J . Phys. Chem. 1987, 91, 5325-5332
The Addition and Dissociation Reaction H Comparison with Theory
+ CO
5325
HCO. 2. Experimental Studies and
Raimo S. Timonen,+ Emil Ratajczak,t David Gutman,* Department of Chemistry, Illinois Institute of Technology, Chicago, Illinois 60616
and Albert F. Wagner* Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60462 (Received: December 29, 1986)
Directly measured low-pressure thermal HCO dissociation rate constants and isotope effects are presented for the first time. The temperature range of the measurements is 637-832 K. A theoretical model developed in the preceding paper is found to be highly consistent with these results and with all available H + CO thermal addition rate constant measurements. The calculations are used to extend the measured dissociation rate constant to combustion temperatures. The calculated low-pressure dissociation rate constant k l in various buffer gases is accurately represented from 300 to 3000 K by k,(Ar) = 3.09 X 10-7 ~ l ~ - 1 7 . 0 / R, Tkl(He) = 3.80 X 1 0 - 7 T ' e - 1 7 , 1 / R r , k,(N2) = 3.07 X 10-7T1e-17.0/RT, and kl(H2) = 5.79 X 10-7T1e-17.0/Rr, where kl is in cm3/(molecule s) and R is in kcal/(mol deg). The calculations suggest that (AI?),,,, the average energy transfer between metastable HCO* and the buffer gas, varies between -40 and -50 cm-I for buffer gases NZ, H2, He, and Ar.
I. Introduction The formyl radical is an important intermediate formed during the high-temperature oxidation of Because the hydrogen atom in H C O is so weakly bound (bond energy 16 kcal/mol), it is lost relatively easily under combustion conditions either by direct decomposition of the radical HCO
+M
-+
H
+ CO + M
(1)
or by H atom transfer reactions, e.g. HCO
+ (H, OH, 0 2 )
-+
CO
+ (H2, H20, H02)
(2)
Quantitative knowledge of the relative importances of these two processes is required for accurate modeling of combustion chemistry. This is due to the fact that decomposition leads to chain branching (since the H atom formed in reaction 1 reacts largely with O2 to yield OH 0) while the H atom transfer reactions are chain-terminating processes (or at least have a chain-terminating character1V2). In spite of its importance, reaction 1 has heretofore never been isolated for direct investigation. The existing knowledge of its rate constant is based on two sources: from studies of the pyrolysis of H 2 C 0 and the oxidation of hydrocarbons (in both flames and shock tubes)' and from the limited amount of knowledge of the kinetics of the reverse reaction at and near ambient temperature 1). Because (combined with the t h e r m ~ c h e m i s t r yof ~ - reaction ~ the experimental studies which have obtained rate constants for reaction 1 (the forward reaction) have all involved complex systems in which this particular reaction was not a major rate-determining step, the suggested values of k , they report are not highly quantitative. For this reason, there is a tendency in combustion modeling studies to rely more heavily on calculated rate constant parameters for k l using the direct measurements of k-, for the addition r e a c t i ~ n l ? ~
+
H
+ CO + M
-.
HCO
+M
(-1
1
These measurements have all been done at room temperature4s5 or over a very narrow temperature range near room temperature.6 The values of k l at combustion temperatures, which are based on measurements of k - ] , have their own uncertainties associated with them due to the very limited knowledge of the temperature dependence of kl,to the assumptions needed regarding the efficiencies of collider gases at high temperatures, and to some extent 'Permanent address: Department of Physical Chemistry, University of Helsinki, Helsinki, Finland. f Permanent address: Department of Physical Chemistry, Medical Academy, Wroclaw, Poland.
0022-3654/87/2091-5325$01.50/0
by a small lingering uncertainty regarding the thermochemistry of the formyl radical. In order to gain more direct knowledge of the thermal decomposition of HCO, we have now studied this reaction over a limited temperature range (637-832 K) using three different collider gases, He, N2, and Ar. The reaction was studied in a heated tubular reactor coupled to a photoionization mass spectrometer. To support and extend the measurements, we have also performed complementary rate constant calculations. These calculations employ the isolated resonance model of reaction dynamics described in the previous paper' (hereafter called paper l). Parameters needed to complete the theoretical model were chosen to obtain the best possible agreement with measured rate constants of reaction 1, with the hydrogen-deuterium isotope effect of k l (also reported here), and with values of k-, obtained in prior investigations of reaction -1 at or near ambient temperature. HCO is a prime candidate for applying the isolated resonance theory. Because of the weak bond energy of H C O and its large frequencies, the resonance vibrational states of metastable HCO* remain discrete and do not overlap into a continuous distribution of states. Furthermore, the availability of the three-dimensional potential surface for this system calculated by Harding,* the relative simplicity of the molecule, and the new significant body of quantitative information on the kinetics of both the forward and reverse reaction provide the information and conditions needed to develop and test this new theory of chemical reactivity. The calculations presented here and in paper 1 constitute the first step of a series of increasingly detailed theoretical studies of the kinetics and dynamics of H C O using this new framework. The experimental studies are described in section 11. In section 111, the theoretical model is presented and calculated rate constants are compared to the measured values. Section IV is primarily a discussion of the final values chosen for the adjustable parameters in the theoretical model and of the calculation of dissociation rate constants at combustion temperatures. Section V presents a (,l) Warnatz, J. In Combustion Chemistry; Gardiner, W. C., Ed.; Springer-Verlag: New York, 1984; Chapter 5. (2) Westbrwk, C. K.; Dryer, F. L. Prog. Energy Combust. Sci. 1984, I O , 1-57. (3) Benson, S. W.; ONeal, H. E. Kinetic Datu on Gas Phase Unimolecular Reactions; NSRDS-NBS 21; US.Government Printing Office: Washington, DC, 1970. (4) Hikida, T.; Eyre, J. A,; Dorfman, L. M. J . Chem. Phys. 1971, 54, 3422. (5) Ahumada, J. J.; Michael, J. V.; Osborne, D. T. J . Chem. Phys. 1972, 57, 3136. ( 6 ) Wang, H. Y.; Eyre, J. A.; Dorfman, L. M. J . Chem. Phys. 1973, 59, 5199. (7) Wagner, A. F.; Bowman, J. M. J . Phys. Chem., preceding paper in this issue. (8) Romanowski, H.; Lee, K.-T.; Bowman, J. M.; Harding, L. B. J . Chem. Phys. 1986, 84, 4888.
