J. Phys. Chem. 1990, 94, 2453-2464
collaborative program in material science. We thank Drs. R. E. Huie and S.S.Emmi for helpful comments on the manuscript.
74-95-3; CHBr3.Br, 75-25-2; CBr4.Br, 558-13-4; CIHSBr, 74-96-4: CH30C6H4w?61 19-32-0;CH3OC6H4OH+,34471-10-8; CH@C&OH, 150-76-5; Br', 7726-95-6; 1,3,5-trimethoxybenzene,621-23-8; triphenylamine, 603-34-9; N,N,N',N'-tetramethyl-p-phenylenediamine, 100-22-1;hexamethylbenzene, 87-85-4; cyclohexene, 110-83-8.
Registry No. DMSO, 67-68-5; DBM, 74-95-3; (CH,)*S(Br)O,6768-5; CHBr3, 75-25-2; CBr4, 558-13-4;C2HSBr.Br,74-96-4: CH2Br2.Br,
+
-
2453
Rate Constants for the Reactions 0 C2H2and 0 4- C2D2 Products, over the Temperature Range 850-1950 K, by the Flash Photolysis-Shock Tube Technique. Determination of the Branching Ratio and a Further Theoretical Analysis -+
J. V. Michael* and A. F. Wagner Chemistry Diuision,Argonne National Laboratory, Argonne. Illinois 60439 (Received: June 26, 1989; In Final Form: October 10, 1989)
-
-
Overall rate constants for the reactions 0 + C2H2 products and 0 + C2D2 products have been measured between -850 and 1950 K by the flash photolysis-shock tube (FP-ST) technique. The results can be well represented by the Arrhenius exp(-2740 & 167 K/T), equations k l H = (1.78 i= 0.18) X 10-10exp(-2714 118 KIT), and kID= (1.73 i= 0.24) X where both are expressed in units of cm3 molecule-' s-'. The branching ratio for the process 0 + C2H2 HCCO + H has been estimated by comparison experiments to the reaction 0 + H2 OH + H, under identical conditions of first-order 0-atom depletion, photolyte concentration, and flash energy. The result is that the H-atom-producing channel amounts to 0.80 0.15 of the overall reaction between 900 and 1200 K. The present results on 0 + C2H2are compared to earlier lower and higher temperature studies. A three-parameter evaluation of the overall rate behavior is derived from the present and all earlier studies, and the result, between 195 and 2500 K is k , = 1.2 X 10-'7p.09exp(-786 K/T) cm3 molecule-' s-I. The theoretical studies on the title reactions by Harding and Wagner are reviewed and extended in order to understand the theoretical implications concerning the overall rate behavior.
*
-
-
*
Introduction The reaction of O(3P) atoms with acetylene 0 + CzH2 products (1) has long been considered to be important in hydrocarbon oxidations since acetylene can be an intermediate in a fuel-rich system.' Therefore, the detailed mechanism involved in the oxidation of acetylene has been crucial to the further understanding of hydrocarbon combustion chemistry. It was originally proposedZthat reaction 1 occurred through the abstraction process 0 + C2H2 CZH O H (la) because both induction times and product growth rates in the oxidation were substantially controlled by the slowest chain branching reaction, H + O2 O H + 0, as in the H2 oxidation. It was therefore supposed that the two oxidative mechanisms should be closely related. However, this was soon questioned by Fenimore and Jones3 who, on the basis of flame studies, suggested that 0-atom consumption must proceed through the adduct paths 0 CzHz H HCCO (lb) 0 C2Hz CHZ CO (IC) Several lower temperature studies followed which essentially confirmed that the adduct paths were indeed i m ~ o r t a n t . ~The -~
-
-
+
-
+ +
+
-+
+
+
( I ) (a) Bittner, J. D.; Howard, J. B. Prog. Astronaut. Aeronaut. 1978,62, 335. (b) Warnatz, J.; Bockhorn, H.; Moser, A.; Wenz, H. W. Symp. (Inr.) Combust., [Proc.], 19th. 1982 1983, 197. (2) (a) Bradley, J. N.; Kistiakowsky, G. B. J. Chem. Phys. 1961,35, 264. (b) Kistiakowsky, G. B.; Richards, L. W. Ibid. 1%2,36, 1707. (c) Hand, C. W.; Kistiakowsky, G. B. Ibid. 1962, 37, 1239. (d) Glass, G. P.; Kistiakowsky, G. B.; Michael, J. V.;Niki, H. Ibid. 1965, 42, 608. (e) Glass, G. P.; Kistiakowsky, G. B.; Michael, J. V.; Niki, H . Symp. (Int.) Combust., [Proc.], loth, 1964 1965, 513. (3) Fenimore, C. P.; Jones, G. W. J . Chem. Phys. 1963, 39, 1514. (4) Jonathan, N.; Marmo, F. F.; Padur, J. J . Chem. Phys. 1965.42, 1463. ( 5 ) Arrington, C. A.; Brennen, W.; Glass, G. P.; Michael, J. V.; Niki, H. J . Chem. Phys. 1967, 43, 5 2 5 .
