3828
J . Phys. Chem. 1988, 92, 3828-3833
systems should answer many of these questions in the near future.
rate constant suggests that strongly interactive exit channels cross the attractive entrance channel at long range. The intramultiplet mixing rates of Cd(3Po,2)with Cd(3Pl) are not rapid in Ar buffer gas. A weak Cd2* emission, tentatively associated with the Cd2(l~,~n,,) state, which could be formed by three-body recombination with Cd(3P2),was observed at high Ar and Cd concentrations. Qualitative observations of the CO(a311) Cd reaction suggest a close similarity with the N2(A) reaction.
Conclusions The excitation-transfer rate constants of N2(A) to Cd are large with the favored channels being those with conservation of electron spin and large N,(A-X) FC factors. Our data suggest that Cd(3Po)and Cd(3P2)are important products, as well as Cd(3Pl). These results follow the same trends that were observed for N2(A) with Cu atoms,s and large excitation-transfer rate constants to metal atoms generally can be expected. Another way to express the Franck-Condon idea is to note that R(N2,A) in the entrance channel is larger than in the exit channel (for N,(X,v”=O), and favorable crossings with the entrance channel potential require stretching of N2(X) in the exit channel. The very large quenching
+
Acknowledgment. This work was performed under the auspices of the U S . Department of Energy by Lawrence Livermore National Laboratory under Contract No. W-7405-ENG-48. We thank the reviewers for thoughtful criticism. Registry No. N,, 7727-37-9; Cd, 7440-43-9; CO, 630-08-0.
Kinetic Isotope Effects in the Gas-Phase Reaction of Hydroxyl Radicals with Ethylene in the Temperature Range 343-1173 K and at 1-atm Pressure Andong Liu,+ William A. Mulac, and Charles D. Jonah* Chemistry Division, Argonne National Laboratory. Argonne, Illinois 60439 (Received: July 20, 1987)
-
-
-
-
The rates of the reaction of ethylene and ethylene-dowith OH and OD were determined. The following reactions were examined: OH + C2H4 products (HH); OD + C2H4 products (DH); OH + C2D4 products (HD); OD C2D4 products (DD). These reactions show different reaction pathways at different temperatures. Below 560 K there is a weak negative activation energy which is characteristic of the OH addition to the double bond. kHHand kHD were the same at 1.65 X 1O-I2 exp(480/T) cm3/(molecuIe s) while kDDand kDH were the same at 1.35 x exp(480/T) cm3/(molecule s). Above 720 K, all rate constants show a positive activation energy of 4-5 kcal/mol and both primary and secondary kinetic isotope effects were observed. The high-temperature pathway was attributed to the H abstraction from ethylene by the OH. A conventional transition-state-theory calculation (TST) successfully reproduced the temperature and isotope dependence of the H abstraction rate constants.
Introduction The reaction of hydroxyl radicals with ethylene is an important reaction in both combustion and atmospheric chemistry and has attracted much attention in recent The experimental data at lower temperatures (less than 560 K) are consistent with a reaction mechanism which goes through the addition of the O H radical to the T bond of the ethylene molecule and subsequent collisional stabilization of the energetic adduct. This Lindemann-type mechanism can be described by the following scheme:I6 OH
+ C2H4
OH + CzH4 -% CzH3 + H 2 0 (3) The rate constant for O H disappearance would then be kl k = k3 + -(11) k-1 1+k2WI Since studies of the kinetic isotope effect are useful to gain insight into reaction mechanisms that are occurring,’* we have measured the rate of the reaction of O H with ethylene for all combinations of hydrogen and deuterium. Similar studies have
k k-I
C2H4-OHt
+
(1)
(1) Liu, A. D.; Mulac, W. A.; Jonah, C. D. Int. J . Chem. Kinet. 1987, 19,
(C2H4-OH)+ + M
-k C2H4-OH + M
25.