0 1987 American Chemical Society
5326 The Journal of Physical Chemistry, Vol. 91, No. 20, 1987
L. =
He buffer gas
_____
..........................
0.0
10.0
20.0
TlME (msec)
Sld'6 1.05
1.10
1.15
1.20
1.25
1.50
1.35
1.40
1.45
1.50
1.55
1.60
1OOO/T
Figure 1. Low-pressure limit thermal dissociation rate constants for HCO decomposition vs. inverse temperature for various bath gases. The symbols denote measurements, and the lines denote the theory. The insert shows a measured HCO' decay profile and a fitted exponential function through the data points. For conditions of this experiment,see
Table 1.
Timonen et al. HCO with free radicals produced during photolysis had negligible rates. This independence was expected since the initial HCO and CH, concentrations produced by the photolysis of CH,CHO were below 3 X IOio molecules/cm3 (based on a measured upper limit of 0.2% for the extent of acetaldehyde decomposition during each laser pulse). The results of the latter tests indicated that H C O did not react with C H 3 C H 0 to a measurable extent either homogeneously or heterogeneously. Calculation of k , from the measured H C O decay constants required knowledge of k3 above 600 K where it could not be measured. The magnitude of k3 above 600 K had to be inferred from the observed values and temperature dependence of this rate constant between 300 and 500 K. When the total gas density was kept constant, k, was found to be independent of temperature in this 200-deg interval (usually varying less than 4 s-l). For this reason, it was assumed that k , remained temperature independent between 500 and 832 K, the highest temperature used in this study. Sets of experiments (which included measurements of k , below 500 K and of k above 650 K) were always performed at a constant total gas density to assure a minimum change in k,. For the presumed mechanism for HCO loss, the experimentally determined decay constant k has the form
k = k, summary of the findings of this study. 11. Experimental Studies A . Apparatus and Procedure. The experimental apparatus and procedures used to reduce the data have been described Pulsed 308-nm radiation from a Lambda Physik EMG lOlE excimer laser was directed along the axis of a heatable 1.05-cm-i.d., coated (with boric acid) tubular quartz reactor. Gas flowing through the tube at 5 m/s contained CH,CHO (or C H 3 C H 0 and C D 3 C D 0 in the experiments conducted to also measure the hydrogen isotope effect of k , ) and the bath gas (He, Ar, or N2). The bath gas was always in great excess (>99.9%). Gas was sampled through a 0.08-cm-diameter tapered hole in the wall of the reactor and formed into a beam by a conical skimmer before it entered the vacuum chamber containing the photoionization mass spectrometer. As the gas beam traversed the ion source, a portion was photoionized and then mass selected. Temporal ion signal profiles were recorded from a short time before each laser pulse to 10-28 ms following the pulse by using a multichannel scalar. Typically, data from 5000 to 30000 repetitions of the experiment were accumulated before the data were analyzed. Formyl radical decay profiles were exponential in shape under all conditions. They were fit to an exponential function ([HCO], = [HCO]oe-k') by using a nonlinear least-squares procedure (e.g., see insert in Figure 1). Below 500 K, H C O decomposition was too slow to be observable. H C O loss between 300 and 500 K was due solely to heterogeneous processes:
HCO
-
heterogeneous loss
(3)
The H C O decay constants ( k ) were independent of temperature in this 200-deg range (31-34 s-l in a typical set of experiments). Above 500 K the decay constant increased, first slowly and then rapidly with increasing temperature (to over 500 s-l near 800 K). This increase is interpreted as due solely to the growing importance of HCO thermal decomposition, reaction 1. The mechanism for H C O loss (reactions 1 and 3) was tested for its completeness. First, experiments were performed to determine whether HCO could also have been reacting with the free radicals in the system or with acetaldehyde. Under each set of experimental conditions, the decay constant was measured as a function of laser intensity (to vary the free-radical concentrations) and acetaldehyde concentration. (Each was varied by at least a factor of 2 . ) The H C O decay constant was always found to be independent of both. The former test indicated that reactions of (9) Slagle, I . R.; Gutman, D. J . A m . Chem. SOC.1985, 107, 5342-47. (10) Timonen, R. S.; Gutman, D. J . Phys. Chem. 1986, 90, 2987-91. ( I 1) Timonen, R. S.; Ratajczak, E.; Gutman. D.J . Phys Chem.. in press.
