J . Phys. Chem. 1988, 92, 2196-2201
2196
describe homogeneous chemical kinetic rate processes.
mixing intensity on the final product yields. They have shown that the final product yield in a series-parallel reaction, Le., a reaction that has consecutive and/or competing reactions, is sensitive to flow velocity and the geometry of mixing. This is not unexpected in light of the difficulty in scaling a reaction up from the laboratory to the industry processing level where the mixing conditions may vary considerably. In summary, assumptions that mixing is instantaneous and complete within a miniscule volume in stopped-flow instruments have led to a disregard for experimental determinations of the regime of the reacting system as was suggested for steady-flow experiments by Hartridge and Roughton in 1923. The invariance of the kinetic rate to changes in the flow velocity in steady- and stopped-flow experiments indicates that the determined kinetic rate was for a homogeneous system. The inescapable conclusion that must be faced is that the interpretation of kinetic rate data obtained from stopped-, accelerated-, or pulsed-flow experiments where the homogeneity of the reaction regime has not been experimentally described is of questionable value in its ability to
Acknowledgment. We acknowledge the discussions and suggestions received from our colleagues in the field of chemical engineering, in particular Herbert L. Toor and Robert S. Brcdkey. A very special acknowledgment is given to the late Stanley Corrsin, whose guidance in the field of turbulence was indispensable. In the field of chemical spectroscopy, we are grateful to the Tracor Northern Co. for the loan of their UV-vis rapid scanning instrument and to members of their staff, especially Robert Compton, for their continuing support. Also we thank the Nicolet Instrument Co. for making FTIR rapid scanning instrument time available and especially their employees, Warren Vidrine and Stewart Yaniger, for their assistance. We acknowledge Helmut Beinert and George Blondin for their interest, encouragement, and criticism of the manuscript. Shirley Hickman and Kim Gaffney are thanked for their assistance in preparing the final manuscript and figures, respectively. This work was supported by Update Instrument, Inc.
Kinetics of Hydrogen and Hydroxyl Radical Attack on Phenol at High Temperatures Y. Z. He, W. G. Mallard, and W. Tsang* Chemical Kinetics Division and Center for Fire Research, National Bureau of Standards, Gaithersburg. Maryland 20899 (Received: May 22, 1987; In Final Form: September 28, 1987)
The kinetics of hydrogen and hydroxyl radical attack on phenol have been studied in single-pulse shock tube experiments. The hydrogen atoms are formed through the unimolecular decomposition of hexamethylethane (C,H,,) to two tert-butyl radicals which rapidly decompose to hydrogen atoms and isobutene. The hydrogen atoms react with phenol via abstraction of the phenolic hydrogen and displacement of OH. From the yields of isobutene and benzene we derive the ratio of the rate for these two processes over the temperature range 1000-1 150 K and pressures between 2.5 and 5 atm. In the presence of added methane, benzene yield is depressed due to the reaction of hydrogen with methane. Since the rate of H atom reaction with methane is known, the rate constant ratio can be used to derive absolute rate constants. Using a rate expression for k(H + CH4 CH, + H2) = 2.4 X 10" exp(-7000/7) L/(mol.s), we find k(H + C6X50H H, + C6H50)= 1.15 X 10" exp(-6240/T) L/(mol.s) and k(H + C6H50H C6H6 + OH) = 2.21 X 10'oexp(-3990/T) L/(moh). The reaction of hydrogen atoms and phenoxy radicals represents an added complication in these studies. We find k(H + C6H50 C&@H) = 2.0 X 10" L/(mol.s). The substitution of large quantities of carbon monoxide in place of methane leads to increased yields of benzene due to the conversion of the displaced hydroxide radicals to hydrogen atoms and their reaction with phenol. On the basis of k(OH + CO C 0 2 + H) = 7 X IO' exp(0.000927') L/(mol.s), we find k(OH + C6H@H C6H50+ H,O) = 6 X lo9 L/(mol.s) at 1032 K. From the equilibrium constant the rate expression for the displacement of a hydrogen atom by hydroxyl radical is k(OH + C6H6 H 4- C6H50H)= 13.4 X lo9 exp(-5330/T) L/(mobs). Comparisons with OH disappearance rates in high-temperature benzene systems are in agreement with the conclusion that the primary process is the abstraction of a ring hydrogen.
