J. Phys. Chem. 1986, 90, 437-440 the structure of vinylketene, CHz=CH-CH=C=O, or cyclobutenone. Since the latter is known to readily isomerize into the former under present conditionsZZwe conclude that vinylketene is the initial product of FA t h e r m o l y s i ~ : ~ ~ (,\)-CHO
+
CHz=CH-CH=C=O
t CO ( 3 )
At about 1170 K the amplitude 16, reaches a flat maximum indicating that vinylketene finally decomposes, probably to propyne and CO. The actual pathway of reaction 3 must involve a biradical formed by Cz-O or Cs-O bond fission followed by suitable H-atom shifts. Although elementary Hiickel MO calculations predict the Cz-O bond to be. slightly weaker and hence that this path should be preferred,z the fact that decomposition of all intermediates is expected to be fast precludes a clear choice to be made based on present data. Assuming an A factor A , = 1015.3s-l for the ring-opening step as in 2-methylfuran and & = 1 below 1200 K,I3 we arrive at the high-pressure Arrhenius expression log (k3,s3-') = 15.3 - 67.0/8. The activation energy E3 = 67.0 kcal/mol is about 5-6 kcal/mol smaller than that associated with the ring opening of furan, suggesting that the formyl group further stabilizes the biradical by that amount. A similar effect has already been observed in the pyrolysis of acetylcycloalkanes.'*6 Other alternatives such as considering that the unsubstituted biradical formed in furan decomposition is more stable than previously estimated, the difference being account for by the activation energy (22) W. S.Trahanovsky, B. W. Surber, M. C. Wilkes, and M. M. Preckel, J . Am. Chem. SOC.,104, 6779 (1982). (23) We have recently confirmed this assignment by IR spectrophotometric and gas chromatographicanalysis of the products of the vacuum pyrolysis of FA. M. A. Grela and A. J. Colussi, to be submitted.
437
of the ensuing H-atom shifts, seem less likely. Obviously the usual simplifications required to estimate the heats of formation of these and other biradicals, such as the assumption of noninteracting radical centers, are either too drastic or even contradictory in this and similar cases in which extensive delocalization over the entire framework needs to be invoked. There is no basis to suspect that wall reactions may have qualitatively or quantitatively affected present results. In fact unimolecular reaction theory correctly predicted the observed variation of the rates of decomposition of furan, 2-methylfuraq and 2,5-dimethylfuran in a similar setup as function of molecular complexity, as expected for homogeneous processes.6 If 2-furaldehyde should decompose during rather than after collision with the silica walls on account of its greater polarity due to the presence of the formyl group, then one would expect similar decomposition mechanisms for the three aldehydes, at variance with present observations. In any event, as it emerges from these studies, the furan ring appears to be considerably less stable than other heterocycles, such as pyridine,25 adding a novel feature to the interpretation of the high-temperature behavior of cellulose-related materials such as coal, wood, and their derivatives. Further work is in progress.
Acknowledgment. Financial support by CIC and CONICET of Argentina is gratefully acknowledged. Registry No. Benzaldehyde, 100-52-7;2-butenal, 41 70-30-3; 2-furaldehyde, 98-01-1. (24) H. Hiraoka, J . Phys. Chem., 74, 574 (1970). (25) B. D. Barton and S.E. Stein, J . Chem. SOC.,Faraday Trans. 1,77, 1755 (1981). (26) J . K. Tarlouw, P. C. Burgers, and J. L. Holmes, J . Am. Chem. SOC., 101, 225 (1979).
Measurements of the Pressure Dependence of the HOz Radical Self-Disproportionation Reaction at 298 K Michael J. Kurylo.* Philip A. Ouellette, Center for Chemical Physics, National Bureau of Standards, Gaithersburg, Maryland 20899
and Allan H. Laufed Office of Basic Energy Science, Department of Energy, Washington, D.C. 20545 (Received: July 26, 1985)
Flash photolysis kinetic absorption spectroscopy was used to investigatethe gas-phase disproportionationreaction of hydroperoxy radicals at 298 K. Measurements of k l / u (where k l is the rate constant and u is the H 0 2 absorption cross section) were made as a function of N2 and O2 pressures between 25 and 600 torr. Our observations of the linear dependence of k , on total pressure as well as of the existence of a finite bimolecular (zero-pressure) reaction component are in good agreement with other recent investigations. An analysis of our data using the equation kl = k,' + ~ N ~ [ +Nk ~o 2][ 0 2yields ] k l o = 1.88 X cm3 molecule-' s-l, kN2= 5.95 X cm6 molecule-z s-l, and ko2 = 4.53 X cm6 molecule-* s-I. An error band of f20% is assigned for 95% confidence limits. Together with the earlier studies, the present work provides a detailed data base upon which to make rate constant recommendations for atmospheric modeling.
