S. W. MAYERAND L. SCHIELER
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Activation Energies and Rate Constants Computed for Reactions
of Oxygen with Hydrocarbons by S. W. Mayer and L. Schieler Laboratories Division, Aerospace Corporation, El Segundo, California 90646 (Received February 6 , 1968)
A study has been made of a procedure for computationally estimating activation energies and rate constants of bimolecular transfer reactions for atomic or molecular oxygen with hydrocarbons, hydrogen, and water in the gas phase. The procedure is modified from the Johnston-Parr bond-energy method, previously applied to abstraction by radicals in the doublet electronic state. One modification is based on the doubled spin repulsion that could arise in the activated complex because of the two parallel-spin electrons characteristic of triplet states such as those for atomic or molecular oxygen. The modified procedure based on doubled repulsion provides better agreement between computed and experimental activation energies or rate constants for abstraction by triplet 0 or 0 2 . A modification in which the alkyl radicals of the hydrocarbons are treated as point masses is also examined briefly. Computations of activation energies and rate constants are made for abstractions by the singlet excited states: O(lD,), O(IS), 0 2 ( l A g ) , and OZ(~Z,+).
A chain-propagation step in the combustion process for a hydrocarbon is the abstraction by atomic oxygen of a hydrogen atom from the hydrocarbon. This reaction is written in the following equation with the ground electronic states indicated
+
+
~ ~ ( 1 2 o) ( 3 ~=) ~ ( 2 2 ) OH(~II)
(1) During the past few years, rate measurements by improved techniques1-* have provided rather dependable activation-energy (Eo)and rate-constant ( k ) data for this important abstraction reaction in several cases where R was an alkyl, hydroxyl, or hydrogen radical. An objective of the present study was to compare these experimental values for Eo and k with the values computed by a modification of the bond-energy-bond-order m e t h ~ d ~for - ~calculating Eo and k. This method is based on an activated-complex treatment using several trial postulates interrelating dissociation energy, bond order, and bond length. The method does not use adjustable parameters. Computations of kinetic data by the modified method are also reported herein for the abstraction of hydrogen by ground-state or excited molecular oxygen and by excited atomic oxygen, in addition to the abstraction by ground-state atomic oxygen shown in eq 1. The generalized hydrogen atom abstraction reaction can be written
+B = R
*
n1
H*
n2
- B = R + HB
(2)
where nl and n2 are the bond Orders, in the transition state, of the breaking bond R. . .H and the forming bond H. . .B, respectively. This study is concerned with cases in which the abstracting species is an Oxygen atom or molecule. The potential energy of forming the The Journal of Physical Chemistry
9
V
=
+
DRH- DRHnlP - D H B ~V ,~ ~ ( 3 )
where D is the bond dissociation energy, and p and q are the slopes of the log (dissociation energy) us. log (bond order) lines. Equation 3 produced rather good agreement (e.g., within 2 kcal/mol) between computed and experimental Eo when it was tested for reactions where the radical B had only one unpaired electr0n.~16I n these cases B consisted of only univalent species such as atomic hydrogen, atomic halogens, CFa, CHS, or C2H6radicals. The origin of the parallel spin repulsion in the transition state for such cases can be illustrated by the following representation of the reaction, where the arrows indicate the direction of electron spin
RTlH
Modified Computation Procedure
RH
transition state is postulated on a trial basis to be equal to the energy required to break the bond RH to R * . * H of bond order n1 in the transition state, less the energy supplied by the forming of H* .B to bond order n2,plus a repulsion energy V , arising from the parallel electron spins on R and B.4 By using the trial postulate4~6that the bond energy at zero bond order corresponds to the binding energy of a noble gas diatomic pair, the potential energy of forming the transition state can be expressed as
+ TB = R T * * * . / H . * - T=BR t + HlTB
(1) A. A. Westenberg and N. de Haas, J. Chem. Phys., 46, 490 (1967). (2) A. A. Westenberg and N. de Haas, ibid., 47, 1393 (1967). (3) W. E. Wilson and A. A. Westenberg, Eleventh Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, Pa., 1967, p 1143. (4) H. S. Johnston and C. Parr, J. Amer. Chem. Soc., 85, 2644 (1963). (6) H. S. Johnston, “Gas Phase Reaction Rate Theory,” The Ronald Press Co., New York, N. Y., 1966. (6) S. W. Mayer, 14. Sohieler, and H. 8. Johnston, J. Chem. Phys., 45,386 (1966).