(2)
(2) Klein, T.; Barnes, I.; Becker, K. H.; Fink, E. H.; Zabel, F. J . Phys. Chem. 1984, 88, 5020. (3) Zellner, R.; Lorenz, K. J . Phys. Chem. 1984, 88, 984. (4) Tully, F. P. Chem. Phys. Lett. 1983, 96, 148. (5) Bartels, M.; Hoyermann, K.; Sievert, R. Symp. (Int.) Combust., [Proc.],19th 1982, 61. (6) Farquharson, G. K.; Smith, R. H. Ausr. J . Chem. 1980, 33, 1425. (7) Niki, H.; Maker, P. D.;Savage, C. M.; Breitenbach, L. P. J . Phys. Chem. 1978.82, 132. (8) Atkinson, R.; Perry, R. A,; Pitts, J. N., Jr. J . Chem. Phys. 1977, 66,
With this mechanism, the overall rate constant will be both pressure and temperature dependent. The rate constant will be
1197. (9) Meagher, J. F.; Heicklen, J. J . Phys. Chem. 1976, 80, 1645. (10) Overend, R.; Paraskevopoulos, G. J . Chem. Phys. 1977, 67, 674. (11) Howard, C. J. J . Chem. Phys. 1976, 65, 4771. (12) Gordon, S.; Mulac, W. A. Inr. J . Chem. Kinet., Symp. 1975, No. 1 ,
The results from the measurements show Arrhenius behavior with an activation energy of -1 kcal/mol and an A factor of about 2 x 10-12 cm3/(molecule s).1-4,7,8,10.12.13,15.17 Recent work has shown that the reaction rate decreases at higher temperatures, showing that the addition channel becomes less However, at temperatures above 720 K the rate of O H disappearance increases.’ This was attributed to the reaction
(13) Davis, D. D.; Fischer, S.;Schiff, R.; Watson, R. T.; Bollinger, W. J . Chem. Phys. 1975, 63, 1707. (14) Morris, E. D., Jr.; Stedman, D. H.; Niki, H. J . Am. Chem. SOC.1971, 93, 3570. (15) Greiner, N. R. J . Chem. Phys. 1970, 53, 1285. (16) For example: Laidler, K. J. Chemical Kinetics, 2nd ed.; McGraw-
‘On leave from the Institute of Low Energy Nuclear Physics, Beijing Normal University, Beijing, China.
Hill: New York, 1965; pp 143 and 175-178. (17) Atkinson, R. Chem. Reo. 1986, 86, 69. (18) Collins, C. J.; Bowman, N. S., Eds. Isotope Effecrs in Chemical Reactions; ACS Monograph 167; Van Nostrand Reinhold: New York, 1970.
0022- 3654,/ 88 ,/ 2092-3828 $0 1.50/ 0 I
789
0 1988 American Chemical Societv -
The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 3829
Reaction of Hydroxyl Radicals with Ethylene O.D.
I
0.003
.
0.002
-
0.001
.
/
150007
. . .. . . ..
0.000
I
0.0
"
0.24
'
.
1
'
'
-
'
I
"
0.48 0.72 TIME ( ms )
-
*
I " " 1
0.96
Figure 1. A typical O D decay profile at 973 K, 1-atm total pressure, for reaction O D C2D4. [C2D4] in the reaction cell was 0.97 X lOI5 molecules/cm3. The solid line is a nonlinear-least-squares fit to a pseudo-first-order decay.
+
been done with a more limited set of isotopic substitution^.^^^^ The kinetic isotope effect shows the involvement of a particular H (or D) atom in the rate-determining step. Thus, if the high-temperature reaction that we had previously observed' was due to a hydrogen abstraction, there would be an isotope effect. Further insight was obtained by comparing conventional transitionstate-theory (TST) calculations for all four isotopic variants with the experimental data.
Experimental Section The experimental details have been described previously in ref 1 and the references cited therein; only the basic principles and the details specific to this experiment will be given here. A mixture of water (or D 2 0 ) at 6 Torr, the reactant gas, and Ar flowed through a reaction cell which was in an oven. An electron beam pulse created OH radicals in the reaction mixture. The absorption of the OH (OD) was measured by means of a lamp which was created by a microwave discharge in a helium-water mixture. The light was selected by an interference filter and detected with a photomultiplier. The output of the photomultiplier was digitized by a Biomation 8100 transient recorder and signal-averaged with a computer. The data were analyzed by using a nonlinear least-squares program. The absence of contamination of the measured rates by radical-radical reactions (including OH-OH) was shown by determining that the rate constant is independent of the initial radical concentration. A sequence of experiments as a function of water concentration showed that water had no effect on the measured rates. The mixture of C2D4 and Ar was made in this laboratory. C2D4 was from ICN Biomedicals (98% C2D4 and 2% C,D,H) and diluted in U H P Ar (99.999%). The mass spectrometric analysis of the mixture was as follows: C2D4, 13.4 f 0.8%; C2D3H,0.4 f 0.1%; and Ar, 86.2 f 1.0%. The concentration of C2D4 in the reaction cell was of the order of 1015 molecules/cm3 while the initial concentration of O H was estimated at 1012-1013molecules/cm3 from the second-order decay of OH in the absence of the reactants. A typical time profile of the observed decay of OD radicals reacting with CzD4 is shown in Figure 1. The solid line is the nonlinear least-squares fit which gives the pseudo-first-order rate constant. A nonlinear least-squares fit was used because i t is easier to weight each time point for the error. (In our experiments all time points on a trace are equally weighted.) Also, there will be values less than the long-time limit if the decay is followed long enough and such points cannot be included in a semilogarithmic plot. Two examples of the determination of the bimolecular rate constants from pseudo-first-order rate constants are shown in Figure 2. The intercepts of these plots reflect primarily (19) Brauer, B.-E., personal communications.