0022-3654/90/2094-2453$02.50/0
most compelling of these was that of Jones and Bayes8 who directly observed both ketyl and methylene radicals in a photoionization mass spectrometric flow tube experiment. Because of this earlier interest, there is an extensive experimental literature on reaction 1 both with regard to absolute rate constant^"^ and probable p r o d ~ ~ t s ~ , ~ ~from ~ 2 'the ~ ~reaction. '~~~~-~~
(6) Brown, J. M.; Thrush, B. A. Trans. Faraday Sot. 1967, 63, 630. (7) Williamson, D. G.; Bayes, K. D. J. Phys. Chem. 1969, 73, 1232. (8) Jones, I. T. N.; Bayes, K.D. (a) Symp. ( i t . ) Combusr., [Proc.],14th, 1972 1973, 277. (b) Proc. R . SOC.London, A 1973, 335, 547. (9) Westenberg, A. A.; deHaas, N. J . Chem. Phys. 1969, 73, 1181. (10) Hoyermann, K.; Wagner, H. gG.; Wolfrum, J. Z. Phys. Chem. (Frankfurt a m Main) 1969, 63, 193. (11) James, G. S.; Glass, G. P. J , Chem. Phys. 1969, 50, 2268. (12) Aleksandrov, E. N.; Arutyunov, V. S.; Koslov, S. N. Kinet. Catal. 1981, 22, 391. (13) Homann, K. H.; Wellmann, Ch. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 527. (14) Lohr, R.; Roth, P. Ber. Bunsen-Ges. Phvs. Chem. 1981. 85, 153. (15) Frank, P.; Bhaskaran, K. A.; Just, Th: Symp. (Int.) Combust., [Proc.],Zlst, 1986 1988, 885. (16) Mahmud, K.; Fontijn, A. J . Phys. Chem. 1987, 91, 1918. (17) Russell, J. J.; Senkan, S. M.; Seetula, J. A,; Gutman, D. Symp. (Int.) Combust., [Proc.],22nd, 1988, 1989, 1007. (18) Williamson, D. G. J . Phys. Chem. 1971, 75, 4053. (19) Kanofsky, J. R.; Lucas, D.;Pruss, F.; Gutman, D. J . Phys. Chem. 1974. 78. 3 11. (20) Blumenberg, B.; Hoyermann, K.; Sievert, R. Symp. (Int.) Combust., [Proc.],16th, 1976 1977, 841. (21) Homann, K. H.; Schweinfurth, H. Ber. Bunsen-Ges. Phys. Chem. 1981, 85, 569. ( 2 2 ) Clemo, A. R.; Duncan, G. L.; Grice, R. J . Chem. SOC.,Faraday Trans. 2 1982, 78, 1231; 1983, 79, 637. (23) Buss, R. J.; Baseman, R. J.; He, G.; Lee, Y. T. Report BNL51714; Brookhaven National Laboratory, Upton, NY, 1983; p 176. (24) Homann, K. H.; Wellmann, Ch. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 609.
0 1990 American Chemical Society
2454
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990
It is now generally agreed that the two adduct channels, reactions l b and IC, dominate even at high temperatures. The importance of reaction la in the combustion mechanism has been questioned. All experimental evidence to date suggests that the abstraction pathway does not compete effectively with the adduct reactions under most experimental conditions. With this being the case, it is now possible to devise a mechanism for the oxidation of acetylene that can explain most featuresz6 with k , , = 0. In addition to the experimental investigations, reaction 1 has also been theoretically rationalized by using ab initio potential energy surfaces for both the 3A’ and 3A“ statesz7(hereafter, simply designated as A’ and A” states). It would appear that channels l b and I C can originate from both states but only under the assumption that the A’ state is either rapidly interconverted to the A’’ state or the resultant vibrationally hot adduct is collisionally stabilized. Subsequent RRKM calculations** indicate that the adduct lifetimes are small but are not smaller than a rotational period as indicated by direct molecular beam observation^.^^ Hence, stabilization, at least up to 1 atm of argon, is not an important process being at most only 4-8% in the lower temperature region, 300-850 K. In the theoretical study,z8consideration was also given to the possibility of the abstraction reaction la, and it was shown to be negligible below 2500 K on the condition that the value for the heat of formation of C2H radicalsz9 at 0 K is 134 f 2 kcal mol-I. Therefore, reactions l b and IC, in this theoretical view, account for nearly 100% of the reaction over the complete temperature range. Lastly, the branching ratio of products was theoretically estimated and compared to earlier experimental data. The theoretical predictions of overall rate constants are in good agreement with most lower temperature studies within the combined errors of the experiments.28 However, a disagreement exists between theory and experiment in the high-temperature regime above 1000 K. There are two shock tube s t u d i e ~ ’ ~between * ’ ~ 1500 and 2500 K that give rate constant values about 2 times larger than theoretically predicted. These values were obtained from fits of [O] and [HI profiles to a complex chamical mechanism. The recent high-temperature flash photolysis-resonance fluorescence (HTP) direct determination by Mahmud and Fontijn16 seemed to corroborate the shock tube data. However, the region of temperature overlap between the HTP and shock tube studies was only 10 K. It is possible that the mechanism used for obtaining k l in the shock tube studies was not complete and that the disagreement with theory is not real but is instead caused by this incompleteness in mechanism. This possibility has supplied the motivation for the present direct study. Flash photolysis-shock tube (FP-ST)30rate constant results that substantially overlap the temperature ranges of both the shock t ~ b e ’ ~and . ‘ ~ lower temperature d e t e r m i n a t i o n ~ ~ ’ are ~ . I presented. ~*~~ In addition, branching ratio determinations for reaction l b are given for three temperature ranges. Lastly, a further theoretical analysis is presented that is based on the earlier calculations of ref 28. Experimental Section The experiments were performed with the FP-ST technique. In this technique, a transient species is formed axially in the shock (25) (a) Vinckier, C.; Schaekers, M.; Peeters, J. J. Phys. Chem. 1985,89, 508. (b) Peeters, J.; Schaekers, M.; Vinckier, C. Ibid. 1986, 90, 6552. (c)
