presence of two competing elementary processes, hydrogen abstraction and ring opening. Thus, KIE for the competitive reaction scheme shown in Table I11 was simulated and the results are shown in Figure 3. The input quantities for this calculation were our experimental Arrhenius parameters (abstraction mechanism) and Marsh and Heicklen's Arrhenius parameters (ring opening mechanism). The theoretical value ED - E H = 1200 cal mol-I for a primary KIE and A2(H)= A,(D) were assumed. Slight changes in the latter assumptions do not change the result significantly. The KIE simulation, shown in Figure 3, differs from the experimental KIE at a very high level of statistical significance. This is conclusive evidence that hydrogen abstraction is the sole reactive channel for O(3P)+ Etox. The lack of visible chemiluminescence also bears on the question of mechanism. The intermediate for the ring expansion process would be 1,2-dioxetane, for which the heat of formation has been estimated as 0 kcal Combination of this estimate with AH40(3P)),AHf(Etox), and E , = 1800 cal mol-l (for ring opening) leads to the prediction that the transition state for ring opening attack would be chemically activated 1,a-dioxetane having ca. 50 kcal mol-l of excess vibrational energy. Bogan et al. have recently reported the observation of formaldehyde (A1A2 XIA1) chemiluminescence in the range X 340-500 nm from the reaction CzH, + 02(lA ).20 This reaction proceeds via a 1,2-dioxetanecomplex with ca. 50 kcal mol-l of excess vibrational energy. Despite the very high activation energy (compared to the present work) of 21 kcal mol-l, observed for the latter reaction, a high resolution spectrum was obtained and chemiluminescence was easily seen in the darkened room, at a reactor temperature of 400 K. The hypothetical reaction O(3P)+ Etox 1,2-dioxetanewould proceed (at least initially) via a triplet potential energy surface presumably leading to a preponderance of HCH0(3A2)z1 rather than HCHO(lA2). This might make such a reaction difficult to confirm via chemiluminescence. Nevertheless, the absence of visible chemiluminescence is consistent with the results of the KIE experiments. C. Evaluation of the Rate Parameters. The leastexp(-(5250 f squares rate parameters, h2 = 10(9~28*0~08) 150)/RTJ,are, as noted above, chemically reasonable al-
-
-
2072
The Journal of Physical Chemistty, Vol. 82, No. 19, 1978
though somewhat low. The error limits (fa) represent a measure of experimental precision but not of absolute accuracy. Inspection of Figure 2 suggests an error limit of a factor of 2, particularly at low temperature. The room temperature measurements of kz are least accurate and are considered to be only 3 to 5 times larger than the smallest constant which can be measured in our apparatus. Hence we recommend realistic error limits of a factor of f 3 at 300 K and a factor of f1.5 at 700 K with linear scaling of the limits at intermediate temperatures. Kinetic modelers and others. who desire consistent sets of rate constants for hydrogen abstraction from various C-H bonds by O(3P) might wish to raise our A and E , values. We would recommend that the maximum values of kz,at the temperatures 300 and 700 K, be retained, such that Arrhenius parameters so adjusted would have unsymmetrical error limits. D. Secondary Reactions and Overall Mechanism. Having established that the initial reaction in the system is
O(,P)
+ C2H40
-
C2H3O + OH
(2)
we consider the possible secondary reactions and an overall mechanism capable of explaining the observed final products. Reaction 2 is very slow, thus rates of consumption of the radical products CzH3O and OH via secondary reactions are expected to be much faster than the observed consumption of Etox. The principal path for loss of OH is the fast reaction 0 OH 02 H
+
+
+
The CzH30 product of (2) will be initially formed with excess internal energy and may undergo immediate unimolecular fragmentation or rearrangement to more stable vinoxy,22or structure, followed by either unimolecular or bimolecular reaction. Using the maximum possible energy content of CzH3O [obtained from the reactants' A",, E,, and A",(OH)] the only exothermic unimolecular reactions are CzH30*-+HzCC0 H AH2 -6.0 (8)
+
+
CH3 CO AH L - 35.9 (9) Reasonable bimolecular loss channels for CzH3O are the reactions 0 + CzH30 HCHO HCO (10) -+
--
+
+ HCHO + H HzCCO + OH
CO
COz + CH3
(11) (12)
(13)