+ k,[M]
(4)
where k , is expressed as the low-pressure limit of the thermal dissociation rate constant. At the elevated temperatures and low pressures of these experiments, reaction 1 is at the low-pressure limit (see section 111). The rate constants for reaction 1 were obtained from this equation by using the decay constants measured in experiments performed above 637 K, the rate constants for reaction 3 (which were measured below 500 K), and the measured total gas pressure in the tubular reactor. Experiments to measure k , were conducted only above the temperature at which the H C O decay constant, k , was at least 3 times greater (to as much as 17 times greater) than the measured wall-loss rate constant. With this precaution, small unexpected changes in k, with increasing temperature would not significantly affect the accuracy of the values of k , obtained from the first-order decay constants. It was this condition which determined the lowest temperature of each set of experiments. The highest temperature used at each gas density was fixed by the requirement that the measured H C O decay constants had to be below 600 s&. Above this value the accuracy of the measurements of the decay constant diminishes.I2 A final test of the experimental procedure and of the proposed mechanism involved determining whether the measured secondorder rate constants for reaction 1 were independent of bath gas density. Three sets of experiments were performed over a twofold density range (when He was the bath gas), and this independence was observed (see section IIB). The hydrogen isotope effect of reaction 1 was measured in those experiments in which He was the bath gas. In these experiments both CH,CHO and CD3CD0 were present. Laser photolysis produced both HCO and DCO simultaneously. HCO and DCO decay profiles were recorded alternately during an experiment to assure that both profiles were recorded under the same experimental conditions as well as during the same time interval. Separate values of k3 for HCO and DCO were measured at each density at temperatures below 500 K. The bath gases He (minimum 99.995%), Ar (minimum 99.996%), and N2 (minimum 99.998%) were obtained from Linde and used without purification. Acetaldehyde (99.995%) was obtained from Mallinckrodt, and acetaldehyde-d, (>99%) was obtained from Aldrich. Both were degassed by freeze-pumpthaw cycles and used without additional purification. B. Experimental Results. The conditions of all experiments and results obtained are presented in Table I. The measured rate constants and isotope effects are displayed in Figures 1 and 2 together with the calculated values (see section 111). The estimated (12) Moore, S. B.; Carr, R. W. I n t . J . Mass Spectrom. Ion Phys. 1977, 24. 161.
H
’
+ C O e H C O Reaction 3’00
The Journal of Physical Chemistry, Vol. 91, No. 20, I987
TABLE I: Conditions and Results of Experiments To Measure the Thermal Dissociation Rate Constant k , for HCO or DCO with Various Bath Gases M
HCO + H+CO (He buffer gas)
2.75-
10-16[M], k’(H),“ k’(D),” 1015k1(H),cm3/ k,(H)/ T , K molecules/cm3 s-’ s-I (molecule s) k,(D) M = He
2.50 0
2.25
0
-
k3(H)*= 37 SKI
k3(D)b= 31
786 832
3.5 1 3.51
186 258
644 675 708 745 786
5.31 5.28 5.24 5.26 5.27
644 675 708 743 786
7.08 7.10 7.09 7.06 7.07
340 479
k,(D)
k,(H) = 36 s-’ 98 142 171 299 441
I, 1.20
I
THEORY
,
I
1.25
1.30
I
1.35
1.45
1.40
1.50
1.55
1.60
116 168 238 341 586
Figure 2. Ratio of low-pressure limit thermal dissociation rate constants for HCO and DCO vs. inverse temperature for He bath gas at different
gas densities. The symbols denote measurements, and the line denotes the theory. For conditions of the experiments, see Table I. error limits on kl vary from f 15% in the middle of the temperature range covered to f20% at both temperature extremes. The estimated uncertainty in the isotope ratio, k,(H)/k,(D), is somewhat less: f10% at the middle of the temperature range covered and f15% at the extremes. The reduced uncertainty in the isotope ratio is due to the fact that its measurement does not require knowledge of the gas density in the reactor and because some possible minor systematic errors would cancel in the calculation of this ratio. The values of k l and kl(H)/kl(D) which were measured as a function of bath gas density (done only for He) show no systematic dependence on buffer gas concentration as is required if k l is the low-pressure limit of the dissociation rate constant. The magnitudes of the fluctuations of k l observed in the three density ranges studied are consistent with the 15-20% uncertainty estimates for the measurements of k,. The dependence of kl on the identity of the buffer gas is slight (see Figure 1). The insert in Figure 1 shows a representative HCO’ ion signal profile measured during one of the experiments to determine k l . The magnitude of the isotope ratios k,(H)/kl(D) is quite substantial, about 2.00-2.25 (see Figure 2). No temperature dependence in this ratio is discernible. If a minor one exists, it is obscured by the uncertainties of the measured rate constant ratios. The lines in both Figures 1 and 2 are the calculated values of k l and k l ( H ) / k l ( D ) discussed in section 111. 111. Theoretical Studies A . Introduction. The theoretical model used here to calculate thermal rate constants for reactions 1 and -1 was described in detail in paper 1. It employs a form of chemically activated RRKM theory that has been specially adapted to treat the extremely sparse density of H C O metastable vibrational states. Tunneling is suppressed in these calculations for the reasons discussed in paper 1. Summation over total angular momentum is explicitly performed. The tumbling rotational degree of freedom in HCO is treated adiabatically during unimolecular dissociation. The Troe formulaI3 for the ratio of the stabilization rate constant to the gas kinetic rate constant for buffer gas-metastable H C O ~~
2.0 1.9
s-l
1.2 2.0 2.6 5.0 7.7
2.0 2.3
1.9 2.4 2.3
SKI
1.2
1.9 2.9 4.4 7.8
2.5 2.3 2.1
1.8 1.7
M = N2
lOOO/T
~~
= 31
61 77 111 143 210 64 89 131 200 352
s-I
8.6 12.6
k3(D) = 31
k,(H) = 32 S-I
,.”*
5327
~
~
~~
~
(13) Troe, J. J . Chem. Phys. 1977,66,4745. The efficiency factor derived here is for low-pressure thermal dissociation, the reverse of addition. The ratio between the addition and dissociation nonequilibrium rate constants from the master equation has been shown to be the equilibrium constant (Troe, J. Annu. Reo. Phys. Chem. 1978, 29, 223) which implies the derived efficiency factor applies to low-pressure addition as used here.
k,(H) = 32 s-I 643 673 673 705 740 780
7.15 7.09 7.15 7.09 7.05 7.07
85 139 127 207 337 5 20
0.76 1.5 1.3 2.5 4.3 6.9
M = Ar
k,(H) = 31 637 667 701 737 780
S-I
91
7.13 7.18 7.18 7.15 7.14
137 190 304 489
0.84 1.5 2.2
3.8 6.4
“k’(H) and k’(D) are the directly measured HCO* decay constants. Photolytic sources [CH,CHO] and ([CH,CHO] + [CD3CDO])were in the range of (1.1-1.4) X I O l 3 molecules/cm3. bk3(H)and k,(D) are the HCO wall rate constants measured in the temperature range 300-500 K (see text).