Introduction The gas-phase self-disproportionation reaction of ~0~?lays an important role in both and combustion chemstry, In the atmosphere it is the principal source of HZOz,while in both areas it serves as an effective chain termination step for HO, reaction cycles. A still further importance arises from the use of this reaction as a reference in other kinetic studies involving H02. Our understanding of the complex kinetic picture sur?Guest worker at the National Bureau of Standards.
rounding HOz self-reaction has improved considerably with recent laboratory indicating that the rate constant for this process consists of both a pressure-independent bimolecular reaction HO2 + H0z HzO2 + 0 2 (la) -+
(1) S. P. Sander, M. Peterson, R. T. Watson, and R. Patrick, J . Phys. Chem. 86, 1236 (1982). (2) R. Simonaitis and J. Heicklen, J . Phys. Chem., 86, 3416 (1982). (3) C. C. Kircher and S. P. Sander, J . Phys. Chem., 88, 2082 (1984).
This article not subject to U S . Copyright. Published 1986 by the American Chemical Society
438
The Journal of Physical Chemistry, Vol. YO, No. 3, 1986
Kurylo et al.
and pressure-dependent termolecular reaction HO2
+ H02 + M
--*
HZ02
+0 2 +M
(1b)
(each with its own unique temperature dependence). Thus, the rate constant for the overall reaction, k l , is given by the equation kl
= kia + kibkM1
where [MI is the molecular density of the inert diluent, M. This recognition explains some of the difficulties encountered in comparing earlier results in which the two reaction components were not mathematically separated. Such separation is not a problem when comparing low-pressure studies since reaction l a should be independent of the identity of inert diluent gas and the contribution due to reaction l b is negligible at low pressure. In fact, a number of direct low-pressure measurements of ki show excellent agreement when normalized to account for differences in the absorption coefficients used to calculate the H 0 2 concentration. The values reported for k,, (in units of lo-'' cm3 molecule-' s-l) are as follows: Simonaitis and Heicklen,2 1.5-1.7; Cox and burrow^,^ 1.3-2.5; Thrush and T ~ n d a l l 1.6 , ~ f 0.2; Takacs and Howard: 1.5 f 0.3; and Sander,' 1.5 f 0.4. Consistent with these results is the linear extrapolation of the higher pressure data from Sander et al.' (1.7 f 0.2). The situation regarding high-pressure measurements of k , is consideraly less definitive since early investigations did not include systematic variation of the molecular density or of the identity of the inert diluent. From the standpoint of atmospheric modeling, there are three studies involving N2as a carrier gas but only two of these report a pressure variation. cm3 At 1 atm of N2, the following values of k l (in units of molecule-1 SKI)are reported: Sander et aI.,l 3.0; Simonaitis and Heicklen,2 2.9; and Patrick and Pilling,* 3.7. Data from the first cm6 two groups can be used to calculate klb = 5.6 X molecule-2 s-l. For M = O,, the only existing pressure-dependent data are those of Sander et al.' For evaluation purposes, however, the situation is complicated due to the observations by these authors of experimental difficulties (attributable to radical diffusion) which limit their measurements to pressures above 100 torr. Simonaitis and Heickleq2 on the other hand, conducted experiments at pressures as low as 5 torr without apparent experimental difficulty in a nearly identical experimental setup. In an effort to expand the pressure-dependent data base needed for atmospheric m ~ d e l i n gand ~ ~ 'to~ determine its reliability, we have recently concluded an investigation of the pressure dependence of the title reaction a t 298 K for N2 and O2 pressures between 25 and 600 torr employing the technique of flash photolysis kinetic absorption spectroscopy. Experimental Section
