J . Phys. Chem. 1986, 90, 6552-6557
6552
but on models of guest-host interaction (Lennard-Jones and Devonshire or Kihara potentials) in which there has been some force fitting of the interaction parameters to give agreement with experimental dissociation pressures, including those of the hydrates of argon and krypton which have been found6 not to be structure I hydrates at all. Previous estimates based on compositions alone are free of such assumptions but are generally restricted to hydrates of large guest molecules where negligible occupancy of the small cages may be assumed. These include the results of van der Waals and Platteeuw,2 who based their estimates on the composition of bromine hydrate which was erroneously assumed to be a structure I hydrate, of Davidson,I9 who attempted to find a value which was consistent with the range of compositions available in 1972 for structure I hydrates, and of Dharmawardhana et al.,3who measured the equilibrium composition of cyclopropane hydrate. The value of Holder et aLZ0is based on a reanalysis of Dharmawardhana's data. The present value of 1297 f 110 J/mol for xenon hydrate is in good agreement with other recent values for structure I hydrates. (17) John, V. T.; Papadopoulos, K. D.; Holder, G. D. AIChE J . 1985, 31, 252. (18) Barakhov, S. P.; Sawin, A. Z . ; Tsarev, V. P. Z h . Fiz. Khim. 1985, 59, 1039. (19) Davidson, D. W. In Water: A Comprehensiue Treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 2, p 115. (20) Holder, G. D.; Malekar, S. T.; Sloan, E. D. Ind. Eng. Chem. Fundam. 1984, 23. 123.
(We believe the error limits cited in ref 16, 18, and 20 to be greatly underestimated.) It is noteworthy that there appears to be no substantial difference between the chemical potentials of the water lattices which contain molecules as diverse as xenon (van der Waals radius 4.58 A) and cyclopropane (5.84 A). Although the uncertainty is considerable, it is probable that there is some significance in the measurement of a somewhat larger value of Os/OL for xenon in the D 2 0 hydrate (0.77 f 0.02) than in the H 2 0 hydrate (0.73 & 0.02) near 0 "C. Hafemann and Miller found2I that the dissociation pressure of xenon deuteriohydrate at -12.0 O C was 8% higher than for the hydrate. If this is true at 0 O C , use of the Langmuir constants found here for the hydrate predicts that Os/OL should be higher by 0.014 and ApN0 by 3 0 J/mol for the deuteriohydrate than for the hydrate of xenon. Similar observations led to an estimate2' that deuteriation of the water lattice increases ApWoby 25 J/mol for the type I hydrate of cyclopropane. Registry No. Xenon hydrate, 60212-94-4; '29Xe,13965-99-6 (21) Hafemann, D. R.; Miller, S. L. J . Phys. Chem. 1969, 73, 1398. (22) de Forcrand, R. C.R . Hebd. Seances Acad. Sei., Ser. C 1925, 181, 15.
(23) Braun, B. Dissertation, Bonn, 1938. (24) Berecz, E.; Balla-Achs, M. Gas Hydrates; Elsevier: Amsterdam, 1983; p 176. (25) Cady, G. H. J . Phys. Chem. 1983, 87, 4437. (26) Child, W . C. J . Phys. Chem. 1964, 68, 1834.
Ketenyl Radical Yield of the Elementary Reaction of Ethyne with Atomic Oxygen at T = 290-540 K J. Peeters,* M. Schaekers, and C. Vinckier Department of Chemistry, Katholieke Universiteit Leuuen, 3030 Heverlee, Belgium (Receiued: March 1 1 , 1986)
The ketenyl radical yield of the elementary reaction between ethyne and atomic oxygen was determined at T = 287 and 535 K, at a pressure of 2 Torr (He). Use was made of the flow reactor technique, in combination with molecular beam mass spectrometry. First, a detailed investigation was made of the kinetics of formation and destruction of HCCO in C,02/H systems; by use of the absolute HCCO concentrations thus obtained, the sensitivity of the MBMS apparatus to HCCO could be determined. The HCCO yield of the elementary C2H2+ 0 reaction was then derived in C 2 H 2 / 0systems from the observed stationary HCCO concentration and from the known HCCO destruction rate, at a given total C2Hl + 0 reaction rate. In this way, the HCCO yield of the elementary C2H2+ 0 reaction with 2a error was found to be 59% f 20% at 287 K and 64% f 19% at 535 K.
