J. Phys. Chem. 1981, 85,3828-3831
3828
and Dombi call this combined repulsion and stabilization energy the end-group contribution. It consists of the energy of an unstretched bond between A and B which is weighted by a factor involving the Morse parameter for an A-B bond and by an additional factor containing the electron affinities of A and B. In cases where other atoms are bound to A or B, the electron affinity is considered to be that of the whole group of atoms. In both methods the maximum of the sum of these energies along the path is taken to be the energy of activation. The configuration of the A-H-B complex at this energy maximum is assumed to correspond to that of the transition state in the activated-complex theory. Both methods evaluate the structure of the transition state, determine force constants and vibrational frequencies,and through the activated-complex theory determine the Arrhenius parameters. As a test of these two methods, we have calculated activation energies for the following reactions: CzH + Hz, CH4, CzH6,and CN + Hz and CHI. The CN radical has an electronic structuregvery much like that of C2Hso that similar behavior is to be expected. For the BEBO calculation, a simple transition state was assumed with the usual vibrational analysis leading to the evaluation of the partition functions required for the activated-complex theory. This allowed us to calculate Arrhenius frequency factors. The particular version of BEBO used incorporated the modifications proposed by Gilliom.lo The detailed computer code of the established BEBO procedure, which does not differ in substance from that of Gilliom, is being published elsewhere.ll All of the experimental results for the CzH reactions were measured at room temperature. Thus there are no direct measurements of the activation energies. These can, however, be estimated from the observed rate constants and the BEBO calculated frequency factors through use of the Arrhenius relation. This was (9) J. Pacansky and G . Orr, J. Chem. Phys., 67, 5952 (1977). (10) (a) R. D. Gilliom, J. Chem. Phys., 65, 5027 (1976); (b) R. D. Gilliom, J.Am. Chem. Soc., 99,8399 (1977). In ref. 6, Berces and Dombi claim that Gilliom’s value of 0.45 for the anti-Morse constant in the BEBO triplet repulsion energy should be reduced by a factor of 2 in order t o reproduce his published results. We were able to obtain his results without any such reduction. (11) R. L. Brown, J. Res. Nutl. Bur. Stand. (U.S.), in press.
done for the C2H reactions shown in Table I, which lists the observed rate constants, the frequency factors calculated by the BEBO method, the derived experimental activation energies, and the activation energies calculated by the BEBO and BSBL techniques. For the BSBL method, only the potential energy of activation was calculated. This will differ somewhat from the Arrhenius energy parameter. Such a difference is shown for the BEBO energies. For these, the first energy listed is the potential energy of activation like that given for the BSBL calculations. The energy in parentheses was determined by differentiating the logarithm of the calculated rate constant with respect to 1/T and is a representation of the actual Arrhenius parameter. All of the data used for calculating the activation energies are shown in Table 11. We can see from Table I that, for the C2H abstraction reactions, the values of k derived from the BEBO preexponential factor and activation energy are from lo3 to lo9 slower than those experimentally measured, which is quite unsatisfactory. It should be noted that the value for the maximum activation energy may be derived by assuming a frequency factor equal to the collision rate. This leads, for example in the case of CzH + CH4,to a maximum E, = 3.3 kcal/mol or about 9 kcal/mol less than that calculated by the BEBO method. Alternatively, the BSBL method yields far more accurate estimates of activation energies for these reactions than does the BEBO technique. One possible explanation12for the superiority of BSBL may lie in its method of handling the end-group interaction. BEBO is least satisfactory in cases where the end groups have large electron affinities; this is the case for the reactions considered here. If one considers the transition state to be made up of two one-electron bonds A-H.B and one additional antibonding electron shared by A and B, then the repulsion between A and B would be lowered if either or both had a strong tendency to attract this extra electron. BEBO takes no direct account of the electron affinity of these end groups. Acknowledgment. This work was supported in part by the Planetary Atmospheres program of the NASA. (12) Z. B. Alfassi and S. W. Benson, Int. J.Chem.Kinet., 5,879 (1973).