Since a second-order decay rate is concentration dependent, an essential requirement in the real-time measurement of second-order radical kinetics is the homogeneity (Le., uniformity) of the radical concentration over the entire reaction cell. This, in turn, is coupled to the need for adequate detection sensitivity so that both the initial radical concentration and the decay rate can be determined with the desired precision. These requirements were satisfied through modifications of an earlier vacuum UV flash photolysis design." The present apparatus incorporates a 1-mlong Pyrex flash photolysis cell constructed in a conventional (4) R. A. Cox and J. P. Burrows, J . Phys. Chem., 83, 2560 (1979). (5) B. A. Thrush and G. S. Tyndall, Chem. Phys. Lett., 92,232 (1982). (6) G. A. Takacs and C. J. Howard, J . Phys. Chem., 88, 2110 (1984). (7) S. P. Sander, J . Phys. Chem., 88, 6018 (1984). (8) R. Patrick and M. J. Pilling, Chem. Phys. Lett., 91, 343 (1982). (9) W. B. DeMore, J. J. Margitan, M. J. Molina, R. T. Watson, D. M. Golden, R. F. Hampson, M. J. Kurylo, C. J. Howard, and A. R. Ravishankara, Evaluation No. 7 of the NASA Panel for Data Evaluation, J.P.L. Publication 85-37, 1985. (10) D. L. Baulch, R. A. Cox, R. F. Hampson, J. A. Kerr, J. Troe, and R. T. Watson, J . Phys. Chem. ReJ Data, 13, 1259 (1984). (1 1) G. H. Atkinson, A. H. Laufer, and M. J. Kurylo, J . Chem. Phys., 59, 350 (1973).
..
W
0
(Y"
\,,
,w
I
.YO c L
T Figure 1. Schematic of flash photolysis apparatus: E, electrodes for flash lamp; F, inlet for filter cell; G, gas inlets for reaction tube; L, inlet for Xe flash lamp; 0, O-ring connectors; R, reaction tube; T, inlets for temperature controlling fluid; W, quartz window assemblies.
cyclindrical tube designi2 (see Figure 1) and situated in a White celli3 for enhanced transient absorption sensitivity. The inner reaction tube was approximately 30 mm i.d. with the size of the outer tubes chosen to allow for a 3-5-mm spacing between the concentric cyclinders. The positioning of the windows within the cell defines a monitoring region characterized by uniform photolysis flux and temperature regulation. An aluminized mylar reflector surrounding the cell helps to ensure a homogeneous light flux from the Xe flash lamp along this central region. The flash itself was generated by a triggered discharge (175-500 J) in -30 torr of Xe and was characterized by a half-life of < 5ps. The temperature of the cell was controlled at 298 K by circulating water from a thermostatted bath through the outer jacket. The filter chamber between the flash lamp annulus and the inner reaction tube was filled with air for the present experiments. Thus the wavelength distribution of the photolysis flash was limited only by the low wavelength Pyrex cutoff (-300 nm). H02 was monitored in real time (following its flash photolytic production) by recording its absorption of radiation from a xenon arc lamp utilizing a 0.3-m monochromator-photomultiplier assembly connected to a microprocessor-controlled transient digitizer. In this way absorption decay profiles from numerous experiments (flashes) could be signal averaged, resulting in signficant enhancement of signal-to-noise ratio. Through appropriate changes in monochromator wavelength and slit width settings, we were albe to verify the absence of any effects (due to monitoring wavelength or resolution) on the kinetics. Reaction mixtures were prepared by mixing calibrated flows of the desired gases just prior to their admission into the cell. The total flow rate was chosen to allow for complete sample replenishment every 3-5 flashes (-30 s). For most of the experiments, HOz was generated by the commonly used reaction sequence C1,
+ hv (A > 300 nm)
C1 + CH30H CH20H
-
+0 2
-
CHzOH
-+
CH2O
2C1
+ HC1
+ HO2
This mechanism has the advantage of a rapid, pressure-independent production of H 0 2 . This is to be contrasted with the reaction pair C1+ H2 H
-
+0 2 +M
HC1+ H
+
HO2 + M
in which HOz production dominates over the reaction H Clz -+ HCl C1
+
+
only at high O2 partial pressures (>300torr). Nevertheless, a few experiments were conducted using this second sequence to examine the "chemical cleanliness" of our reaction system. The ran es of concentrations for the experiments reported here system) were (in units of molecule/cm3) as follows: Cl2, (3-10) X lo1$ CH,OH, (2-10) X 02,(1-7) X 10'' (for experiments where N2 was the diluent gas). The desired total pressure was then achieved by the addition of N2 or 02.For the (12) R. T. Watson, S . P. Sander, and Y. L. Yung, J . Phys. Chem., 83, 2936 (1979). (13) J . U. White, J . Opt. SOC.Am., 32, 285 (1942).