-
-
-
-
-
Introduction The importance of phenol as an intermediate in the oxidative degradation of aromatic structures is ~ell-established;'-~ however, there are very few studies on its reactions with the reactive radicals found in high-temperature combustion. In this paper we report on our determination of the rates and mechanisms of hydrogen atom attack in a single-pulse shock tube at temperatures of 1000-1 150 K. In addition, the rate constants for H combination with phenoxy and O H attack on phenol are determined. This work is a continuation of our earlier study of the hydrogen-induced decomposition of t01uene.~ There, hydrogen atoms (1) Hsu, D. S . Y.; Lin, C. Y.;Lin, M . C. In Twentieth Symposium (Internafional)on Combusfion;The Combustion Institute: Pittsburgh, 1984; p 623. (2) Bittner, J. D.; Howard, J. B. In Eighteenth Symposium (Inrernarionn on Combustion; The Combustion Institute: Pittsburgh, 1980; p 1105. (3) Venkat, C.; Brenzinsky, K.; Glassman, I. In Nineteenth Symposium (Internafional)on Combustion;The Combustion Institute: Pittsburgh, 1982;
p 143.
-
were generated in large excesses of toluene through the decomposition of hexamethylethane to two tert-butyl radicals and the subsequent rapid decomposition of the tert-butyl radicals to hydrogen atom and isobutene. The contribution from the displacement reaction was determined from the measured benzene. The isobutene that is detected (for sufficiently small concentrations of hexamethylethane) is a measure of the total hydrogen atoms released into the system. The difference between the isobutene and benzene concentrations reflects the hydrogen atoms that have been lost through abstraction of the benzylic hydrogen. Having determined the relative rates of displacement and abstraction from the isobutene to benzene ratio, the rate constants are placed on an absolute basis by comparison to the H CH4 reaction. This is done by adding a sufficient excess of CH4, so that benzene yields decreased as a result of the competition between the hydrogen attack on CH4 and toluene. Since the rate constant for the process H + CH4 is well-e~tablished,4.~ the decrease in benzene yields can
+
(4) Robaugh, D.; Tsang, W. J . Phys. Chem. 1986, 90,4159
This article not subject to U S . Copyright. Published 1988 by the American Chemical Society
Hydrogen and Hydroxyl Radical Attack on Phenol then be used to convert the ratio of rate constants to an absolute basis. If one substitutes phenol for toluene, it is possible to carry out the same experiment and obtain similar information regarding H atom attack on phenol. In addition, since OH from the displacement reaction is more reactive than CH, from toluene, it has been possible to deduce the rate of O H attack on phenol. This was accomplished by examining the increase in benzene yield when a large excess of C O was added to the reaction mixture. C O reacted with OH, in competition with phenol, and produced H atoms. These atoms could undergo subsequent reactions with phenol, producing more benzene. Here as for methane the use of accurate rate data for the reaction OH + COS sets our rate constants on an absolute basis. Finally, it also proved possible to determine the rate constant for H combination with phenoxy. The OH radical reacts with benzene at low temperatures. At about 330 K the reaction is reversed, and in experiments where OH decay is directly monitored this is manifested by a drastic decrease in the apparent rate constant for OH disappearance with temperat~re.~?'As the temperature is further increased, the rate constant begins a monotonic increase which is usually interpreted in terms of the abstraction of the ring hydrogen.* These results suggest that at low temperatures O H does not displace hydrogen atoms from the aromatic ring but adds to form a stable adduct. At high temperature this adduct is no longer stable but decomposes to yield O H and benzene. The same adduct would be formed by the addition of hydrogen atom at the site of the OH in phenol, and its decomposition will lead to displacement of the OH and the production of benzene. In this study we measure the rate of displacement of O H by H and calculate the rate constant of the reverse reaction through detailed balancing. The main problem in the study of the reactivity of phenol, or for that of any organic molecule of moderate complexity, is the possibility of multiple reaction channels. The powerful modern methods which follow the disappearance of small reactive radicals such as O H or H can only measure a total rate constant for reactant disappearance. Measuring the formation of a product permits us to directly determine the rate constant for at least one of the channels. Since we also monitor the number of reactive species released into the system, we are able to infer some details of the other reactive channels. The specific reaction pathways of concern in the present study are H
OH
+ C~HSOH
+
C 6 H 5 0+ Hz
-
+ C6H50H C 6 H 5 0+ HzO OH + C & 5 C6H5OH + H
k, koH
+
The rate constants for the first three reactions are determined in this work. The last reaction is the reverse of the second and as noted earlier can be calculated. In addition, a number of other processes can affect the interpretation of our measurements. The rate constants for these processes, in particular H
-
+ C6H50
C6H5OH
are obtained by computer modeling. The modeling also leads to a better set of rate parameters for the other reactions. The rate constant for abstraction must be related in some manner to the bond strength of the 0-H bond. The phenoxy-H bond is weakened by resonance relative to the OH bond in water or methanol. McMillen and Golden9 assign a bond dissociation energy of 362 kJ/mol compared to 437 kJ/mol for the O H of aliphatic alcohols. However, for toluene4 the full extent of the decrease in the C-H bond strength due to benzyl resonance energy ( 5 ) Tsang, W.; Hampson, R. F. J . Phys. Chem. ReJ Dura 1986, 15, 1087. (6) Tully, F. P.; Ravishankara, A. R.; Thompson, R. L.; Nicovich, J. M.; Shah, R. H.; Kreutter, N. M.; Wine, P. H. J. Phys. Chem. 1981, 85, 2262. (7) Perry, R. L.; Atkinson, R.; Pitts, J. N. J . Phys. Chem. 1977, 81, 296. (8) Madronich, S.; Felder, W. J . Phys. Chem. 1985, 89, 3556. (9) McMillen, D. F.; Golden, D. M . Annu. Rev. Phys. Chem. 1982, 33, 493.