CONSTANTS COMPUTED FOR REACTIONS OF OXYGENWITH HYDROCARBONS I n order to estimate the spin repulsion between R and B in the transition state, it was assumed on a trial basis that V , is similar to that of the repulsive, triplet state of H2(3Zu+)and that V , can be expressed as an antiMorse function such as the one used by Sato for triplet
Hp4
/3 where
Table I : Properties” of the Bond Involving the Abstracted Hydrogen Atom
we
= (1.2177 X
107)~,(p/De)1’a cm-I
(4)
is the vibrational wave number (in cm-l);
De is the dissociation energy, in kcal/mol (to the minimum of the potential energy curve) ; and duced mass, in atomic weight units.
p
is the re-
Results and Discussion In Table 11, computed activation energies and rate constants are summarized for the abstraction reaction of ground state O(3P) with hydrogen, water, methane, ethane, n-propane, n-butane, and acetaldehyde in the gas phase. Activation energies computed by the modified procedure are presented in Table I1 for comparison with the experimental values. Also shown in Table I1 are the activation energies calculated by the
Bonddissociation energy, kcal/mol
Vibrational wave number, om -1
109.5 123.4 106.7 51.0
4405
*
Compound
When B has more than one unpaired electron (e.g., if B is triplet oxygen or quartet atomic nitrogen), the problem arises of choosing between using the JohnstonParr method4 of computing V , or modifying it because of increased repulsion between R and B due to the two or three parallel-spin electrons on B. I n the present study, the modification was adopted of doubling V , if B had two parallel-spin electrons. This modification was applied to abstraction by O(3P) or 0 2 ( 3 Z g - ) ; it restores the factor in the Sat0 type of expression to 1.0.4 Johnston (ref 5, p 221) has pointed out that experimental preexponential factors in abstraction reactions do not usually decrease greatly as the number of atoms in the radical R increases. This relative constancy of the preexponential factor can be attributed to the probability that most of the force constants for polyatomic R are not extensively altered in the transition state. The estimation of bending force constants in the transition state is not dependable when R or B are not monatomic.6 For these reasons, in this study the modification of treating R and B simply as if they were monatomic mass points was tested as a convenient method of estimating the preexponential factors for comparison with experiment. This modification cannot be completely correct, but it is believed that in many reactions the net correction arising from changes in bending force constants of R in the transition state is small. For those reactions having exceptionally low steric factors,5 this modification should be considered particularly undependable. Molecular parameters used in the computations are summarized in Table I. The Morse parameter /3 used4 for computing V , can be calculated from the relationship
2629
105.1 102
104 105 93
3760 3735 3600 3000 3000 3000 3000 3000
Bond length, X 10-8 om
0.742 0.96 0.971 0.96 1.09 1.09 1.09 1.09 1.09
‘ Data from D. R. Stull, Ed., “JANAF Thermochemical Tablea and Supplements,” Dow Chemical Co., Thermal Research Laboratory, Midland, Mich., 1967; C. T. Mortimer, “Reaction Heats and Bond Strengths,” Pergamon Press Inc., New York, N. Y., 1962. This dissociation energy, De, includes the zeropoint vibrational energy of the bond. For propane and butane, De is weighted for the presence of secondary hydrogen bonds. The De of acetaldehyde applies to the CH bond of the aldehyde group.
’
unmodified procedure in which the spin repulsion between R and O(3P) is assumed equal to that arising from only a single unpaired electron on the abstracting oxygen atom. Examination of the results for computed Eoin the table shows that the modified procedure gave better agreement with experiment for each reaction. In the abstraction from ethane, for example, Eo computed by the modified procedure was 0.7 kcal/ mol higher than the experimental value of 6.8 kcal/mol, whereas the unmodified procedure produced an Eowhich was 3.3 kcal/mol lower than the experimental value. For all seven reactions, the mean value by which Eo computed via the modified method differed from experimental Eo was 0.8 kcal/mol. The unmodified method produced Eoresults which were lower than experimental Eoby a mean of 2.6 kcal/mol. This difference of 2 or 3 kcal/mol between computing procedures for Eo is reflected in the rate constant results at 30OoK, since the exponential factor is sensitive to such differences at 300°K in contrast with the decreased sensitivity a t high temperatures.s In the aforementioned abstraction from ethane, the rate constant computed by the modified procedure is within a factor of 2 of the experimental value. The rate constant calculated on the basis of single repulsion, however, is a factor of 100 larger than that of the experimental IC a t 300°K. The tunneling effect6 in hydrogen atom abstractions, moreover, would tend to raise the computed rate constants if a correction for tunneling were applied. No tunneling correction was used for the computations summarized in Table 11, since there is considerable disagreement about the method of making this correction.2ss If the method6 based on the unsymmetrical volume 73, Number 7 July 1968
