3583
J. Phys. Chem. 1995,99, 3583-3591
CH(a4Z- and/or X2n)Formation in the Reaction between Ketenyl Radicals and Oxygen Atoms. Determination of the CH Yield between 405 and 960 K Jozef Peeten,* Werner Boullart, and Katia Devriendt Department of Chemistry, University of Leuven, Celestijnenlaan 200F,B-3001 Leuven, Belgium Received: November I , 1994; In Final Form: December 20, I994@
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Recently, the minor reaction channel HCCO 0 CH(a4Z- and/or X 2 n ) C02 (r2b) was identified and quantified at 290 K; in an accompanying ab initio study, a CH(a4Z-)-forming and a CH(X211)-producing pathway were characterized. Presently, the C02 plus CH yield k d k 2 was determined at 405, 500, 650, and 960 K from the C02 produced in low-pressure C2Hd0 systems, measured by the discharge-flow/molecular beam sampling mass spectrometry technique. The only critical parameters are the rate constant kl, of the primary reaction channel C2H2 0 HCCO H, which is well established, and the ratio kJk2 of the rate constants of the reactions HCCO H (r3) and HCCO 0 (r2), which was determined here simultaneously. In the temperature range of interest, the k3/k2 ratio was found to be nearly constant, with an average value of 1.45 f 0.30 (20 error). In the determination of the C02 plus CH yield k2dkz from the observed C02, contributions of additional C02 sources were corrected for by kinetic modeling. In this way, kzdkz was found to be 0.079 f 0.033 at 405 K, 0.110 f 0.049 at 500 K, 0.132 f 0.059 at 650 K, and 0.149 f 0.070 at 960 K (overall 95% confidence range). Using the known k2, the values of k2b at the four temperatures were derived; they can be fitted by k2b = (4.9 f 2.6) x lo-" exp[-(560 f 300)/(T/K)] cm3 molecule-' s-'. The increase of k2b with temperature is in agreement with the earlier prediction based on an ab initio characterization of the HCCO 0 reaction surfaces. Finally, it is argued that the reaction channel r2b is an important CH-source in hydrocarbon flames.
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Introduction The formation of ketenyl radicals, along with triplet methylene, in the reaction of acetylene with oxygen atoms was fiist suggested by Fenimore and Jones in 1963.' Although the product distribution has been a matter of controversy for two decades, all recent ~ t u d i e s ~agree - ~ that HCCO is the dominant primary product, with a yield of 80 & 15% nearly independent of temperature for T = 290- 1200 K:
+
C2H2 0
-
HCCO
-
+H
CH2(X3Bl)
(r 14
+ CO
(rib)
Since the major fate of acetylene, a common intermediate in
all hydrocarbon flames, is attack by oxygen atoms?*6the abovementioned studies establish HCCO as a key species in combustion processes. The kinetics of ketenyl reactions have also been the subject of several studies in the past. In the mid eighties, Vinckier et ale7and Peeters et reported rate coefficient measurements of the HCCO 0, HCCO H, and HCCO i0 2 reactions at T = 286 and 535 K. Determinations of the rate constants of the reactions with 0 and H at T = 1500-2500 K by Frank et aL9 are in good agreement. Peeters et al.'O and Boullart and Peeters3 have highlighted the HCCO H reaction as a source of singlet CH2(a1A1), which, due to its high reactivity toward closed-shell molecules such as C2H2, may be responsible for the formation of higher poly-unsaturated hydrocarbon species in flames. Further studies, by several groups including ours, dealt with the reactions of HCCO with 0 2 , C2H2, N2O and Boullart et al.14 studied the HCCO NO reaction over an extended temperature range (T = 290-670 K) and
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@Abstractpublished in Advance ACS Absrracts, February 15, 1995.
0022-365419512099-3583$09.00/0
proposed it as one of the principal "natural" NO-removal pathways in flames.14 In a recent kinetic study of room temperature C2H2/0 systems by Peeters et al.," a minor channel of the HCCO 0 reaction was newly identified as a potentially important CH formation route:
+
HCCO
+ 0 -2CO + H
-
(r2a)
CH(a4Z- and/or X 2 n )
+ CO,
(r2b)
Reaction channel r2b could be quantified from the observed production of the stable coproduct COS, as this reaction was found to be the major C02 source in the C2HdO systems investigated. In this way the CH plus C02 yield of HCCO 0 could be derived with fair precision: kzdk2 = 0.062 f 0.024 at T = 290 K. Furthermore, Peeters et al.15 argued that reaction r2b is the probable source of quartet CH(a4X-), which was identified spectroscopicallyin C2H210 systems by Nelis et al.16 and which was invoked by Phippen and Bayed7 to explain residual chemi-ionization observed in CzHdO systems upon removal of CH(X211)by added C b . At the same time, Peeters et ruled out other possible CH(a4X-) sources. In a complementary ab initio chara~terization'~ of the HCCO 0 potential energy surfaces, two CH-forming (minor) pathways were discerned, one yielding CH(a4X-) and the other CH(X211); both were expected to become faster at elevated temperatures. Reliable predictions of the quartet and doublet CH yields of reaction r2b could not be made however, due to an uncertainty of about 3 kcallmol on the relative energies of the calculated stationary points and transition states. The available kinetic information on CH(a4X-) reactions is limited,l8 and therefore the importance of CH(a4X-) chemistry in flames is still somewhat speculative at this stage. Beside the chemi-ionization reaction CH(a4X-) 0 HCO+ e-,''
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0 1995 American Chemical Society
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Peeters et al.