7'he Journal of Physical Chemistry, Vol. 92, No. 8, 1988 2197 TABLE I: Experimental Mixtures
mixture
HME,
phenol,
CH,,
CO,
DDm
%
%
%
102 163 50 22 99 97 97 64
2.0 0.97 3.1 2.6 2.3 1.7 1.7
1.8
4.6 9.4 9.4 29.5
is not reflected in a corresponding decrease in the activation energy for the abstraction process relative to that of the alkanes. Data on the rates of attack of reactive radicals on an -0-H grouping are sparse. The only gas-phase information that we have been able to find are for reactions with hydrogen peroxide5 and water. The latter is not satisfactory for comparative purposes due to the strength of the 0-H bond which leads to an endothermic process. The corresponding reaction in phenol is strongly exothermic. The resonance stabilization in the phenoxy radical brings the bond energy of the phenoxy 0-H bond to about the same value as that in H202.9 However, there are uncertainties with respect to the mechanism of hydrogen atom attack on the latter. In nonaqueous solution tert-butoxyl radicals abstract the hydrogen from phenol with a very large rate constant.1°
Experimental Section The experimental procedure is similar to that used in our earlier study with respect to t ~ l u e n e .Table ~ I contains a summary of the gas mixtures that were studied. The experimental strategy involves carrying out experiments in a variety of reactant concentrations and thus determining the conditions where clear-cut mechanistic interpretations are possible. We then use experiments under these conditions to determine rate constants. Gas chromatography with a silicone oil column and flame ionization detection is used for analysis. Hexamethylethane was from Wiley 0rganics;l' phenol was from both Mallinckrodt and Aldrich, and no difference was observed in results for the two suppliers. Gas chromatography did not reveal the presence of significant quantities of impurities. Except for vigorous degassing, all the chemicals were used without purification. Argon was Matheson UHP grade and methane Matheson Research grade. The use of the shock tube in the present investigation assures truly thermal reactions, the total absence of surface effects, and short reaction times. With the sensitivity of gas chromatographic detection, which permits studies at high dilutions, reaction mechanisms for complex molecular processes are simplified and quantitative studies are possible.12 The main products that are detectable with flame ionization from the decomposition of hexamethylethane in phenol are isobutene and benzene. This is in contrast to the situation with toluene where much methane and ethane are formed from the methyl radical displaced by the hydrogen atom. The hydroxyl radical that is displaced in the present study cannot lead to any hydrocarbon product. At the highest temperatures we detect C3 products such as allene and, interestingly, increasing concentrations of cyclopentadiene. The former is presumably from the decomposition of isobutene. The latter is due to the decomposition of phenoxy radical to form cyclopentadienyl and CO and the subsequent abstraction of a hydrogen to form cyclopentadiene. All of the experiments used in the analysis of the rate parameters are (10) Denisov, E. T. Liquid Phase Reaction Rate Constants; IFI/Plenum: New York, 1974. (1 1) Certain commercial materials and equipment are identified in this paper in order to specify adequately the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or equipment is the best available for the purpose. (12) Tsang, W. In Shock Waves in Chemistry; Lifshitz, A., Ed.; Marcel Dekker: New York, 1981; p 60. (13) Tsang, W. J . A m . Chem. Soc. 1985, 107, 2812. (14) Baker, R. R.; Baldwin, R. R.; Walker, R. W. Trans. Faraday SOC. 1970, 66, 2812.
2198
The Journal of Physical Chemistry, Vol. 92, No. 8, 1988
He et al.
TABLE II: Rate Constants Used in Model reactions
n
HME = 2(fert-butyl) tert-butyl = H + isobutene H + PhOH = PhH + OH H + PhOH = PhO + HZ OH + PhOH = PhO + HzO H + HME = HME* + H2 O H + H M E = HME* + H2O HME* = tert-butyl + isobutene PhO + H = PhOH H + CH, = Hz + CH3 C2H6 = CH3 + CH3 CO + OH = C02 + H
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -1.8 1.o
a t a temperature substantially lower than required for the formation of the secondary products in order to avoid these complications.