S. W. MAYERAND L. SCHIELER
2630
Table 11: Activation Energies and Rate Constants Computed by Modified Procedure and by Single Repulsion
Reaction
+ + + + + + + + + + + + +
Hz 0 = H OH HOH 0 = 2OH CH4 0 = CHa OH CzHa 0 = CzHs OH n-CaHs 0 = CaHT OH n-CrHio 0 = C4H9 OH CHaCHO 0 = CHaCO OH
Activation energy, -kcal/molExptl Computed Single"
10.2* 19.5' 8.7b 6.1b 5.7d 4.2' 2.3d
11.2 18.9 8.8 6.8 6.9 4.5 3.0
Log k a t 300°K,
-cc/mol Exptl
6.1 17.6 4.6 2.8 3.8 2.3 1.1
Computed
Single"
-cc/mol Exptl
5.6 0.0 7.3 8.8 8.7 10.6 10.8
9.5 1.1 10.3 11.7 11.0 12.2 12.4
11.3 10.2 11.5 12.0 12.7 12.6 12.5
Bet-
6.0 0.3 7.5 8.9 9.7 10.5 11.3
Log k et 100O0K, secComputed Single"
11.5 10.0 12.0 12.7 12.7 13.3 12.5
12.8 10.6 13.0 13.8 13.5 14.1 13.4
'
a V , not doubled; spin repulsion assumed from only a single unpaired electron on O(aP). Reference 1. R. S. Brokaw, ref. 3, p 1071. K. Schofield, Planetary Space Sci., 15, 643 (1967). L. Elias and H. I. Schiff, Can. J. Chem., 38, 1657 (1960).
Eckart barrier is used for estimating a tunneling correction in the ethane abstraction, a mean tunneling correction factor of about 2 would be applied to the computed k's at 300°K listed in Table 11. This tunneling factor would make k computed by the modified procedure about 60% larger than the experimental k. The k computed by the single-repulsion assumption would disagree with the experimental k a t 300°K by a factor of 200 if this tunneling factor were applied. The mean deviation between the experimental log k and the log k computed by the modified procedure is 0.37 at 300°K. Only in the case of the abstraction from propane is this deviation in log k greater than 0.5. If the propane case is omitted, the average excess of the experimental log k over this computed log k is only 0.23, which corresponds to deviation by a factor of 1.7. A small tunneling correction could improve the agreement further. Inasmuch as these rate constants were computed with the use of the modification that neglects any changes in the force constants for the radical R when it is in the transition state, the agreement with experimental k suggests that in some abstraction reactions it is feasible to treat R as a point mass. The case of propane may represent an example where R should not be so treated. Alternatively, in the case of propane the method may give relatively poor agreement because other trial postulates fail or, less probably, because the experimental results may not be accurate. I n view of the unestablished dependability of the trial postulates, it clearly is highly probable that they would not be obeyed by some reactions. Rather, it is surprising that these very simple postulates can provide the good agreement seen in Table I1 and in previous studies. 4,6--8 The computing procedure that assumes single repulsion produces rate constants at 300°K which exceed the observed rate constants by a mean factor of 100. This large disagreement is attributable mainly to the low Eocomputed when single repulsion is assumed for O(3P), since the trial postulate that R can be treated as a point mass was used throughout this study. At T h e Journal of Physical Chemistry
1000"K, where the tunneling effect is generally negligiblels the disagreement between the single repulsion computed and the experimental k had dropped to a factor of 15 because the deviation in Eo has a smaller effect a t 1000°K than a t 300°K. The modified procedure (ie,, doubled V , because of triplet oxygen) provided a mean deviation a t 1000°K between the experimental and the computed log k of 0.33, which corresponds to a mean factor of 2.1. The propane reaction a t 1000°K did not exhibit the marked disagreement noted at 3OO0K, apparently because of the aforementioned effect of higher temperatures in diminishing the importance of Eo. To supplement the computations made for abstraction by O(aP), a set of calculations for abstraction by the singlet excited electronic states O(lD) and O(%)
Table 111: Activation Energies and Rate Constants" Computed for Reactions with Ground-State and Excited Molecular Oxygen Oz('2g -)
0d1Ag)
Reactant, Hydrogen 58 35 4 x 10-80 1 x 10-14 3 3 x 104
Eo,kcal/mol k (at 300'K) k (at 1000'K)
k (at 300'K) k (at 1000'K)
Reactant, Water 72 49 4 x 5 x 10-42 3X 60
Eo,kcal/mol
57
Eo,kcal/mol
k (at 300'K) k (at 1000'K) a
RH
Reactant, Methane 34
6 X
6
10-26
4 X 6 X lo4
Oa(1Zg")
20 1 x 10-6 1 x 106
34 3 1
x x
19 2 5
x 10-0 x 108
10-14 106
The rate constant k , in units of cc/mol sec, for the reaction 0 2 = R HOz.