3584 J. Phys. Chem., Vol. 99, No. 11, 1995
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TABLE 1: Initial Composition of Investigated Mixtures other processes of possible relevance are the fast CH(a4X-) (Concentrations in lOI3 Molecules cm-9 at a Total Pressure NO reaction, for which a high rate constant of (4.2 f 0.7) x of 2 Torr (He Bath Gas) lo-” cm3 molecule-’ s-l was measured recently,’* and the CH(a4Z-) NZ HCN N(4S) reaction, which in contrast mixture [CZ”lo [OIO [0210 to CH(X2n) N219 is a spin-allowed process and hence a T = 405 K 1 15.0 24.4 24.5 candidate contributor to prompt NO formation in flames at high 2 12.9 14.4 13.9 temperatures. 3 10.4 20.7 17.5 Irrespective of the state(s) in which the CH from reaction T=500K r2b is formed, this channel merits further investigation because 1 9.5 20.1 22.1 in hydrocarbon flames it might produce CH at a rate comparable 2 17.3 11.8 17.0 to that of CH2(X3B1) H CH(X211) H2, which is generally 7.7 19.2 3 21.1 considered to be the principal CH-source in flames, but which T=650K is thought to slow down severely at higher ternperature~.~’?~~ In 1 9.0 14.0 22.4 this context it is worth repeating that both the CH(a4Z-) and 2 7.5 8.8 11.6 CH(X2n) yields of HCCO 0 are expected to increase with 3 5.5 11.5 19.7 temperature. Obviously, the verification of the latter is of critical T = 960 K importance to establish the role of reaction r2b as a CH-source 3.6 5.8 12.6 in flames. 4.2 6.6 19.8 4.9 6.4 16.8 Therefore, we now have extended the quantification of the 3.7 7.4 26.4 CH(a4Z- and/or X2n) yield of the HCCO 0 reaction to nearly lo00 K. The CH yield was again derived from the measurement Carbon dioxide and 0 2 were monitored at an electron energy of the stable coproduct C02. At the same time, this study allows of 70 eV, and C2H2 was monitored at 14.4 eV; HCCO signals verification of the temperature dependence of the ratio of the were recorded at 12 eV, and the electron energy for both 0 rate constants of the two dominant HCCO destruction reactions and H atoms was 15.4 eV. in these systems, HCCO 0 and HCCO H. Absolute concentrations of the molecules C2H2, 02, H2, and Experimental Section C02 were established from measured flows of certified highpurity gases and from the total pressure. The instrumental The conventional discharge-flow/molecularbeam sampling sensitivities for 0 and H atoms were determined by partial mass spectrometry technique (D-FMBMS) used in this investigation has been described elsewhere;20its major characteristics dissociation of 0 2 or H2, respectively, in the microwave discharge and application of the discharge odoff method.2o will be repeated here briefly. The flow reactor consists of a cylindrical quartz tube (i.d. = Gases and mixtures, used without further purification, were 16.5 mm) equipped with a discharge side arm,a movable central He (99.9996%, L’Air Liquide) as discharge-inlet carrier gas, injector tube, and an additional side inlet to admit (helium) He (99.994% L’Air Liquide) as additional carrier gas, and carrier gas. The reactor is treated with a 10% HF solution to certified 1-10% mixtures of C2H2 (99.6%), N2O (99.5%), 0 2 suppress radical loss on the reactor walls. Oxygen atoms were (99.998%), H2 (99.999%), and COZ (99.999%) in UHP He generated in a microwave discharge through a flow of N20 (99.9996%) (all UCAR). diluted by He.15 At the beginning of the reaction zone, Le. the downstream 4-24 cm part of the reactor tube, a C2H2/He Results mixture is added through the central injector. The major The quantification of the HCCO 0 CH C02 reaction advantage of using N2O rather than 0 2 as oxygen atom source was undertaken in C2HdO systems at temperatures of 405,500, is that at a dissipated microwave power of 75 W, the N20 650, and 960 K. At each temperature, three or four reaction N2 0 dissociation is nearly complete (-98%) in our mixtures were investigated; the initial mixture compositions are conditions. Except for some 0 2 , which may arise in part by shown in Table 1. All experiments were carried out in CzHdO recombination of 0 atoms on the walls of the 100 cm long systems without initial H atoms, so as to promote consumption reactor tube, no other potentially interfering species such as NO of HCCO by 0 atoms rather than by H atoms. In all the were detected. The much lower [02] obtained when generating mixtures the absolute C2H2, 0, H, 0 2 , and C02 concentration 0 atoms from Nz0 will reduce additional COZproduction via versus time profiles were recorded; at T = 405, 650, and 960 reactions involving 0 2 , such as CHz(X3B1) 0 2 and HCCO K, also the relative HCCO profiles were monitored. Small 02, as discussed below. isotopic contributions of C3H4 to the mass spectrometricHCCO All experiments were carried out at a total pressure of 2 Torr signals were duly corrected for. (298% helium) and at T = 405-960 K. The reactor tube was equipped with a heating mantle ensuring a uniform temperature 1. Methodology. Similar to the room-temperatureinvestigaprofile. Depending on temperature, the flow velocities ranged tion,15 the determination of the CH plus C02 yield of the HCCO from 37 to 71 d s and the corresponding maximum reaction 0 reaction was based on the measurement of the absolute times from tmsx = 6.5 to 3.5 ms. amounts of C02 formed in the investigated mixtures at various reaction times. Of course the use of C02 as a tracer for CH Qualitative and quantitative analysis of the mixtures investigated was achieved by molecular beam sampling mass formation in the (minor) reaction channel r2b of HCCO 0 spectrometry. Samples were taken downstream of the reactor requires that the observed C02 production is chiefly due to this through a 0.3 mm pinhole in a quartz cone, giving access to reaction. At room temperature15this condition was met. First, the first of two differentially pumped low-pressure chambers. the rate of C02 generation was observed to be directly After mechanical modulation to allow phase sensitive detection, proportional to the product of the HCCO and 0 concentrations. the resulting molecular beam enters the second low-pressure Second, COz formation by the other possible sources, CH2(X3B1) chamber which houses an electron-impact ionizer and an 0 2 (r7a, see Table 2), HCCO 0 2 (r4a), CH(X211) 0 2 Extranuclear quadrupole mass spectrometer. A lock-in amplifier (r12c). C2H 0 2 (r17a and b), HCO 0 (r19a), and HC3O discriminates beam ions from background ions. 0 (r21a), could be calculated using known kinetic data and was