2
0
4
1.20
[C,D,
6
8
15
I
I O molecule cm.'
Figure 2. The observed pseudo-first-order rate constant k'of O H and O D + C2D4 at 973 K vs concentration of added C2D4.
+ C2D4
TABLE I: Summary of Experimental Data on OH + C2H9 OD + C2H4, OH + C2D8 and OD C2D4of This Work" T, K k X 10l2 T , K k X 10l2 T,K k X 10l2 OH C,H, 343 6.78 703 i.58 943 2.30 973 2.60 730 1.29 373 6.02 748 1.47 403 5.20 990 2.51 773 1.70 423 2.92 5.04 1042 794 1.65 483 4.24 1087 3.53 800 1.51 523 3.20 4.12 1099 855 1.85 563 4.01 3.46 1136 873 2.32 603 3.14 1163 4.28 901 2.15 653 2.06 1173 4.03
+
+
343 373 403 483 563
6.14 4.75 4.34 3.52 3.23
OD 603 653 703 748 773
333 473 603 653 703
6.85 4.29 3.59 1.53 1.09
OH 723 773 798 873 923
383 393 448 523 603
4.91 4.28 4.23 3.20 3.10
OD 653 708 748 801 873
+ C2H4 2.94 1.79 1.32 1.26 1.53
873 973 1073 1173
1.88 2.23 2.62 3.52
973 1023 1073 1123
1.85 1.95 2.10 2.36
973 1023 1173
1.30 1.86 2.34
+ C2D4 0.79 1.13 1.29 1.50 1.62
+ C2D4 1.47 0.84 0.88 1.08 1.13
"All rates were measured at 1-atm total pressure of Ar and are in units of cm3/(molecule s). The estimated error limits is &lo%.
the rate of O H disappearance by reactions with itself. The intercept decreases with decreasing of the dose of the electron beam (lower O H concentration), but when the dose of the electron beam was varied by a factor of 10, the slope of the plot (the second-order rate constant) was constant within the experimental accuracy. The overall errors of these bimolecular rate constants were estimated at *lo% which reflect the accuracy of this experiment.
Results and Discussion The measured rate constants for OH and O D radicals with C2H, and C2D4 are given in Table I. The data for OH and OD with C2D4 are new as are some high-temperature points for CzH4. Previous data are included in the table to facilitate comparison.' The data are plotted vs 1000/T in Figure 3 with previous experimental and are compared in different (20) Smith, G. P.Int. J. Chem. Kinet. 1987, 19, 269.
3830 The Journal of Physical Chemistry. Vol. 92, No. 13. 1988
Liu et al.
P ,o II
sx
10
-13
""I""I
1""l""I""l 0.5
1.0
1.5
2.0
1OOQITIK)
2.5
1. 0
1.3
+
Figure 3. Experimental results of rate constants of OH/OD CIH,/ C2D, of this work ( 0 . 0 ,0 , m) and selected data of OH + C,H, from other authors: ( A ) ref 4; (I) ref 2: ( X ) ref 7; (+) ref 8; (v)ref I z : (e) ref 2 0 (0)ref 21.
'. .. ..
(21) Relative mCawemenU of Westenkg and Fristrom (Symp. Int. Combust.. (Prm.1,10th 1965. 473) and have been recalculated by W. E. Wilson. Jr. Data appeared in Figure C2 of Wilson's article (J.P h p . Chcm. Re/. Dot0 1912, 1. 564).
0.0
0.5
1.0
1.5
2.0
2.5
3.0
1.5
10OOITtK)
Arrhenius plot of rate constants of OD + C2H,/C,D4. The lines are computer fits. At low temperatures the fit is a least-squares fit of the data to k ( 7 ) = Ae-E/RT,and at high temperatures it is a fit of the calculated TST rate constants to k ( n = CP cxp(hS'*(T)/R) erp(AHoa(7)/RQ. See text far details. Figure 5.