Data Analysis and Results All of the rate constants that we will report are based on internal standards. This eliminates the main source of error in determining rate expressions from single-pulse shock tube studies, the uncertainty in the time-temperature history of the experiment. Our internal standard for determining the relative rate constants for abstraction and displacement is the decomposition of hexamethylethane (HME, C8H18). The rate expression is’, k(CgH18
-
2C4H9’) = 3
X
eXp(-34500/T)/S
= kdec
As H M E concentration is increased, other paths for its destruction may become important. These reactions and their rate constants have been incorporated into a simple kinetic model in order to estimate their effect on the estimated temperature and to correct the calculation of the rate constants for small secondary effects. The reactions and the rate parameters used are shown in Table 11. These calculations have shown that the secondary processes account for such a small fraction of the H M E destruction that the maximum errors in the estimated temperature from these sources is less than 5 K. In our earlier paper on hydrogen atom attack on toluene, we expressed our results in terms of the rate constant for the decomposition of hexamethylethane. This is an explicit demonstration of the use of the internal standard in our measurements. In the present case, due to the subsequent modeling, we express all our results in the Arrhenius form. This simply involves converting our results from a function of kdcc to a function of temperature by using the rate expression given above. For hydrogen atom attack on phenol, the rate constants are calibrated against the rate expression for hydrogen atom attack on methane4s5 k ( H + CH4 CH, + H,) = 2.4 X 10” exp(-7000/7‘) L/(mol.s) = kM
-
while for OH attack the rate expression used as the standardS is k(OH CO C02 H ) = 7 x lo7 exp(0.00092T) L/(mobs)
+
+
+
The absolute uncertainties in all the rate expressions that are derived from these rate expression are at least as great as those of the reference reaction rate constants which are in the range of factors of 1.2-1.5. The processes of interest have relatively low activation energies when compared to the unimolecular decompositions that we have previously studied using the comparative rate technique. This technique works best when the activation energies of the reference reaction and the reaction studied are nearly the same so that the inherent uncertainty in the time-temperature history is modeled by the reference reaction. The large differences between the activation energiek of these reactions and the reference appear to violate these guidelines. However, the rate-determining step for quenching the hydrogen atom attack on phenol is the generation of the hydrogen atoms. The hydrogen atom source,
A / (L/ (mo1.s)) 3.00 X 8.00 x 2.21 x 1.15 X 6.00 x 4.00 X 1.62 x 8.00 x 2.50 X 2.40 X 3.22 X 1.76 x
10l6 1013 10’0 10” 109 10” 109 10’3 10” 10”
loz2 105
E*/ (kJ/mol) 289.1 157.1 33.1 51.9 0.0 40.6 6.7 157.1 0.0 58.6 381.0 0.0
ref 12 13
this work this work this work 4 14 13 this work 4 5 5
hexamethylethane decomposition, is itself the reference reaction and has a high activation energy. In addition, the quenching of the hydrogen atom attack is as sharp as that of the unimolecular reactions previously studied. The uncertainties in the physical conditions such as the reaction time-temperature history will not have a serious effect on the determination of the rate constants for the various paths of hydrogen atom reactions as long as the differences in the activation energies of rate constants for these paths are small. In this case this means that the activation energies for both the reactions of hydrogen atom with phenol and the reaction of hydrogen atom with methane should be roughly equal in order to minimize error. In most complex reactions it is necessary to determine not only the rate of disappearance of the reactant but also the relative rates of the product channels. In the case of the reaction of H atoms with substituted benzenes the primary paths a t our reaction temperatures will be the displacement of the substituent group or the abstraction of an H atom from this moiety. The direct abstraction of a ring hydrogen is expected to be substantially slower. In order to evaluate both of these channels, we measure one of the products, benzene, and derive the other product by difference. Assuming sufficiently small H M E to phenol ratios, negligible depletion of phenol, very fast hydrogen atom disappearance rates within the time scales of our experiments, and the reactions of OH with phenol yielding negligible quantities of hydrogen atoms, the relationships between rate constants and product concentrations are as follows: A. rate of hydrogen atom formation = rate of isobutene formation B. rate of isobutene formation = rate of benzene and phenoxy formation
C. rate of benzene and phenoxy formation =
( k + kd) [phenol] D. rate of benzene formation = (kd)[phenol] From these relations we derive to a first approximation the relationship between the experimentally determined isobutene and benzene concentrations and the rate constants for abstraction and displacement. [isobutene] / [benzene] = ( k , kd)/ kd
+
Simple rearrangement isolates the ratio of rate constants for abstraction to displacement and leads to the relation [isobutene]/[benzene] - 1 = k,/kd = R The left-hand side of this equation is the fundamental experimental observable used throughout this work. For convenience, we designate this experimental quantity as R. A necessary consequence of this treatment is that hydrogen atoms are present in steady state. It will also become clear from the subsequent discussion that the assumptions intrinsic in this treatment are, after minor corrections, consistent with the results of our experiments. Experimentally, this study was more difficult than the work on toluene because of the slower rate of hydrogen attack on phenol relative to that on toluene. It was therefore necessary to work at much higher aromatic to hexamethylethane ratios for phenol
The Journal of Physical Chemistry, Vol. 92, No. 8, 1988 2199
Hydrogen and Hydroxyl Radical Attack on Phenol 1.5
eo..