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CH Yield of HCCO
J. Phys. Chem., Vol. 99, No. 11, 1995 3585
K
TABLE 2: Reaction Mechanism Used in the Model Calculations To Derive the CH plus COZYield of HCCO Absolute COZProfllesQ k(cm3molecule-' no rla rlb da r2b r3a r3b r4a r4b r5a r5b r6 r7a r7b r7c r7d r8 r9a r9b r10 rll r12a r12b r12c r13a r13b r13c r14 r15 rl6a/b rl7a/b r17c r18 r19a r19b r20 r21a r21b r21c
reaction CzHz
+0
A
+
+
2
---
+
2.0 x 10-10
120
2-4 7-9
2.9 x 10-lo
120
7-9
-
+
2.7 x
430
3 8, 12, 13
+
+ + + HC30 + H
--- + - + +
---c3oz++ - +
+
(see text) 19,28
1.35 x 8.0 x 10-7 1.8 x 10-l'
-1.36
4.7 x 10-2
or -3.28
1.8 x 10-14 3.5 x 10-10
0.93
29 30 630 (see text)
1430
-61
24 31-33 34
(RRKM estimate)
1.0 x 10-10 1.0 x 10-10
35 30,36 34
5.5 x 10-1'
(see text)
(estimate)
2.3 x
(branching 30:45:25 at 290 K, changing linearly to 52:37:11 at lo00 K) C3H2+H4C3H3 CzH CzHz C&Iz + H C2H 0 CH(4Z- and/or ZII) CO + COZ CzH 0 2 CH(4X-and/or CO HCO (branching 5050) CZHZ+ H CZH3 HCO 0 C02 H -CO+OH (branching 5050) HCO H-Hz+ CO HCsO 0 C2H COz HCCO + CO
+ + +
2.09
this work
- ++ + - + -- + + -. + + - + + + - + +
+ +
ref
1.2 x 10-17
+
+
s-l)b
EJR 786
+
HCCO H -CHZ(~BI)+ CO (branching 80:20) HCCO 0 2 CO H CH(4X- and/or zII)+ COZ (branching) HCCO H CHz(lA1) + CO CHZ(~BI) + CO (branching 93:7) HCCO 02- COz HCO (H CO) products (branching 35:65) CHZ(~B~) 0 CO 2H -CO Hz (branching 60:40) CHZ(~BI) + H CH('II) + Hz CHz('B1) 0 2 COz Hz (2 H) HzO + CO HzCO 0 products (branching 40:34:16:10) CHZ(lA1) He CHZ(~B~) + He CH('II) + CZHZ- C3H2 + H C3H HZ (branching 90:lO) CH(TI) 0 CO H CH('lI) H C + H2 CH('II) 02 HCO 0 -CO OH -COz H (branching 33:33:33) C3Hz O-C2H H CO + CO -CZHZ(~B~)
+
n
+ 0 from the
4.7 x 10-9 1.6 x 1.0 x 10-10 1.3 x lo-''
-0.58 -300
6 6 37 6,37 38
4.0 x 10-14 1.0 x 10-10
285
(estimate) 39 29
5.0 x lo-"
-320
29 40,41 (estimate)
1.0 x 10-10
H
(estimate) (branching 33:33:33) (estimate) 1.0 x 10-10 r22 HC3O + H CzHz CO a Only the reactions with a reduced sensitivity coefficient > 1% are listed. Listed rate coefficients apply always to the total rate constant, which is expressed as k = A T exp[-EJRT]. found to amount to only a quarter of the measured C02 production; it could therefore be corrected for with sufficient confidence. This does not necessarily apply to the high-temperature conditions. The predominance of HCCO 0 COz i- CH in the overall COz production might be less pronounced because of (i) the somewhat increased [O2]d[O]o concentration ratios at elevated temperatures due to the enhanced 0 2 production by 0 recombination on the reactor walls and (ii) the known (or expected) positive temperature dependence of the additional CO2-forming reactions involving molecular oxygen. Therefore, all experimental conditions had to be judiciously optimized for a maximum COz production by reaction r2b relative to formation by the additional sources.
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The dominance of HCCO 0 in the total C02 production should manifest itself by a correlation between the experimental C02 formation rates and the iHCCO[o] concentration product over the entire time span. The latter was verified for the Table 1 mixtures at 405, 650, and 960 K (in the 500 K mixtures the ketenyl profiles were not monitored). The pertaining d[COzl/ dt versus iHcco[o] plots are shown in Figure 1. The clear correlation found for each case is consistent with the HCCO 0 reaction as the dominant COz formation route in the investigated mixtures. Both the scatter and the non-zero d[COzl/ dt for small iHCCO[o], i.e. for longer reaction times, can be attributed to additional COz-sources involving 02,which become relatively more important at longer reaction times where the [Oz]/[O] ratio becomes higher.
+
Peeters et al.
3506 J. Phys. Chem., Vol. 99,No. 11, I995
I Q,
-a
d
T=405K
0.81015 .
Q
-2
A MIXTURE 2 MIXTURE 3
n
0.4
c
b Y U
h
v)
0
2.5
0
5
7.5
10
2.01015
T=650K
scheme,15in the sense that there are no important new reactions or channels opening up. We therefore use the room-temperature reaction scheme described and validated recently by Peeters et al! and adopted already in our quantification of reaction r2b at 290 K.15 The mechanism displayed in Table 2 comprises all known reactions relevant to C02 production. The kinetic coefficients were taken from the literature or estimated from analogous reactions. 3. Critical Rate Parameters. Determination of the Ratio of the Rate Constants for the Destruction of HCCO by H (1-3)and 0 Atoms (r2). Only a limited number of reactions and associated rate parameters have a significant impact on the total C02 production in the investigated C2Hd0 systems, and we will confine our comments to such processes. Before undertaking a sensitivity analysis to identify all processes of any significance, it is useful to highlight first the critical parameters that control the bulk of the C02 formed. In light of the experimental correlation above, one can write for the bulk C02 formation rate Ub(c02):
Since the average lifetime of HCCO in the pertaining high [O] conditions is only -0.05 ms, while the time scale for the change of the HCCO concentration is several ms, the quasisteady-state principle can be applied for [HCC0].14J5 The destruction of HCCO is due to its reaction with 0 (12)and with H (r3); in all our experimental conditions, wall termination and destruction by C2H2 and 0 2 account for at most a few percent*J2J3 and can therefore be neg1e~ted.l~Therefore, for t 2 0.2 ms,
0
2
1
3
4
5
and after substitution in eq 1 and rearrangement,
Figure 1. Correlation between the experimental COz formation rate and the i~cco[O]concentrationproduct for T = 405, 650 and 960 K, a.u. = arbitrary units.
