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Kinetics of the Thermal Reaction of H Atoms with Propyne Claudette M. Rosado-Reyes,* Jeffrey A. Manion, and Wing Tsang National Institute of Standards and Technology Chemical Science and Technology Laboratory, Physical and Chemical Properties DiVision 100 Bureau DriVe, Gaithersburg, Maryland 20899-8380, USA ReceiVed: December 31, 2009; ReVised Manuscript ReceiVed: March 2, 2010
The reaction of hydrogen atoms with propyne (CHtCCH3) was investigated in a heated single pulse-shock tube at temperatures of 874-1196 K and pressures of 1.6-7.6 bar. Stable products from various reaction channels (terminal and nonterminal H addition, and by inference H abstraction) were identified and quantified by gas chromatography and mass spectrometry. The rate constant for the channel involving the displacement of methyl radical from propyne (nonterminal H addition) was determined relative to the methyl displacement from 1,3,5-trimethylbenzene (135-TMB), with k (H + 135-TMB f m-xylene + CH3) ) 6.70 × 1013 exp(-3255/T[K]) cm3/mol · s,
k(H + propyne f CH t CH + CH3) ) 6.26 × 1013 exp(-2267 ⁄ T[K]) cm3 ⁄ mole · s Our results show that the acetylene to allene yield is approximately 2 at 900 K, and decreases with increasing temperature. The rate expression is:
k(H + propyne f CH2dC d CH2 + H) ) 2.07 × 1014 exp(-3759 ⁄ T[K]) cm3 ⁄ mole · s This is a lower limit for terminal addition. Kinetic information for abstraction of the propargylic hydrogen by H was determined via mass balance. The rate expression is approximately
k(H + CH3C t CH f CH t C-CH2 + H2) ) 1.20 × 1014 exp(-4940 ⁄ T[K])cm3 ⁄ mole · s and is only 10% of the rate constant for acetylene formation. All channels from H atom attack on propyne at combustion temperatures have now been determined. Comparisons are made with results of recent ab initio calculations and conclusions are drawn on the quantitative accuracy of such estimates. Introduction The formation of polycyclic aromatic hydrocarbons (PAH) is a critical step in the formation of soot during the combustion of hydrocarbon fuels. Key cyclization steps that can initiate the production of aromatic rings are believed to involve reactions of resonantly stabilized hydrocarbon radicals, such as benzyl(C6H6-CH2•), propargyl(CHtCCH2•), and allyl(CH2dCHCH2•) radicals.1 Of particular importance is the reactivity of hydrogen atoms with unsaturated organic compounds, which are always present in rich systems. These processes can lead to resonance-stabilized hydrocarbon radicals. The reactivity of H atoms is such that for their attack on any unsaturated hydrocarbons of moderate complexity there are multiple reaction channels, including contributions from addition and abstraction channels. The relative importance of these pathways determines the significance of subsequent chemical processes. For H attack on propyne, nonterminal addition (ntadd), terminal addition (tadd) and abstraction (abst), must be considered, * To whom correspondence should be addressed.
10.1021/jp9122858
The abstraction of the acetylenic hydrogen can be ignored, since such reaction is endothermic by over 110 kJ/mol. The radicals formed by H addition (reactions 1a and 2a) can undergo the following reactions,
Simple beta C-C bond fission reaction from 1-propenyl radical (reaction 1b, -1b; dc-c) leads to the formation of acetylene. Terminal addition (reaction 2a) leads to 2-propenyl
This article not subject to U.S. Copyright. Published 2010 by the American Chemical Society Published on Web 04/15/2010
Thermal Reaction of H Atoms with Propyne
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TABLE 1: Summary of Previously Obtained Data for the Reaction of Hydrogen Atoms with Propyne H + propyne f
rate constant (cm3/mol · sec)
T (K)
P (bar)
k (1000 K)
ref
products products products products CH3CHdCH CH3CdCH2 f HCtCH + CH3 CH3CdCH2