bonds are broken during the addition or decomposition, one would not expect to see a primary isotope effect and only a secondary isotope effect would be expected for the reactions HH-DD. (For an explanation of the terminology used for kinetic isotope effects, seeTable9.1 onp287ofref22.) When k,[M] >> k.,,thereaction will be close to the high-pressure limit and the kinetic isotope effects kHH/kHDand koH/kDo will be close to unity?% However, a t lower pressures a n inverse isotope effect would be predicted from the statistical-weight effects for unimolecular decomposition of the excited adduct. Data of Brauer indicated a ratio of kHH/kHo 0.75 a t r m m temperature and 2 Torr'q while Niki et al? measured 0.97 f 0.06 a t 700 Torr. For propene, Tully and Goldsmith found k(C,H6)/k(CID6) = I in 600 Torr of He from 293 to 481 K for the O H + propene reaction.'] Work in this laboratory on O H + C,H,/C,D, has shown that k(H)/k(D) = 1 below 398 K and < I at higher temperatures. Thus, it seems likely that at 1 atm the O H addition reaction is close to the high-pressure limit up to 563 K. The data of Zellner and Lorenz also would suggest that our data should be a t or near the highpressure limit? In particular, our results at 523 K are the same as the extrapolated high-pressure limit rate constant within experimental and extrapolation error? Sato and cc-workers found that a pressure of 500 Torr was sufficient to be in the high-pressure limit for the reaction of H + ethylene at 450 K?4 One would expect that it would be easier to reach the high-pressure limit for O H + ethylene because there will be three additional degrees of freedom. The O H rate is about 22% higher than that for OD, and this ratio is nearly temperature independent. There are several factors which could cause this. Qualitatively, one might expect that for O D more of the external rotational freedom is converted into internal energy of a transition complex. This would make the equilibrium constant for the transition-state @ smaller for OD than for O H . The bigger internal rotational and vibrational entropy of the OD group will partially compensate for this effect. To quantify this effect, the transition-state calculation was made to estimate the ratio of Arrhenius A factors for the second-order high-pressure limited addition reaction (reaction I ) . Ethylene was taken as a model wmpound. The length of the newly formed C-0 bond was estimated as 1.83 A, 0.4 longer than the normal C-O bond. This is a tight transition state and has been found to fit the experimental results well. The calculation gave the ratio of A factors for A(HH)/A(DH) = 1.29 and A(HD)/A(DD) = (221 Robinson. P. I.: Holbroak. K. A. Unlmoleculor Reactions:. Wilev, Inl;&iencc: London. 1972; (a) p301: (b) p 288. (23) Tully. F. P: Goldmith. J E M Chtm Phyr b i t . 1985. 116. 345. (24) S u g ~ a m K..O!azaki. . K.:Sm.S.Bull. Chrm.Sm. Jon. 1981.54. 2872
The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 3831
Reaction of Hydroxyl Radicals with Ethylene
TABLE 11: Assumed Vibrational Frequency Changes (cm-I) in Activated Complexes for OH (OD) a Model Compound)" C2H40Hi C2H40Di C2D40Hi C-H str (2989) CH, r (810)
C2D40D*
Frequencies Removed from Reagentb C-D str (2200) C-H str (2989) CD, r (586) CH, r (810)
C-D str (2200) CD2 r (586)
Frequencies Added to Activated Complexes( 0 - H str (3700) C- .H. e 0 asym str (rc) C. -Dee 0 asym str (rc) C. .Ha e 0 sym str (2200) C- -D. .O sym str (1 500) C=C- *(H--0-D) b (280) C=C* .(D*-0-H) b (270) Ha .O-D b (500) D. -0-H b (450) C. *H**O b (450) C. *Dee 0 b (350)
0-D str (2500) C. .D. -0 asym str (rc) C- .De sym str (1 500) C=C* .(De*O-D)b (270) Dm.0-D b (350) C.*D**Ob (350)
0-D str (2500)
0 - H str (3700)' C. .Ha -0 asym str (rc)c C..H..O sym str (2200)' C=C. *(H..O-H) b (280)d H**O-H b (600)' C**Ha-0 b (450)d
+ CzH4 (CzD4)Reactions (Ethylene Is Used as
a
0
astr is stretch, r is rock, asym str is asymmetric stretch, sym str is symmetric stretch, b is bend. *Frequencies of ethylene and ethylene-d4 were from ref 35. 'Reference 27. dReference 31; C..H-.O b reduced from 600 to 450 cm-I. 'Reference 26. /Adjustment was made to deuterium substitution'by analogy.