Peeters, J.; Boullart, W.; Van de Ven, P.; Vinckier, C. Presented at the Joint Meeting of the French and Italian Sections of the Combustion Institute, Amalfi, 1987; paper 2.12. XIIIth International Conference on Photochemistry, Budapest, 1987, p 69. (26) Miller, J. A.; Mitchell, R. E.; Smooke, M. D.; Kee, R. J. Symp. (In?.) Combust., [Proc.], 19th, 1982 1983, 181. (27) Harding, L. B. J . Phys. Chem. 1981, 85, IO. (28) Harding, L. B.; Wagner, A. F. J . Phys. Chem. 1986, 90, 2974. (29) (a) Wodtke, A. M.; Lee. Y . T. J . Phys. Chem. 1985,89,4744. (b) Shiromaru, H.; Achiba, Y . ;Kimura, K.; Lee, Y. T. Ibid. 1987, 91, 17. (c) Chen, Y . ;Jonas, D. M.; Hamilton, C. E.;Green, P. G.;Kinsey, J. L.; Field, R. W. Ber. Bunsen-Ges. Phys. Chem. 1988, 92, 329. (30) (a) Burns, G.; Hornig, D. F. Con. J . Chem. 1960,38, 1702. (b) Emst, J.; Wagner, H. gG.; Zellner, R. Ber. Bunsen-Ges. Phys. Chem. 1978,82,409. (c) Niemitz, K. J.; Wagner, H. gG.; Zellner, R. 2. Phys. Chem. (Frankfurt am Main) 1981, 124, 155.
Michael and Wagner -AD
--
L
r---
DRIVER
!y--
-
+,
i
Q )
GV
I
Sample Inlet
*P 1 P
+
P
7m
Figure 1. Schematic diagram of the apparatus. P, rotary pump. D, oil diffusion pump. CT, liquid nitrogen baffle. GV, gate valve. G, bourdon gauge. B, breaker. DP, diaphragm. T, pressure transducers. FL, flash lamp. C, capacitor. PS, power supply. M, microwave power supply. F, atomic filter. RL, resonance lamp. A, gas and crystal window filter. PM, photomultiplier. DS, digital oscilloscope. MP, master pulse generator. TR, trigger pulse. DF, differentiator. AD, delayed pulse generator. LT, lamp trigger transformer.
tube by flash photolysis, and its temporal behavior is observed radially as it is removed by chemical reaction. The technique has already been described31 and has been used to measure several rate constants over quite large ranges in t e m p e r a t ~ r e . ~ ~ The present experiments were performed in a redesigned and newly built apparatus33that is schematically illustrated in Figure 1. The 304 stainless steel shock tube is fabricated from 4 in. 0.d. X 14 gauge tube and is about 7 m in length. The incident shock wave velocity is measured by fast pressure transducers, T, and are subsequently differentiated, DF, and recorded on channel two of a digital oscilloscope, DS. The trigger pulse, TR, for both the oscilloscope and the flash lamp is supplied by a master pulse, MP, that is initiated by the first transducer signal. This master pulse is delayed by a preset delay, AD, that then drives a trigger transformer, LT, giving a fast high voltage pulse. This pulse then supplies the trigger for an N2 flash lamp, FL. Photolysis occurs only in the hot central region of the reflected regime, and the measured radial distance across this photolysis region is 4.2 cm at the photometer position of 6 cm from the endplate. In the present experiments, atoms are detected by atomic resonance absorption spectroscopy (ARAS). The photometer system consists of an atomic resonance lamp, RL, and a solar blind photomultiplier, PM. All window materials are optical grade MgFz including the lenses on the shock tube. The lamp runs continuously and is powered by a 2450-MHz microwave generator, M. An atomic filter section,34F, is located in front of the resonance lamp. It is a simple fast discharge flow system and is designed to remove all resonance radiation from the lamp. The flowing gas is -0.5 Torr of the diatomic molecule of the atom to be photometrically detected (e.g., O2 in the case of 0-atom experiments). The atomic species is formed by an electrodeless microwave discharge, M, upstream from the photometer light path. Hence, a large concentration (- 1OI4 ~ m - can ~ ) be produced before and/or after a shock tube experiment in order to measure the fraction of the light detected by the photomultiplier tube that is resonance radiation. When this fraction is known, I, can be simply (31) (a) Michael, J. V.; Sutherland, J. W.; Klemm, R. B. Inr. J . Chem. Kine?. 1985, 17, 315. (b) Michael, J. V.; Sutherland, J. W. Ibid. 1986, 18, 409. (32) (a) Michael, J. V.; Sutherland, J. W.; Klemm, R. B. J . Phys. Chem. 1986, 90, 497. (b) Sutherland, J. W.; Michael, J. V.; Klemm, R. B. Ibid. 1986, 90, 5941. (c) Sutherland, J. W.; Michael, J. V.; Pirraglia, A. N.; Nesbitt, F. L.; Klemm, R. B. Symp. (In?.)Combust., [Proc.],Zls?,1986 1988, 929. (c) Michael, J. V.; Sutherland, J. W. J. Phys. Chem. 1988, 92, 3853. (e) Pirraglia, A. N.; Michael, J. V.; Sutherland, J. W.; Klemm, R. B. J . Phys. Chem. 1989, 93, 282. (33) Michael, J. V. J . Chem. Phys. 1989, 90, 189. (34) (a) Lee, J. H.; Michael, J. V.; Payne, W. A,; Stief, L. J. J . Chem. Phys. 1978, 69, 3069. (b) Miller, J. C.; Gordon, R. J. Ibid. 1983, 78, 3713.