collisions is used. The gas kinetic rate constant is derived from a standard formula13 with Lennard-Jones parameters. The input required for the calculation are (1) the structure, frequencies, and energetics of HCO, HCO* (the conventional transition state on the HCO potential energy surface), and H CO; (2) the Lennard-Jones parameters for the gas kinetic collision rate constant for HCO* M collisions; and (3) the average energy transferred between buffer gas and HCO* per collision, ( AE)lol. The last quantity sets the ratio of the stabilization rate constant to the gas kinetic rate ~ 0 n s t a n t . I ~ B. Fixed Parameters. Almost all of the parameters required in these calculations are fixed without reference to thermal rate constant experiments with which the theoretical results will be compared. The parameters include the structure and vibration frequencies of H CO, HCO*, and HCO, which were obtained from the empirically modified ab initio potential energy surface determined by Harding.* The vibrational states of C O and HCO which have been obtained by using this global surface are in good agreement with spectroscopic observation^.'^ A trajectory study of hot H atom inelastic collisions with CO, which used this same HCO surface, also obtained good agreement with observed product internal energy state distributions.’’ The use of this surface in the current study constitutes a further test of its use, this time to obtain quantitative thermal rate constants for reactions 1 and -1.
+
+
+
(14) Bowman, J. M.; Bittman, J. S.;Harding, L. B. J . Chem. Phys. 1986, 85, 911. (15) Gieger, L. C.; Schatz, G. C.; Harding, L. B. Chem.Phys. Lett. 1985, 114, 520.
5328 The Journal of Physical Chemistry, Vol. 91, No. 20, 1987 The empirical modifications used in obtaining the Harding surface involved employing two potential energy parameters which are known with a higher degree of accuracy than is currently obtainable from the ab initio calculations. These two parameters are also required for the RRKM calculations in the current study. They are the addition reaction barrier height, fl, and the dissociation reaction endothermicity, E,. (In paper 1 and here potential energy parameters include zero-point vibrational energies. and E , is Therefore, fl represents AHO,[H+CO-HCO*] AHoo[HCO+H+CO].) The value of E , was determined from the heats of formation for H, CO, and HCO. While the first two quantities are very accurately known, the value of AHfOo[HCO] is somewhat uncertain. There are four different determinations based on studies involving photoionization, photodecomposition, recombination (of H C O to form glyoxal), and equilibrium (I H 2 C 0 HI + HCO). As discussed in the Appendix, a consensus value derived from these studies gives AHfOo[HCO] = 10.3 f 1.0 kcal/mol. The corresponding value of E , is 14.1 i 1.O kcal/mol. The empirical modifications in the Harding potential energy surface yield essentially the same value, 14.2 kcal/mol. The other potential energy parameter, v, was adjusted slightly in the current study (see below). The temperature dependence of the energy transfer parameter LE)^^^ must be assumed. The temperature dependence of this quantity has been found to be very small or even absent in several systems in which it was determined.'6s'7 For HCO, rate constants for either addition or dissociation have not been measured over a sufficiently large enough temperature range and with sufficient precision and accuracy to determine the temperature dependence of this parameter for collisions of H C O with any bath gases. Therefore, for the calculations reported here, ( AE) was assumed to be independent of temperature. The remaining unadjusted parameters include the LennardJones parameters for the gas kinetic rate constants for collisions between HCO* and the bath gas. They were taken from a tabulation'* of these parameters for all the buffer gases considered here. H C O is not listed, so the parameters for HCCH were used for this radical. C. Adjustable Parameters. The two parameters which were adjusted to achieve optimum agreement between experiment and calculation are the values of v and ( AE)tot. v largely determines the temperature dependence of the dissociation and addition rate constants. Changing ( AE),Otprovides the only means available to scale the magnitude of the calculated rate constants without significantly affecting their temperature dependence. This latter parameter determines the fraction of gas collisions between HCO and the bath gases which result in stabilization. The Harding surface contains a value for based on the quoted value of the activation energy of k-, reported by Dorfman et aL6 Here fi is adjusted to achieve the best agreement not only with the temperature dependence of k-, but also with that of k, and the isotope effect of k, which were determined in the current study. Hence, the final value of fl reported below is an improved value of this potential energy which can be used for "fine tuning'' the Harding potential energy surface. D. Calculated Rate Constants. The calculated values of k,, k-', and k,(H)/k,(D) that are in best overall agreement with the experimental values are presented as lines in Figures 1-4. Figures 1 and 2 show the measured and calculated rate constants (both k, and k,(H)/k,(D)) from the current investigation. Figures 3 and 4 present the measured values of k-, of Dorfman et al.436and of Michael et aL5 along with the calculated values. These calculated rate constants were obtained by using the following values of the adjustable parameters: fl = 1.5 kcal/mol, and ( A E ) , , , = -45 cm-I (for He), -50 cm-I (for Ar), -40 cm-l (for Hz). and -45 cm-' (for Nz). I n general, agreement of cal-
Timonen et al.
H + CO + HCO (H2 buffer gas)
+
~~
(16) Oref, 1.; Rabinovitch, B. S. J . Chem. SOC.,Faraday Trans. I 1984, 80, 769. (17) Heymann, M.: Hippler, H.: Troe, J. J . Chem. Phys. 1984, 80, 1853. (18) Hippler, H.: Troe, J.; Wendelken, H. J. J . Chem. Phys. 1983, 78, 6709.