Reactions of Ethynyl Radicals. Rate Constants with CH4, C2ti6, and C2D6 Allan H. Laufer National Bureau of Standards, Chemical Kinetics Divisions, Center for Chemical Physics, Washington,D.C. 20234 (Received: May 5, 198 1; I n Final Form: August 2 1, 198 1)
The rate constants for the abstraction of H atoms from CHI, C2H6, and D atoms from C2D6 by C2H (ethynyl) radicals have been determined by using a flash photolysis-kinetic spectroscopic technique. The values obtained, cm3 molecule-l s-l, respectively. (6.5 f 0.4) X and (3.1 f 0.5) X at 297 K, are (1.2 f 0.2) X The rate constants are independent of added helium over the pressure range 20-700 torr. The kinetic parameters were determined by monitoring the acetylene product spectroscopically using CzH-CF3 as the source of ethynyl radicals.
lene-containing systems which may be as diverse as the planetary htmosphere of Jupiter and pyrolysis of hydrocarbon systems. However, there have been few direct
(1) W. Lange and H. Gg. Wagner, Ber. Bunsenges. Phys. Chem., 79, 165 (1975). (2) A. H. Laufer and A. M. Bass, J. Phys. Chem., 83, 310 (1979).
This article not subject to US. Copyright. Published 1981 by the American Chemical Society
Reactions of Ethynyl Radicals
of any direct measurement of C2H reactivity with other simple molecules. In particular, the reactions of C2Hwith alkanes usually have been omitted from models of complicated systems; their inclusion must lead to greater accuracy in predictive capability. The experiment to be described entailed the flash photolysis of a suitable C2H precursor with subsequent measurement of the CzH2 produced by reaction 1 using kinetic spectroscopic methods. C2H + RH = C2H2 + R (1) Previous work on the reaction of ethynyl radicals with alkanes has been sparse. In the two cases extant, the C2H was prepared by photolysis of C2HBr3p4at 253.7 nm. The rate of reaction 1 relative to reaction of the ethynyl with parent (reaction 2) was deduced from product yields of C2H + C2HBr = C4H2 + Br (2) both C2H2and C4Hzas a function of the concentration of added alkane. For the alkanes, CHI or C2H6, the values obtained in the two studies for the k l / k 2 ratio agree quite well and are 0.02 and 0.5, respectively. The reaction system was complicated by inclusion of NO in the C2HBr-RH mixture. NO is an effective scavenger for CzH.4 The kinetic system therefore involved multiple reaction pathways for ethynyl radical removal which complicated the system and made interpretation more difficult. Evidence for the complexity of the CzHBr photolysis, even in the absence of additives, has been demonstrated recentlye5 Alternate sources of C2H are available. The most convenient is photolysis of C2H2itself.2 However, the only absorption attributed to C2H is in the infrared.6 An ultraviolet system has been reported,7abut the validity of the assignment has been q u e s t i ~ n e d .Attempts ~ ? ~ ~ to observe CzH,by absorption, in the vacuum-ultraviolet region between 125 and 180 nm were unsu~cessful.~ This eliminates the possibility of direct observation in our apparatus of the temporal history of the ethynyl radical. In addition, CzH2is negated as a convenient source of C2H since it is not possible to differentiate spectroscopicallythe formation of product C2Hzfrom the photolysis substrate. Yet another source of C2H is the photolysis of 3,3,3trifluoropropyne (CF,C2H)2rEin the near-ultraviolet. As a plausible precursor to C2H,the fluoropropyne has certain advantages. The absorption spectrum of CF3C2Hexhibits weak absorption in the region of 152 nmtwhere C2H2has an extremely strong absorption feature (C-X).9 Further, the remaining photofragment, CF3, does not contribute to CzH2formation nor does any product which may result from its secondary reaction have an overlapping absorption with C2HP Finally, CF3C2Hexhibits a relatively large absorption in the 180-nm region. Under our experimental conditions, therefore, CF3C2Hmay be photolyzed while the reactant alkanes remain photochemically inert since their absorption spectra begin at wavelengthsless than 155 nm,lo the transmission limit of the reaction vessel. (3) A. M. Tarr, 0. P. Strausz, and H. E. Gunning, Trans. Faraday SOC., 61, 1946 (1965). (4)C. F. Cullis, D. J. Hucknall, and J. V. Sheperd, Proc. R . SOC. London, Ser. A , 335,525 (1973). (5)A. H. Laufer, J. Phys. Chem., 83, 2683 (1979). (6) D. E. Milligan, M. E. Jacox, and L. Abouaf-Marguin, J. Chem. Phys., 40,4562 (f967). (7)(a) W.R.M. Graham, K. I. Dismuke, and W. Weltner, Jr., J. Chem. Phys., 60,3817 (1974); (b) D. P.Gilra, ibid.,63,7163 (1975). (8) D. F. Howarth and A. G. Shemood, Can. J. Chem., 51,1655(1973). (9)G.Herzberg, “Molecular Spectra and Molecular Structure”, Vol. 111, Van Nostrand Co., Princeton, NJ 1967. (10)(a) R. D. Hudson, Reu. Geophys. Space Phys., 9,306 (1971);(b) J. R. McNesby and H. Okabe, Adu. Photochem., 3, 157 (1964).