0
+ C2Hzand 0 + C2D2Reactions
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 2455
calculated from the observed signal (at long time) that is measured in a shock wave experiment. Of course, during an experiment the atom filter is not operational. A combination gas filter and crystal window filter section, A, is located in front of the photomultiplier tube. This filtering section serves to help spectrally isolate the resonance line transitions, and various combinations of optical filter and gas filter are used depending on which atomic species is to be detected. Experiments are performed in the reflected shock wave regime. After the reflected wave has cleared the photometer position (6 cm from the endplate), the master pulse fires the flash lamp through the preset delay and trigger transformer. Atoms are formed photochemically from a source molecule that is present in a premixed experimental gas sample. This gas is introduced into the tube at a known initial pressure, temperature, and density. The final reflected shock regime pressure, temperature, and density are calculated from the initial values, the measured Mach number, and corrections for nonideal shock wave behavior, as described p r e v i o ~ s l y . The ~ ~ ~attenuation , ~ ~ ~ ~ ~of the atomic species is followed as it reacts with a reactant molecule that is also present in the premixture. The output from the photomultiplier, which monitors the photometric absorption, is recorded on channel one of the digital oscilloscope, DS. In the present experiments, the attenuation of the signal due to 0-atom absorption is used for the measurements of overall rate constants. However, H atoms are monitored as a product in the determination of the branching ratio for reaction lb. For the 0-atom studies, dry N 2 is used as the filtering gas in A, the crystal window is CaF, (A L 125 nm), and the atomic filter gas is Oz. The resonance lamp contains - 2 Torr of X , = in He, and it runs at 35 W of microwave power. Therefore, the resonance lamp is similar to lamp B as described by Pamidimukkala et a1.j5 For the H-atom studies, dry air is used as the filtering gas in A. The deep window in the absorption spectrum of O2at 121.6 nm, combined with the optical cutoff of MgFz, serves to spectrally isolate the Lyman-a transition. The resonance lamp contains -2 Torr of ultra-high-purity H e and runs at 30 W of microwave power. Under these conditions, there are sufficient hydrogeneous impurities to give measurable signal, and the lamp is nonreversed with a Doppler temperature of -450 K, as described previ~usly.~~ Hence, absolute H-atom concentrations at any temperature greater than 700 K can be derived from the curves of growth that are totally determined by the oscillator strength of the Lyman-a transition. It should be noted that the flash lamp fires -200 p s after passage of the reflected shock wave so that the base-line value for zero absorptions can be assessed from the signal before photolysis (both H and 0 atoms) and/or the signal after long times (when 0-atom concentration decays to zero). The H e that was used as the driver gas was supplied by Air Products and Chemicals, Inc., and was high-purity grade (99.995%). The He and O2that were used in the resonance lamp were ultra-high-purity grade (from Airco Industrial Gases, 99.995%) and extra-dry grade (from Air Products and Chemicals, Inc., 99.6%), respectively. N O was used as the source of 0 atoms. It was obtained as technical grade from Matheson Gas Products and was further purified by bulb-to-bulb distillation at -183 OC in an all-glass vacuum line. The middle third was retained and was subsequently used in mixture preparation. Ar, as the diluent in the experimental gas, was obtained from M G Industries (Scientific Grade, 99.9999%) and was used as received. C2H2 was obtained from Linde, Inc. as technical grade. It was subjected to bulb-to-bulb distillation at -100 OC, and the middle third was retained. This procedure removed the acetone stabilizer as shown by subsequent mass spectrometric analysis (total impurities, > [O], little reactant is consumed, and [R] is essentially a constant. Therefore, the rate for removal of [O] is -dio1/dt =
k b i [Ol [R]
(5)
and this equation integrates to give In
[o],= -kbi[R]t c
(6)
Equation 6 is rigorously correct if 0-atom removal by secondary reactions is negligible. This point will be discussed further below. Transmittance of 0 atoms at t = 0, To,for the triplet resonance transition (130.2, 130.4, and 130.6 nm) is regulated by the energy of the flash lamp such that the value is never less than 0.77. At these high values of T , Beer's law strictly holds,35and therefore
T, = ( Z f / Z O ) = exP(-dOl,~)
(7)
where u is the effective absorption cross section and 1 is the optical path length. The time dependent absorbance, (ABS),, is defined as In (T;'), and therefore, (ABS), = u[O],l
(8)
The relationship between (ABS), and the bimolecular rate constant is then found by combining eqs 6 and 8 In (ABS), = -kbi[R]t
+ c'
(9)
In the experiment, (ABS), is measured, and, according to eq 9, the natural logarithm of it should yield a straight line when plotted against time. The negative slope of the line is kbi[R]. Since [R] is known from the mole fraction in the premixture and the reflected shock regime density, k b i can be calculated for the temperature and density of the given experiment. Figure 2 shows typical experimental plots of both TI and In (ABS), against time for an experiment with C2H2as the reactant. The results for 0 C2H2(820-1921 K) and for 0 C2Dz (857-1980) are given in Table I and are plotted in Arrhenius form in Figures 3 and 4. The lines shown in the figures are given by the equations
+
+
klH = (1.78 f 0.18) X
exp(-2714 f 118 K/T) cm3 molecule-' kiD
Chem. Phys. 1981, 75, 11 16.