..
+
.t
**
.03
The deviations from these values shown by the mixtures with lower phenol/HME ratios are due to the contributions from the reaction of hydrogen with hexamethylethane and phenoxy radicals. In particular, the change in slope is due to the hydrogen phenoxy reaction. Indeed, it was our failure to fit these data on the basis of our simple mechanism (in contrast to our earlier situation with toluene) that forced us to use detailed kinetic modeling. The modeling did show that even for the two mixtures with the highest phenol/HME ratios there are some contributions from the other H atom sinks. Computer modeling of all the results has been used to refine the initial estimates of the rate constants and will be discussed below. Returning to our results under limiting conditions, we translate this rate constant ratio into absolute values by adding a competitive channel for the H atoms for which we know the rate parameters and observe the effect on our experimental observable (R). The upper two data sets in Figure 1 show the effect of adding large quantities of methane into the reaction mixture. The analysis of these results follows the same logic as in the absence of methane except that the hydrogen consumption term now includes the effect of the methane so that only the second assumption is altered: B. rate of isobutene formation = (ka + kd) [phenol] + kM[CHII
.07
.9 1
.95
.99
1.03
1 ooorr Figure 1. Ratio of apparent abstraction and displacement rate constant versus I / T (based on rate expression for hexamethylethanedecomposition as given in the text) for various mixtures: 102 ppm hexamethylethane, 2%phenol (*); 163 ppm hexamethylethane, 0.97% phenol ( 0 ) ; 50 ppm hexamethylethane, 3.1% phenol (A); 22 ppm hexamethylethane, 2.6% phenol (+); 101 ppm hexamethylethane, 2.15% phenol, 4.6% methane (m); 97 ppm hexamethylethane, 1.7% phenol, 9.4% methane (0).Lines are the results of our modeling work. The broken line is our final result for k,/k, as based on the rate expressions given in Table 11.
than was the case for toluene. Since there is a practical upper limit to the amount of phenol that can be used in these experiments, we are forced to detect very low levels of isobutene and benzene. Furthermore, the rate constant ratio ( R ) depends on the difference between the concentration ratio and unity; thus when the ratio of concentrations is near one, errors in measurement will be amplified when translated into rate ratios. This was especially serious in the analysis of low levels of benzene where it appeared that at concentrations below 1.O ppm the precision of our measurements decreased drastically, thus setting a lower limit to operating levels. In addition, for phenol, displacement was favored in comparison to abstraction by about two to one. This is exactly the reverse of the situation for toluene. Since we obtain the contribution from our abstraction channel by difference, the uncertainty is necessarily increased. Figure 1 contains the results of studies with varying quantities of HME, phenol, and methane. The curved lines represent the fits that are based on our computer simulation (to be discussed subsequently). Initially, we will treat the data in terms of the limiting mechanism discussed above. The lower four data sets show data with no added methane. The results are expressed in terms of the experimental quantity R , which, were the analysis given above complete, would show no effect of the ratio of phenol to HME. At sufficiently large ratios of phenol to H M E this appears to be the case-the data for the phenol/HME ratios of 600/1 and 1200/1 are statistically indistinguishable, and a single least-squares line has been fit to both sets of data. Under these conditions this ratio is a direct measure of the ratio of the rate of abstraction to displacement. However, at lower phenol to H M E ratios the experimentally observed ratio is increased due to contributions from hydrogen-loss processes other than the reactions with phenol. These processes violate the assumption (B above) that all of the hydrogen atoms react with phenol by either displacement or abstraction. We therefore begin by using the results from the two sets of experiments with the highest phenol/HME ratio and derive the following least-squares relation for the ratio abstraction to displacement: R = 30.1 exp(-4020/T) N ka/kd
Now the experimental ratio of isobutene/benzene can be related to the following rate expression isobutene/benzene = ((ka + kd)[phenoll + kM[CH41~/kd[pheno11 which can be simplified and related to the experimental quantity R RM = k,/kd k~[CHi]/kd[pheIlOl]
+
where the subscript M is used to indicate the presence of methane, and the phenol concentration on the right-hand side is that in the mixture with methane. Note that the ratio of the abstraction to displacement rate constants is just the quantity determined in the experiments without methane by the limiting value of R a t high phenol to H M E ratios. If we denote this limiting value of R as Ro, then we may rearrange the equation above to RM - R, = k ~ [ c H d/kd[phenOl] ] from which we can derive kd
= kM[CH,l/([phenol]*(R~ -