H 0 2 Radical Self-Disproportionation
H2 system, the O2concentration was
-
1019and the H2concentration was -3 X 10l8. Reagents had the following stated purities: C12, 99.96%, used after redistillation; C H 3 0 H , Spectral Grade, used after vacuum drying and redistillation; 02,99.99%; N2, 99.999%; H2, 99.9999%. For the ranges of concentrations indicated, the production of H 0 2 by either mechanism occurs on a time scale of 10-20 ~s (considerably faster than its decay rate via reaction 1. As previously mentioned, the determination of kl requires a knowledge of the absolute initial concentration of H 0 2 , [HO,], which, for absorption measurements, requires an accurate measure of the analysis path length. This was accomplished for two, four, and eight passes in the White cell by recording the light absorption of various mixtures of CH3Br in He (or C12in He) and calculating the path length from Beer’s law by using published absorption cross s e ~ t i o n s . l *The ~ results from these optical measurements were in good agreement with predictions based on a simple physical measurement of the window-to-window distance indicating an eight-pass analysis path length of 450 f 15 cm. Using this pathlength and the H 0 2absorption coefficients recommended in ref 9 we can calculate [H0210from the initial absorption in each experiment. We thus find that the indicated range in [Cl,], coupled with the previously mentioned threefold variation in flash intensity, yielded initial H 0 2 concentrations from 5 X 10l3to 50 x i o i 3 molecules/cm3.
Results and Discussion The standard kinetic analysis of second-order decay curves involves a linear least-squares fitting of the reciprocal concentration vs. time. For experiments in which concentration is determined by optical absorption, a fit of reciprocal optical density using Beer’s law can be made. For the title reaction, however, the linearization of the second-order rate equation is complicated due to a residual light absorption by product H202. It can be shown that such linearization can still be achieved if the final (postflash, postreaction) light intensity, I,, is used in computing the optical density rather than the preflash value, Io:
where
B = In (I,/Z) Bo = In (Im/Z3
In these equations, Z‘is the transmitted light intensity immediately following the flash (corresponding to [HO2I0). The determination of kl using eq I is quite sensitive to the choice of Z,, however. Depending on the range in absorption over which the analysis can be. extended, an underestimation (or overestimation) of I , of only a few tenths of a percent can lead to an increase (or decrease) in the value computed for kl of between 10 and 50%. Due to the “long tail” nature of a second-order decay, an accurate measure of I , would necessitate the inconvenience of following the absorption out to extremely long times in order to avoid a systematic error. In principle, one can circumvent this problem somewhat by calculating I , from a measurement of Io, the computer fit of Z’,and an assumed product yield for H2O2 However, uncertainties and Z’translate directly into errors in Z,. We have in uHO2,uHZo2, attempted to avoid this potential source of systematic error in our rate constant determination by utilizing a three-parameter nonlinear least-squares fitting of eq I in which “best fit” values of Z’, I,, and kl are simultaneously determined. One should note that the calculated value for k,is linear dependent on the values used for the absorption coefficients of both H 0 2 and HZ02.For the present work we have utilized the cross sections recommended in ref 9. All rate constants determined were independent of analysis wavelength between 215 and 230 nm, monochromator resolution from 2 to 3 nm, and the ranges of [Cl,], [CH,OH], and flash intensity mentioned earlier. The majority of the measurements were conducted a t X = 225 nm with a 3 nm (fwhm) resolution. Under these conditions, in a single-shot experiment a 3% ab-
The Journal of Physical Chemistry, Vol. 90, No. 3, 1986 439
z
96 . o -
0
H m m H
x ln z
92
.Ot
a
E +
00.01 0 .o
1
I
5
2.5
.o
T I M E .
1 7.5 1 0 .ia
m s .