+ hu
s-I
(10)
= (1.73 f 0.24) X exp(-2740 i 167 K/T) cm3 molecule-' s-I (11)
where the errors are given at the one standard deviation level. The individual points deviate from the line expressed by eq 10 by f20%
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990
2456
1.000
1)
Michael and Wagner
-
0.975
-
0.950
-
/
m
._ E 2 Y Y
O+C2D2
.. .
/*
..
m L
t0.925
Y
0.900 2.75
3.50
3.25
3.00
3.75
-26' 0
\, "
2
"
4
"
6
"
8
10
104 KIT
12
I 14
+
Figure 4. Arrhenius plot of the data from Table I (0 CzD2experiments). The line in the figure is calculated from eq 11 in the text.
from reaction l b is directly determined with the ARAS technique. Since the curves of and the optical path are known, the absolute [HI, profile can be determined following flash photolytic initiation. In the absence of secondary reaction complications, the formation rate for H atoms, from photolyte photolysis through reaction lb, would then follow the simple result [HI, = [Hl-(1 - exp(-k,[C,H,lt)J
-5
where [HI, = BR[OIo with BR, the branching ratio, being k l b / k 1 . Since the photolyte concentration is always kept low in the present type of experiment, the controlling factor for [O], is the photolyte concentration, [PI, and the photolytic flash energy, FE; Le., [O], 0: FE[P], where it is assumed that the photolytic absorption is proportional to FE. Since FE can be accurately reproduced from one experiment to another, it is only necessary to have a calibrating experiment that uses the same [O], in order to compare with the results for [HI, from a parallel branching ratio experiment. For this purpose the reaction chosen is
\
-
b
-24-
0
6,
+ H2
-+
OH
+H
(13)
In this case [H2] is kept high enough so that the decay constant from reaction 13 is similar to that for reaction 1. But under these conditions, the subsequent reaction
0)
5
E
m
OH
E
>
(12)
-25-
+ H2
-+
H20
+H
is fast on the time scale of the experiment ( k I 4 / k l 3= 4-8 for 800 IT I1200 K),32c*d so that two H atoms are formed for every one initial 0 atom. With only these kinetics, an expression similar to eq 12 is expected to hold
5 c a
[HI, = [HI-11 - exp(-ki,[H2lt)l *L"
0
(14)
2
4
6
8
10
12
14
104 KIT
+
Figure 3. Arrhenius plot of the data from Table I (0 C2H2experiments). The line in the figure is calculated from eq 10 in the text.
whereas the deviation of the points from eq 11 is f23% with both values determined at the one standard deviation level. It is obvious by inspection that there is no isotope effect within experimental error. Branching Ratio Determinations. The branching ratio for reaction 1 to form H atoms, k l b / k 1 has , been measured in three temperature ranges. In these studies, H-atom product formation
(15)
where [HI, = 2[0],. The top panel of Figure 5 shows an example of the behavior in the H2 system. [HI, is measured following photolyte photolysis. For reasons discussed below, the photolyte used in this example is SO2. The dashed line is calculated from cm3 molecule-I~-~ and [HI- = 9.51 eq 15 with k , , = 5.3 X X 10" cm-,. The rate constant value is only 35% greater than expected from a recent FP-ST study on the 0 + Hz reaction.32c In order to examine whether secondary reactions might be perturbing the H2-SO2system more than expected from the simple considerations given above, the experiment shown in the top panel of Figure 5 was modeled with a numerical simulation of the chemical mechanism. In constructing the mechanism, certain processes can be eliminated from consideration. The abstraction
0
+ C2H2and 0 + C2D2Reactions
The Journal of Physical Chemistry, Vol. 94, No. 6,1990 2451
1 0.25
0.50
0.75
Attempts were initially made to observe photochemically produced H atoms in separate experiments with only C2H2-Ar mixtures. [C2Hz] was the same as that to be used for the branching ratio experiments. With [C2H2]= ~(3-4)X 1014~ m - ~ , photochemical formation of H atoms was substantial when an unfiltered N z flash lamp was used. Therefore all subsequent experiments (including the H2-SO2 experiments) were carried out with a Suprasil filter in front of the flash lamp. Even so, H-atom formation could be detected, due no doubt to the fact that the absorption coefficient for C2H2at the most intense line from the photolysis lamp, 174.4 nm, is -45 cm-I atm-I, base e, 0 0C.38 Therefore, for each branching ratio determination, it was necessary to measure this photochemical concentration, [HI , so that it could be subtracted from the value that was formeBhin the reactant experiments. This level also takes into account H atoms that are produced from the apparently fast reaction, C2H + C2H2 C4H2 H ( k = (3-15) X IO-" cm3 molecule-' S - I ) . ~Under ~ the present conditions, the atoms from this fast reaction would be formed with a pseudo-first-order rate of formation of (1-6) X lo4 s-', and this is much larger than the decay constant for 0 C2H2that is used in the branching ratio experiments. In direct observations, temporal buildup or decay could not be observed, in agreement with this fast formation rate. The steady levels of [HIphfrom these experiments are given in Table I1 along