3
8
MICHAEL (fixed T) THEORY
0
I
0.5
0.0
1.0
1.5
20
2.5
3.0
8.5
lOOO/T Figure 3. Low-pressure limit thermal addition rate constant vs. inverse temperature for H, bath gas. The symbols denote the measurements in ref 4-6 (see text). The line denotes the theory. ,."
1.0-
0.5
0 0
I
-
. 0
0
3? ;*
ul
m "
'
0
Ar buffer gas
.
1.04
-6
>E
H, buffer gas m.
d" 0 0
0.5
0
,..
_ I _ -
0.5 0.0
200.0
400.0
600.0
800.0 1000.0 1200.0 1400.0 1600.0
P(t0rr)
Figure 4. Pressure dependence of the local low-pressure limit thermal addition rate constant (see text). The symbols are measurements from ref 4 and 6 . The lines denote the theory.
culation with any particular kind of rate constant (e.g, only the addition rate constants or only the dissociation isotope effects) could be improved by further parameter variation, but only at the expense of the desired overall agreement with all measured rate constants and isotope effects. 1. Comparison of Theoretical and Measured Values of k, and k,(H)/k,(D). The theoretical results for the low-pressure limit of the dissociation rate constant are all within the experimental error limits of the measured values. The theoretical ratios kl(H)/k,(D) fall within or somewhat below the lower limits of the measured values. The calculations confirm the lack of any significant temperature dependence for this ratio. The discrepancy between theory and experiment for this isotope effect is probably real and reflects approximations made in the calculation of either the dynamics (see paper 1) or the potential energy surface. 2. Comparison of Theoretical and Measured Values of k-,. The calculated low-pressure limit of the addition rate constant in H2 is compared to three different sets of measurements in Figure 3. Only one study6directly determined a temperature dependence. While the scatter in the measured values of k-, is small (&15%),
H
+ CO
F=
The Journal of Physical Chemistry, Vol. 91, No. 20, 1987 5329
H C O Reaction
the relatively narrow temperature range covered (298-375 K) makes the activation energy for the addition reaction rather uncertain. Values of of from 1.3 to 2.3 kcal/mol produced calculated rate constants with activation energies consistent with these measurements. There is some uncertainty introduced into these calculations because the apparent accuracy of the temperature dependence measurements of k-, reported by Dorfman cannot be presumed from the apparent precision of these rate constants. This is due to the fact that there are other measurements of k-, at room temperature using H2as a buffer gas which lie outside the precision limits of the Dorfman results. The first is by Michael5 and the second is also by D ~ r f m a n .These ~ additional measurements were done at a variety of pressures (50-1400 Torr). To estimate a precision in the measured values of k-, in these latter studies, “local” low-pressure limit values (i.e., k,,,/[M], where kappis the measured second-order rate constant for H C O addition) were calculated. It is these resulting local low-pressure limits which are plotted separately in Figure 3. The apparent precision of the Dorfman measurements in the ambient-temperature study is the same as in his study in which temperature dependence of kl was measured. The Michael ambient-temperature measurements of k_, show comparable precision yet are displaced below those of the Dorfman study. An unfortunate limitation in these calculations is the fact that temperature dependencies of k , and k-, are not available for the same bath gas. A temperature dependence of k-, is available only for H2 which could not be used under current conditions as a carrier gas in the flow reactor experiments for safety reasons. Thus, the more extensively measured temperature dependence of k , cannot be directly linked to that of k-,. The theoretical values of k-, (shown in Figure 3) were designed to fit the more extensive Dorfman measurements instead of the Michael measurements which were made only at room temperature. As seen in this figure, the calculated k-, has an activation energy that is near the lower limit of the range determined by the precision of the experimental measurements. The calculated temperature dependence of k-, could be increased by increasing the value of v, but only at the expense of decreasing the agreement with the observed temperature dependence of k , (see Figure 1). The calculated values of k-, show small undulations as a function of temperature and a reversal in temperature dependence at very high temperatures (>1500 K). The undulations (which are discussed in paper 1) are due to several minor approximations in the calculations. The temperature reversal is due primarily to the increased difficulty of stabilizing HCO* formed from very hot H and CO reactants. The magnitude of this effect depends to some degree on the choice of temperature dependence of ( AE),,, (chosen to be independent of temperature in the current study). The last measurements of k-, which were considered are those which were obtained with different bath gases at ambient temp e r a t ~ r e . ~In. ~Figure 4, a selection of these measurements for H2, Ar, and He as buffer gases are presented as a function of the local low-pressure limit discussed above, Le., the addition rate constant at each pressure divided by the concentration of buffer gas at that pressure. The theoretical results are displayed as solid lines. If the calculated results were exactly at the low-pressure limit, there would be no dependence on pressure for this rate constant. The calculations indicate that the low-pressure limit had not quite been reached in these studies. However, the data displayed in Figure 4 have precision limits which are greater than the anticipated pressure dependencies. Hence, no deviation from the low-pressure limit is observed in these data. As mentioned above, the theoretical study favored the temperature-dependent measurements of k-, for H2 buffer gas reported by Dorfman over those determinations for this bath gas as obtained by Michael at only one temperature (see upper panel in Figure 4). For He (the lower panel), there are only the Michael measurements for comparison with the calculations, and for this bath gas the theoretical results are at the high end of the measured low-pressure limits. For Ar, there are measurements by both Michael and Dorfman, and the calculated values of Ll lie in the
+
He
-
0
0
001
0
0
= Tme et a]. (law mota=)
A
= Tme et a]. (CS,)
0
0
A r H2
-
0.0
m
~e
0
4b.0
0
17.0.0
0
0
A
000 0
60.0
= Bmwn and Miller (H02+He) = Rssent Study (HCO)
160.0
200.0
ub.0
280.0
3210.0
PEL&----
\~
\
,.......
......................................................