Due to their importance in combustion chemistry, reactions of ethyne have since long been the subject of extensive studies. It has been shown that the reaction of ethyne with atomic oxygen proceeds via two important primary reaction channels:'-4 C2H2+ 0 CH2 CO AH = -47 kcal mol-' (la) C2H2
+0
--
+
HCCO
+H
AH = -19 kcal mol-'
(1b)
Past attempts to determine the relative importance of both reaction channels resulted in widely varying estimates for the branching ratio 0.1 < k i , / k , < 0.97.2-4-6 In several recent studies, ( I ) Vinckier, C.; Schaekers, M.; Peelers, J. J . Phys. Chem. 1985,89, 508. (2) Williamson, D. G.; Bayes, K. D. J . Phys. Chem. 1969, 73, 1232. (3) Kanofski, J. R.; Lucas, D.; Pruss, F.; Gutman, D. J . Phys. Chem. 1974, 78, 311. (4) Vinckier, C.; Debruyn, W. S y m p . (Int.) Combusr. [Proc.] 17rh 1979, 623. ( 5 ) Blumenberg, B.; Hoyermann, K.; Sievert, R. S y m p . (Int.) Combust. [Proc.] 16th 1976, 841.
0022-3654/86/2090-6552$01.50/0
it was concluded that H C C O formation becomes important at elevated temperature7,*or a t high collision e n e r g i e ~while ,~ CH2 production dominates at room t e m p e r a t ~ r e .On ~ the other hand, a b initio calculations without planarity constraints locate the transition states for both exit channels at nearly the same energy, about 10 kcal mol-' below the barrier for the addition of 0 to C2H2;I0since the transition state leading to C H 2 formation, involving a 1,2-H migration of the initial formylmethylene adduct, is expected to be tighter than that for C-H fissure, the a b initio results, in the framework of chemical activation RRKM theory, (6) Williamson, D. G. J . Phys. Chem. 1971, 75, 4053. (7) Lohr, R.; Roth, P. Ber. Bunsenges. Phys. Chem. 1981, 85, 569. (8) Aleksandrov, E. N.; Arutyunov, V. S.; Kozlov, S. N. Kinet. Katal. 1981, 22, 513. (9) Clemo, A. R.; Duncan, G. L.; Grice, R. J . Chem. Soc.. Faraday Trans. 2 1982, 78, 1231. ( I O ) Harding, L. B. Annual Report Theoretical Chemistry Group, Argonne National Laboratory, 1984, p 3.
0 1986 American Chemical Society
Ketenyl Yield of C2H2+ 0
The Journal of Physical Chemistry, Vol. 90, No. 24, 1986 6553
favor formation of HCCO, regardless of temperature. The aim of the present study is to determine the rate constant of channel l b and hence the HCCO yield klb/kl at T = 300-600 K from measured absolute H C C O concentrations in C 2 H 2 / 0 systems.
Procedure In a C 2 H 2 / 0system, the quantity klbcan be derived from the value of the quasi-stationary HCCO concentration: [HCCO1st = klb[C2H21 [ o l / c k i [ x i l
(1)
I
with C i k i [ X i ]being the total H C C O removal rate (s-l) due to the reaction H C C O Xi products
+
-
The nature of the major species responsible for HCCO destruction in C 2 H 2 / 0 systems and the magnitudes of the associated rate constants ki have been determined in previous work'.'' (Xi = 0, H , 02,and C2H2). The molecular beam sampling mass spectrometric (MBMS) t e c h n i q ~ e , ' * described ~%'~ in the next section, allows accurate measurements of the absolute concentration of the species C2H2,0, H , and 02,figuring in eq I. The remaining quantity in that equation is the absolute concentration of HCCO; it can be derived from the corresponding MBMS signal i(HCC0) provided that the sensitivity of the MBMS apparatus for HCCO, S ( H C C 0 ) e i(HCCO)/[HCCO], is known. The required calibration of the MBMS instrument for HCCO was achieved by using the reaction H
+ C302
-
HCCO
+ CO
AH = -13 kcal mol-'
(2)
as a source of HCCO. Reaction 2 has been investigated extensively by Faubel and Wagner.I3 Quantification of the rate of H C C O formation in C 3 0 2 / H systems is straightforward since reaction 2 yields exclusively HCCO, all other possible pathways being highly endoergic. Also, stabilization of the short-lived H C 3 0 2intermediate (lifetime C s according to R R K M estimates) is negligible at a pressure of a few Torr. Besides k2, also the total HCCO removal rate Cjkj[X,] must be known in order to establish the absolute HCCO concentration in a C302/H system. If all necessary kinetic information relating to the destruction of HCCO would be available, one could again take recourse to a stationary-[HCCO] equation, analoguous to eq I for C 2 H 2 / 0systems. However, since there is a lack of reliable data on possible H C C O removal reactions in C302/H systems such as H C C O C3O2, we opted for an alternative approach, where the time history of the total HCCO removal rate is obtained from the known time-dependent HCCO formation rate and from the observed time history of the relative H C C O concentration i ( H C C 0 ) . The method can be regarded as an extension of the well-known "approach to the stationary state" technique. Once the time evolution of the HCCO destruction rate ur(t) = Cjk,[Xj] is known, the absolute [HCCO] can be calculated at each point in time. Combination with the corresponding i ( H C C 0 ) signals then yields the sensitivity factor S sought here. The actual numerical procedure is more fully detailed in a later section. It should be stressed that calibration factors S ( H C C 0 ) thus obtained in C 3 0 2 / H systems can be transposed without correction to the C 2 H 2 / 0systems of interest here provided that all parameters affecting the MBMS sensitivity, Le., temperature, total pressure, and nature of the diluent gas (He > 97%), are identical.