with the experimental conditions. The normalized values, [HIph/[C2H2]FE,are then used to correct the H-atom concentrations that are observed in the branching ratio experiments. In order to test whether H atoms could be substantially depleted in secondary reactions with acetylene, a few experiments were made with the larger [HI that can be produced from the photolysis of NH3. The [C2H2]was the same as that used in the branching ratio studies. NH3 was chosen as photolyte because the subsequent reaction of NH, with C2H2is quite slow, and there is no evidence that H atoms are formed as a product.40 Though there was a slight temporal attenuation of [HI, it was entirely attributed to the reaction H + NH3.32a Experiments with and without C2H2 gave the same results, within experimental error, indicating that C2H2is a spectator and is not appreciably reacting with H atoms in the reaction H C2H2 (+ M) C2H3 (+ M), under the present shock wave conditions. This is in complete accord with estimates based on lower temperature m e a ~ u r e m e n t s . ~This ~ reaction should have a rate constant of 1 4 X cm3 molecule-' s-l in which case the pseudo-first-order decay constant for H-atom removal would only be 1140 s-l. In order to minimize effects from secondary reactions, the branching ratio experiments were carried out with flash energies such that [HI I 7 X l o 1 '~ m - ~Use . of this low concentration level should make all atom-atom, atom-radical, and radicalradical reactions relatively unimportant on the time scale of these experiments. However, the radical intermediates might significantly react with the larger concentrations of reactant and/or photolyte molecules. Ketyl, HCCO, from reaction l b might react with acetylene giving H atoms. This process has been considered in flow reactor experiments with corresponding s i m ~ l a t i o n s , and 2 ~ ~the ~ ~products ~ are presumably C3H3 CO. The rate constants used in the and 5 X cm3 molecule-' s - ~ . ~ ~ ~ simulations are 1.7 X Even if the larger of the two values were used, the pseudo-firstorder rate constant for the removal of ketyl would only be -200 s-I, and H atoms are apparently not a product anyway. Methylene is probably formed exclusively as the triplet state in reaction IC, but even if singlet methylene were formed, the singlet would be entirely quenched to the triplet state at the high
-
+
:i I
I
C
1
O
b
"
0.2
0.4
"
'
0.6 '
'
0.8 I
'
t/ms Figure 5. Typical branching ratio experiments showing [HI, against time for 0 + H2 and 0 C2H2reactions. Top panel: H-atom growth in 0 + H, at 1015 K and [H2] = 1.408 X 10l6~ m - ~(---) . Calculated with eq 15 as described in the text. (-) Calculated from a numerical simulation as described in the text. Bottom panel: H-atom growth in 0 + C2H2at 1019 K and [C2H2]= 3.372 X loi4 (---) Calculated with eq 12 as described in the text. (-) Calculated from a numerical simulation of the mechanism given in Table 111 as described in the text.
+
+
+
reactions of 0 + SO2, OH SO,,and H SO, are strongly endothermic and are therefore negligible, and the addition reactions between the same species are all third order and, thus, are also unimportant secondary reactions under the present conditions. Hence, the four major reactions (both forward and reverse) in the H2-02 reaction mechanism are sufficient in describing the system. These reactions with appropriate rate cons t a n t ~ were ~ ~ then ~ ~ included ~ ' in the numerical simulation with the same initial [O], = [H],/2 and value for k13that was used in the eq 15 analysis. The result of this simulation is shown as the solid line in the top panel of the figure. The conclusion of this comparison is that secondary reactions (primarily reaction 14) slightly perturb the approach to steady state but do not affect the final value of H-atom concentration, [HI,, under the present conditions. Therefore a determination of [HI, in the H2-S02 system will give 2[010. This same value of [O], can be used in the branching ratio experiments if the same photolyte concentration and flash energy are employed. Table I1 lists values for [HI from these experiments for use with corresponding branching ratio experiments. Two values were obtained under each condition, and the normalized values, [H],/[P]FE, are generally accurate to -*IO% for each condition. There are additional complications that must be considered before attempting the branching ratio experiments. Photochemical formation of H atoms from the reactant, C2H2,should be minimal at the concentration of acetylene that is used in the branching ratio experiments. Also, H-atom formation or depletion, through secondary reactions, should either be very fast or very slow compared to the time scale of the experiment. With [C2H2]= -(3-4) X I O i 4 ~ m - the ~ , decay constant for the removal of 0 atoms is -2500-7500 s-l over the temperature range, 900-1 200 K. (37) (a) Harding, L. B.; Wagner, A. F. S y m p (Znt.) Combust., [Proc.], 22nd. 1988 1989,983. (b) Albers, E. A,; Hoyermann, K.; Wagner, H. gG.; Wolfrum, J. Symp. (Znr.) Combust., [Proc.], 13th, 1970 1971, 81.