+
+
(7) S. W.Mayer, J. Phys. Chenz., 71,4169 (1967). (8) 9. W. M ayer, L. Schieler, and H. S. Johnson, ref 3, p 837.
REACTION OF RECOILTRITIUM WITH METHYLS~LANES was made for each reactant listed in Table 11. Since singlet rather than triplet atomic oxygen was the abstracting species, Vr was not doubled in this set of calculations. The products and the RH reactant were again taken to be in their ground states. I n each case, it was found that the computed activation energy did not exceed 1kcal/mol. This result was not unexpected, since the energetic, excited states can usually supply the energy required by activation energies such as those shown in Table 11. The computation also showed that the bending force constant in the transition state was erg/rad2 throughout this series of less than 1.2 X abstractions by O(lD) or O(lS). Therefore, as previously discussed,6 these abstractions by singlet atomic oxygen should be treated by a collision method rather than a transition-state method. This result agrees with the viewpoint that abstraction by O(lD) or" O(lS) is very rapid.g Finally, a set of computations was made for the 0 2 (IAg), or abstraction of hydrogen atoms by 02(321g-), O2 (I&+) to form ground state HOz
2631
RH
+ 02
7
R
+ HOz
(5)
where R H was H B ,HzO,or CH,. (In view of the triplet Vr was doubled as in nature of ground state 02(32g-), the modified computing procedure.) For every reaction in this series of computations, it was found that the activation energy was within 1 kcal/mol of the endothermicity of the reaction. Computed rate constants (and activation energies) for H atom abstraction by molecular oxygen are presented in Table 111. It is evident that the rate constants in Table I11 are much lower than the rate constants for abstraction by atomic oxygen (Table 11). Consequently, these computations support the view that combustion initiates via reaction with atomic oxygen much more readily than by reaction with molecular oxygen.
Acknowledgment. The authors are grateful for the valuable correspondence with Professor H. S. Johnston of the University of California a t Berkeley, Berkeley, California. (9) W. B. DeMore, J . Chem. Phys., 47, 2777 (1967).
Reaction of Recoil Tritium with Methylsilanes
by Judith Witkinl and Richard Wolfgang Department of Chemistry, Yale University, New Haven, Connecticut 06611 (Received February 7, 1968)
The reactions of hot hydrogen atoms, in the form of tritium recoiling from nuclear reactions, with methylsilanes have been studied. Reaction types found are similar to those with homologous hydrocarbons and are in accord with the previously postulated reaction models. A greater reactivity of silanes, especially for abstraction processes, appears related to the weakness of the Si-H bond. Yield patterns of reactions involving rupture of C-Si bonds correlate with known properties of silicon bonds and inertial restrictions on relaxation motions.
Introduction The discovery that tritium recoiling from nuclear processes reacts as hot atoms2 has led to an intensive study of this species. Nearly all work, from the initial characterization of the basic abstraction and displacement interactions2 to the identification of the factors controlling these reactions, has been done using hydrocarbon The resultant body of information provides a prototype example of the nature of hot-atom chemistry. The present work was undertaken to determine whether the generalizations drawn from hydrocarbons are applicable to other systems. Silanes were chosen because the variety of possible products is sufficiently large that it should be possible to identify any significant changes in mechanism. Furthermore, while
silanes have obvious similarities to hydrocarbons, there are also some significant and interesting differences. Prominent among these is the greater size of the silicon atom, the relative weakness of the bonds it forms, and the possible availability of d orbitals which tends to stabilize distortion of its compounds from tetrahedral (1) Work performed in partial satisfaction of the requirements for the M.S. degree. (2) M. El-Sayed and R. Wolfgang, J . Amer. Chem. Soc., 79, 3286 (1957). (3) D. Urch and R. Wolfgang, ibid., 83, 2982 (1961). (4) W. Breckenridge, J. Root, and F. 51. Rowland, J . Chem. Phys., 39, 2374 (1963); 43, 3695 (1965). (5) R. Wolfgang, Progr. Reaction Kinetics, 3, 99 (1965). (6) R. Wolfgang, Ann. Rev. Phys. Chem., 16, 15 (1965).
Volume 73, Number 7 July 1968