1.32 at 300 K, which are in reasonable agreement with the experimental result of 1.22. The ratio of A factors for ethylene/ eth~1ene-d~ are A(HH)/A(HD) = 1.01 and A(DH)/A(DD) = 1.03, which are also in good agreement with the experiment. Alternate reaction channels for the energy-rich adduct might also explain the results. Our discussion of possible channels will be based on the detailed discussion of Zellner et aL3 and Bartels et al.5 For example, possible channels might be C,H,-OHt
k4
C2H50
4
OCH;, CH,CHO
+ CH, +
(4)
H
The overall rate would then be
kHH/kDH and kHD/kDD (OH VS OD). The kinetic isotope effects here support the suggestion that the reaction is an H (or D) atom abstraction from ethylene. To better understand these results, calculations using conventional transition-state theory (TST) were carried out for the H atom abstraction reaction. TST has been shown to be useful for the quantitative interpretation of the temperature dependence of rate constants for bimolecular reactions.26 It has been used in simulation and extrapolation of the measured rate constants of O H with alkanes,27halo alkane^^^^^^ 0 atom reactions with alk a n e ~ , and ~ ~ ethylene.32 ,~~ The history and validity of this technique have been discussed recently by Cohen and Benson.z8 The formula we used for calculating the rate constants is
kl
k =
(111) k-l k,[MI + k4 Such a channel would give a primary isotope effect and the O D reaction would be slower because reaction 4 has both an 0-H break and a C-H formation. (See Figure 7 of ref 3 for details.) However, Zellner et aL3 have shown that reaction 4 is not important a t pressure above 40 mbar at room temperature. They have also shown that k-l > k4 at all temperatures. Also, one would expect the overall rate to increase with temperature, contrary to the experimental results, because there is a positive activation energy for (4).3 Thus, although reaction 4 could explain the isotope effects, other evidence shows that it is not important under o u r conditions. Tully et al. have reported OD formation in the reaction of OH with C3D623which was attributed to a rapid scrambling between H and D in the adduct. Similarly, Schmidt et al. have reported OD formation in the OH C2Dzreaction, but only in the presence of oxygen.25 They have given a detailed discussion of the mechanism.zs If intramolecular rearrangements were important in the rate-determining step for OH ethylene, they would lead to a primary isotope effect where the OD rate would be considerably slower than OH. To see if such a rearrangement is occurring, we did a similar experiment to that described in ref 23. The formation of O H was investigated in the reaction of OD + CzH4. The kinetics were measured in both the presence and the absence of C2H4 at temperatures of 343, 383, 653, and 878 K. A small decay signal (less than 10%) was observed in both cases, but the difference signal was zero within our accuracy (better than 1% of the total signal). The signals are presumably due to small amounts of H,O in the D 2 0in the cell and overlap of the spectrum. Thus, isotope scrambling does not explain the isotope effect seen in this temperature regime. High-Temperature Regime (723-1 173 K ) . The high-temperature data show a positive activation energy of approximately 4-5 kcal/mol. In addition, there are major kinetic isotope effects kHH/kHD and kDH/kDD (C2H4 VS C2D4) and minor ones for 1+
+
+
(25) Schmidt, V.;Zhu, G. Y . ;Becker, K. H.; Fink, E. H. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 321.
Q7') = 2.84 X 1 0 - 1 2 pexp(AS'*(T)/R)
exp(-AHo*(T)/R7') (IV)
where ail of the reactants go to products (transmission coefficient K = 1). k(7') is the rate constant at temperature T (cm3/(molecule s)), and AS' *(7') and AHo *(7') are the activation entropy and enthalpy, respectively. (The standard state is 1 atm.) The entropy was calculated by using the technique of BensonZ6where C2H4 was taken as a model compound. AH0*(300) was adjusted to fit the experimental data, and A H o * ( T ) was calculated from AHo*(300) by using ACpo*(T,,,)AT. The calculation for the activated complex was done for two different structures. The bond lengths of C-H, H - 0 , and 0-H were assumed to be 1.2, 1.3, and 1.0 A, respectively, for both structures. For the linear structure, the C-H-0 bond angle is 180'. For this structure there is only one internal rotation of the 0-H group about the axis of the C-H bond. In the nonlinear structure, the C-H-0 bond angle is 160'. For this structure, there will be two internal rotations (about the C-H and the H-0 bonds). For the OH + ethane reaction, Tully et al. calculated a linear transition state.33 A nonlinear transition state was used by Cohen et al. for O H + alkanesz7and haloalkanes.28 Mahmud et al. used both for 0 ethylene.32 The results from the linear transition state are in better agreement with our data and will only be discussed here. The vibrational frequencies that we used for the activated complexes are given in Table 11. Only two of the frequencies from ethylene34 needed to be changed. The C-H stretch (2989 cm-') becomes the reaction coordinate (rc), and the CH, rock (810
+
~~~
~~~~~
~~
~~~~~~
(26) Benson, S. W. Thermochemical Kinetics, 2nd ed.;Wiley: New York, 1976. (27) Cohen, N. In?. J . Chem. Kinet. 1982, 14, 1339. (28) Cohen, N.; Benson, S . W. J . Phys. Chem. 1987, 91, 162. (29) Cohen, N.; Benson, S. W. J . Phys. Chem. 1987, 91, 171. (30) Cohen, N.; Westberg, K. R. Int. J . Chem. Kinet. 1986, 18, 99. (31) Cohen, N.; Westberg, K. R. J . Phys. Chem. R e j Data 1983, 12, 531. (32) Mahmud, K. Marshall, P.; Fontijn, A. J . Phys. Chem. 1987, 91, 1568. (33) Tully, F. P.; Droege, A. T.; Koszykowski, M. L.; Melius, C . F. J . Phys. Chem. 1986, 90, 691. (34) Arnett, R. L.; Crawford, B. L., Jr. J . Chem. Phys. 1950, 18, 118.