+
-
+
+
~~
~
~~
(38) Okabe, H. Photochemistry o f s m a l l Molecules; Wiley: New York, 1978; p 273. (39) (a) Lange, W.; Wagner, H. gG. Ber. Bunsen-Ges. Phys. Chem. 1975, 79, 165. (b) Laufer, A. H.; Bass, A. M. J . Phys. Chem. 1979,83, 310. (c) Stephens, J. W.; Hail, J. L.; Solka, H.; Yan, W.-B.; Curl, R. F.; Glass, G . P. Ibid. 1987, 91, 5740. (40) Bosco, S. R.; Nava, D. F.; Brobst, W. D.; Stief, L. J. J . Chem. Phys. 1984,81, 3505. (41) Payne, W. A,; Stief, L. J. J . Chem. Phys. 1976, 64, 1150.
2458
Michael and Wagner
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990
-
TABLE I: Rate Data for the Reaction 0 + CzH2 Products P,/Torr
M,'
kls,/d
Ps/(10'8 ~ m - ~ ) TJKC ~
k , / ( 1O-I2 cm3 s-') P,/Torr C2H2Reactant
1.767 1.809
2268 1537 1428
1.474 1.301 1.372
976 852 888
Xc2H2= 1.291 X IO4 11.9 10.84 9.2 10.96 8.1 10.98
10.65 10.87 10.74 10.82 10.98
2.264 2.377 2.546 2.539 2.457
3931 5042 7895 7301 6749
1.814 1.954 2.069 2.079 2.043
1323 1446 1638 1631 1536
Xc2H2= 9.134X 1 0-5 23.7 10.79 28.2 10.72 41.8 10.93 38.4 10.87 36.2
10.93 10.89 10.93 10.91 10.84
2.558 2.701 2.784 2.715 2.564
3733 3298 4277 2550 3508
2.120 2.220 2.295 2.235 2.108
1648 1822 1921 1840 1656
42.7 36.0 45.2 27.7 40.4
15.84 15.75 15.73 15.75 15.99 15.96
2.069 2.214 2.342 2.404 2.291 2.165
6030 10057 12163 14769 8252 7381
2.429 2.616 2.774 2.861 2.765 2.593
1135 1278 141 1 1474 1353 1224
15.9 24.7 28.1 33.1 19.2 18.3
15.94 15.81 15.96 15.59
2.033 1.936 1.805 1.723
3626 3077 2111 1525
2.399 2.232 2.041 1.854
1097 1008 894 826
11.7 10.7 8.0 6.4
15.93 15.90 15.90 15.80 15.89
2.494 2.358 2.287 2.159 2.165
8952 8746 5332 3555 5213
2.996 2.833 2.753 2.567 2.590
1573 1424 1344 1215 1221
32.7 33.8 21.2 15.2 22.0
15.88 15.83 15.90
2.552 2.627 2.456
5201 6241 4497
3.060 3.1I8 2.957
1634 1728 1526
29.5 34.7 26.4
15.86
2.600
4992
3.106
1690
34.0
10.78 10.70 10.87
I .909
M:
klst/s'I
p5'(101*
cm-3)c
T,/KC
k , / ( 10-l2 cm3
s-l)
1.918 2.060 2.086
281 1 3195 3472
1.492 1.664 1.694
984 1117 1143
14.6 14.9 15.9
2.452 2.194 2.196 2.094
7034 3247 3315 1650
2.003 1.761 1.797 1.691
1529 1250 1252 1 I46
38.4 20.2 20.2 10.7
2.524 2.679 2.560 2.536
2703 3239 3349 2909
2.086 2.217 2.110 2.093
1609 1795 1650 1622
31.4 35.5 38.5 33.7
2.108 2.037 1.865 1.958 2.007 1.986
5226 4428 3268 3901 4767 5576
2.506 2.388 2.142 2.280 2.364 2.296
1 I73 1 IO5
13.4 11.9 9.8
1.818 1.821 1.737
2587 2820 2570
2.047 2.066 1.905
902 905 835
9.8 10.6 10.5
2.087 2.011 1.799 1.883
2314 2071 1691 2189
2.484 2.336 2.028 2.174
1 I41
10.2 9.7 9.1
15.61 15.82
2.384 2.615
3690 6870
2.811 3.104
1452 1713
24.5 38.4
= 4.726X lo-' 15.97
2.481
3390
2.999
1554
23.9
2.534 2.691
4575 6035
3.030 3.203
1621 1800
36.6 45.7
2.529
4627
3.002
1.949 2.002 1.940 1.776
3640 2701 2982 1242
1.548 1.593 1.534 1.350
1009 1057 857
19.7 14.2 16.3 7.7
2.422 2.193 2.303 2.220
3761 3028 4304 3047
2.023 1.804 1.912 1.823
1485 1241 1360 1273
20.1 18.2 24.4 18.1
2.432 2.349 2.407 2.377
2771 1940 2986 2201
2.006 1.949 2.008 1.975
1502 1410 1469 1440
30.3 21.9 32.7 24.5
Xc2Hz= 4.122X
10.89 10.95 10.87 10.88
Xc2H2= 1.558X
15.97 15.87 15.87 15.79 15.80 15.56
938 1022 1062 1043
11.0
12.9 15.6
Xc2H2= 1.291 X
15.80 15.90 15.75
Xc2H2= 9.134 X IO+