2.4 × 1011 1.5 × 1013exp(-1006/T) 3.61 × 1013exp(-1233/T) 3.79 × 1011 5.79 × 1012exp(-1560/T) 6.5 × 1012exp(-1010/T) 2.40 × 1013exp(-1152/T)
Low Temperature 298 195-503 215-460 298 195-503 195-503 215-460
0.003 0.001-0.024 0.007-0.8 0.003 0.001-0.024 0.001-0.024 0.007-0.8
NA 5.5 × 1012 1.1 × 1013 NA 1.2 × 1012 2.4 × 1012 7.6 × 1012
Brown et al. (1967)11 Wagner et al. (1972)12 Whytock et al. (1976)13 Michael et al. (1977)14 Wagner et al. (1972)12 Wagner et al. (1972)12 Whytock et al. (1976)13
products HCtCH + CH3 HCtCH + CH3 HCtCH + CH3 HCtCH + CH3
7.2 × 1013exp(-2270/T) 1.3 × 105 T2.5exp(-503/T) 2.57 × 1013exp(-962/T) 3.16 × 1014exp(-4094/T) 3.46 × 1012 T0.442exp(-2749/T) 1.72 × 1014 T-0.01exp(-3590/T) 3.16 × 1014exp(-4094/T) 6.26 × 1013exp(-2267/T) 1.90 × 1014exp(-3160/T) 1.74 × 107 T1.98exp(-2275/T) 4.63 × 104 T2.62exp(-2248/T) 2.07 × 1014exp(-3759/T) 3.39 × 1014exp(-4094/T) 3.57 × 104 T2.825exp(-2426/T) 1.2 × 1014exp(-4940/T)
High Temperature 1200-1400 1200-1570 1158-1477 1200-1400 250-2500 250-2500 1200-1400 870-1145 1200-1400 250-2500 250-2500 870-1145 1200-1400 250-2500 870-1145
1.3-4.0 1.7-2.6 1.2 1-4 1.01325 10.1325 1-4 2-3 1-4 10.1325 101.325 2-3 1-4 ∞ 2-3
7.4 × 1012 2.5 × 1012 9.8 × 1012 5.3 × 1012 4.7 × 1012 5.1 × 1012 5.3 × 1012 6.5 × 1012 8.1 × 1012 1.6 × 1012 3.5 × 1011 4.8 × 1012 5.7 × 1012 9.4 × 1011 8.9 × 1011
Bentz et al. (2007)10 Hidaka et al. (1989)34 Fernandes et al. (2005)15 Bentz et al. (2007)10 Miller et al. (2008)16 Miller et al. (2008)16 Bentz et al. (2007)10 This Work Bentz et al. (2007)10 Miller et al. (2008)16 Miller et al. (2008)16 This Work Bentz et al. (2007)10 Miller et al. (2008)16 This Work
HCtCH + CH3 HCtCH + CH3 H2CdCdCH2 + H H2CdCdCH2 + H H2CdCdCH2 + H CH2CtCH + H2 CH2CtCH + H2 CH2CtCH + H2
radicals with three possible reactive channels (reactions 2a-2d). The first involves C-H bond scission resulting in the formation of allene. The second leads to the starting compound and therefore is not detectable. We have also included the possibility of a 1,2-hydrogen shift into allyl radical. Such reactions for alkyl radicals have activation energies that are too large to compete with C-C and C-H bond cleavage.2,3 However, the formation of a resonance-stabilized radical means that this is a much more exothermic process and so the possibility of a small contribution from this process cannot be ignored. Finally, abstraction of methyl hydrogen from propyne leads to the resonance-stabilized propargyl radical, thermally stable except at the highest temperatures. In combustion systems it is believed to be an important intermediate involved in the formation of the first aromatic ring.4-7 Hence, the relative yields of acetylene to propargyl are of considerable importance with respect to the role of propyne in sooting systems. This paper is concerned with experimental studies on the mechanism and rate constants of hydrogen atom attack on propyne in a heated single-pulsed shock tube, as a continuation and an extension of earlier work of H-atom attack on unsaturated compounds from the National Institute of Standard and Technology Shock Tube Laboratory. This experimental study focused on the aforementioned multichannel sequence of reactions, although the potential energy surface of the reaction of propyne with H atoms is complex.8-10 There has been considerable work on H-atom attack on propyne, both experimental and theoretical. The available literature data are compiled in Table 1. Much of the earlier work was near room temperature and involves observing the temporal behavior of H atoms.11-14 Mechanisms were derived on the basis of various assumptions. Their applicability to the higher temperatures of interest here is uncertain. More recent studies are of direct applicability. Fernandes et al.15 studied the thermal unimolecular decomposition of allyl radicals under shock tube conditions. They extracted the rate constant for the reaction of H + propyne under high temperature conditions, by modeling experimental H-atom concentration-time profiles. Bentz and co-workers10 studied the kinetics and mechanism of the H + propyne reaction in a shock tube at 1200-1400 K, and a pressure range of 1.3-4 bar. An overall