Reactions 10 and 11 are addition-fragmentation reactions of 0 with either vinoxy22or e p o ~ y e t h yradicals. l~~~ Reaction 12 giving ketene can occur via direct abstraction of hydrogen from C2H30of any structure, followed by bond rearrangements of the CzH20fragment. If reaction 12 occurs, the product ketene must be formed with less internal energy than the ca. 70 kcal mol-l needed to form CH2 and CO by unimolecular fragmentation, since no evidence was found for CH2 or the Cz and higher C, products which would result from its presence. Reaction 13 is envisioned as the addition-fragmentation reaction of 0 with acetyl radical. Methyl radical from (9) and/or (13) would not be easily seen because the reaction CH, + 0 -HCHO + H (14) occurs on every collision.24 Ketene from (8) and/or (12)
D. J. Bogan and C. W. Hand
would also be consumed rapidly by HZCCO + 0 -+ HCHO + CO (15) The rate of consumption of HCHO by 0 has been measured by Niki,25and is two orders of magnitude greater than kz. That we easily observed HCHO when it is so rapidly destroyed indicates a large rate of formation, and strongly suggests that the principal paths of reaction are those leading to HCHO. Once formed, formaldehyde should be lost by the reactions of Niki's mechanism:26 0 + HCHO OH + HCO (16) 0 + HCO CO + OH (17) 0 + HCO C02 + H (18) OH + HCO ---* H2O + CO (19) OH + wall products wall (20) to which for completeness we add
--
+
+
H + wall 1/2Hz+ wall (21) This mechanism, in particular the molecular simplicity and small number of final products, is entirely consistent with our experimental observations. I t is not possible to observe growth and decay of intermediates in the above scheme, since their very detection strained the limits of the apparatus (ca. 1O1O species ~ m - ~ ) , Reliable information on species growth and/or decay was obtained only for H2 and CO, both of which increased monotonically with increasing contact time, as expected. At long contact times the ratio of products, [CO]/ [CO,] 3. All other carbon-containing products are minor and a reasonable carbon mass balance was obtained using only CO, C02, and reactant Etox. E. Relationship to Other Studies. The reaction of O(3P)with the isoelectronic molecule, cyclopropane, was studied by Scala and WuZ9via Hg sensitized photolysis of a static sample followed by gas chromatographic analysis of the products. Experiments were done both in the gas phase at room temperature and in a 77 K matrix. It was inferred from the results, particularly the observation of oxetane in the 77 K experiments (presumably following warm up), that an insertion reaction occurred. Huie and Herron,la in reviewing O(,P) reactions, believed it unlikely that cyclopropane deviates from the pattern of hydrogen abstraction observed for other alkanes. They emphasized that the quantitative product analyses of Scala and Wu are typical of hydrogen abstraction, and that the absence of products characteristic of abstraction and coupling reactions of cyclopropyl radical is inconclusive because O(3P) is expected to react at least lo4 times faster with cyclopropyl than with the parent cyclopropane. The reaction of bicyclo[l.l.0]butane with O(,P) has recently been studied.30 Mercury sensitized photolysis of NzO at 0.9 atm and room temperature was used with GC product analysis. Two reaction paths were identified, consistent with addition (but not necessarily insertion), and concurrent C-C bond rupture forming short-lived 1,4 biradicals. Identification of the expected cleavage products of the postulated biradicals was used as evidence of the reactive paths. It is interesting to note that the total strain energy of the bicyclo[l.l.O]butane ring system has been This is significantly larger estimated as 68.4 kcal m01-l.~~ than the 27.6 kcal mol-l estimated for cy~lopropane.~~ The reaction of O(3P)with ethylene episulfide was found by Lee et to be very fast with a near zero activation energy. This fact, together with the results of product analyses conducted in a discharge flow-mass spectrometer system, was cited as evidence that reaction proceeds by
The Journal of Physical Chemistry, Vol. 62, No. 79, 1976 2073
Charge-Pair Recombination
direct addition of O(3P)to sulfur, forming the sulfoxide. The reaction is presumably facilitated by the presence of low-lying 3d orbitals on sulfur. On the basis of the above considerations, it appears unlikely that insertion pathways with low activation barriers exist for the reactions of ground state O(3P) with the saturated three-membered heterocycles. Acknowledgment. We thank Dr. M. C. Lin for helpful discussion and Professor R. B. Timmons for his continued interest and encouragement in this work.
