1601
ADDITION REACTIONS OF H AND D ATOMS
From this equation the concentration is easily calculated.
where fo =
DO -'
Bo
fN
=
CjK+' = g,
0
WO Bo
go = -
- f,C,+P+'
The procedure is to obtain a value of PjK+lfrom the predictive equation, calculate g,, j j , and then CjK+I, compare these values with the predicted values, and if they are not within the required error repeat the procedure using the calculated CjKtl values as the predictive values. Repeat this procedure until the required accuracy is attained. A computer program has been written to solve these equations for first- and second-order reactions. l 2
Mass Spectrometric Studies of Rate Constants for Addition Reactions of Hydrogen and of Deuterium Atoms with Olefins in a Discharge-Flow System at 3 0 0 ° K by E. E. Daby, H. Niki,*and B. Weinstock Scient& Research S t a f , F w d Motor Company, Dearborn, Michigan 48131
(Reeeiaed December .29, 1970)
Publication costs assisted by the Ford Motor Company
Absolute rate constants for the addition reaction of H and of D atoms with a number of olefinic hydrocarbons have been determined directly at 25" using mass spectrometric detection in a fast discharge-flow system. The rate constants obtained range from 0.7 to 9 x 10'1* cm8 molecule-' sec-', and their ratios agree well with relative values reported by CvetanoviE and coworkers. The relevant reaction scheme is H
+
+ (o1efin)I
kf(f) kf
R1*; Rl* k,_ Rz (olefin)rI;R1* -% R1. Under the experimentalconditionsused,the observed bimolecular rate constants yield krcs, directly in most cases. The systematic variations of rate constant with molecular structure of the olefins are discussed.
Introduction When atomic hydrogen reacts with olefinic hydrocarbons, chemically activated alkyl radicals are formed. The subsequent unimolecular dissociation of these adducts has been the subject of extensive experimental and theoretical studies.' The absolute rate constants for the initial addition reactions are known to a much lesser degree2 with the exception of ethylene. Values of the absolute rate constant for the addition of atomic hydrogen to ethylene have been determined by a variety of experimental techniques, but show an order of magnitude spread and a critical choice of the most reliable value is difficult to make.3 Several measurements of relative rates for olefins also lack consistency, with the exception of three independent photochemical studies by CvetanoviC: and coworker^.^-^ In Table I, mean
values of the relative addition rates obtained by Cvetanovi6's group are compared with those of other systematic studies.',* In a previous note from this laboratory, mass spec(1) B. 8. Rabinovitch and D. W. Setser, Advan. Photochem., 3, 1 (1964). (2) For reviews mior t o 1964: R . J. CvetanoviE, ibid., 1, 115 (1963); B. A. Thrush, Progr. React. Kinet., 3, 65 (1965). (3) See, for example, Table I of ref 6. (4) K . R. Jennings and R. J. Cvetanovi6, J . C'hem.*Phys.,35, 1233 (1961). (5) G . R. Woolley and R. J. CvetanoviO, ibid., SO, 4697 (1969). (6) R . J. Cvetanovii! and L. C. Doyle. ibid., 50, 4705 (1969). (7) (a) P. E. M . Allen, H. W. Melville, and J. C. Robb, Proc. Roy. Soc., Ser. A , 218, 311 (1953); (b) J. N. Bradley, H. W. Melville, and J. C. Robb, ibid., 236, 318 (1956). (8) K. Yang, J. Amer. Chem. Soc,, 84, 719, 3795 (1962).
The Journal of Physical Chemistry, Vol. 76, No. 10, 1971
1602
E. E. DABY,H.NIKI, AND B. WEINSTOCK Dischorqe
Table I: Literature Values of the Relative Rates for H Olefins a t 25"
+
Allen Melville, and Robbl
Olefins
Mu I ti holed Outle t CvetanoviC,
Y angs
et al.6
Sea I Pyrex
c=c/
\ \
C
0.76
C
dC
'C C
\
3.85
1.06
0.49
0.72
0.83
0.52
0.90
0.98
2.05
1.28
C
c=c
/-
'c c=c-c=c
Pump
Figure 1. Schematic diagram of the discharge-flow apparatus coupled to a time-of-flight mass spectrometer.