10-~~~~~, --._.__._._..__.__....___.__ --- , lo-2 -.-.-.-._.-. 100.0
0.5
1.5
1.0
20
2.5
3.0
3.5
lOOO/T Figure 6. Comparison of calculated values of the thermal dissociation rate constant in Ar bath gas vs. measured values. The symbols for the ref 27; V,ref 28; 0 , ref 29; - - -,ref measured values a r e ---, ref 26; 1; 0,measurements of the current study; and 0 (or A ) , ref 4 (or ref 5) which a r e measurements of addition rate constants converted to dissociation rate constants via the equilibrium constant. a-,
outside the range of conditions which have been used in experimental investigations. The theoretical model was used to calculate rate constants for k , as a function of temperature from 300 to 3000 K. The results for Ar as the collision partner are shown in Figure 6 along with the results obtained in the current study as well as from less direct determination^*^-^^ of k , , which are listed in the review of these rate constants by Warnatz.’ The lack of sensitivity of flame studies and shock tube investigations to k , is responsible for the almost 2 orders of magnitude range of its values obtained in the indirect determinations of k , which are displayed in Figure 6. The lowtemperature addition measurements4,’ are plotted in the same figure after conversion to k , values by using the calculated equilibrium constant. The extrapolated results from the current study agree closely with the Arrhenius expression for k l recommended by Warnatz’ which is based on an evaluation of all prior determinations of k , and k-,. The agreement with this expression becomes poorer at very high temperatures due to the non-Arrhenius behavior of k , at high temperatures. (This high-temperature falloff is the dissociation counterpart to the high-temperature addition behavior discussed in section 111and illustrated in Figure 3.) The calculated values of k , between 300 and 3000 K for all bath gases were fit to the form k , = A7ne-Ea/RTfor use in combustion modeling studies (here R is the gas constant). The results obtained are k,(Ar) = 3.09 X 1 0 - 7 T ’ e - 1 7 0 / R T
(5)
k,(He) = 3.80
X
10-7T1e-17 IIRT
(6)
k , ( ~=~3.07 )
x
1 0 - 7 ~ ~ ~ - 1 7 0 / ~ ~ (7)
(26) Meyer, E.; Olschewski, H . A,; Schecker, H. Gg.; Troe, J.; Vasatko, H.; Wagner, H. Gg.; Zabel, F. “Institut fur Physicalische Chemie der Universitat Gottingen, Final Scientific Report”, 1970, as reported in: Baulch, D. L.; Drysdale, D. D.; Duxbury, J.; Grant, S . J. Evaluated Kinetic Data for High Temperature Reactions; Butterworths: London, 1972; Vol. 3. In ref 1, p 253, Figure 43, there is plotted an unreferenced measured thermal dissociation rate constant that is most likely from this reference. (27) Schecker, H. G.; Jost, W. Ber. Bunsen-Ges. Phys. Chem. 1969, 73, 521. (28) Browne, W. G.; White, D. R.; Smookler, G. R. Symp. (In?.) Combust., [Proc.] 1969, 12, 1035. (29) Bowman, C. T. Symp. ( I n t . ) Combust., [Proc.] 1975, 15, 869.
H
+ C O + H C O Reaction
The Journal ofPhysica1 Chemistry, Vol. 91, No. 20, 1987
k1(H2) = 5.79 X 10-7T1e-170/Rr
(8)
k, is in cm3/(molecule s) and E , is in kcal/mol. Above 500 K, the fit using this functional form is within 6% of the calculated rate constants. (For convenience, the exponent of the T factor has been set to -1. If allowed to vary, that exponent would range from -1 .OO to -1.03 and the fitting error above 500 K would drop to 5%.) Over the temperature range 1000-3000 K, these extrapolations represent the most reliable estimate available of the dissociation rate constant of H C O at high temperatures. Since the results in Figure 6 and eq 5-8 are for the low-pressure limit, all the buffer gas sensitivity of the rate constant resides in a multiplicative factor of k,, the stabilization rate constant. The formulas and parameters used to determine k, in the calculation are all described in the previous section. This information and the fits presented above allow one to modify these low-pressure rate constants for other bath gases. As discussed in the preceding paper, the calculations predict that the high-pressure limit for thermal addition or dissociation will be anomalous and will be proportional to a thermally averaged width of HCO* scattering resonance states. As Figure 8 of the preceding paper illustrates, at room temperature, significant deviations from the low-pressure limit should occur only above 10 atm. This conclusion is based on a low estimate of 1 cm-' for the average resonance width. If the resonance width were higher, the pressure at which deviation from the low-pressure limit occurs would also be higher. At 1000 K, these pressure limits have increased still further (by about an order of magnitude). Thus, under essentially all conditions encountered in combustion processes, reaction 1 may be considered to be in the low-pressure limit. As mentioned in the Introduction, the main sensitivity in combustion modeling to the rate constant of reaction 1 is in the temperature range where this reaction successfully competes with other reactions which also consume HCO. The reactions of HCO with H, OH, and 0, are particularly important in this regard.] The H C O H reaction has a near-temperature-independent rate constant of 1 X cm3/(molecule and the H C O + O H rate constant is of similar magnitude, 1.8 X cm3/(molecule s ) . ~ , The H C O 0, reaction has a temperature-independent rate c ~ n s t a n tof~ 7~ x, ~ ~ cm3/(molecule s). Under typical combustion conditions ([M]/[O,] = lo), the consumption of HCO by the H C O 0, reaction is at least 10 times that by the H C O M pyrolysis below about 1000 K. By 1500 K, the two reactions consume H C O at an equal rate. By about 3000 K, the loss due to pyrolysis is 10 times that due to H C O 0,. The H C O + H and H C O O H reactions will be additional important processes competing with either H C O pyrolysis or the HCO 0, reaction only if the H or OH mole fractions exceed 3 X (1000 K) to 3X (3000 K). C. Comments on the Magnitude of k-]. An early investigation5 of the addition rate constant k-' drew attention to the apparently anomalously low value of k-', fully 2 orders of magnitude smaller than that for the H 0, reaction (a reaction whose reactants have masses, structures, and frequencies which are quite similar to those of the H C O reaction). The theoretical model for H C O can account for this large difference in rate constants for what appear to be very similar addition reactions. First, compared to H CO, H 0, has no barrier to addition.f5 If p were reduced to zero keeping all other parameters of the H C O model the same, the calculated value of k-, increases by about a factor of 14. Second, if E , is increased to the larger bond energy for ~ ) ,increases nearly another factor HO, (about 54 k ~ a l / m o l ~k-I of 8. This second increase is due to the fact that, at the lowpressure limit, the rate constant is proportional to the density of
+
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+
+
+
+
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(30) Timonen, R. S.; Ratajczak, E.; Gutman, D. J . f h y s . Chem., in press. (31) Harding, L. B.; Wagner, A. F. Symp. (Znt.) Combust., [Proc.],in press. (32) Temps, R.; Wagner, G. Gg. Ber. Bunsen-Ges. f h y s . Chem. 1984,88, 415. (33) Veyret, B.; Lesclaux, R. J . Phys. Chem. 1981, 85, 1918. (34) Timonen, R. S.; Ratajczak, E.; Gutman, D. J . f h y s . Chem., in press. (35) Dunning, T. H., Jr.; Walch, S. P.; Goodgame, M. M. J. Chem. Phys. 1981, 74, 3482.