(10) G. Marsh and J. Heicklen, J. fhys. Chem., 71, 250 (1967). (11) D. J. Bogan, Ph.D. Dlssertation, Carnegie Mellon University, 1973. (12) A. N. Wright and C. A. Wlnkler, “Actlve Nitrogen”, Academic Press, New York, N.Y., 1968. (13) R. H. Obenauf, Jr., Ph.D. Dissertation, Carnegie Mellon Universlty, 1972. (14) J. G.Dlllard, K. Draxl, J. L. Franklln, F. H. Field, J. T. Herrbn, and H. H. Rosenstock, Nafl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 25 (1969). (15) C. W. Hand and R. H. Obenauf, Jr., J. Phys. Chem., 76, 269 (1972). (16) C. E. Treanor, Math. Comput., 20, 39 (1966). (17) D. J. Smith, D. W. Setser, K. C. Kim, and D. J. Bogan, J. phys. Chem., 81, 898 (1977). (18) K. J. Lakller, “Theories of Chemical Reactii and Rates”, Waw-HUI, New York, N.Y., 1969. (19) H. E. O’Neal and W. H Richardson, J . Am. Chem. SOC.,92, 6553 (1970). (20) D. J. Bogan, R. S. Sheinson, and F. W. Willims, J. Am. Chem. Sm., 98, 1034 (1976). (21) N. J. Turro and P. Lechtken, Pure Appl. Chem., 33, 363 (1973). (22) (a) D. A. Ramsay, J. Chem. phys., 43, S18 (1965); (b) R. F. Anderson and D. Schulte-Frohlinde, J. Phys. Chem., 82, 22 (1978). (23) (a) L. Cracco, I. Glassman, and I. E. Smith, J . Chem. Phys., 31, 506 (1959); (b) S. W. Benson and H. E. O’Neal, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 21 (1970); (c) K. W. Watklns and W. W. Word, Int. J . Chem. Kinet., 6, 855 (1974). (24) (a) N. Washida and K. D. Bayes, Chem. phys. Lett., 23,373 (1973); (b) I. R. Slagle, F. J. Pruss, Jr., and D. Gutman, Int. J . Chem. Nnet., 6, 111 (1974). (25) H. Nlki, J. Chem. Phys., 45, 2330 (1966). (26) D. L. Baulch, D. D. Drysdale, D. G. Horne, and A. C. Lloyd, “Evaluated Kinetlc Data for High Temperature Reactions”, Vol. 1, University of Leeds, Leeds, England, 1972. (27) W. E. Wilson, Jr., J . Phys. Chem. Ref. Data, 1, 535 (1972). (28) W. E. Jones, S. D. MacKnight, and L. Teng, Chem. Rev., 74, 407 (1973). (29) A. A. Scala and W. T. Wu, J . Phys. Chem., 74, 1852 k:970). (30) J. J. Havel and K. H. Chan, J . Am. Chem. Soc., 97,5800 ( 1975). (31) S. W. Benson, “Thermochemical Kinetics”, Wlley, New York, N.Y., 1968, Appendix A.1.