C
C=
,C=
13.3
C/
23.5
7.5
trometric determinations of absolute rate constants were reported for the reaction of H and of D atoms with cis- and trans-butene-2 in a discharge-flow system at 300°K.0 For these reactions, the absolute rate constants obtained by this technique agreed well with those of other workers, who used entirely different experimental method^.'^'^ This paper describes an extension of the mass spectrometric studies to a large variety of olefins. Experimental Section Reactions of H and of D atoms with olefins have been studied in a fast discharge-flow reactor coupled to a Bendix Type 14 time-of-flight mass spectrorneter.l1 A schematic diagram of the apparatus is shown in Figure 1. The flow reactor was fitted to a Bendix fast-reaction chamber. The reaction was monitored directly by sampling the reacting gas into the mass spectrometer through a pinhole (-200-p diam) drilled in a Teflon sheet or through a miniature nozzle (-3mm length) formed in a Teflon sheet. The olefins were introduced into the reactor through a multiholed outlet probe, whose position was adjustable by means of a sliding rubber vacuum seal, lubricated with silicone grease. Exposure of the greased section of the probe to the atomic hydrogen was prevented by using a long side arm (-20 cm), which was flushed with a small fraction of the diluent helium. The olefin was diluted with a carrier gas, which helped to prevent back diffusion of atomic hydrogen into the probe and also to provide a fast response to flow adjustment of the olefin. The reactor pressure was monitored through this probe with an Octoil oil manometer, which was read with a cathetometer to hO.01 Torr. The axial pressure gradient in the reactor was at most 2% of the total The Journal of Physical Chemistry, Vol. 76, No. 10,1971
pressure. The average of all pressure readings during a run was used to calculate the linear Aow velocity. The reaction temperature was measured to be 300 k 2°K with a thermocouple attached externally to the reactor wall. Heat generation by the reaction was assumed to be negligible, since the olefin concentration was generally maintained a t an extremely small fraction (-0.01%) of the diluent gas. The reactor walls were coated with G.E. Drifilm to minimize heterogeneous recombination of atomic hydrogen. The extent of the wall recombination was determined by generating H atoms free of H2 as a product in the reaction of 0 atoms with C2Hz in the presence of an excess of 0 atoms.12 The results showed that less than 5% of the total H atoms were recombined under all the experimental conditions used. Atomic hydrogen was generated by dissociating molecular hydrogen in a microwave discharge. In most runs, molecular hydrogen was highly diluted with He carrier gas, and a large fraction (-50%) of Hz could be converted to H atoms. The H-atom concentration was determined directly from the extent of the H2-to-H conversion, and also by the NOCl titration method.13 Results obtained by the two methods agreed within 5% for H-atom concentrations of the order of lo1* atoms per om3. The impurity 0-atom concentration was determined to be always less than 1% of the Hatom concentration. The mass spectral signals for H and H2 varied linearly with concentration in the range of 10l2 to l O I 4 particles per cm3. The mass spectral sensitivities for H and Hz remained constant to * 5 % over the period of half a day, after an initial 1-hr con(9) E. E. Daby and H. Niki, J . Chem. Phys., 51, 1255 (1969). 44, 252 (1967). (10) W. Braun and M. Lensi, Discuss. Faraday SOC., (11) See, for example, J. V. Michael and H. Niki, J . Chem. Phys., 46, 4969 (1967); H. Niki, E. E. Daby, and B. Weinstock, Symp. (Int.) Combut. [Proc.],l d t h , 277 (1969). (12) J. M. Brown and B. A . Thrush, Trans. Faraday Soc., 63, 630 (1967). (13) L. F. Phillips and H. I. Schiff, J . Chem. Phys., 37, 1233 (1962); F. Kaufman and F. P. Del Greco, S y m p . (Int.) Combust. [Proc.], 9th, 659 (1963); M. A. A. Clyne and B. A . Thrush, Proc. Roy. Soc., Ser. A, 275, 544 (1963); A. A. Westenberg and N. deHass, J . Chem. Phys., 43, 1550 (1965). (14) R. E. Harrington, B. S. Rabinovitch, and R. D. Diesen, ibid., 32, 1245 (1960).