temperature-dependent rate expression k(H + propyne)ov was determined by monitoring H atoms, produced from C2H5I photolysis, by atomic resonance absorption spectrometry. They analyzed in detail the entire reaction process via ab initio calculations. This lead to high-pressure rate expressions, calculated from transition state theory, and hence the branching ratios for all processes included in reactions 1, 2a and 2b, and 3. Also temperature- and pressure-dependent unimolecular rate coefficients and branching ratios were calculated by RRKM analysis for the unimolecular decomposition steps of 1- and 2-propenyl radicals. More recently, Miller et al.16 performed ab initio calculations and RRKM analysis on the transformations of C3H5 radicals (allyl, 1-propenyl, and 2-propenyl). Their conclusions from the RRKM analysis did not differ qualitatively from those obtained previously (see references therein). There are, however, significant quantitative differences, as indicated in Table 1, where rate constants at an intermediate temperature are tabulated under the most favorable conditions. Note that there are no experimental data on the branching ratios. This is an important quantitative gap that we fill in this investigation. Note that propyne contains only three heavy atoms and the computational results should be a good measure of the quantitative reliability of theory. The uncertainties will undoubtedly be larger for larger molecules. The results from the literature data are presented in Figures 1 and 2. They are illustrative of the large number of past determinations and the apparent discordance in the results. The scatter in the data is not necessarily due to errors in the measurements because the importance of the various channels can vary with the experimental conditions. It is essential to distinguish between measurements of the total rate constants and those of the branching ratios. The former are relatively easy to carry out with modern techniques since they involve measurements of the H-atom concentration. The latter is more difficult since it involves the identification of products. Thus, many of the branching ratio values are based on estimates with different degrees of uncertainties. The totality of such studies is difficult to interpret since different mechanisms may be operative at the various temperatures. Unambiguous results can only be obtained by direct detection of reaction products. This
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Rosado-Reyes et al. Reaction System. Two chemical sources are responsible for the production of H atoms, hexamethylethane (HME) and t-butylperoxide (t-BP, (CH3)3CO-OC(CH3)3). The thermal decomposition of HME takes place via
HME f 2t-butyl f 2i-C4H8 + 2H
Figure 1. Overall rate constants from the literature for the reaction [H + propyne f products] from experimental work.
The reaction can be monitored by the formation of isobutene and the disappearance of HME. The isobutene concentration is a measure of the number of H atoms released into the system. In single pulse shock tube experiments, no real time measurements are made and all results are derived from concentration measurements from samples extracted after the heating period. The extent of this reaction is also used to determine the temperature of the experiment by means of its rate expression of k (HME f 2 t-butyl) ) 1016.40 exp(-34 400/T) s-1 .20 To cover lower temperatures, experiments were also carried out using a small amount of t-butylperoxide in enormous excesses of H2 (∼20%) to generate H atoms. The reactions are
(CH3)3CO-OC(CH3)3 f 2C(CH3)4O f 2CH3C(O)CH3 + 2CH3 2CH3 + 2H2 f 2CH4 + 2H
Figure 2. Literature rate constants for specific channels in the H + propyne reaction.