Furthermore, as detailed later, extensive kinetic modeling calculations using kinetic data from the literature revealed that all other CO2-sources combined can explain on average only 30-40% of the observed C02. One can therefore conclude that the experimentally monitored absolute C02 production in the investigated mixtures forms a sound basis for the quantification of reaction channel r2b. It may be noted already that the slopes of the d[COz]/dt versus i~cco[O]plots- equal to ~ ~ ~ C H C with C OCHCCO , the instrumental sensitivity for HCCO-show a pronounced increase with temperature. Given the known slightly negative temperature dependence of the instrumental sensitivity for any species in our experimental setup, the increasing slopes toward higher temperatures definitely point to a positive temperature dependence of the HCCO 4-0 CH CO2 rate coefficient k2b. 2. Reaction Mechanism. Since the C02 generation in the C2HdO systems investigated is not uniquely due to the HCCO 0 CH C02 reaction channel r2b, it is obvious that an accurate determination of the CH plus C02 yield of reaction r2 from the total C02 production implies that one has to account for the contributions of all additional C02 formation paths. This is achieved by kinetic modeling, requiring the knowledge of the C2HdOlH reaction mechanism at elevated temperatures and hence the temperature dependences of the rate constants and the product distributions of all relevant reactions. In the 405960 K temperature range, the reaction mechanism is not expected to differ significantly from the room-temperature
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Thus, the parameters or quantities that control the C02 production by reaction r2b are the branching fraction kzdk2, which is sought here, the partial rate constant of the primary reaction kla, the ratio of the rate constants kdk2, and the absolute [CzHzI, [OI, [HI and [COz] concentrations. The total rate constant kl of the primary reaction has been the subject of numerous studies covering a wide T-range. It is now well established; a recent survey by Michael and Wagner2 of all the available data in the range T = 195-2500 K yields the following three-parameter expression: kl = (1.2 x 10-17)P09 exp[-786/ (T/K)] cm3 molecule-’ s-l, which is used in the present study. The HCCO yield of the primary reaction, as already mentioned in the introduction, is also known with fair precision; a temperature-independent value k& = 0.80 is adopted throughout this work. The ratio kdk2 as such was derived by our group7 for T = 286 and 535 K from the quasi-stationary HCCO concentration in C2Hd0 systems as given by eq 2. Replacing [HCCOIstby iHCCO,st/CHCCOand rearranging gives
Hence, kdk2 can be found from the intercepthlope ratio of the straight line obtained when plotting the left-hand side of eq 4 versus [O]/[H]. The instrumental sensitivity , CHCCO, need
CH Yield of HCCO -?
=!
+ 0 at 405-960
K
J. Phys. Chem., Vol. 99, No. 11, 1995 3587
. T=650K
(0
-
.E 1 5 v
x0 1 0 1
/MIXTURE1 MIXTURE2 A MIXTURE3 0 0
(u
I, 0
1
I 3
2
[OIWI Figure 2. Plot of left-hand side of eq 4, ([C~H~~[O~)/(~HCCO[HI), in arbitrary units, versus [O]/[H] for the three mixtures at T = 650 K. The intercepthlope ratio is equal to k&.
TABLE 3: Determination of the kJlk2 Ratios at T = 290-960 K and Comparison with the Literature Data T (K) kdk2 ref this work 290 1.5 f 0.2 405 1.4 f 0.2 this work this work 650 1.3 f 0.1 960 1.7 f 0.2 this work 1.3 f 0.2 Vinckier et al.' 286 535 1.4 f 0.4 Vinckier et aL7 1.5" Frank et al? 1500-2500 Error margin not given. not to be known, since it is common to slope and intercept. Thus, at 286 and 535 K, k3/k2 values of respectively 1.3 f 0.2 and 1.4 f 0.4 (2a error margins) were d e r i ~ e d . ~ A similar treatment of the present iacco, EC2Hz1, [OI, and [HI data of the mixtures studied at T = 405, 650, and 960 K will allow a determination of the kdk2 ratio at these temperatures. All mixtures at a common temperature were treated simultaneously. As an example, the plot of eq 4 for T = 650 K is shown in Figure 2. The high correlation found at each temperature c o n f i i s that the underlying HCCO reaction scheme still holds for temperatures up to 960 K. The k3/k2 values obtained here are summarized in Table 3. Also included is the kdk2 result derived from the concentratiotdtime profiles in the mixtures for the earlier k2dk2 determination at 290 K.15 For completeness, the k3/k2 results of Vinckier et aL7 and of Frank et aL9 are also added. The indicated error margins are the 95% statistical confidence limits. From Table 3 it can be seen that all determinations agree well with one another; no significant temperature dependence is observed in the 290-2500 K range. The average kdk2 ( f 2 o ) is 1.45 f 0.30. 4. Sensitivity Analysis. For each of the investigated mixtures, sensitivities of the absolute C02 concentration to the various rate parameters of the C2H2 oxidation mechanism were derived by kinetic m ~ d e l i n g . ~It should be noted that the measured [CZH~],[O], and [HI concentration profiles were incorporated in these calculations. At each step of the numerical integration procedure the profiles of these species were generated from high-order Chebychev polynomials fitted to the experimental profiles. The straightforward advantage of such a procedure4 is that one can limit the number of reactions in the model to these that immediately affect the concentration of the species under investigation, in this case C02. Resulting sensitivity spectra for the lowest and the highest temperature are shown in Figure 3. This analysis was carried out using the optimum values of the k2dk2 branching fraction obtained in the following subsection. Reduced sensitivity coefficients are defined as Si = 6 In [CO2]/6 In pi, with Si,in
D
Figure 3. Sensitivity spectrum of C02 for mixture 1 at T = 405 K and for mixture 1 at 960 K. Only model parameters for which the reduced sensitivity coefficients S 2 2% are shown. Parameter is either total rate constant (filled bars) or branching fraction (open bars). Branching fractions are respectively k&, k2dk2, k$k,h$h,k1dk12, k13Jki3, ki9&19, and k21&21. percent, expressed as a root mean square statistic over the full time span and pi the pertaining kinetic parameter. Only reactions with Si 2 2% are shown. In agreement with eq 3, the most influential parameters are kl, and kzdkz, while the smaller impacts of k2 and k3 oppose one another. There is also some sensitivity toward the rate coefficients of (i) the secondary reactions HCCO 0 2 (r4) and CH2(X3B1) -I-0 2 (r7), which both (can) yield C02 in one of their product channels, and (ii) the reactions CH2(X3B1) 0 ( r 3 , CH2(X3B1) H (r6), CH(X2n) C2H2 (r9),CH(X2n) 0 (rlO), and CH(X2rI) 0 2 (r12), which together control the C02 formation via the latter reaction, r12. Of course, the sensitivity of the absolute C02 concentration to the above depends on the values adopted for the corresponding rate parameters. Therefore, some explanation regarding the latter is desirable. The kinetic data available on the CH2(X3B1) 0 2 reaction (r7) do not cover our entire T-range. Vinckier and Debruyn20 obtained k7(23 = 2.2 x lo-" exp[-750/(T/K)] cm3 molecule-' s-l, for T = 295-575 K while Bley et al.22measured somewhat higher values: k7(23 = 1.5 x lo-" exp[-505/(T/K)] cm3 molecule-' s-l for T = 233-433 K. In this work, for T = 405, 500, and 650 K the k7 values were calculated from k7(r) = 1.8 x lo-" exp[-630/(T/K)] cm3 molecule-' s-l, the mean of the above two expressions. Dombrowsky and Wagner23 found that this reaction exhibits a negative temperature dependence in the range T = 1000-1800 K. They fitted their k7 determinations and the results of the above two studies by the following three-parameter expression: k7(n = (7.8 x lo-"). (500/T)3,3exp[- 1445/(T/K)] cm3 molecule-' s-l, which was used here for our 960 K experiments. For all temperatures we
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3588 J. Phys. Chem., Vol. 99, No. 11, 1995
Peeters et al.