References and Notes (1) (a) R. E. Huie and J. T. Herron, frog. React. Kinet., 8 , 1 (1975); (b) F. Kaufman, ibid., 1, 1 (1961). (2) J. N. Bradley, “Flame and Combustion Phenomena”, Methuen, London, 1969. (3) (a) “The Natural Stratosphere of 1974”, CIAP Monograph 1, US. Dept. of Transportation, DOT-TST-75-51, 1975 avallable from National Technical Information Service, Springfleld, Va. 22151, document no. PB246-318. (b) F. S. Rowland and M. J. Mollna, Rev. Geophys. Space Phys., 13, 1 (1975). (41 J. N. Pitts. Jr., and B. J. Finlayson, Angew. Chem., Int. Ed. Enol., 14. lf1975). (5) (a)’R. j.Cveknovic, Adv. Photmhem., 1, 115 (1963); (b) J. Chem. fhys., 23, 1375 (1955). (6) (a) J. R. Kanofsky, and D. Gutman, Chem. Phys. Lett., 15,236 (1972); fb) . . J. R. Gilbert. I. R. Slaale, R. E. Graham, and D. Gutman, J. Phys. Chem., 80, 14 (1976); (4J. J. Have1and K. H. Chan, J. Org. Cheh., 42, 569 (1977), and earlier papers in the atomlc oxygen series of Havel and co-workers cited herein. (7) (a) I. R. Slagle, R. E. Graham, and D. Gutman, Int. J. Chem. Kinet., 8, 451 (1976); (b) J. H. Lee, R. 6. Timmons, and L. J. Stief, J. Chem. fhvs.. 64. 300 (1976). (8) R. 2. Bonanno, R.‘ 6. Timmons, L. J. Stif, and R. 6. Klemm, J. Chem. Phys., 66, 92 (1977). (9) D. J. Bogan, J. Phys. Chem., 81, 2509 (1977).
Charge-Pair Distribution and Recombination Kinetics. The Role of Non-Gaussian Diffusion William H. Hamlll
‘
Department of Chemlstry and Radiation Laboratoty, Unlverslfy of Nofre Dame, Notre Dame, Indlana 46556 (Received May 8, 1978) Publicatlon costs assisted by the U S . Department of Energy
Charge-pair recombination is sometimes accompanied by luminescence,the intensity of which usually depends upon time according to the Debye-Edwards equation, I = at-m, with a and m constant. For Coulombically correlated charge pairs this simple equation contains both the initial radial distribution and also the transport mechanism. The rate of recombination is expected to have the same time dependence for otherwise comparable nonluminescent systems, with the integrated rate laws depending upon m < 1,m = 1,and m > 1,with no special significance attaching to the case m = 1. The transport mechanism is expected to involve electron hopping in medium temperature solids with a time-dependent mobility or diffusion coefficient. In liquids, diffusion will be classical. Data for rates of recombination for polar and nonpolar systems over a range of temperature have been examined. For many systems the surviving population n is described by n = aJ’t-” dt from t to a. It is a consequence that the radial distribution is given by d In nJd In R = constant.
Introduction It has been shown that the time-dependent decay of recombination luminescence intensity I ( t ) in alkanes is independent of irradiation dose and scintillator concentration. It is the same for high-energy radiation and UV irradiation.2 It arises from the recombination of isolated, Coulornbically correlated charge pairs. Consequently, I ( t ) is a transform of the original radial distribution function of charge pairs, n(R). For alkanes the number-radius dependence, d In n l d In R = (constant), was shown to be 0022-3654/78/2082-2073$0 1.OO/O
consistent with various experimentalresults? Considerable new relevant evidence has accumulated since this early work and the problem of ion recombination deserves reexamination. The Debye-Edwards relation
I = at-m (1) with a and m constants, was derived for the kinetics of ion-pair recombination in terms of trap-to-trap diffusion, but it ignores the Coulomb effect. Time t was defined 0 1978 American Chemical Society