5331
states above the dissociation barrier. The deeper the potential well, the higher is the density of states. The combination of these two factors accounts for the observed 2 orders of magnitude difference between the recombination rate constants of the H + CO and H 0, reactions. In the original experimental s t ~ d i e sof~ ,the ~ H C O reaction, the presence of the addition barrier, p,was attributed to an avoided crossing between a repulsive A' state arising from the reactant asymptote, H + CO('Z), and A' ground state of HCO, which correlates with H + C O ( 3 ~ ) In . fact, the actual activated complex has a bent geometry' (bond angle of 117') where such symmetry classifications do not apply. The two states involved in the avoided crossing in the collinear geometry are about 20 kcal/mol apart in the bent geometry of the transition state,36and no avoided crossing is possible. The recombination activation energy is actually what .is expected of radical attacks on P electronic systems.
+
+
V. Summary The first direct measurements of the HCO thermal dissociation rate constants and its deuterium isotope effect are presented in this paper. The isolated resonance RRKM theory introduced in paper 1 has been used to calculate rate constants for both reactions 1 and -1 under all conditions which have been used to study experimentally both the HCO dissociation reaction and the H + CO addition reaction. The dynamics theory employs the recently developed Harding potential energy surface for HCO, with some fine tuning of its barrier to addition. The success of the calculations complements earlier agreement between theoretical studies which have employed the Harding surface to model other properties of the H C O system quantitatively, including the HCO vibration spectrum and the final C O vibrational distribution in hot H atom collisions with CO. The close agreement of the calculated and measured thermal dissociation rate constants was achieved by using two adjustable parameters. These parameters are the barrier to recombination p (1.5 kcal/mol) and ( the average energy lost by HCO* in buffer gas collisions (values from -40 to -50 cm-' (see section 111)). The value of p is consistent with addition barriers for similar reactions. The values of ( AE)totare somewhat lower than expected from measurements on other systems. However, theoretical arguments have been advanced which suggest this is a consequence of the unusually low dissociation energy of HCO. The quality of the agreement between theory and experiment provides confidence that the theoretical model can be used to predict the behavior of the H + C O system outside of the range of conditions already studied experimentally. Rate constants for H C O decomposition from 300 to 3000 K have been calculated and fit by using standard functional forms to provide the best currently available estimates of the dissociation rate constant at combustion temperatures. The theory used here contains significant approximations that can be confirmed or corrected by more detailed dynamics calculations which are in progress. Future papers in this series will develop the model used for this reaction. There is a need for more experimental work, especially on the addition reaction. In particular, temperature-dependent addition rate constants with Ar, He, or N, as buffer gases and isotope effects of the addition rate constant at room temperature would provide the additional information needed for testing and perfecting more detailed theoretical treatments of this system and for calculating still more reliable dissociation rate constants at very high temperatures. Finally, a somewhat unconventional experiment, one which measures the high-pressure limit of the addition rate constant (which should occur at more than 100 atm of pressure), would yield results which could be used for a direct test of the foundations of the theory.
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Acknowledgment. This work was supported by the Office of Basic Energy Sciences, Division of Chemical Sciences, U S . (36) Private communication with L. B. Harding
J . Phys. Chem. 1987, 91, 5332-5336
5332
Department of Energy, under Contract W-3 1-109-Eng-38 and Contract DE-AC02-78ER14.593. R.S.T. thanks the Natural Science Research Council of the Academy of Finland for a fellowship. We also thank Dr. Irene R. Slagle and Dr. James Miller for advice and help.
Appendix: The Heat of Formation of HCO Experimental values for AH?o[HCO] come from four different sources: photoionization studies, photodecomposition studies, HCO self-recombination studies, and iodine-formaldehyde.studies. The most direct photoionization experiments are those of W a r n e ~ k , ~ ’ H C O + H+ + e- at who measured the threshold for H,CO room temperature. When corrected38 to 0 K, this threshold, together with J A N A F values39of heats of formation of H, H’, e- and H 2 C 0 , gives AHfoo[HCO] = 12.1 f 1.8 kcal/mol. The best photodecomposition studies40 measured the onset of H C O production as a function of photon energy in the laser-induced decomposition of HzCO at room temperature. When corrected , ~ ~ resulting value to 0 K either e m p i r i ~ a l l yor~ ~t h e o r e t i ~ a l l y the
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(37) Warneck, P. Z . Naturforsch., A 1974, 29, 350. (38) Guyon, P. M.; Berkowitz, J. J . Chem. Phys. 1971, 54, 1814. See also: Guyon, P. M.; Chupka, W. A.; Berkowitz, J. J . Chem. Phys. 1976,64, 1419. (39) Chase, Jr., M. W.; Curnutt, J. L.; Downey, Jr., J. R.; McDonald, R. A,: Syverud, A. N.; Valenzuela, E. A. J . Phys. Chem. ReJ Data 1982, 1 1 , 695 and references therein. (40) Reilly, J. P.; Clark, J. H.; Moore, C. B.; Pimentel, G. C. J . Chem. Phys. 1978, 69, 4381.