Two different methane mixtures are shown in Figure 1. Note that in the present cases the phenol to hexamethylethane ratios are only 200 to 1. Unlike the results in the mixtures without methane, these mixtures are not affected by unaccounted H atom reactions since the large concentrations of methane reduce the relative importance of the reactions other than those included in the elementary analysis. The least-squares relations for the raw data RM for the two methane mixtures are RM = 67.6 exp(-3650/T) for 4.6% methane RM = 67.9 exp(-3230/T)
for 9.7% methane
The statistical uncertainties in these expressions are 10% in the activation parameter and about the same in the preexponential. Using the analysis above, we can calculate the rate of displacement of OH from phenol by H atoms. The resulting rate constant for displacement kd = 1.78 x 10'' exp(-3760/T) L/(mOl*S) varies by a maximum of 12% between the two methane mixtures used. The small variation between the results of the two mixtures is confirmation of the assumption that the relative importance of the secondary reactions in the methane mixture is small. This result combined with the ratio k,/kd from above gives a rate constant for the abstraction k, = 5.36
X 10"
exp(-7780/T) L/(mol.s)
2200
The Journal of Physical Chemistry, Vol. 92, No. 8, 1988
These rate parameters were then used as initial values in a kinetic model calculation. All of the secondary reactions were included, and every mixture was analyzed. The sources of the other rate constants used in the calculation are given in Table 11. Since the reaction takes place entirely in the post-reflected-shock gas, the model is essentially a fully mixed batch reactor model with no corrections for transport necessary. The thermal reservoir provided by the high concentrations of phenol and the low extents of phenol decomposition ensures that the experiments are isothermal. Table I1 contains the set of rate expressions that we used in modeling the experimental data that gave the “best fit” of our results as shown by the lines in Figure 1. We emphasize again that the modeling was necessary in order to include the reaction of hydrogen atoms with phenoxy radicals. These phenoxy radicals, unlike the benzyl radicals in the comparable toluene case, cannot be removed by combination. The recombination process forming the C-C bond from the stable keto form of the phenoxy radical,I5 or for that matter any 0-0bond that may be formed: is expected to lead to a bond that is so weak that, under our experimental conditions, combination can be expected to be reversed in contrast to the C-C bond in bibenzyl which is stable. The only fast reaction for phenoxy removal is H C 6 H 5 0 C 6 H 5 0 H which is also a sink for hydrogen atoms. Without modeling, the limiting analysis used to account for the toluene results cannot reproduce the magnitude and temperature dependence of the high H M E concentration results. The isobutene yield still represents the total hydrogen atom production, but the difference between the isobutene and the benzene yields is not a result of the abstraction alone. The rate constant for abstraction calculated from this difference is as a result too large. The experimental rate constants and parameters for the hydrogen abstraction process given above are too large, and the detailed modeling leads to a lowering of the A factor by a factor of 5 and of the activation energy by 13 kl/mol. The overall rate constant is lowered by about 25%. Using the set of rate constants given in Table 11, we can illustrate the role of the H phenoxy reaction. For the mixture with the lowest phenol/HME ratio, the fraction of H atoms used up by the recombination goes from 7% a t 1000 K to 40% at 1150 K. As manifested through the calculation of the abstraction channel by difference, this is a very large and observable effect. In contrast at the highest phenol/HME ratio, the fraction of H atoms involved in recombination varies from 0.5% to 10%. While this is still not negligible, it represents a relatively small difference. The results of these experiments permit a relatively accurate determination of the rate constant for the combination of hydrogen atoms and phenoxy radicals. Since the rate constant for displacement is directly associated with benzene yields, the adjustments as expected are much smaller. We expect that the rate expressions that we give have uncertainties of a factor of 2 in the A factor, 6 kJ/mol in the activation energy, and 20-25% in absolute rates. Figure 2 contains data on the effect of added carbon monoxide. The result of adding CO into this system is to provide a route for the OH radicals produced in the displacement reaction to react and produce additional H atoms. The O H radicals have two reaction paths-reaction with the added CO and abstraction of H atoms from phenol. The added H atoms from O H reaction with C O will in turn produce more benzene by displacement of OH from phenol, resulting in a decrease in the observed isobutene/benzene ratio and in R. Very large concentrations of C O are needed to change the experimental ratio, demonstrating that the rate constant for O H attack on phenol is much larger than that for reaction with carbon monoxide. The very size of the difference in rate constants makes the experimental effect very small and does not permit a determination of the temperature dependence. The initial data analysis sets
+
-
+
Rco = (isobuteneo/(benzeneO + benzeneco) - 1)
where the benzeneco is added benzene resulting from the reaction between C O and OH. This can be converted into relative rate (15) Mahoney, L. R.; Weiner,