TABLE 4: k2dk2 and k a Determination at T = 290-960 K and Associated Overall 2u Error Margins, Average Deviations between the Experimental and Calculated Absolute KO21 Profiles in the C2HdO Systems, and Fraction of C02 Calculated at Time Equal to 0.5 r- Originating from HCCO 0
+
T 6) 290" 405
CH
+ COz yield (k;?dkz,
average of
1oo([co21cdc - [cozlexp)/[co2l,xp
k2,,(crn3molec-' s-')
5.5 f 2.5%
(0.72 f 0.32) x lo-" 8% 7.9 f 3.3% (1.16 f 0.49) x 10% 500 11.0 f 4.9% (1.72 f0.76) x lo-'' 14% 650 13.2 f 5.9% (2.18 f 0.98) x lo-'' 6% 960 14.9 f 7.0% (2.62 f 1.23) x 10-l' 8% Results at 290 K,15 recalculated assuming that the reaction CH(XZII) 02 produces 33% COZ.
c02
from HCCO 75% 70% 65% 60% 60%
+0
+
adopted the product distribution determined recently by Alvarez and Moore24at 290 K, with the C02 plus H2 (or 2 H) channel(s) accounting for 40% of the products. The same authors also measured CO and H2CO yields of 34% and 16%, respectively. These results are in quantitative agreement with the findings of Rowland et aLZ5who reported a [CO]/[C02] yield ratio of approximately 1. In view of the 4: 1 [CO]/[CO2] product ratio reported by Dombrowsky and Wagner23at 1000-1800 K, the assumed 40% C02 yield is probably an overestimate at 960 K. On the HCCO 0 2 reaction, r4, only very few data are at hand. The only reported h measurements at elevated temperatures are by Peeters et al.*; their k-data for T = 286 and 535 K can be fitted by the expression: k4 = 2.7 x exp[-4301 (TK)] cm3 molecule-' s-'. Regarding the C02 yield from HCCO 02, only an upper limit can be estimated. This estimation is based on the discrepancy between k4 values measured at room temperature by Peeters et aL8 and by Murray et al.12 on the one hand and by Temps et al.13 on the other. The first two agree on a 290 K k4-value of 6.0 x cm3 molecule-' s-'. The markedly lower k4 = 2.3 x cm3 molecule-' s-l obtained by Temps et can be ascribed to HCCO regeneration via reaction of 0 atoms, produced in HCCO 0 2 0 HCO CO, with the large excess of C2H2 present in their C2H2/0 systems. Hence, their low k4 value may be considered as an upper limit for the rate coefficient of the C02producing reaction channel. The moderate sensitivity to the rate parameters of the other reactions listed above is mainly due to the formation of C02 H assumed here in the fast reaction between CH(X211) and 0 2 (r12); reactions r5 to r12 control the concentration of the precursor CH(X211). The CH(X211) 0 2 reaction can proceed via three highly exothermic reaction channels:
+
+
+
-
+
+
+
+
CH(XII) + 02
-HCO + -CO+OH -COz+H
0
AHr (kcdmol) -76 -159 -184
(r12a) (r12b) (r12c)
There are no data on the C02 yield of this process; in the literature, including in evaluations, one usually mentions only the reaction channels r12a and r12b. There is only the evidence of Lin26 for C02 chemiluminescence in CHBrd02 systems, which he attributed to the highly exothermic reaction channel r12c. In our analysis, the product yield ratio of this reaction was arbitrarily set to 1:1:1. In the context of the literature, the assumed 33% C02 yield is to be regarded as a rather high value. The impact of the uncertainty of the COz yield of reaction r12 on the calculated C02 production and the probable systematic error it induces in the quantity k2dk2, will be addressed in the Discussion. Regarding the CH(a4Z-) 0 2 reaction, it is obvious that the amount of C02 produced by this process can at most be only a fraction of the C02 formed together with the CH(a4Z-); at the given concentrations of 0, H, and 0 2 , a large if not dominant part of the quartet CH is expected to react with
+
0 and H. Moreover, contrary to CH(X211), quartet CH(a4Z-) does not possess the unique combination of a vacant orbital plus a lone pair required for insertion into a o-bond or cycloaddition to a z-bond; hence C02 production in CH(a4Z-) 0 2 is mechanistically highly unlikely. We therefore did not consider this process. The rate coefficient expression for the CH2(X3B1) H reaction (1-6) at T = 300-1000 K listed in Table 2 was obtained from work in progress at this l a b ~ r a t o r y ; ~ ~ the measured drop-off of the rate constant in this T-range is less steep than implied by the recently recommended rate e x p r e s s i ~ nwhich , ~ ~ was based essentially on data at 300 K and at T > 1500 K. 5. Determination of the CH plus C02 Yield of HCCO 0. Above, evidence was presented that the bulk of the C02 production in our systems arises by the HCCO 0 reaction. Hence, as follows from eq 3, k2dk2 can be derived analytically in good approximation from the measured [COz] formation rates and [C2H2], [O], and [HI concentrations. However, rather than using such an analytical approach, we opted for 'comparative' kinetic modeling 4 ~ 1 5to extract kzdkz from the experimental data. The reason is that kinetic modeling provides a straightforward way for taking into account directly the additional COz production by all sources. It must be stressed that such a k2d k2 determination should not be regarded as the result of 'fitting experimental data to a complex reaction model', because the modeling serves merely to correct for minor contributions from other COZ sources. In the comparative kinetic modeling procedure, absolute C02 concentration profiles are calculated for a range of values of the kzdk2 parameter and compared with experimental profiles. The parameter optimum, i.e. the kzdkz value that provides the best match, is obtained via a two-dimensional variant of the response surface method4,27which is essentially a least-squares approach. Assuming a normal error distribution, the objective function to be minimized takes the following form:
+
+
+
+
m;
(5) j
i
with the response R a measure of the goodness of fit, mi the number of degrees of freedom of the ith profile, and n the number of profiles at a given temperature. All the mixtures investigated at the same temperature are treated here simultaneously. The reaction mechanism is that (partly) displayed in Table 2. Again, the experimental [CZHZI,[OI, [HI, and [OZ] profiles were incorporated in the modeling, via third-order Chebychev polynomials. After a coarse location of the parameter optimum, the response was calculated for some 20 values of kzdkz in the region of interest. The resulting response curve was then fitted by a quadratic polynomial from which the optimum kzdkz value was obtained. Statistical 95% confidence margins were obtained using the quasi-rigorous 'likelihood ratio' Table
CH Yield of HCCO
+ 0 at 405-960
K
J. Phys. Chem., Vol. 99,No. 11, 1995 3509
4 lists the optimum kzdk2 values for each temperature; the 290
K result15 is also included. Column 3 shows the corresponding partial rate constants k2b using the k2 = 2.0 x exp[-120/ (T/K)]cm3 molecule-' s-l expression for the total rate constant of HCCO 0. The latter was constructed from the k2 measurements by Vinckier et al.' (T = 286 and 535 K) and by Frank et al? (T = 1500-2500 K). The indicated 2 a error margins for k2dk2 as well as k2b include both the statistical error (95% confidence range) and the possible systematic errors, as detailed in the next section. The results displayed in Table 4 show that both the CH yield of HCCO 0 and the absolute magnitude of the partial rate coefficient k2b exhibit a positive temperature dependence. The k2b data for T = 290-960 K can be fitted by an Arrhenius-type law: k2b = (4.9 f 2.6) x lo-" exp[-(560 f 300)/(T/K)] cm3 molecule-l s-l, implying an activation energy of 1 kcal/mol. The temperature dependence of the kzdkz branching fraction for T = 290 -960 K is given by kdk2 = (0.25 f 0.12) exp[-(440 f 250)/(T/K)] . The latter suggests that in the high-temperature limit the HCCO 0 reaction may give about one quarter C02 CH. The average deviation between the experimental [CO2] profiles and those calculated with the optimum kzdk2 values ranges from 6 to 14% (See column 4 of Table 4). Examples of the CO2-profile fits are shown in Figure 4. The last column of Table 4 lists the calculated average contributions of the HCCO 0 reaction to the total calculated C02 concentrations at a reaction time equal to half t-. Thus it is found that HCCO 0 accounts for 60-75% of the total C02 production, consistent with the strong correlation between the C02 formation rate and the iHCCO[o] product. The remainder, 25-40%, is due to additional C02 producing reactions: HCCO 0 2 (r4a), CH2(X3B1) 0 2 (r7a), C2H 0 2 (r17a and b), HC30 0 (r21a), HCO +O (r19a), and CH(X211) 0 2 (r12c). It was found that reaction r12, with an assumed C02 plus H yield of 33%, is by far the most important single additional C02 source under our conditions. Its calculated contribution to the [CO2] measured at t = 0.5 t- ranges from 10 to 20%,depending on temperature. However, it should be kept in mind that the assumed yield k12Jk12 of 0.33 is probably an overestimate; the lack of information on this yield will of course entail a fairly large possible systematic error on the derived value of k2b, as discussed below. None of the other minor CO2-producing reactions contributes more than a few percent of the total C02.
+
MIXTURE 3
0
2
6
4
+
-
+
+
+
2
I
/
+
+
+
1
MIXTURE2
+
+
6
4
Time (ms) 0
1
2
3
4
5
+
Discussion
1. Evaluation of Systematic Errors. Possible systematic errors in the reported k2dk2 determinations will arise in the first place from uncertainties in the quantities that control the C02 production via HCCO 0. As follows from eq 3, these are: the partial rate constant kl,, the rate constant ratio k3/k2, and the absolute concentrations of C2H2, 0, H, and C02. The last four were measured each with an estimated standard error of 5%. The uncertainties on the parameters kl, and k3/k2 were addressed previously; the following standard errors were adopted: a(k1) = 0.1 x kl?' U(klJk1) = 0.1?-4 and ~(k3/k2) 0.15 as determined here. Another important cause of systematic errors is the uncertainty of the C02 yield of the CH(X211) 0 2 reaction (r12), the most important additional C02 source here. The assumed k12Jklz = 0.33 could be off by 0.33, such that one has, roughly, 24k12Jk12) 0.33. The impact of each of these uncertainties on the kzdk2 determinations was evaluated by kinetic modeling; the resulting total (statistic and systematic) errors were calculated using the classical error propagation rule. Thus, for all temperatures, the combined relative 20 errors (or
+
+
1
2
3
4
Figure 4. Examples of experimental [COz] profiles (A) and profiles calculated (-) using the k& optima listed in Table 4.