The Journal of Physical Chemistry, Vol. 85, No. 25, 198 1 3829
With CF3C2Has a precursor, the reactions of C2Hwith CH4, CZH6, and C2D6have been examined in a flash photolysis-kinetic spectroscopic experiment. Rate constants for the abstraction reaction 1 a t room temperature have been determined.
Experimental Section The vacuum-ultraviolet flash photolysis apparatus used in conjunction with kinetic absorption spectroscopy, also in the vacuum-ultraviolet region, has been described in previous publications from this l a b ~ r a t o r y . ~In~ ~the present experiments, the reaction cell, fabricated from Suprasil, was subject to a photolysis flash through N2 of 2450 J. The light pulse decays to 10% of its maximum intensity ca. 7 p s following initiation. Spectroscopic analysis was performed by using a Garton-type flash lamp of 2-ps pulse width triggered, a t preset delays, with a photomultiplier-oscilloscope delay circuit. The vacuumultraviolet output was focused, through LiF optics, upon the slit of a 2-m Eagle vacuum spectrograph. The instrument dispersion was 2.8 A/mm in first order, and spectra were recorded on Kodak SWR plates. A single flash, through 60-pm slits, produced adequate plate darkening. C2H2concentrations were determined with the strong absorption at 152 nm by calibration with samples of known concentration of C2H2. Plate-transmission data were obtained by using densitometry and previously determined characteristic curves of the plate response. Analysis of hydrocarbon products through C4was done, following the photolysis flash, by rapid withdrawal of a sample from the center of the reaction vessel through stainless-steel tubing and injection onto a 7-m long, 6-mm o.d., stainless-steel chromatograph column packed with 30% (w/w) squalane on Chromosorb P. The flame ionization detector was calibrated with known samples. Acetylene, obtained commercially, was purified by repeated trap-to-trap distillations from 196 to 77 K. There were no hydrocarbon impurities as determined by chromatography, and photolysis indicated that acetone, often present as an acetylene stabilizer, was absent as indicated by lack of product formation attributable to methyl radicals. The remaining hydrocarbons were obtained commercially and used without further purification. In all cases, analysis by chromatography confirmed the absence of impurities. In addition, the c2D6 was analyzed by mass spectrometry to assure that the D atom percent (99 at. 9%) agreed with the data of the supplier (Merck, Sharpe and Dohme of Canada). 3,3,3-Trifluoropropyne was obtained from Peninsula Chemical Co. The material, as supplied, had a hydrocarbon impurity to the extent of 6.5%. The impurity was not removable by simple trap-to-trap distillation, and photolysis of the impure material unfortunately yielded C2H2. Therefore, the trifluoropropyne was exhaustively purified by chromatography until photolysis no longer resulted in C2H2production. Ultrapure helium (99.999%) was used without further purification. In a typical experiment, samples of precursor (CF,C2H) and alkane were prepared as mixtures in helium; aliquots were taken such that the desired concentrations were present in the reaction vessel which was then pressurized with added helium to the appropriate pressure. Before photolysis the sample was allowed to mix for 7-15 min, depending upon the total pressure. All experiments were performed at room temperature, 297 K. Results and Discussion Several preliminary experiments were carried out to ascertain the optimum conditions for determination of the
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The Journal of Physical Chemistry, Vol. 85, No. 25, 1981
rate parameters for the ethynyl reactions. It is known that the photolysis of neat CF3CzHis complicated by the formation of a nonvolatile solid polymer.8 Independent of the reaction sequence which leads to the cyclic polymer, its relative importance with respect to the chemistry of C2H was minimized by titrating the C2H formed in the primary photolysis with added alkane; analysis for product C2H2was by gas chromatography. No other hydrocarbon products, through C4 other than C2H2,were observed. Photolysis of the neat alkane at the concentrations necessary to achieve a C2H2plateau indicated no photodecomposition, again determined by product analysis. The absence of photolysis was anticipated on the basis of the known alkane absorption spectrum.1° In the system the chemistry is simply that of CzH and RH to form CzH2 without complicating alternate processes; the sole fate of the ethynyl radicals was reaction with alkane (reaction 1). Since the final products do not include any hydrocarbons other than C2H2,it may be presumed that the fate of the secondary radical, R, is by reaction with C2HCF3which is present in large excess. Then the temporal history of C2H2formation is an accurate measure of kl. A t fixed concentrations of alkane, the C2H2yield was independent of added helium over the range of 20-700 torr. The extinction coefficient of C2Hzat 152 nm has been measured,llaJ’ but the two existing values differ by 1order of magnitude. Since absorption at 152 nm is a convenient method to determine