+
Experimental Section The experimental setup has been described in detail previo ~ s l y . ~Basically, J~ it consists of a quartz fast-flow reactor, with a continuous flow of reagents. Sampling occurs through a pinhole in a quartz cone, giving access to the first of two differentially ( 1 1) Schaekers, M. Ph.D. Dissertation, Faculty of Sciences, K. U. Leuven, 1985. (12) Vinckier, C.; Debruyn, W. J . Phys. Chem. 1979, 83, 2057. ( 1 3) Faubel, C.; Wagner, H. Gg. Ber. Bunsenges. Phys. Chem. 1977,81, 684.
0
1
3
2
5
t /ms
-
TABLE I: Determination of the Rate Constant k 2 of the Reaction Products at the Experimental Conditions as in Figure 1 C302+ H run [HI, mol cm-3 /cobs,, f u, s-l k2 f u, cm3 mol-' s-l 158 f 9 10.4 f 0.60 X 10" A 1.51 X B 2.01 X 183 f 32 9.1 f 1.59 X 10" C 2.76 X lo-'' 222 f 13 8.05 f 0.47 X 10" 303 f 35 10.0 f 1.2 X IO" D 3.02 X 9.4 1.0 x 10" av
*
pumped low-pressure chambers. In the first stage, the gas jet is mechanically chopped to permit phase-sensitive detection. The molecular beam that enters the second low-pressure chamber is ionized by means of electron impact, at an electron energy only a few electronvolts above the ionization potential of the molecule or radical being monitored. Ion mass selection is achieved with an Extranuclear Labs Quadrupole mass filter. Oxygen and/or hydrogen atoms are generated in a microwave discharge through a mixture of oxygen and/or hydrogen in helium. Ethyne, also diluted in helium, is added to the main reagent stream through an axial movable central injector. The reaction time can be varied between 0 and 10 ms. The reactor, which is passivated with HF, can be heated up to 600 K by means of heating tape wrapped around it. The pressure is kept constant at 2 Torr. Carbon suboxide is prepared from malonic acid following a standard p r 0 ~ e d u r e . l ~The purified product contains over 99% suboxide, with carbon dioxide as the only important impurity.
Results and Discussion 1. Reaction of C3O2 with Hydrogen Atoms. Evaluation of the rate of formation of HCCO in the reaction of carbon suboxide with hydrogen atoms (reaction 2) requires knowledge of the rate constant k2. The easiest way to perform a determination of k2 is to monitor the pseudo-first-order decay of C3O2 at a large excess of hydrogen atoms. In this way, complications by secondary reactions are easily avoided. However, it appeared that carbon suboxide catalyzes the recombination of hydrogen atoms on the reactor wall. This effect could be suppressed to a large degree by the addition of a small amount of molecular oxygen (about 10 mTorr), a method already described by Fa~be1.l~The presence of molecular oxygen appears to inhibit the heterogeneous reactions. The decay of the carbon suboxide concentration as a function of reaction time, in the presence of a large excess of hydrogen atoms, was monitored by means of the most important fragment ion of C302,C 2 0 + . Several pseudo-first-order plots, all at a temperature of 535 K, are shown in Figure 1. The concentration ratio 10 < [H],/[C302], < 20 is high enough to prevent loss of carbon suboxide in secondary reactions. It has been ascertained exper(14) Miller, F. A,; Fateley, W . G.Spectrochim. Acta 1964, 20, 253. (15) Faubel, C. Ph.D. Dissertation, Gottingen, 1977.