Figure 2. Example of an H 0 2 absorption decay curve. [HO$ = 5 X 1014molecules/cm3. Accumulation of 20 flashes. Solid line IS a fit to the data using eq I. TABLE I: Rate Constant Measurements for Reaction 1 as a Function of Pressure k, x cm3 molecule-’ s d P,torr M N2 M = 02 25 50 100 200 300 400 500 600
1.87 1.85 2.1 1 2.33 2.61 2.51 2.80 3.24
1.90 1.94 2.16 2.32 2.45 2.41 2.68 2.70
sorption could be recorded with a signal-to-noise ratio of 1:l (corresponding to [H0210of 2 X 1013molecules/cm3). By signal averaging as many as 150 experiments, this signal-to-noise ratio can be increased significantly thereby improving markedly the instrumental detection sensitivity toward H 0 2 . As stated, our goals in this study were to expand the limited data base for the O2 pressure dependence of reaction 1 and to resolve the experimental anomalies of ref 1 and 2 which might influence the reliability of the Nz pressure dependence recommended from these measurements. To do this, experiments were conducted over the pressure range 25 to 600 torr using both nitrogen and oxygen and diluent gases. Our observations were consistent with the two-component interpretation of reaction 1; Le., kl increased linearly with total pressure. However, below 150 torr, we observed a systematic departure from this linearity similar to that noted by Sander et al.’ (The decrease in kl with decreasing pressure appeared to level off and k, even began to increase below 75 torr.) We were able to explain this phenomenon by repeating more than 100 runs over the complete pressure range indicated with four-, two-, and one-pass analytical configurations. The anomalous pressure effect diminished in the four-pass and disappeared in the two- and one-pass arrangements supporting the interpretation of a diffusion-controlled(inverse pressure dependent) wall loss of H02. In the eight-pass (and, to a lesser extent, four-pass) configuration, the analytical light beam at times passed very close to the cell walls. Consequently, at pressures where the H 0 2 can diffuse even a few millimeters during its kinetic lifetime, accelerated wall removal can be important. These effects would be observed in our studies and those of ref 1 but not of ref 2 where a single light pass through the center of the cell was employed. For the majority of the results reported here (all measurements < 200 torr) a two-pass configuration was used. This path length was sufficient to monitor HOz at concentrations as low as 5 X 1013molecules/cm3 with a signal-to-noise ratio of 3:l for a signal averaging of 25 experiments. A typical experimental decay curve is shown in Figure 2 along with the fit of the data to eq I. At each total pressure, a minimum of twenty decay curves were recorded (each decay curve being the signal average of between 20 and 150 flashes). The uncertainty on the rate constant determined from a decay curve (one standard deviation from the
440 The Journal of Physical Chemistry, Vol. 90, No. 3, 1986 3.5
1.SI
I
1
2mm.o
o.a
~i05.0
I
600.0
8mm.m
P CTorr3 Figure 3. Plot of the k , data from Table I vs. total pressure. The upper and lower solid lines are fits to the N2 data (Labeled N) and O2 data (labeled 0) respectively using eq 11.