3832 The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 TABLE I11 Calculated Thermodynamic Parameters of Activation at 300, 1200, and 2100 K for the Reactions of OH and OD with C2H4 and CzD, at High Temperature by TST"
OH+ C2D4
OD+
-33.16 0.40 2.92 5.20 -24.64 0.46 1.40 8.79 1.00 x 10-13
-33.20 0.50 3.55 4.51 -24.64 0.50 2.10 9.49 3.11 X
-33.31 -0.66 3.92 5.20 -24.84 1.09 2.10 9.55 2.80 X
10-14
10-14
T = 1200 K -39.94 -40.04 -1.24 -2.36 10.39 10.74 5.88 6.58 -24.91 -25.09 2.28 2.31 3.02 3.09 32.91 33.20 4.15 X 3.67 X 10-12 10-12
-40.08 -2.25 1 1.74 5.88 -24.71 2.31 3.99 33.64 3.05 X 10-12
-40.19 -3.42 12.23 6.58 -24.80 2.33 4.05 33.81 2.84 X 10-12
T = 2100 K -42.72 -42.82 -2.35 -3.47 13.86 14.22 6.44 7.13 -24.77 -24.94 2.20 2.21 5.05 5.13 57.06 57.50 1.30 X 1.44 X 10-11 10-11
-42.86 -3.36 15.20 6.44 -24.59 2.15 5.99 57.62 1.26 X
-42.97 -4.53 15.69 7.13 -24.67 2.16 6.05 57.87 1.19X
IO-"
lo-"
4.021
4.065
4.138
4.174
2.024
2.046
2.082
2.100
OH+
OD+ C2H4 CzH4 T = 300 K
So 'translation
ASo'totation 'vibration
rot
mo'int
So 'total
*c.oo"
AH , kcal/mol AGO',
kcal/mol
k(300), cm3/ (molecule s)
so 'translation AS'
'rotstion 'vibration
a0 l i n t rot ~o'tofal
*CPOO'* Ah' , kcal/mol AGO' kcal/mol
k( 1200), cm3/ (molecule s)
aso'translalion aso'lotatlo" aso'vibration rot
as0',t
ASo'total AC.DO0'* AH , kcal/mol AGO', kcal/mol
!+loo),
cm3/ (molecule s)
average ACuo'-
-33.05 1.52 2.71 4.51 -24.32 0.24 1.40 8.70 1.18 x 10-13
OH +
OD + OH + OD + C2H4 C2D4 C2D4 lo'*, cm3/ 3.48 f 0.19 2.55 f 0.13 1.72& 0.04 1.38 f 0.03 C2H4
A X
(molecule s) n B, cal/mol
2.01 f 0.01 2.04 f 0.01 2.11 & 0.00 2.13 f 0.00 585 f 1 1 591 f 10 1305 f 5 1312 f 4
A X IO'*, cma/
2.53 & 0.01 2.29f 0.00 2.69f 0.01 2.55 2 0.01
(molecule s) n E , cal/mol E,, kcal/mol
300 K 1200 K 2100 K
2.05 520 f 4
2.05 570 f 3
2.05 1390 f 3
2.05 1430 f 4
1.74 5.41 9.07
1.79 5.46 9.12
2.61 6.28 9.94
2.65 6.32 9.98
'The rate constants are k = A T @ / R T .The indicated error limits are one standard deviation of nonlinear least-squares fit. Activation energy E, = B nRT.