S. A. J . Am. Chem. SOC.1972, 94, 5 8 5 .
He et al. 1
’ I
,
I
.aa
I
1
,
I
I
.Q .92 34 .sa .sa 1 ooofr Figure 2. Effect of added CO on abstraction to displacement rate constant ratio: 97 ppm hexamethylethane, 1.7% phenol, 9.7% CO (M); 64 ppm hexamethylethane, 1.8% phenol, 29.5% CO (*). Solid line is our calculated result for a 280:l phenol/hexamethylethane mixture without .a4
.0a
co.
constants for OH attack on phenol and CO from the difference between k0and &, where Rois the experimental R for the same phenol/HME ratio. The resulting equations generate an infinite series since the H atoms released into the system produce more OH which in turn produces more H atoms, and so forth. Due to the smallness of the branching ratio, the series was truncated and all terms greater than second order in H atoms were discarded. The resulting equation was solved for the ratio of the rate constants for O H reaction with phenol and CO. Due to the rather high uncertainty of the CO data and the approximate nature of the analysis, this value was only used as an initial input to the model. Once all of the other rate constants were set by fitting the various HME/phenol mixtures and the CH4 mixtures, the value of the OH + phenol rate constant was adjusted to fit the CO mixture data. The resulting rate constant is given in Table 11. It is also possible to use the data in Figure 1 to determine the rate constant for hydrogen atom attack on hexamethylethane. We have carried out a similar calculation using the data on toluene4 and obtained a value that, on a per hydrogen atom basis, is equal to the published rate constant for hydrogen atom attack on ethane. In these studies, when we compare our relative abstraction and displacement processes at high and low hexamethylethane concentrations, the difference is due to the reaction H hexamethylethane which produces two isobutenes without any additional hydrogen atom production. The rate constant derived from this data is essentially that found in the toluene work.
+
Discussion The results of this study are indicative of the chemical reactivity of phenol in high-temperature systems. Specifically, phenol can be expected to be much more reactive in oxidative systems where OH attack is a predominant mode of reaction than in pyrolytic situations where attack by H atoms would predominate. The reaction of phenol with H atom can be compared with our earlier report for toluene. In that work the rate expression for displacement and abstraction were given as C6H.5 + CH,) = k ( H C&,CH, 1.2 XIO1o exp(-2587/T) L/(mol.s)
-
k(H
+ C6HsCH3
-
C6HsCH2 f H J = 1.2 X lo1’ exp(-4138/T) L/(mol.s)
These rate constants are factors of 2 and 6 faster than the comparable values for phenol, and the ordering of the reaction channels is reversed. Thus for phenol, displacement is favored over abstraction. This represents mechanistic hindrance to aromatic oxidation since displacement produces the unoxidized structure. More generally, it is interesting to compare data on the abstraction rate constants for a variety of systems presented in Table 111. Two things become apparent. First, the A factor is approximately constant even upon comparison of such different systems as
Hydrogen and Hydroxyl Radical Attack on Phenol TABLE 111: Rate Parameters for H
+ R-H
-
R*
The Journal of Physical Chemistry, Vol. 92, No. 8, 1988 2201
+ H2
log (A/no.
R-H R*
bond, nm
E,/(kJ/mol)
of H atoms)
CH3 CZHS i-C3H7 t-C,H, PhCH2 PhO OH
440 41 1 398 390 368 362 498
58.6 40.6 34.7 29.3 34.3 51.9 95.8
10.78 10.32 10.53 10.94 10.60 11.02 11.20
ref 5 5 15 15 4
this work 5
methane and phenol. Second, the change in bond energy is not reflected in a comparable change in the activation energy for the highly resonance stabilized radicals such as benzyl and phenoxy. This is in contrast to the alkanes where a decrease in the bond energy is more fully reflected in a decrease in activation energy. On the other hand, it is possible that we are beginning to see contributions from the abstraction of a hydrogen atom from the ring. The upper limit of ring hydrogen abstraction by hydrogen as given by Nicovich and RavishankaraI6 is only a factor of 5 smaller than the rate constant that we determined. This may have some effect on the rate expression presented here. Our rate expression for the displacement of the hydroxide group from phenol is very similar to that for the displacement of a methyl grouping from toluene! The overall effect of a factor of 2 decrease in rate constants is apparently due to an increase in activation energy of 6 kJ/mol. The equality of the A factor is indicative of similar transition states for the addition of a hydrogen atom at the ipso site and the absence of steric effects. With this rate expression we can calculate, through the equilibrium constant,” the rate expression for the reverse displacement of H atoms by an OH. This leads to the expression k(OH