6554
The Journal of Physical Chemistry, Vol. 90, No. 24, 1986
Peeters et ai. provided the mixture composition is selected properly, it is possible to obtain a reaction system where the carbon suboxide as well as the molecular oxygen concentration remain constant regardless of the reaction time. Under such circumstances, the destruction of HCCO by C3O2 and O,, as well as on the reactor wall, will each be pseudo first order and can be taken into account as one single reaction 02,C,02, wall
HCCO
products
(4)
The evolution of the ketenyl radical concentration with time can then be expressed as d [ H C C O ] / d t = k,[C,O,][H] - k,[HCCO][HI - k,[HCCO] (11)
1
0
1
I
I
1
2
3
[ H I / IO-'
Since the concentration of HCCO is directly related to the mass spectrometric signal "i" by means of the sensitivity S
i(HCC0) = S[HCCO]
mol cm-3
Figure 2. Determination of k , at 5 3 5 K from a plot of the C,O, decay constant kobsdvs. [HI: k , f 2a = (9.1 f 1.4) X 10" cm3 mol-l SKI.
imentally that a constant concentration of atomic hydrogen was maintained throughout the reaction zone. The observed first-order decay constants kOMat T = 535 K with the corresponding values of k2 are given in Table I. The average rate constant k, obtained is equal to (9.4 f 1.0) X lo'] cm3 mol-] s-l. When, on the other hand, a plot is made of the first-order decay constant kob4vs. the hydrogen atom concentration as shown in Figure 2, a straight line can be drawn to pass through the origin, and from its slope a weighted value of k , f 2u = (9.1 f 1.4) X 10" cm3 mol-' s-I can be derived. Both values are in good agreement; the value derived graphically will be used further in this work. It is about 15% lower than the value of 1.1 X 10l2cm3 mol-' s-I derived from Faubel's expres~ion;'~~'~ the latter was determined in the temperature region 290-450 K. There can be no doubt that a large part of the HCCO radicals formed in the investigated C 3 0 2 / H systems subsequently react with hydrogen atoms. The rate constant of reaction 3, with 95% confidence limits, is equal to (1.55 f 0.45) X lOI4 cm3 mol-' s-I at 535 K as determined in our earlier work.'
HCCO
-
+H
products
(3)
Concerning the nature of the reaction products of reaction 3, several channels are possible:I3 HCCO H --t C H , C O (3a) HCCO H C20 H2 (3b)
+ +
HCCO
-+
+H
+
+ +
C,H,O
(3c)
A preliminary investigation revealed the formation of methylene radicals to be dominant; an accurate determination of the branching ratio k3,/k3 remains the object of a further investigation. Mass spectrometric interference by C3H4prohibited any conclusion about the formation of C 2 0 radicals. 2. Determination of the Absolute HCCO Concentration in C 3 0 2 / HSystems. 2.1. Evaluation of the Problem. Since the ketenyl radical is the only primary product of the reaction between carbon suboxide and atomic hydrogen, a knowledge of the rate constant k2 permits the calculation of the rate of formation of HCCO. The aim of this investigation is to relate mass spectrometric signals of HCCO, i(HCCO), to absolute concentrations [ H C C O ] . In order to achieve this, besides the rate of formation of the ketenyl radical, also its rate of destruction has to be known. The most important destruction reaction of HCCO in this system is the very fast' reaction 3. Destruction of HCCO can also occur with carbon suboxide as the reaction partner. Also, as mentioned in the above paragraph, molecular oxygen had to be added to the reaction mixture in order to suppress wall reactions. As a consequence, destruction of HCCO with molecular oxygen will also occur,II while at the same time neglection of wall termination of HCCO might lead to biased results. Thus, at first sight, the reaction system appears to be fairly complex. However,
(111)
eq I1 can be transformed into
d i ( H C C O ) / d t = k , S [ C 3 0 2 ] [ H-] ( k , [ H ] + k J i ( H C C 0 ) (IVa) Equation IVa allows the simultaneous determination of S and of k4 from the time history of the HCCO signal, provided that the rate constants k 2 and k , as well as the time evolution of the C 3 0 2 and H concentrations are known. The value of k , at 535 K has been determined in earlier work:' k 3 = (1.55 i 0.45) X lOI4 cm3 mol-I s-'. For k2, the value of (9.1 i 1.4) X 10" cm3 mol-' s-I obtained above was adopted. The determination of the parameters S and k4 was performed with the DUD program,I6 a least-squares method for nonlinear parameter estimation. The program makes direct use of the set of differential equations that govern the kinetics of the system; an analytical solution is not required. Specifically, there is no need for the explicit regression