of AHfoo[HCO]is 9.7 f 1.2 kcal/mol. HCO self-recombination studies are the basis for the JANAF value39for AH?,[HCO] of 10.3 f 2.1 kcal/mol. The last m e a ~ u r e m e n involves t~~ an equilibrium study of I H 2 C 0 H I + H C O in which the activation energies for the forward and reverse directions are separately measured. The difference of these energies, corrected to 0 K, together with the known39 thermochemistry of I and H I gives AHfo0[HCO]. In the measurements, the forward activation energy is measured to within f0.2 kcal/mol. However, the reverse reaction activation energy is not directly measured. Rather, the difference of that activation energy from one for a secondary reaction is directly measured with an uncertainty of about f0.9 kcal/mol. This secondary reaction activation energy is estimated to be between 0 and 1 kcal/mol, for an uncertainty of f0.5kcal/mol. The final value of AHfoo[HCO]is 9.9 f 1.6 kcal/mol where the final uncertainty is the sum of those for the individual measurements. The four measured values of 12.1 f 1.8, 9.7 f 1.2, 10.3 f 2.1, and 9.9 f 1.6 kcal/mol have an overlapping range of about 2 kcal/mol centered at about 10.3 kcal/mol, suggesting a consensus value of 10.3 f 1.0 kcal/mol. Registry No. HCO, 2597-44-6; H, 12385-13-6; CO, 630-08-0; D2,
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7782-39-0.
(41) Moortgat, G. K.; Seiler, W.; Warneck, P. J. Chem. Phys. 1983, 78, 1185. (42) Walsh, R.; Benson, S: W. J . Am. Chem. Soc. 1966, 88, 4570.
New Dynamic Behaviors in a Closed Iodide-Catalyzed Bromate Oscillator. Experiments and Their Mechanistic Interpretation Peter Ruoff,*+ Margit Varga, and Endre Koros* Institute of Inorganic and Analytical Chemistry, L. Eotvos University, H- 1443 Budapest, Hungary (Received: March 4, 1987; In Final Form: May 19, 1987)
When iodide ion is initially present in a closed, uncatalyzed bromate oscillator with 4- [2-(methylamino)propyl]phenol as the organic substrate, a dramatically higher number of oscillations (at most over 100) can be generated than is observable in the absence of iodide ion (3-6 oscillations). The mixing order of reactant solutions was found to have a major influence on the number of oscillations observed. This can be explained by the recently found “clock-typebehavior” of the bromate-iodide reaction. The iodide-catalyzed oscillations are explained in terms of a recycling of iodine between oxidation states +I and -I where reactive iodine(+I) intermediates react rapidly with the organic substrate and thus prevent further effective oxidation of iodine to iodate by bromate. Bromide ions are produced by subsequent reactions, and control of oscillations is interpreted by analogy to the Field-Koros-Noyes theory, with bromide ion as the control intermediate. Similarities to the iodide-bromate reaction performed under batch and CSTR conditions are discussed. We found the first example of a bistability between an oscillatory and a nonosciliatory state in a closed system.
Introduction Bromate oscillatorst.2are homogeneous oscillatory chemical reactions in which an organic substrate is brominated and oxidized by bromate ion in aqueous acidic solutions. They can be divided into two major groups. The first consists of the catalyzed or “classical”’ bromate oscillators, where a metal ion serves as a catalyst. The other main group includes the so-called uncatalyzed systems where no metal ion catalyst is p r e ~ e n t . ~Basic . ~ mechanisms have been established for both classes: the FieldKoros-Noyes (FKN)5 mechanism for the catalyzed case and the Orban-Koriis-Noyes (OKN)6 mechanism for uncatalyzed systems; the OKN mechanism is a minor modification of the FKN mechanism. ‘Permanent address: Department of Chemistry, Rogaland Regional College, Ullandhaug, N-4004 Stavanger. Norway.
0022-3654/87/2091-5332$01.50/0
The important feature in both mechanisms is that bromide ion has a basic function as a control intermediate switching the system between an oxidized and a reduced state, corresponding to a low and high bromide ion concentration, respectively. Model calcul a t i o n ~show ~ ~ ~that main features appear to be reasonably well (1) Noyes, R. M. J . Am. Chem. SOC.1980, 102, 4644. (2) See reviews in: Oscillations and Traveling Waues in Chemical Systems; Field, R. J., Burger, M., Eds.; Wiley: New York, 1985. (3) (a) Koros, E.; Orbln, M. Nafure (London)1978,273, 371. (b) Orbln, M.;Koros, E. J . Phys. Chem. 1978, 82, 1672. (4) (a) Orbln, M.; Koros, E. In Kinetics of Physicochemical Oscillators; Franck, U. F., Wicke, E., Eds.; Deutsche Bunsengesellschaft fur Physikalische Chemie: Aachen, 1979. (b) Koros, E.; Orbln, M.; Habon, I. J . Phys. Chem. 1980, 84, 559. (5) Field, R. J.; Koros, E.; Noyes, R. M. J . Am. Chem. Soc. 1972, 94, 8649. (6) Orbin, M.; Koros. E.: Noyes, R. M. J . Phys. Chem. 1979, 83, 3056.
0 1987 American Chemical Society