is a key advantage of the single-pulse shock tube experiments. Although there were a number of earlier experimental investigations on the reaction of hydrogen atoms with propyne, most of the work was carried out at room and lower temperatures. There remain a number of questions concerning the relative importance of the various channels, particularly at higher temperatures (relevant to combustion systems). The present shock tube study involves direct measurements of two of the possible products, acetylene and allene, and inferences derived from the total H-atom concentration released into the system. The single-pulse shock tube has unique capabilities for carrying out such studies. These involve the short reaction time, the absence of surface effects and the capability of working under conditions where the only reactions under study are those involving the decomposition of the initially formed radicals. As a result, the products formed are a direct measure of the fundamental radical reaction processes. The resulting rate constants will provide a basis for subsequent comparisons and will allow one to estimate rate constants of the reactivity of H atoms with organics. Experimental Section Experiments were carried out in a heated single-pulse shock tube. Details of the apparatus and general procedures have been published previously.17-19
(3)
(4) (5)
Due to the rapid formation and disappearance of methyl radical, this method is used to generate a precise amount of hydrogen atoms. This is, however, all that is necessary to determine the relative rates of H atom attack on a substrate. In this system, chlorocyclopentane is used as the temperature standard. The thermal decomposition of chlorocyclopentane into cyclopentene and hydrogen chloride is characterized by a rate expression of 4.47 × 1013 exp(-24 570/T) s-1.21 Rate constants for the reaction of H atoms with propyne were determined from relative rate studies utilizing 1,3,5-trimethylbenzene (135TMB) as the competitor. In our experiments, 135TMB undergoes a methyl displacement reaction upon H atom attack, leading to the production of a unique product m-xylene (1,3-dimethylbenzene),
The rate constant for reaction 6, k(950-1100 K) ) 6.7 × 1013 exp(-3255/T) cm3/mol · s,22 is traceable to that of H attack on methane or k(CH4 + H f CH3 + H2) ) 2.4 × 1014 exp(-7000/T) cm3/mol · s in the temperature range of 1000-1200 K.23 135TMB as well as propyne can serve as a radical scavenger, quenching chain decompositions. Some of the experiments were carried out without the 135TMB standard. In those cases the interest was focused on the relative yields of H-atom attack on propyne alone. Mixtures used in the present study are listed in Table 2. The use of a variety of mixtures was designed to validate the postulated reaction mechanism. Most experiments were carried out at pressures of 1.6-2.6 bar. However, to examine the effect of pressure on acetylene and allene yields, we specifically
Thermal Reaction of H Atoms with Propyne TABLE 2: Gas Mixtures Used in the Present Experimentsa mixture
componentsb
A
5000 ppm propyne, 100 ppm CCP, 25 ppm t-BP, 5000 ppm 135TMB, 20% H2 5000 ppm propyne, 200 ppm HME, 5011 ppm 135TMB 6021 ppm propyne, 100 ppm HME, 3000 ppm 135TMB 10323 ppm propyne, 132 ppm HME 10000 ppm propyne, 15 ppm HME 6400 ppm propyne, 100 ppm CCP, 25 ppm t-BP, 9300 ppm 135TMB, 20% H2
B C D E F
a The remaining balance is argon. b CCP ) chlorocyclopentane; 135TMB ) 1,3,5-trimethylbenzene; t-BP ) t-butylperoxide; HME ) hexamethylethane (Note: 1% ) 10 000 ppm).
J. Phys. Chem. A, Vol. 114, No. 18, 2010 5713 Others products observed in smaller concentrations include propene, from HME decomposition, and 1,3-dimethyl-5-ethylbenzene. Propene arises from the isomerization of t-butyl radical via a 1,2 hydrogen shift, followed by β-fission of methyl. The formation of propene accounts for approximately 3% the decomposition of hexamethylethane.24 Ethane and 1,3-dimethyl5-ethylbenzene formation results from methyl recombination reaction and the addition reaction of methyl with 3,5-dimethylbenzyl radical intermediate, respectively. Methyl Displacement Channel (via Nonterminal Addition). A direct measure of the relative rate of methyl displacement is obtained by comparing the yields of m-xylene (reaction 6) and acetylene (reaction 1b), normalized for the initial concentrations of the target molecules or,
k1 /k6 ) [acetylene][135TMB]i /[m-xylene][propyne]i Figure 3 presents an Arrhenius plot of k1/k6, the relative rate constants for displacement of methyl radical from propyne and 1,3,5-trimethylbenzene. The following relative rate expression is obtained
log(k1/k6) ) (0.4291 ( 0.035)1/T-(0.0293 ( 0.04); (874-1041 K)
Figure 3. Rate Constant for displacement of methyl from propyne by atomic hydrogen relative to that of 1,3,5-trimethylbenzene.
conducted a set of experiments with mixture F at pressures between 6.2 and 7.6 bar and temperatures of 823-895 K. Two different gas chromatographic columns were used in the analysis of the reaction mixture. Light organics (C1-C4) were separated on a 2.5 m HayeSep N column (80-100 mesh) operated isothermally. Heavier species were analyzed using a 30 m, 0.53 mm I.D., 5% phenylmethylsiloxane column. Retention times and response factors of the species under analysis were determined from samples of pure compounds. Reaction mixtures were allowed to homogenize for at least 24 h prior to carrying out the shock tube studies. All hydrocarbon samples were from Aldrich Chemicals and were used without purification. The only significant impurity in the samples was a small amount of allene in the propyne. This was subtracted from the products that were formed during the course of the reaction.