+ C6H6
-
+
C6HjOH H ) = 1.34 X 1O’O exp(-5330/T) L/(mol.s)
Under our experimental conditions this is equal to a rate constant of approximately los L/(mol.s). This can be compared with the rate expression for the disappearance of O H in the presence of benzene as determined by Tully et a1.,6 k(OH C6H6 C6H5 HzO) = 1.4 X 1Olo exp(-2260/T) L/(mol.s), which is a factor of 15 higher at our temperatures. Clearly, near 1000 K the abstraction of ring hydrogen is overwhelmingly favored over displacement as the primary route for OH reaction with benzene. Displacement reactions of the type discussed here are not elementary processes; rather they are due to the sequence of reactions
+
+
OH
C6H6
ki
-
C6H60H
kx
C6H@H
-
H
and can thus be expressed in terms of the relation k(OH
+ C6H6
C6H5OH
+ H ) = k f ( k , / ( k ,+ k,))
In the present instance we have determined the overall rate. Extrapolating from the results of Tully et aL6 near room temperature, this leads to k,/k, = 9. As expected, the preferred mode
of hydroxycyclohexadienyl (C6H60H) decomposition is the ejection of the hydroxyl radical. Our results on OH attack must be due to reaction with the phenolic H, since the rate constant for attack on the ring is ~ e l l - e s t a b l i s h e dand ~ ~ ~is a factor of 10 smaller. Indeed, H abstraction by O H on all hydrocarbons appears to have on a per hydrogen atom basis somewhat smaller rate constants at our temperatures. Thus, under high-temperature conditions the preferred mode of O H attack on phenol is the abstraction of the phenoxy hydrogen. This is in agreement with the results of Perry et al.19on O H reaction with cresol if the factor of 4 higher rate in comparison to toluene6 is attributed to abstraction of the hydrogen on the OH group. In addition, one may compare the abstraction by OH of the H from formaldehyde5 and hydrogen peroxide5 where the C-H and 0-H bond strengths, respectively, are essentially the same as the 0-H bond in phenol. There the published rate constants are very close to our value. The enhanced reactivity that we observe for O H is in contrast with the data for abstraction by hydrogen atoms, where our rate constants are very similar to those for hydrocarbons. Unfortunately, the great difference in reactivity between carbon monoxide and phenol prevented us from working under conditions where the observed effect is much larger, and so our results on O H attack must be viewed as having large error limits. Further work to confirm these results would be worthwhile. The derived rate constant for hydrogen atom combination with phenoxy radical, 2.5 X 10” L/(mol.s), is very large. Comparable numbers are 1.5 X 10” L/(mol.s) for H CH3,55 X 1Olo L/ (mol-s) for H C2H5,5and most recently 5 X 1Olo L/(mol.s) for H + H02.*0 All of these values are at room temperature. Thus, our number in the 1000 K range is especially valuable. It is line with our recent observations that combination rates involving resonance stabilized radicals seem to be especially large.17 The rate constant that we determined for hydrogen atom attack on hexamethylethane is exactly the same that we determined from our earlier study on the induced decomposition of t ~ l u e n e .This ~ provides a very satisfactory self-consistency check of our results. That is, the relative rate constant links between hydrogen attack on methane, toluene, and phenol is confirmed by the sequence of hydrogen atom attack on hexamethylethane, toluene, and phenol. Since we have previously shown that the rate constant for H attack on hexamethylethane is the same as that for hydrogen attack on ethane on a per hydrogen basis, this establishes the characteristic value for abstraction by hydrogen of a primary hydrogen. Thus, the methodology that we have employed permits extremely accurate determination of relative rate constants in the 1000 K region. Systematic studies of a similar nature can thus build up a data base of an accuracy similar to that which now exist for stratospheric chemistry. This should be a major consequence in the modeling of all high-temperature phenomena involving hydrocarbons. At the same time it will provide a basis for the development of predictive theories.
+
+
Acknowledgment. This work was supported by the Department of Energy, Office of Renewable Technology. Registry No. H, 12385-13-6; O H , 3352-57-6; PhOH, 108-95-2; ( t -
(16) Nicovich, J. M.; Ravishankara, A. R. J . Phys. Chem. 1984,88,2534. (17) Stull, D.; Westrum, E. F.; Sinke, G . C . The Chemical Thermodynamics of Organic Molecules; Wiley: New York, 1969. (18) Tsang, W. J . Phys. Chem. 1986, 90, 1152; 1984,88, 2812.
Bu),, 594-82-1; OPh, 2122-46-5; PhH, 71-43-2. (19) Perry, R. A.;Atkinson, R.; Pitts, J. N. J. Phys. Chem. 1977,81, 1607. (20) Keyser, R. J. Phys. Chem. 1986, 90, 2994.