nonlinear least-squares fit) was typically less than 5%. The mean values of kl obtained by averaging the results at a each pressure of N, and O2 are given in Table I. The standard deviation of the mean for these data sets was typically 10%. Several higher pressure experiments performed with the C12/H2/02 source of H 0 2 agree well with the results shown here, although exact comparison requires a precise determination of the third-body efficiency of H2. These data are plotted vs. the pressure of N 2 or O2in Figure 3 along with the weighted (reciprocal of the square of the standard deviation of the mean) nonlinear least-squares fit to the equation
This fitting procedure forces the Nz and O2 data to a common value of the bimolecular (zero pressure) rate constant, kiO,and yields the results
k,O = 1.88
X
10-l2 cm3 molecule-' s-l
ko, = 4.53
X
cm6 molecule-2 s-I
kN2 = 5.95 X
cm6 molecule-2 s-l
The two data sets can also be analyzed independently to yield separate slopes in intercepts. The values of klO,ko,, and kN, obtained from such a treatment agree (within 10%) with the rate constants listed above as determined in a composite analysis. The latter is a statistically more rigorous treatment and was chosen as the proper way to present these results. Based on our observations for potential errors in the calculation of the second-order rate constant from absorption decay data as well as the measurement reproducibility we assign a 20% uncertainty to our complete data base. This represents our best appraisal of 95% confidence limits. A similar mathematical analysis of the composite N 2 / 0 2data set from ref 1 yields the parameter values
k I 0 = 1.70 X
ko2 = 3.69
X
k N 2= 5.64
X
-
As can be seen, our data differ from those of ref 1 by 10%in the bimolecular component. For the O2 system, this difference increases to 15% at 700 torr; while for the N2system, it drops to -8% at this same pressure. These differences are similar for the N2 data set of ref 2 when the latter are normalized to the same absorption cross section values used in the present work. In addition, our extrapolation of the bimolecular component compares quite favorably with the body of low-pressure determinations given in the Introduction and recently reviewed by Sander.' Several different sources (Le., lot numbers) of N2, 02, CH,OH, and C12 were used in these experiments without any statistically meaningful change in the results. Some experiments were per-
-
Kurylo et al. formed using premixed samples of C12/CH30H/N2(or 02).Even when this mixture was completely light protected, there was evidence of a background reaction: H 0 2 decay experiments gave irreproducible results. This problem completely disappeared when the gases were mixed (via a flow controller assembly) immediately before entering the photolysis cell. We thus believe our data to be free from systematic error and concur with the present assessment9 regarding the two-component nature of reaction 1. The present results along with those of ref 1 provide an excellent framework upon which to base recommendations for the pressure dependence of HOz self-reaction in air. The N2data from both studies are also supported by the N 2 experiments of ref 2. The pressure dependencies from these three data sets can be averaged to give a recommended pressure dependence in air at 298 K of
kai, = 5.41
X
cm6 molecule-* sei
While our value (and that of ref 1) for the bimolecular component ( k I o agree ) well with low-pressure determinations, it is important to emphasize the extrapolative nature of klo as determined from predominately high-pressure measurements. Even though our data extend down to 25 torr, the value of klo that we report is based on a linear least-squares fit over the complete pressure range. Thus, a proper evaluation of the bimolecular reaction component should give higher weighting to direct, very-low-pressure measurements. Very recently, Kircher and Sander3 and Patrick et al.14 have presented an elaborate discussion of the mechanism for H 0 2 disproportionation based on the latest laboratory data. While the present study confirms the data base in the zero-pressure and low-pressure limits, no further insight regarding detailed mechanistic behavior can be gained from RRKM calculations similar to those performed by these authors since such calculations are dependent on unknown structural properties of the H 2 0 4adduct intermediate. Similarly, the ( k vs. p ) falloff curves predicted from these calculations can only be verified by experiments conducted at total pressures near 100 atm. Finally, during the present study a number of experiments were conducted at 280 K to check on the sensitivity of the measurements to small changes in rate constant. Despite the 20% uncertainty limits assigned to our rate constant determinations, we technically should be able to see changes in decay rates of less than this amount given a large enough sampling of rate constants. At this lower temperature we observed increases in k l , and klbof slightly greater than 10% and 20%, respectively. These increases can be compared to the 14% and 24%values predicted based on the work described in ref 3 and support the observation of a negative temperature dependence for each of the two reaction components. The discussion of earlier workers regarding the atmospheric significance of reaction 1 are appropriate to this study as well. As mentioned in the Introduction, H02 disproportionation is the sole source of atmospheric hydrogen peroxide. Reaction 1, followed by reaction 2 is the net equivalent of reaction 3. O H + H202 H2O HO2
-
+
OH
+ HO2
+ H2O + 0 2
Thus the sequence represents a reaction cycle for the destruction of odd hydrogen radicals (HO,). Rate constants for reaction 1 are thus necessary for calculating equilibrium concentrations of H202in the atmosphere which in turn can be compared to ambient measurements. In addition, they can be used to predict the rate of removal of tropospheric H02.
Acknowledgment. The authors express their gratitude to Dr. W. Braun (NBS) for his assistance in the design and modifications of the apparatus used in this work. The research described herein was conducted at the National Bureau of Standards with the support of the National Aeronautics and Space Administration (Agreement W- 15,816) and the Chemical Manufacturers Association (Agreement FC 82-402). (14) R. Patrick, J. R. Barker, and D. M. Golden, J . Phys. Chem., 88, 128 (1984).