The uncertainties listed above are (σ and are a measurement of precision only. Experimental uncertainties in comparativerate single-pulse shock tube studies, mostly systematic in nature, were discussed earlier.18 We estimate that the relative rate constants should be accurate to within (10%, and the estimated uncertainty in the relative activation energies is approximately 5 kJ/mol. Relative to the standard reaction of displacement of methyl from 135TMB,22 where k6 ) 6.70 × 1013 exp(-3255/ T) cm3/mol · sec, we obtain,
k1 ) 6.26 × 1013 exp(-2267/T)cm3 /mol · s; (874-1041 K) Expanded uncertainties in the absolute parameters are estimated to be about a factor of 1.4 in the rate, 10 kJ/mol in the activation energy, and a factor of 3 in the A-factor, taking into account the uncertainties in the parameters for the standard
Results The important products that were observed in the HME and propyne mixtures are i-butene, acetylene, allene, ethane, and methane. i-Butene forms as a result of the decomposition of hexamethylethane, whereas the other products come from hydrogen atom attack on propyne. m-Xylene is observed when 135TMB is added to the mixtures. Acetone (from its decomposition) is also found when t-butylperoxide is present in the system. In the presence of chlorocyclopentane, cyclopentene is formed. Methane and ethane originate from methyl radicals produced from displacement reactions of propyne and 135TMB and subsequent recombination reactions. The amount of methane and ethane that is formed is dependent on the nature of the mixture studied and has no direct bearing on these experiments.
Figure 4. Relative rate constant for methyl vs hydrogen displacement from propyne by H atoms. The apparent dramatic change in the rate above 1110 K is due to propyne isomerization (see text). (Note: 1% ) 10 000 ppm.)
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Figure 5. Comparison of rate coefficients.
Rosado-Reyes et al.
Figure 6. Pressure dependence of the acetylene and allene yields.
reaction, measurements, and due to possible experimental systematic errors. Allene Formation (via Terminal Addition). Figure 4 presents the ratio of acetylene to allene yields with respect to temperature at pressures between 2 and 3 bar. There is a dramatic increase in allene yields above 1100 K. This result is a consequence of the isomerization of propyne into allene. Restricting the analysis to only the linear portion of the graph (see Figure 4), the following fit for the relative rate constant is obtained,
log k(acetylene + CH3)/k(allene + H) ) (0.6481 ( 0.064)1/T-(0.520 ( 0.07); (900-1041 K) This leads to the following absolute rate expression
k(propyne + H f allene + H) ) 2.06 × 1014 exp(-3750/T) cm3 /mol · s; (900-1041 K) This is a composite rate expression combining the terminal addition of H atom to propyne and the branching ratio for the decomposition of the 2-propenyl radical to form allene and propyne. When comparing the results of the present study at pressures of 1.6-2.6 bar to the computed values of Miller et al.16 at 10 bar (Figure 5), the rate of the allene + H channel shows the largest variation. The determinations differ by about a factor of 2.5-5. Figure 6 shows the effect of pressure on the acetylene and allene yields from two sets of experiments covering 1.6-2.6 bar and 6.2-7.6 bar, respectively. No pressure dependency was observed in this range. Abstraction of H-Atom from Propyne. The difference between the concentrations of isobutene and acetylene represents the H atoms that have disappeared from the system. Note that allene formation conserves the H-atom concentration since for each H atom added to propyne another is ejected from the newly formed radical. The difference between the measured isobutene and acetylene concentrations is taken in order to determine the rate constant for the abstraction reaction. This difference becomes increasingly inaccurate as the contribution from the abstraction channel becomes much smaller than that from the methyl displacement channel, due to the subtraction of two large numbers. For example, Figure 7 presents the concentrations of isobutene and acetylene with respect to one another. The
Figure 7. Yields of acetylene and i-butene with respect to each other during H-abstraction experiments.