function i ( H C C 0 ) = f ( t , p ) with p ( S , k 4 ) the parameter vector. In the DUD program, the parameter vector p is optimized in an iterative numerical procedure, finally leading to the parameter set that minimizes the sum of the squared deviations between measured and calculated HCCO signals. In order to correctly interprete the results, it is important to understand fully the underlying principles of the method applied. It should be emphasized that in essence one derives here the time history of the total HCCO removal rate u,(t) from the observed shape of the measured i ( H C C 0 ) profile and from the known HCCO formation rate Uf(t); a faster destruction will lead to an earlier approach of the quasi-stationary concentration. The absolute concentration [HCCO](t)-and hence also the sensitivity S = i(HCCO)/[HCCO]-follows directly from Ur(t) and v,(t). Of course, in view of the accepted HCCO destruction mechanism, vr(t) is treated here as the sum k 3 [ H ]+ k4, with k 3 [ H ] given. The parameter k4 is independent of the parameter S, but S can be determined only after k4 is derived. Also, since reaction 4 accounts for only a part of the total destruction rate v, but has to bear the full weight of any imprecision regarding v, because k , [ H ] is given, the relative precision of the obtained k 4 can be rather low, while the precision of S is still high. Moreover, whereas the parameter k4 is closely coupled to the input quantity k3, the value found for S will depend only weakly on the chosen input k,; indeed S follows from the total vr(t) as derived from the i ( H C C 0 ) profile shape, while the distribution of u,(t) over reactions 3 and 4 has little bearing on the S value. 2.2. Determination of the Sensitivity for HCCO. The evolution of i ( H C C 0 ) toward the quasi-stationary state was recorded in three experiments at 535 K, always with the C,O, concentration in large excess of the initial H concentration and in the presence = 1.5 x IO-'' mol of molecular oxygen, at a concentration [02]0 cm-,. The constancy within 5% of the C,O, and 0, concentrations over the total reaction time, required to guarantee the validity of eq IVa, was verified experimentally. The initial composition (16) Ralston, M . L.; Jenrich, R. I . Technomerrics 1978, 20, 7 .
+0
The Journal of Physical Chemistry, Vol. 90, No. 24, I986 6555
Ketenyl Yield of C2H2
t/ms
Figure 3. H decay at T = 535 K and [O2lO= 1.5 X lo-" mol ~ m - ~(I). [C3O2lO = 7.0 X lo-", [HI, = 3.3 X mol ~ m - kow ~ , = 196 s-I; (11) [C302],= 4.6 X lo-"; [HI, = 2.45 X mol ~ m - kobd ~ , = 126 s-'; (111) [C3O,lO= 6.1 x [HI, = 2.0 x 10-l2 mol ~ m - kobsd ~ , = 125
d. TABLE 11: DUD Determination of the Parameters S(HCC0) and k4, with Standard Deviation (a) Percentages % B Derived from i(HCC0) Profiles in CqO,/H Systems at 535 K expt S, fiv cm3 mo1-l %B k4, s-I %B a. Only Primary HCCO Formation Considered I 2.64 x 1014 5.1 135 20.4 11
Ill
I I1 111
2.18 x 1014 2.58 x 1014
3.6 1.9
121 149
b. Including Secondary HCCO Formation 2.96 x 1014 4.0 278 2.34 x 1014 2.9 206 2.77 x 10'4 2.3 229
15.7 7.2 9.2 8.0 5.9
of the three investigated mixtures was (I) [C3O2l0= 7.0 X lo-", (11) [C302]o= 4.6 X lo-", [H,] = 2.45 X [HI, = 3.3 X mol cm-,. (111) [C302],= 6.1 X lo-", [HI, = 2.0 X The reaction time could be varied between 1.4 and 6.8 ms. The recorded atomic hydrogen concentration profiles are shown in Figure 3. The decay of [HI is close to exponential in each of the three cases; the observed first-order rate constants are, respectively, (I) kobs,j= 196, (11) kobd = 126, and (111) kobd = 125 s-I. With [C302]constant and with [HI showing an exponential decay, the single additional differential equation besides eq IVa needed to describe the system is d[H1/dt = -kobsdlH1
(IVb)
It is worth mentioning that the observed H decay is in all three cases about 30%faster than attributable to reactions 2 and 3 and the subsequent reaction of H with CH2:17,18
+ H CH2 + C O CH2 + H - C H + H2
HCCO
+
(3a) (7)
Quite probably, the excess H removal is to be ascribed to heterogeneous H recombination, with wall-adsorbed C3O2 acting as ~ata1yst.l~ The signal profiles of HCCO in the three investigated mixtures are shown in Figure 4. From these profiles the unknown parameters in eq IVa, Le., the rate constant k4 and the sensitivity S, were evaluated by using the DUD algorithm. Table IIa lists the results, together with the corresponding variation coefficient B, Le., the percentage standard deviation. The values of Table (17) Bohland, T.; Temps., F. Ber. Bunsenges. Phys. Chenz. 1984,88,459. (18) Bohland, T.; Temps, F.; Wagner, H. Gg., unpublished results.