+
in Table 111. The calculated data were fit to the form k(7') = APe-E/RT. The results are given in Table IV both for n free and n fixed to 2.1. The kinetic isotope effects for the temperature range 300-2100 K are primary isotope effects:
kHH/kHD = 0.99eg121RT; k D n / k D D= 0.94e806/R7
("300-2100K)/R
"he
TABLE IV: Arrhenius Parameters for the Reaction of OH and OD with CzH4and CzD4 Obtained by Nonlinear Least-Squares Fit to TST Results"
C2D4
(300-2100 K) AC,.O*-
Liu et al.
units of entropy and heat capacity are in cal/mol.
cm-I) was changed to a C=C-(H-0-H) bend by analogy to the frequencies of C2H4 and C2H,F. The assignment of vibrational modes is similar to that of Cohen and Benson for OH/haloethane except that H-0-H frequencies were changed from 1000 to 600 cm-' as done by Mahmud et al. in the O/C2H4 reaction,32and the C-H-0 bend was adjusted from 600 to 450 cm-I. The vibrational constants for the deuterium substitution were done mainly by analogy with C2H4 and C2D4 and the expected effects of isotope substitution. Small adjustments were made to improve the agreement with the experimental data. The AHo*(300) values for C2H4 and C2D4 were 2.4 and 3.1 kcal/mol, respectively. The difference between the two enthalpies (0.7 kcal/mol) represents the difference between the barrier height for breaking the C-H and C-D bonds. It is less than the zeropoint energy difference, which is about 1.3 kcal/mol. This is reasonable since the breaking bonds in the transition state are not completely separated, and the remaining zero-point energy reduces the differences in the effective barrier height.22b Similar results were seen for the O H H2/D2 reaction.35 The calculated rate constants are plotted in Figures 4 and 5 for comparison with the experimental data and are in good agreement for all four isotopic variations. The theoretical results are lower at lower temperatures than the experimental results because both the experimental results include the effect of OH addition and the theoretical results do not include the effect of hydrogen tunneling. Results at 300, 1200, and 2100 K are given
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(35)Smith, I. W.M.; Zellner, R. J . Chem. Sot., Faraday Trans. 2 1974, 70, 1045.
secondary isotope effects:
k H H / k D= H 1.1 le4'IRT; k H D / k D D = 1.05e4'IRT If we compare the parameter n (not fixed) in Table IV with the value of averaged AC,*/R (300-2100 K) calculated by TST in Table 111, we find that they are very similar, which is as ex~ e c t e d . ~Benson ~ , ~ ~has indicated that for many radical-molecule reactions, particularly those of importance in flames, the effective value of n between 300 and 1500 K is in the range 2-2.5.36 Our calculated values of n are in good agreement with this. From the TST calculation we see that the primary isotope effects are due to the intermolecular critical energy effect and the secondary isotope effects can be interpreted as the statistical-weight effect. Taking O H / O D + C2H4 reaction as an ex= exp((ASO*HH - A S 0 I D H ) / R ) From . Table ample, kHH/kEDH I11 we can see that at 300 K a net difference of 0.32 eu of A(ASo*) will be obtained from the sum of contributions from external rotation (+1.12), internal rotation (-0.69), vibration (-0.21), and translation (+0.11). This would cause a 17% lower value for the O D reaction. From these results we can also calculate the magnitude of H abstraction at room temperature. The magnitude of that rate is approximately 0.3% of the overall rate constants and is consistent with previous ~ o r k . ~ , ~ , ~ ~ If the C-H-0 bend is 600 cm-] as in ref 32, the agreement with the experimental results is better; the calculated curve does not fall as far below the experimental results. However, since tunneling corrections are not used in this calculation, and since there is almost certainly a component of the O H addition reaction at the lower temperatures, the calculation using 450 cm-' may be a more meaningful one. The activation energy can be calculated from the TST results and will be considerably different for the two different frequencies. The activation energy at 300 K changes from 3.6 to 1.7 kcal/mol as the C-H-0 bend changes from 450 to 600 cm-I. (Reference 27 would suggest a value of 4-5 kcal/moI depending on the value assumed for the bond energy.) Although precise values cannot be determined from these calculations, the general trend of the calculations and the agreement between the calculations and experimental data are strong evidence that the hydrogen abstraction reaction is responsible for the behavior seen at high temperatures. (36)Benson, S.W.Acc. Chem. Res. 1986, 19, 3 3 5 .
3833
J . Phys. Chem. 1988, 92, 3833-3836
Conclusions clearly show that at least two different The reaction mechanisms are occurring in the OH ethylene reaction and depend on temperature. At temperatures below 560 K, the addition reaction is the dominant reaction. Above 560 K, the rate decreases since the reaction is no longer in the high-pressure limit. At temperatures above 720 K, the abstraction reaction becomes dominant. The kinetic isotope effect at the higher temperatures supports this mechanism. TST calculations show excellent agreement with the experimental data. These results clearly confirm the H atom abstraction mechanism at high temperatures. Many uncertainties still remain with these reactions. In particular, the pressure dependence of the addition reaction a t temperatures from 350 to 500 K would be of great interest. This is particularly true because of the controversy about the negative activation energy of the high-pressure data'*2*3,8J5 and the highpress~re.~'In addition, such studies could give further information
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about possible reaction channels for C2H4-OHt such as the Competition between iSOmeriZatiOrl and decomposition Of this Product.