the yield of product C2H2,it was necessary to redetermine the value of E , the extinction coefficient. Absorption data, in the pressure range of 0.5-10 mtorr of C2H2,in 10-100 torr of added helium were fitted to the equation I = Io exp(-qpx). The value of E , determined from the slope of a plot of In (Io/fivs. pressure, was 5950 cm-l atm-l. The newly determined value was used in the present work rather than either of the two previous values (1140011a and 140011bcm-l atm-l). The extinction coefficient was independent of added buffer gas in this pressure region. The abstraction reaction of C2H with C2H6 exhibits no kinetic complications. The preliminary titration experiments indicated exclusive reaction between C2H,derived from 100 mtorr of CFBC2H,and C2H, occurred at concentrations of less than 100 mtorr of added ethane. In the alkane concentration region where the C2H2product concentration is a plateau, the only fate of ethynyl radicals is by reaction 1and the final yield of C2H2is equal to the initial C2H concentration. Based upon such an analysis, photoconversion of the CF3C2Hprecursor was always less than 3%. Under these conditions C2H2was produced in an amount adequate to permit spectroscopic detection, and the reaction proceeded by first-order kinetics. The results are shown in Figure 1, in which the yield of C2H2is plotted vs. time. If the only fate of C2H is to abstract an H atom from the alkane, i.e., follow first-order kinetics, the value of kl may be determined from the half-life of the reaction. However, the rate constant also may be obtained from the - (C2HJt]vs. time plot. The slope of a In [(C2HZ),/(C2H2), preferred value and the standard deviation, for RH = C2H6,obtained from the slope is kl(CZHB) = (6.5 f 0.4) X The curve, fitted to the data, cm3 molecule-’ shown in Figure 1is calculated by using the preferred value of the rate constant. Error bars for several typical points are indicated. There was no evidence for a pressure effect over the range of 20-700 torr of added helium. In terms of the (11) (a) T.Nakayama and K. Watanabe, J . Chern. Phys., 40, 558 (1964); (b) G.Moe and A. B. F. Duncan, J . Am. Chem. SOC.,74,3136 (1952).
O l 0
I
I
I
I
I
100
200
300
400
500
I I
Time (ps)
Flgure 1. C2H2concentration as a function of time following photolysis: (0) 100 mtorr of CF3C2H4- 100 mtorr of C2H6 4- 20 torr of He; (A) 100 mtorr of CF3C2H4- 100 mtorr of C2H64- 700 torr of He; (A)100 mtorr of CF3C2H4- 100 mtorr of C2D, 4- 20 torr of He; (0)100 mtorr -k 100 mtorr of CpD, 4- 700 torr of He. of CF3CH l
primary photodissociation, this suggests that CF3C2H dissociates through a totally repulsive state, which is a significant departure from C2H2photodissociation. The lack of an effect of pressure on the rate constant, in the above range, agrees with previous observations based upon flash photolysis results2using C2H2 as a C2Hprecursor but conflicts with low-intensity experiments using C2HBr as the C2Hprecur~or.~ The effect of inert-gas pressure upon the distribution of products at low intensity has been attributed to translationally “hot” ethynyl radicals. Based upon extinction-coefficient data the active photolysis region in the present experiments is the region of 185 nm (154.5 kcal/mol). The heat of formation of CF3C2Hmay be estimated by using the group additivity scheme12from which -104 kcal/mol may be derived. Since AHf(CF3) = -112.5 kcal/mol13”and AHf(C2H)= 127 k ~ a l / m o l , the l~~ excess energy following photodissociation is 36 kcal/mol. If the excess energy is partitioned between the fragments, in inverse proportion to their respective masses, the ethynyl radical would have ca. 25 kcal/mol additional energy, which is comparable to that in the low-intensity experiments. However, with helium as a quencher and assuming a hard-sphere collision model, about 25% of the excess translational energy will be transferred to the third body per c01lision.l~ The C2H, therefore, will be reduced in enery to that associated with kT in about 10-12 collisions. A t 20 torr, this number to collisions will occur in fraction of a microsecond. The minimum observational delay time achieved in our experiments was 9 p s , by which time the reactive radicals would be entirely thermalized. The rate constants reported are, therefore, representative of thermal species. As an adjunct to the C2H6study, the abstraction by C2H of a D atom from C2D6 (reaction 3) has been examined. CZH + C2D6 = C2HD + C2Db (3) The separation between absorption bands of C2H2 and C2D2in the 152-nm region is 1 A.15 The comparable transition, in C2HD,presumably lies between that for the do and dz isotopes. The absorption feature in this region is quite broad so an exact frequency measurement is difficult; however, the product of reaction 3 appears at higher (12) S. W. Benson, “Thermochemical Kinetics”, Wiley, New York, 1976. (13)(a) JANAF Thermochemical Tables, 2nd Ed. Natl. Stand. Ref. Data Ser. (U.S. Natl. Bur. Stand.), No. 37 (1971); (b) H.Okabe and V. H. Dibeler, J . Chern. Phys., 59,2430 (1973). (14)J. B. Hastead, “Physics of Atomic Collisions”, Butterworths, Washington, DC, 1964,p 43. (15)P. G.Wilkinson, J. Mol. Spectrosc., 2, 387 (1958).