Figure 4. Approach of [HCCO] to the stationary state in the C302/H system at T = 535 K and [O2lO= 1.5 X lo-', mol ~311~~. (I) [C302],= 7.0 X lo-", [HI, = 3.3 X mol ~ m - (11) ~ ; [C3O2l0= 4.6 X lo-", [HI, = 2.45 X mol ~ m - (111) ~ ; [C302],= 6.1 X lo-", [HI, = 2.0
x
mol ~ m - ~ .
IIa were obtained with k2 = 9.1 X 10" and k, = 1.5 X lOI4 cm3 mol-' SKI.As foreseen, the B values for k4 are much larger than those for S. For both S and k4 the standard deviation of an individual measurement from the mean is about 10%. The weighted averages, with corresponding 2a uncertainties are = (2.51 f 0.23) X 1014pV mol-' cm3 and f 4= 143 f 15 s-l; the relative weight factors for each individual determination were taken equal to the inverse square of the appropriate B values. The k4 result can be compared to the known magnitude of k 6 [ 0 2 ]a, major constituting part of k4 HCCO + O2 products (6)
s
-
The rate constant k6 was measured in earlier Stern-Volmer experiments;" the results, as yet unpublished, can be represented by the Arrhenius expression k6 = 1.6 X 10l2exp(-430K/T) cm3 mol-'s-'. Thus, with k6 = 7.2 X 10" at 535 K and with [ 0 2 ] = 1.5 X mol ~ m - one ~ , has k 6 [ 0 2 ]= 1 13 SKI, only slightly lower than the value obtained here. Changing k3 from the mean value] 1.5 X l o f 4cm3 mol-' s-I to the lower limit 1.1 X 1014results in a decrease of 3 by 6% and in an increase of k4 by 27%. Expressed in terms of relative linear sensitivity coefficients, one has ( d S / S ) / ( d k , / k , ) 0.18 and ( d k 4 / k 4 ) / ( d k 3 / k= 3 )-1.0. The much larger effect of a change in the input value of k3 on k4 as compared to that on S is as expected. Taking into account the 2u uncertainties regarding k , (35%), as well as k2 (15%) and [ C 3 0 2 ] (5%), the overall 2u confidence interval for?!. becomes (2.51 f 0.47) X lOI4 pV mol-' cm3. The question of possible systematic errors in the determination of the sensitivity S ( H C C 0 ) must also be addressed. First, as mentioned earlier, the observed [HI decay is about 30% faster than expected; the excess H loss can be ascribed to It H termination on the wall, catalyzed by adsorbed c302.13315 cannot be entirely excluded that the heterogeneous reaction leads in part to additional HCCO production, not counted in eq IVa; however, it is unlikely that this fraction would be important. Faubel and Wagner'3,15observed that the C302-catalyzedH loss is accompanied by formation of H2. Possible secondary formation of HCCO by C 3 0 2+ O H HCCO + C 0 2 (8)
-
with k, = 2.2 X 10l2 cm3 mol-' s-' at 535 K" merits closer inspection. The O H radical can be formed in at least two ways in C 3 0 2 / H systems: (19) Faubel, C.; Wagner, H. Gg.; Hack, W. Ber. Bunsenges. Phys. Chem. 1917, 81, 689.