figure indicates that the concentration of isobutene and acetylene differ from each other by ∼10%. An uncertainty of 2-3% exists for each concentration measurement, and an overall error of up to 50% can be estimated. In addition, there appeared to be a tendency for smaller differences as the reaction temperature increases, thus experiments were carried out with larger propyne to HME ratios. The results are shown in Figure 8. In the case where the propyne/ HME concentration ratio is raised to 700, the H atom concentration (based on isobutene yields) becomes greater than 1. This is contradictory to the postulated mechanism. As a further check, experiments were carried out without HME. It appears that under the present conditions, acetylene can be formed from propyne in the absence of an added source of H atoms. This is barely discernible at 1% propyne mixture but becomes unmistakable at 2% propyne mixtures. It appears that the thermal decomposition of propyne leads to the formation of acetylene. Furthermore, it appears that acetylene formation is dependent on a higher order reaction involving propyne. From the results for the propyne and 135TMB mixtures, it is highly likely that this extra acetylene was generated by H atoms. At higher extents of the reaction, there are no other sources of H atoms. Note that in the present study, the pyrolytic sources of HME and t-BP/H2 were selected in terms of their ease for generating H atoms. It is unlikely that H atoms could arise directly from the unimolecular decomposition of propyne or any possible impurity. At the lower temperatures or before the steep increase in acetylene concentration, it is possible to derive a rate constant
Thermal Reaction of H Atoms with Propyne
Figure 8. Ratio of acetylene to i-butene at different hexamethylethane to propyne ratios vs temperature. (Note: 1% ) 10 000 ppm.)
that can be assigned to the abstraction channel. For nonterminal H addition/displacement versus H abstraction, having a branching ratio of 0.9 at 938 K (see in Figure 7), the following is obtained,
k(H + propyne f propargyl + H2) ) 6.21 × 1011 cm3 /mol · s This value is only about 20% larger than that for a similar process involving the benzylic hydrogen22 but is in contrast to the case for methyl displacement. Using the A-factor for the abstraction of an H atom from toluene,25 one obtains,
k(H + propyne f propargyl + H2) ) 1.2 × 1014 exp(-4940/T)cm3 /mol · s Discussion The rate constant for the reaction of H + propyne f acetylene + CH3 (displacement) is about 2.5 times faster than the H + 135TMB f m-xylene + CH3 (see Figure 3). On a per-methyl basis the results show that H atoms displace methyl radicals from propyne 7.5 times faster than from 135TMB. Since this is a direct measure of nonterminal addition to propyne, one can conclude that this large difference is the consequence of the increased barrier arising from the breaking of the resonance energy of the aromatic ring into a cyclohexadiene structure. This result is indicative of the greater stability of aromatic structures. The rate constant for allene formation is not a direct measure of terminal addition. This is because existing evidence suggests that the breaking of the vinylic C-H bond in 2-propenyl radical is favored over that of the alkyl C-H bond. The actual value of the branching ratio has been determined on the basis of RRKM calculations by Bentz et al.10 to be ∼0.1. This is in rough accord with the value of ∼0.2 derived by Mueller et al.26,27 based on the photofragmentation of 2-chloropropene. On this basis, the total terminal addition to propyne will be a factor of 5-10 larger than that derived from the experimentally observed allene yields. The dominance of terminal addition over nonterminal addition is clear. Terminal addition is thus the main reaction in the H atom addition to propyne. However, the reversal of the 2-propenyl decomposition toward allene at higher temperatures means that the lower stability of 2-propenyl radical is hidden,
J. Phys. Chem. A, Vol. 114, No. 18, 2010 5715 implying that we cannot determine a rate constant for terminal addition. The relative importance of the two processes (reactions 2a, -2a) is dependent on their rate expressions. It can also lead to the observed variation in lower temperature results at varying pressures as a consequence of energy transfer effect. It may well be interesting to carry out a detailed analysis of the lower temperature data. From mass balance considerations, any contribution to terminal addition from allyl formation is excluded. The formation of acetylene from propyne decomposition is an interesting phenomenon. It is probably due to a source of H atoms in the system, as indicated by the concomitant formation of m-xylene in instances where 135TMB is present. The m-xylene and acetylene were observed in a 1:1 ratio, ruling out the direct formation of acetylene from propyne via a molecular process. We note that the interpretation of acetylene pyrolysis itself has always required sources of H atoms.28-30 The fact that the hydrogen atom in propyne pyrolysis leads to acetylene formation may provide a valuable tool for interpreting such results. The data show that acetylene is produced from H-atom attack on propyne at twice the rate of allene at the lowest temperature. The allene channel appears to be more competitive as the temperature increases. We assume that the 1,2 isomerization of 2-propenyl radical, produced from the terminal H atoms addition to propyne, into the resonance-stabilized allyl radical does not contribute. The isomerization of propyne into allene is expected to be responsible for the increasing the concentration of allene and sudden curvature above 1100 K. This is confirmed by determining the rate constant at 1180 K, where k for isomerization can be determined by assuming that allene concentrations above 1100 K are the result of only propyne isomerization,