The Journal of Physical Chemisfry, Vol. 85, No. 25, 1981 3831
Reactions of Ethynyl Radicals
lo
ticipated, it was found that larger quantities of CHI were required to achieve a plateau for C2H2production, implying a lower rate constant than that for C&6. In fact, 500 mtorr was required to achieve a buildup curve with a time history sufficiently short to preclude serious diffusion effects. Kinetic data are shown in Figure 2. A curve with a value of k1(CH4)= (1.2 f 0.2) X 10-l2 cm3 molecule-l s-l has been drawn through the experimental points. There are not any values in the literature with which to compare the absolute values reported here. With respect to rate-constant ratios, the present results yield ;;p/kl(c€Id = 5.7. This ratio is to be compared with that uced from low-intensity experiments equal to 203 or 34.4 Though disagreement is significant, there is no ready explanation except that the photolysis of neat C2HBr is complicated by the presence of excited Br atoms and production of HBr.5 The measured hydrocarbon yields, in a Br-containing system, may be affected by reaction of either Brl or Br3/2atoms or abstraction from HBr by product afkyl radica1s.l' Using C2H2 as a precursor for ethynyl radicals and measuring the decrease in C4H2 production upon addition of various reactants (reactions 4 and 5 ) , Okabe18notes that C2H + C2H2 C4H2 + H (4) C2H + RH -+ CzH2 + R (5) the reaction of C2H with CH4is about 31 times slower than that with C2H2. If k(C2H + C2H2) = 3.1 X cm3 molecule-l then k1(cH4)= 1.0 X cm3 molecule-l s-l, in good agreement with the present work.
1
0 0
100
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300
Time (ps)
+
+
Figure 2. (X and 0) 100 mtorr of CF&H 500 mtorr CH, 25 torr of He; (A)100 rntorr of CF&H -I- 500 mtorr of CH, -I- 200 torr of He.
frequency than C2H2,in agreement with an assignment to C2HD. Kinetic data for reaction 3 are shown in Figure 1 also. The data, plotted logarithmically, yield a straight line through the origin from which k3 = (3.1 f 0.5) X cm3 molecule-l s-l is derived. The H/D isotope effect is 2.2 which, if entirely due to a difference in the activation-energyterm of the Arrhenius expression, is equivalent to 500 cal/mol. By comparison, CH3 abstraction reactions exhibit a kinetic isotope effect in the activation energy of 1500 cal/mol.16 With CH4 as the alkane additive, products of the titration experiments were analyzed by gas chromatography. The column used elutes C2H2shortly following CH4. In the presence of the relatively large amounts of CHI required by the titration experiments, the small yields of C2H2were obscured. The C2H2yield, therefore, was determined, by absorption spectroscopy at 152 nm. As an(16)W.M. Jackson, J. R. McNesby, and B. deB. Darwent, J. Chem. Phys., 37, 1610 (1962).
+
Acknowledgment. This research was supported in part by the Planetary Atmospheres program of the National Aeronautics and Space Administration under Contract W-13,454. (17)L. Batt and F. R. Cruickshank,J. Phys. Chem., 71,1836 (1967). (18)H.Okabe, private communication.