6556 The Journal of Physical Chemistry, Vol. 90, No. 24, 1986
(i)
HCCO
+H
+0 2 C H 2 + 0,
CH2
(ii)
---c
HCCO CH, CH
+ CO O H + H + CO OH + HCO -+
CH2
(3a) (9a)
-
+H
+H
+
4
+ 02'CO
CH2
CH
+ CO
T, K
(3a)
+ H2
kl kS k3
(7)
+ OH
287
535
(7.5 f 0.8) x 10'0 (8.0 2.1) x 1013 (1.0 0.3) x 1014 (3.6 f 1.2) X 10"
(8.5 f 1.7) X 10" (1.1 f 0.1) x 1 0 1 4 (1.5 f o s ) x 1014 (7.2 f 1.9) X IO"
*
k6
(10)
+
wall
products
( 1 1)
at a rate of 100-250 s-I was found to be of little consequence to the results. Certainly, secondary HCCO formation of this importance can affect the S ( H C C 0 ) and k4 values derived from the i(HCC0) profile shape. On the one hand, an increase of the total HCCO production U k t ) will result in higher [HCCO] and hence in lower S ( H C C 0 ) values. On the other hand, the inclusion of secondary HCCO formation, with increasing relative importance at longer reaction times, will also change the total removal rate function vr( t ) required to match the given HCCO-signal profile. Of course, that change will be largest at the longer reaction times. Since vr(t) is made up of k3[H] + k4, with the known part k3[H] decreasing with time, only an increase in the time-independent parameter k4 can satisfy the above requirements. Obviously this results in turn in a larger average value of v, and hence in a lower [HCCO]. Thus, the two effects arising from the inclusion of secondary HCCO formation on both [HCCO] and S ( H C C 0 ) are seen to oppose one another. This view is confirmed by a DUD determination of S and k4 in the frame of the extended mechanism comprising reactions 2, 3a, 4, 7, 8, 9a, 10, and 11 with rate constants for reactions 7-10 as given above and with k l l = 100 s-l. The input values of k2 and k3 were as before: k2 = 9.1 X 10" and k3 = 1.5 X 1014 cm3 mol-' s-l. The results are given in Table IIb. The weighted averages and corresponding 28 uncertainties regarding the average are = (2.66 f 0.33) X lOI4WVmol-' cm3 and L4 = 233 f 36 s-'. As expected, the k4 found here is much higher than the one obtained without considering secondary HCCO, whereas the difference in is slight (increase by 6%). The sensitivity of S to the input value of k , remains low: (dS/S)/(ak,/k,) = 0.22, only slightly higher than before. The effect of a change of k, on the output k4 value is markedly less than before: I(ak4/k4)/(ak3/k3)l = 0.2; the obvious reason is that reaction 4 now accounts for a much larger share
s
s
(20) Himme, B. Ph.D. Dissertation, Gottingen, 1983. ( 2 1 ) Bohland. T.; Temps, F.; Wagner, H . Gg. Ber. Eumenges. Phys. Chem. 1984, 88, 455.
( 2 2 ) Temps, F.; Wagner, H. Gg. Ber. Bunsenges. Phys. Chem. 1984, 88, 410.
(23) Messing, I.; Sadowski, C. M.; Filseth, S. V. Chem. Phys. Lett. 1979, 66(1), 95. (24) Butler, J. E.; Fleming, J . W.; Goss, L. P.; Lin, M . C. Chem. Phys. 1981, 56, 355. ( 2 5 ) Becker, K . H . ; Fuchs, D.; Wiesen, P., unpublished results. ( 2 6 ) Lichtin. 1). A.: Berman, M R.: I in, M. C. Chem. Phys. Lerr. 1984,
lOR(li, 1 8 .
TABLE III: Rate Constants at 287 and 535 K, with 95%Confidence Limits, Used in the Calculation of the Branching Ratio 0 in the C2H2/0 System: Units Are cm3 mol-] s-l
(9b)
Channel 3a is probably the dominant route of the fast HCCO + H reaction, as already mentioned. In several recent studies of reaction 9, C O and/or H C O were found to be major produ c t ~ , ~ ,suggesting ~ ~ . ~ ~that - ~ channels ~ 9a and 9b are dominant. The C H radical, formed in the fast reaction 7,l7*I8is known to react rapidly with 02.23-25 yielding mainly O H C0.26 A model calculation at 535 K with k3c = k3 = 1.5 X k9, = k9 = 4 X 10'2,4,i2,21 k, = 1.5 X 10'4,17.'8and klo = 5 X 101323-25 revealed that in the conditions of our experiments the secondary [HCCO] attains about 30% of the primary [HCCO] at the largest reaction time of 7 ms. This number should be regarded as an upper limit since reactions 5 and 6 that compete with reaction 3 were not considered in the computer simulation; OH termination on the wall OH
Peeters et al.
TABLE IV: Experimental Conditions Used for the Determination of the Branching Ratio p in the C2H2/0 System T (K), 287, 4.3
concn,
mol/cm-' [HCCO] f 20 [C,H,] [OI
[HI [O*l
(5.6 f 1.2)
X
r (ms)
(5.4 f 1.2)