95% confidence margins) on the k2dk2 values were found to be close to f45%. An effect which hitherto has not been touched upon is the gradual increase of the 'initial' 0 atom concentration [Ole at the beginning of the reaction zone as the mixing point (i.e. the exit of the injector tube) is shifted upstream. This increase is due to 0 atom recombination on the wall of the reactor tube and is of course accompanied by a concomitant decrease of the initial 0 2 concentration. For a few of the investigated mixtures, the magnitude of the [O]Oat various positions in the flow reactor was measured by titrating with an excess of NO2 added through the injector tube (instead of C2H2) and measuring the remaining [NOz]. The influence of this effect on the derived kzdkz, as evaluated by kinetic modeling, was found to be fairly small (typically about 7%), and it was not further taken into account. 2. Temperature Dependence of k2b. Figure 5 represents the Arrhenius plot of the kzb values determined in this work together with the earlier result at room tem~erature.'~The corresponding expression, k2b = (4.9 f 2.6) x lo-" eXp[(560 f 300)/(T/K)] cm3 molecule-' s-l implies a fairly high A-factor and an Arrhenius activation energy of E, 1 kcall mol. The reaction channel(s) leading to C02 plus CH(a4X- and or X 2 n ) becomes fairly fast at temperatures approaching those
-
3590 J. Phys. Chem., Vol. 99,No. 11, 1995
Peeters et al. When using the higher k value of 4 x lo-" obtained by extrapolating our k6 data,3O the calculated ratio of the CH production by reaction r2b over that by reaction r6 is still 0.60.
10-12 0
-
,
, 1
,
+
1000 I T(K) ,
I
I
1
3
2
4
Figure 5. Arrhenius plot of the rate constant kzt, of the reaction channel 0 CH C02. Error bars indicate the 2a margins.
HCCO
+
+
of flames. Both the A-factor and the E, value are compatible with the reaction path via the quartet HCC(0)O adduct identified in our earlier ab initio chara~terization.'~The implied initial 0-addition to the carbonyl x-bond was calculated to face an energy barrier of about 3 kcal/mol, with a possible error of 3 kcal/m01.~~ This path, through quartet HCC(O>O,does of course lead to CH(a4Z-) C02. However, the observed magnitude and T-dependence of k2b is also reconcilable with the other pathway identified in the ab initio study,15 Le. initial formation of a doublet HC(0)CO combination product, followed by 0-migration and subsequent C02-elinination to form CH(X2rI), in competition with the much more facile direct fragmentation of the doublet HC(0)CO into 2 CO H. Approximate RRKM calculations predict a CH(X2rI) yield via this path of about 1.6% at 300 K, increasing to -2.5% at 960 K, both values being subject to a possible error of a factor of 3. The calculated increase with T is less than that of the experimental yield k2d k2, but not incompatibly so. 3. Implications for Flame Chemistry. As argued earlier,15 reaction r2b is the most probable source of quartet CH(a4Z-), which was observed directly16 and indirectly" in roomtemperature QHdO systems. The positive temperature dependence of this branching fraction will significantly enhance the importance of CH(a4Z-) production by reaction r2b in the hightemperature oxidation of C2H2. Therefore, chemi-ion formation by CH(a4Z-) 0, nitric oxide removal via CH(a4Z-) NO, and other quartet methylidyne reactions can be expected to become processes of consequence in hydrocarbon flames where C2H2 is formed as an inte.rmediate. Furthermore, in flames the reaction between HCCO and 0 may become competitive with CH2(X3B1) H (r6) as a source of methylidyne radicals, irrespective of the electronic state. A rough estimate of the relative CH formation rates of reactions r2b and r6 in a flame can be made by invoking quasi-steady states for the reactive intermediates involved, Le. HCCO and CH2. Such an estimate was made for conditions typical for the (middle of the) flame front of near-stoichiometric hydrocarbon flames: a temperature of 1500 K and mole fractions z(C2H2) = 0.005, ~ ( 0 2 = ) 0.07, x(OH) = 0.005, ~ ( 0 =)0.003, and x(H) = 0.003. This information is sufficient for a quasi-steadystate calculation as 0 2 , OH, 0, and H can be considered to be the dominant coreactants for removing HCCO and CH2. It is assumed here that both HCCO and CH2 originate from the C2H2 0 reaction while also all singlet CH2(a1A1), which results from HCCO H,3v10 is deactivated to CH2(X3B1). In this calculation all rate constants at 1500 K were taken from the most recent evaluation of kinetic data for combustion modelincluding the branching of the C2H2 0 reaction (70% HCCO versus 30% triplet CH2 yields at flame temperatures) and the rate constant of CH2(X3B1) H. The rate constants for the reactions of HCCO and CH2 with OH are not known; they were both taken equal to be 10-lo cm3 molecule-' s-l. Thus, it was found that the rate of HCCO 0 CH COz (r2b) is 1.35 times that of CH2(X3B1) H CH H2 (136).
+
+
+
+
+
+
+
+
+
+
--+ +
+
Conclusions On the basis of the observed C02 production in C2H2/0 systems, from room temperature to nearly loo0 K, it could be shown that the C02 plus CH yield of the HCCO 0 reaction is appreciable, increasing from about 5% at 290 K to 15% at 960 K. Over this T-range, a rate constant expression k2b = (4.9 f 2.6) x lo-" exp[-(560 f 300)/(T/K)] cm3 molecule-' s-l could be derived for the CO2-plus-CH forming reaction channel. From an earlier ab initio study, it could be argued that the reaction may generate CH in both the quartet a4Z- and the doublet X211 states; it can now be concluded that the formation of the quartet as well as the doublet state by this reaction speeds up considerably at higher temperatures. Finally, it could be shown that in flames the HCCO 0 reaction may be as important a CH source as the CH2(X3B1) H reaction.
+
+
Acknowledgment. The authors acknowledge support from the Belgian National Fund for Scientific Research, the Commission of the European Union, the Belgian Federal Services for Scientific, Technical and Cultural Affairs, and the Belgian Institute for Encouragement of Scientific Research in Industry and Agriculture. References and Notes (1) Fenimore, C. P.; Jones, G. W. J. Chem. Phys. 1963, 39, 1514. (2) Michael, J. V.; Wagner, A. F. J. Phys. Chem. 1990, 94, 2453. (3) Boullart, W.; Peeters, J. J. Phys. Chem. 1992, 96,9810. (4) Peeters, J.; Langhans, I.; Boullart, W. Znt. J. Chem. Kiner. 1994, 26, 869.