(
ln 1 -
)
[allene] ) -k(0.0005 s) [propyne]0
(7)
This treatment leads to a rate constant of 74.9 s-1 at 1180 K and it is in satisfactory agreement with the published rate expression of 7.76 × 1011 exp(-28 000/T) s-1 by Hidaka et al.,31 the rate expression of 2.63 × 1013 exp(-32 763/T) s-1 published by Karni et al.,32 and the rate expression of 3.32 × 108 exp(-19 472/T) s-1 derived here from the propyne and allene experimental yields presented by Lifshitz et al.33 These results are shown in Figure 9. The results for this study and those of Bentz et al.10 and Miller et al.16 provide an interesting and excellent basis for comparison between experimental work and ab initio calculations by different methods. The general trends are shown in Figure 5 and Table 1. The agreement regarding nonterminal addition and then displacement is quite satisfactory. There are, however, some issues to consider. For nonterminal addition/displacement, the activation energy derived by Bentz et al.10 is several kcals/mol larger than that determined here. This is apparently compensated by the higher A-factor. Thus, the agreement at our temperatures may be fortuitous due to the cancelation of errors in the A-factor and activation energies. The calculated rate constant by Bentz et al.10 for propargyl-H atom abstraction is a factor of 1.4 smaller than the present determination. The Bentz et al.10 calculation does not actually match their experimental results. In their shock tube experiments, Bentz et al.10 measured the H + propyne f products reaction rate coefficient by monitoring the H-atom concentration. Because the allene +
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Rosado-Reyes et al. isomerization of propyne to form allene. From mass balance considerations, the abstraction of the propargyl-H atom is smaller by a factor of 3. The most important process is, however, the terminal addition of the H atom to form 2-propenyl radical, where it is not observable at high temperatures where the reaction is reversible. Results from studies involving the direct measurement of H-atom decays in propyne under somewhat higher temperature conditions are in excellent agreement with this investigation. However, the variation in results from ab initio calculations on the individual processes is about a factor of 2. The accuracy of the transition state properties is probably not much different than those for the ground state molecules. Nevertheless, a factor of 2 or more difference in the simulation results may have serious consequences.
Figure 9. Arrhenius plot of the rate coefficient for the propyne a allene isomerization reaction.
H channel conserves the concentration of H atoms, this channel is invisible to the experiments within shock tube time scales. Only the channels of acetylene + CH3 and propargyl + H2 contribute to the measured rate coefficient by Bentz et al. of 7.4 × 1012 cm3/mol · s. Our result is in remarkable agreement over temperature range of this study, being able to reproduce to within 15% the experimental rate expression derived by Bentz et al.10 on the hydrogen atom disappearance. In view of the possible uncertainties in the two sets of experiments, this is all that can be expected. Indeed, the theoretical studies of Miller et al.16 also fail to match the experimental H-atom decay of Bentz et al.10 Thus, theory as applied by Bentz et al.10 does not seem to be able to match experimental observations. We find significant disagreement between our results and those of Miller et al.16 with respect to allene formation. In our study, a variation of nearly a factor of 4.8 in pressure did not reveal any pressure dependence in the ratio of rate constants for acetylene and allene formation. This does not imply that pressure effects on the rate constants are negligible, but that the pressure dependence must be similar for these two processes. This is in contrast to the results of Miller et al.,16 for which there appears to be a significant difference in the pressure dependence for the acetylene and allene formation channels. Since our experimental pressures were lower than the calculated numbers of Miller et al.,16 one would expect that such pressure effects would be accentuated. Derived pressure effects on unimolecular rate constants may arise from the choice of the energy transfer parameter. A direct comparison of the rate constants shows significant differences, varying by 3.5 near 10 bar. Any pressure dependency on this channel must be significant only above 10 bar within our temperature range. The activation energy determined in this study for the allene + H channel is in good agreement with that determined by Bentz at el.10 and Miller et al.16 The discrepancy with the absolute value must be a result of differences in the pressure dependency and A-factor. Conclusions The single-pulsed shock tube was used to study the mechanisms and rate constants for H-atom attack on propyne. The major observed reaction is the displacement of methyl radicals to form acetylene. A slightly less important process (by a factor of 2) involves the hydrogen atom induced
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