15.87 15.63 15.83 15.89
1069 883 995
11.0
XC,,,= 5.751 X
XC,,,
15.85 15.81
2.435 2.462
3451 3851
2.913 2.926
I509 1544
Xc2H2= 4.122X 28.8 15.89 31.9 15.90
15.67
2.575
3916
3.043
1661
40.9
XC,,,= 3.144X I 0-5 15.71
16.08
49.0
C2D2Reactant XC,,,
2.171 2.155 2.349 2.293 2.147
2993 2883 5116 5140 5501
1.780 1.766 1.960 1.868 1.746
1222 1206 1410 1349 1 I94
14.1 13.7 21.9 23.1 26.4
10.88 10.90 10.91
2.459 2.502 2.526 2.499 2.455
4825 6004 4674 4839 7070
2.031 2.093 2.088 2.070 2.042
1532 1581 1609 1578 1523
25.7 31.1 24.2 25.3 37.5
10.92 10.93 10.98 10.94 10.79
2.747 2.778 2.667 2.810 2.538
3857 4137 3610 4930 2802
2.262 2.293 2.223 2.317 2.080
1878 1912 1772 1953 1624
37.5 39.6 35.7 46.7 29.6
10.94 10.95 11.00
10.76 10.84
= 1.192X 10.95 10.86 10.92 10.97
1001
XC2,, = 9.239X 10.87 11.01
10.96 10.91 10.97 10.91
xc202 = 4.553 x
10-5
10.86 10.94 10.95 10.95
0 + C,H2 and 0 + C,D2 Reactions
The Journal of Physical Chemistry, Vol. 94, No. 6,1990 2459
*
TABLE I (Continued) kl/(10-l2
Ps/(
P,/Torr
M,'
kIst/sd
cm-3)c
T5/KC
cm3 s-I)
k , /( 10-l2
Ps/(1o1*
PI/Torr
15.88 15.90 16.00 15.97 15.90
2.106 2.013 1.995 1.804 1.886
3569 401 3 3898 1367 3378
2.505 2.372 2.359 2.046 2.173
1 I63
1075 1058 890 96 1
XClD2= 1.192 X 11.9 15.97 14.2 15.91 13.9 15.97 5.6 15.87 13.0
15.92 15.97 15.92 16.01 15.87
2.324 2.161 2.097 1.915 1.983
8343 505 1 305 1 3069 2627
2.804 2.598 2.508 2.235 2.322
1383 1217 1151 986 1047
XClo2= 9.239 X 32.2 15.73 21.0 15.92 13.2 15.93 14.9 15.87 12.3
15.90 15.89 15.86 15.84 15.93
2.542 2.437 2.308 2.414 2.544
5810 509 1 2195 3645 3753
3.064 2.944 2.774 2.898 3.06 I
1618 1499 1367 1480 1625
41.7 38.0 17.4 27.6 26.9
15.90 15.93 15.77 15.92
2.51 1 2.358 2.551 2.759
440 1 3101 4181 5365
3.020 2.847 3.015 3.276
1587 1419 1638 1881
40.5 30.3 38.5 45.5
x~~~~ = 4.553 x
M,"
kIst/s-l
cm-3)c
T5/Kc
1.859 1.907 1.972 1.946
2070 2336 3004 3396
2.139 2.208 2.3 19 2.265
937 979 1037 1014
8.1 8.9 10.9 12.6
1.905 2.050 2.277 2.187
1252 2208 6703 4128
2.180 2.431 2.746 2.617
977 1334 1242
6.2 9.8 26.4 17.1
2.560 2.473 2.238 2.299
4665 4400 3274 3134
3.058 3.002 2.700 2.769
1644 1539 1294 I357
33.5 32.2 26.6 24.9
2.839 2.669 2.764 2.770
4905 3147 3616 5831
3.348 3.187 3.297 3.299
1980 1765 1880 1888
37.6 27.4 30.5 49.1
1110
cm3 S-I)
10-5
15.82 15.98 15.96 15.90
Xc2D2= 3.600 X 15.92 15.86 15.95 15.93
aThe error in measuring the Mach number, Ms, is typically 0.5-1.0% at the one standard deviation level. bThe sum of the least-squares one standard deviation error and the propagated systematic error in the measured first-order decay constants is estimated to be -&lo%. CQuantitieswith the subscript 5 refer to the thermodynamic state of the gas in the reflected shock region.
pressures of the present experiment^.^, Hence, only the reaction of T H 2 with C2H2must be considered as a source of H atoms. C3H2and C3H3radicals from this reaction have been suggested in two of the latest mass spectrometric Even though H atoms can be formed in one of the channels, the overall rate constant is small. This rate constant has been measured a number of times, and the most recent and direct results indicate a very low value at room temperature$3,44being in one s t u d p