( 5 ) Miller. J. A.:, Kee.. R. J.: Brook. C. K. Annu. Rev. Phvs. Chem. 1996,41, 245.'
(6) . _ (a) . , Hauchecorne. R. Ph.D. Thesis. Leuven. 1990. (b) Peeters. J.: Hauchecome, R.; Boullart, W.; Borms, R. Proceedings of 'the AngloGerman Combustion Symposium 1993; The British Section of the Combustion Institute: Cambridge, 1993; p 144. (7) Vinckier, C.; Schaekers, M.; Peeters, J. J. Phys. Chem. 1985, 89, 508. (8) Peeters, J.; Schaekers, M.; Vinckier, C. J. Phys. Chem. 1986, 90, 6552. (9) Frank,P.; Bhakaran, K. H.; Just, Th. Symp. (Znt.) Combust. [Proc.] 1986, 21, 885. (10) Peeters, J.; Vanhaelemeersch, S.; Van Hoeymissen, J.; Borms, R.; Vermeylen, D. J. Phys. Chem. 1989, 93, 3892. (1 1) Unfried, K. G.; Glass, G. P.; Curl, R. F. Chem. Phys. Lett. 1991, 177, 33. (12) Murray, K. K.; Unfried, K. G.; Glass, G. P.; Curl, R. F. Chem. Phys. Left. 1992, 192, 512. (13) Temps, F.; Wagner, H. Gg.; Wolf, M. Z. Phys. Chem. 1992, 176, 29. (14) Boullart, W.; Nguyen, M. T.; Peeters, J. J. Phys. Chem. 1994, 98, 8036. (15) (a) Peeters, J.; Langhans, I.; Boullart, W.; Nguyen, M. T.; Devriendt, K. J. Phys. Chem. 1994,98, 11988. (b) Langhans, I. Ph.D. Thesis, Leuven, 1988. (16) (a) Nelis,T.; Brown, J. M.; Evenson, K. M. J. Chem. Phys. 1988, 88, 2087; (b) 1990, 92, 4067. (17) Phippen, D. E.; Bayes, K. D. Chem. Phys. Lett 1989, 164, 625. (18) (a) Hou,Z.; Bayes, K. D. J . Phys. Chem. 1992,963685;(b) 1993, 97, 1896. (19) Blauwens, J.; Smets, B.; Peeters, J. Symp. (Int.) Combust. [Proc.] 1977,16, 1055. (20) Vinckier, C.; Debruyn, W. Symp. (Int.) Combust. [Proc.] 1979, 17, 623. (21) Westley, F.; Herron, J. T.; Hampson, R.F.; Mallard, W. G.; NIST Chemical Kinetics Database-Ver. 4.0; NIST Standard Reference Data: Gaithersburg, MD, 1991. (22) Bley, U.; Temps, F.; Wagner, H. Gg; Wolf, M. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 1043. (23) Dombrowsky, Ch.; Wagner, H. Gg. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 1048. (24) Alvarez, R. A,; Moore, C. B. J. Phys. Chem. 1994, 98, 174. (25) Rowland, F. S.; Lee, P. S.-T.; Montague, D. C.; Russell, R. L. Faraday Discuss. Chem. SOC. 1972,53, 111.
CH Yield of HCCO
+ 0 at 405-960 K
(26) Lin, M. C. J. Chem. Phys. 1974, 61, 1835. (27) Frenklach, M. In Combustion Chemistry; Gardiner, W. C., Ed.; Springer-Verlag: New York, 1984. (28) Bahland, T.; Temps, F.; Wagner, H. Gg. Ber. Bunsen-Ges. Phys. Chem. 1984,88, 1222. (29) (a) Baulch, D. L.; Cobos, C. J.; Cox, R. A,; Esser, C.; Frank, P.; Just, Th.; Kerr, J. A.; Pilling, M. J.; Troe, J.; Walker, R.W.; Warnatz, J. J. Phys. Chem. Re5 Data 1992, 21, 411. (b) Baulch, D. L.; Cobos, C. J.; Cox, R. A.; Frank, P.; Hayman, G.; Just, Th.;Kerr, J. A.; Murrels, T.; Pilling, M. J.; Troe, J.; Walker, R. W. Combust. Flame 1994, 98, 59. (30) Devriendt, K.; Van Poppel, M.; Peeters, J. Manuscript in preparation. (31) Langford, 0. A.; Petek, H.; Moore, C. B. J. Chem. Phys. 1983, 78, 6650. (32) Wagener, R. 2.Naturforsch. 1990, 45a, 649. (33) Hancock, G.; Heal, M. R. J. Phys. Chem. 1992, 96, 10361. (34) (a) Bennan, M. R.;Fleming, J. W.; Harvey, A. B.; Lin, M. C. Chem.
J. Phys. Chem., Vol. 99, No. 11, 1995 3591 Phys. 1982, 73, 27. (b) Bennan, M. R.; Fleming, J. W.; Harvey, A. B.; Lin, M. C. Symp. (Int.) Combust. IProc.1 1982, 19, 73. (35) Messing, I.; Canington, Ti Filseth, S. V.; Sadowsky, C. M. Chem. Phys. Lett. 1980, 74, 56. (36) Hading, L. B.; Guadagnini, R.;Schatz, G. C. J. Phys. Chem 1993, 97, 5472. (37) Koshi, M.; Fukudu, K.; Kamiay, K.; Matsui, H. J. Phys. Chem. 1992, 96, 8583. (38) Van Look, H.; Peeters, J. Thirteenth International Symposium on Gas Kinetics; Dublin, 1994; poster A47. (39) Borms, R. Ph.D. Thesis, Leuven, 1992. (40) Timonen, R. S.; Ratajczak, E.; Gutman, D. J. Phys. Chem. 1987, 91, 692. (41) Cherian, M. A.; Rhodes, P.; Simpson, R. J.; Dixon-Lewis, G. Symp. (Int.) Combust. [Proc.] 1981, 18, 385.
JP942954F