Acknowledgment. We gratefully acknowledge helpful discussions with A. F. Wagner and J , v, Michael, The assistance of MS. Toni Engelkemeir in the ana,ysis of our samples was invaluable. None of these experiments could have been done without the able assistance of the Argonne operators, George Cox, Donald Ficht, and Ed Kemereit. This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Science, U.S.-DOE, under Contract W-3 1-109-ENG-38. Registry No. Hydroxyl, 3352-57-6; ethylene, 74-85-1; deuterium, 7782-39-0. (37) Baulch, D. L.; Cox, R. A.; Hampson, R. F., Jr.; Kerr, J. A,; Troe, J.; Watson, R. T. J . Phys. Chem. Ref Data 1984, 13, 1259.
Temperature Dependence of the Rate Constant for the HOP -t CH,02 Gas-Phase Reaction Philippe Dagaut, Timothy J. Wallington, and Michael J. Kurylo* Chemical Kinetics Division, Center for Chemical Physics, National Bureau of Standards, Gaithersburg, Maryland 20899 (Received: August 28, 1987)
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The temperature dependence of the reaction between hydroperoxy and methylperoxy radicals was measured in a flash photolysis ultraviolet absorption apparatus over the temperature range 228-380 K: H 0 2 + CH3O2 CH302H+ O2 ( 1 ) . The data, represented by the Arrhenius expression k , = (3.0 f 1.2) X IO-" exp[(720 lOO)/q cm3 molecule-' s-', are compared to earlier results and discussed in terms of the reaction mechanism. Due to overlapping absorptions of the two radicals and deviations of the complex reaction system from both pseudo-first-order and pseudo-second-order behavior, the rate constants were determined from a detailed modeling of the radical decay curves. A sensitivity analysis of the rate constant determination procedure to the assumed radical absorption cross sections and correlated changes in the rate constants for the H 0 2 and CH302self-reactions was performed, and the results are reported. The present results were also used to assess the effects of secondary chemistry in our measurements of the temperature dependence of the rate constant of the CH302+ CH302 reaction, and the revised Arrhenius parameters are presented.
*
Introduction Recently, we reported the results of a flash photolysis UV absorption spectroscopy study' of the room-temperature gas-phase reaction between H 0 2 and CH3O2 radicals
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H 0 2 + CH302
CH302H+ O2
(1)
These early experiments were designed to explore the effects of total pressure and water vapor concentration on the rate constant, thereby contributing to our understanding of the role of reaction 1 in both tropospheric and stratospheric methane oxidation. A value of k1(298 K) equal to (2.9 f 0.4) X 10-l2 cm3 molecule-' s-l was found, independent of total N 2 pressure (26-600 Torr) and of water vapor concentration (up to 11.6 Torr), in agreement with the most recent determination by McAdam et aL2 as revised by these same author^.^ Nevertheless, significant differences in the absorption cross sections for both H 0 2 and CH3O2 determined by both laboratories in concert with the kinetic measurements raise some questions about the possible fortuitous nature of this rate (1) Kurylo, M. J.; Dagaut, P.; Wallington, T. J.; Neuman, D. M. Chem. Phys. Lett. 1987, 139, 513. (2) McAdam, K.; Veyret, B.; Lesclaux, R. Chem. Phys. Lett. 1987, 133, 30. ~~
(3) Veyret, B., private communication, 1987.
constant agreement. In addition, there remains a factor of 2 difference between these latest k1(298 K) determinations and the earlier result of Cox and TyndalL4 In an effort to gain further kinetic insight, we have extended our investigation of reaction 1 to temperatures between 228 and 380 K. The rate constant determinations were accompanied by detailed measurements over the complete temperature range aimed at detecting the presence of or a change in any product absorption which could be assigned to a shift in reaction mechanism with temperature. As in our room-temperature investigation,] the rate constants were determined from a mixed-order modeling analysis of the radical absorption decay curves. The sensitivity of this determination to changes in the radical absorption cross sections and to the correlated changes in the self-reaction rate constants for both radicals was also studied. Experimental Section The apparatus used for this investigation has been described in detail in earlier publication^.^^^ H 0 2 and CH302radicals were (4) (a) Cox, R. A.; Tyndall, G. S. Chem. Phys. Lett. 1979, 65, 357. (b) Cox, R. A.; Tyndall, G. S. J . Chem. SOC.,Faraday Trans. 2 1980, 76, 153. (5) Kurylo, M. J.; Ouellette, P. A,; Laufer, A. H. J . Phys. Chem. 1986, 90,437.
This article not subject to U S . Copyright. Published 1988 by the American Chemical Society