10-14
535, 5.2 X
10-14
1.05 X 5.07 X lo-" 3.3 x 10-12 1.6 X IO-"
1.09 X 1.06 X 9.58 X IO-'* 2.57 X 10.''
(6.7 f 1.5) X I 0-14 2 04 X 9.86 X IO-'* 2.39 X lo-', 3.7 x lo-"
of the total H C C O removal rate v,. Considering in addition the uncertainties regarding k2 and [C302]besides that of k3,the 20 confidence interval for S ( H C C 0 ) at 535 K is (2.66 f 0.56) X l o i 4pV mol-' cm3. This value will be adopted in the following. The sensitivity at 287 K, in identical conditions of pressure (2 Torr) and mean molecular mass (He 3 99.7%), will be taken equal to that obtained at 535 K, on the grounds that the directly measured sensitivity for propyne-a species of nearly equal mass-shows a change of less than 6% over the 285-600 K range. 3. Quantitative Determination of the Yield of HCCO as a Primary Product of the C2H2 0 Reaction. Once the sensitivity of the MBMS apparatus for ketenyl radicals is known, the absolute HCCO concentration in various systems can be determined. Considering a C2H2-0 mixture with stationary concentrations of intermediates ( t > 5(kdeS,,)-') and defining the HCCO yield of the primary step as P = k,,/k,, one has
+
P=
[HCCOIss(k5[OI -I- k,[HI kl [C,H21 [Ol
k6[021)
(VI
In eq V, k5 is the rate constant of the reaction of HCCO with 0 HCCO
+0
-
products
(5)
This reaction, together with the reactions of HCCO with H (reaction 3) and with O2(reaction 6), accounts for the larger part of the HCCO destruction in C 2 H 2 / 0systems. When the ethyne concentration is kept low enough, the slow reaction between HCCO and ethyne'-27can be kept negligible. In order to determine the branching ratio P , the magnitude of each of the quantities in the right-hand side of eq V has to be known. The actual concentrations of C2H2,0, H, 02,and HCCO at a given reaction time can be measured. Our separate determinations of k , at 287 and 535 K agree within 10% with the generally accepted expression k , = 1.4 X l o i 3exp(-l500K/ T ) cm3 mol-' s-','~ which was used in the calculations. Values for k, and k , were taken from our earlier Reaction 6 between HCCO and O2 has to be taken into account because of the presence of undissociated molecular oxygen; k6 was evaluated from the Arrhenius expression, cited earlier. In summary, the values used for the rate constants appearing in eq V, both at 287 and 535 K, are listed in Table 111. The absolute stationary concentration of ketenyl radicals in the C 2 H 2 / 0system was measured at temperatures of 287 and 535 K. The measured concentrations of all species of relevance at the ( 2 7 ) Jones, I . T . N.; Bayes, K. D. Symp. (Inr.) Combusr. [Proc.] 1 4 t h 1913, 211. ( 2 8 ) Herron, J. T.; Huie, R. E. J . Phys. Chem. ReJ Data 2 1974. 467.
J . Phys. Chem. 1986, 90. 6557-6562 given reaction time in two mixtures at 287 K and in one mixture at 535 K are shown in Table IV. A combination of the data in Tables 111 and IV permits the calculation of the branching ratio p from eq V. The experiments at 287 K lead to a mean value of p = 0.59 f 0.20 for the HCCO yield of the elementary reaction of ethyne with atomic oxygen. The overall 2a error reflects mainly the uncertainties regarding k l , k5 and [HCCO], and includes the uncertainty concerning the change of S with temperature. In the same way, the value p = 0.57 f 0.17 is obtained at 535 K. This result at high temperature, however, has to be corrected for a sampling effect. Because the sampling takes place through a pinhole in the top of a quartz cone, mounted on a water-cooled plate, the temperature at the sampling point will be lower than the reactor temperature. At a reactor temperature of 535 K for instance, measurements indicate a sampling temperature of 400 K. The H C C O mole flux, which at larger distances from the sampling cone is still equal to the quasi-stationary value at the reactor temperature, will tend to adapt to the decreasing temperature when the gas approaches the sampling cone. The reason is that the rate of the H C C O formation process depends much more strongly on temperature than the rates of the HCCO removal reactions.'$28However, the adaption of the HCCO flux proceeds at a limited rate which is closely linked with the HCCO removal rate; the actual extent of the H C C O flux change is largely determined by the temperature profile and by the [O] and [HI profiles. In the experimental conditions at 535 K described in Table IV, a simplified model predicts a H C C O flux decrease of 11% over the cooling region. Correcting for this effect, the branching ratio with 2 a error at 535 K is @ = 0.64 f 0.19.
Conclusion Contrary to recent indirect evidence based on H formation in C2H2/0 our direct approach shows that the elementary reaction of C2H2with 0 results for the larger part in the formation of HCCO, with a yield that is nearly independent of temperature: 59% f 20% at 287 K and 64% f 19% at 535 K. Our findings
6557
are in excellent agreement with very recent theoretical predictions by Harding and Wagner.29 Since only HCCO and CH, are important primary products,' the amount of methylene radicals found in the C2H2 0 reaction is