1603
ADDITION REACTIONS OF H AND D ATOMS ditioning of the microwave discharge, the flow system, and the mass spectrometer. The experiments with D atoms were done similarly. The energy of the ionizing electron beam was kept below 25 eV to obtain an optimum signal-to-noise ratio and minimum interference from cracking patterns of other species present. Four analog outputs were used to monitor reactants and products simultaneously during the course of the reaction. Flow rates of the diluent He (-100 NTP ,ma min-l) were measured with calibrated Matheson flow meters. The lowest gas flow rates (> that result in a regeneration of the original olefin is very small. Consequently, eq 5 reduces to kexptl = Icf(,) and the observed rate of decay of the olefin gives the correct value for the rate of hydrogen addition. This situation can be best illustrated by the reaction of H with butene-2, i.e. H
+ CH3CH=CHCH3
CH&H2-CHCH*3
(6)
+ CHI
(7a)
CH~CHY-CHCH”~-% CH-CHCH3
-%- CH3CH2-CHCH3
(7b)
For chemically activated sec-butyl radicals,’ k, has been shown to be approximately lo7 sec-l, and IC,’ less than 104 sec-l, ;.e., k, >> k,’. This was confirmed in this work by the observation that isotopically scrambled butenes were not an important product in the reaction butene-2. In addition, regeneration of system D the butene-2 or its isomeric species, eq 8, would also be ruled out on the basis of this observation. This conclusion is further substantiated by the absence of a pressure effect on kexptl for this reaction. It is worth noting that at the diluent He pressure used, 0.4-2 Torr, only a fraction of the activated sec-butyl radicals are collisionally stabilized, i.e., k , 1 w . These considerations do not apply to four compounds studied here, propene, isobutene, 2-methylbutene-2, and butadiene-1,4. In the reactions of D atoms with these compounds, extensive isotopic scrambling of the reactant was observed. Thus, in these systems the reactant olefin must be regenerated either by redissociation of the corresponding activated radicals and/or by the secondary reaction of the stabilized radicals with atomic hydrogen. Therefore, the approximation, kexptl = kf(a),is not valid for these compounds and values for k,, k e f , w , and c would be required to evaluate kr(,) from kexpt1 for the system H olefin, i e . , k E . This difficulty has been circumvented by measuring kexptl using D atoms, Le., k ~ .Then, the decay of the completely protonated olefin gives a good approximation of k f ( , ) ; because very little of the completely protonated olefin is regenerated, most of the regenerated olefin contains deuterium. An estimate of the uncertainty introduced by using this approximation can be made by considering the statistical scrambling that occurs in the regeneration of the parent olefin. For example, in the case of isobutene the activated complex is completely symmetrical and contains eight equivalent H atoms and one D atom. In the previous notation, IC,‘ corresponds to the dissociation of a D atom and k , to that of an H atom. I n this case k , is equal to or greater than 8IC,’. It is probably much greater because of the kinetic isotope effect for breaking a C-H bond compared with a C-D bond. Similar considerations show that regeneration of the protonated parent olefin by reaction of the stabilized complex with D atoms is also not significant. Therefore, k D = kexptl is a valid approximation. The values of k~ and k~ obtained in this study are summarized in Table IV and their ratios are given in the last column of that table. For six of the compounds listed, there is no isotope effect within the experimental uncertainty. The ratios are apparently less than unity for propene, isobutene, and 2-methylbutene-2 because k H , which is given in parentheses, is too large for reasons
+
+
and H
+ CHaCH&HCHs
+u(YL-C~H,,) +
+
b(2CzH5 or C Z H ~ CHI)
+ c(C4Hs + Hz)
(8)
(15) R . D. Kelley, 13. Klein, and M . D. Soheer, J . Phys. Chem., 69, 906 (1965); 74, 4301 (1970). (16) R. J. Cvetanovik and R. S . Irwin, J . Chem. Phys., 46, 1694 (1967).
The Journal of Physical Chemktry, Vol. 76,No.10,1971
E. E. DABY,H. NIKI,AND B. WEINSTOCK
1608
discussed previously. For butadiene, the same arguments apply, although the observed ratio is greater than unity. In this case, the experimental uncertainty is probably greater than indicated by the standard deviation because it is a very rapid reaction. Comparison with Previous Measurements. Extensive studies of the rate constants for the reactions of H atoms with olefins have been reported by CvetanoviE and ~ o w o r k e r s . ~ -I~n their work they did not measure absolute rate constants, but rather obtained relative rates. Photochemical methods were used to generate hydrogen atoms and the reactions were studied under high pressure conditions where the addition complex is generally collisionally stabilized. Their rate constants, k H ' , relative to lcH for trans-butene-2 taken as unity are summarized in the last column of Table V. Our results for k H ' and k ~ are ' also included in this table for comparison. The agreement between the two sets of data is seen to be excellent. For the four molecules for which ICD' (and not ICH') should be taken for comparison, the agreement is also good. The only disagreement in the table is our apparent value for k H ' of butadiene, which we stated earlier to be relatively inaccurate. Absolute rate constants have been reported by Melville and coworker^,^ who derived their values from Hatom decay rates rather than olefin decays. I n their
Table V : Comparison of Relative Rates for H and for D Olefin a t 25"
+
__-__ Olefin
c=c
\
c=c/
Cvetanovii-, et al.
This work----
kE'
1.00
1.30
kD'
kEt
1.00
1.00
0.87
0.80
1.83
1.42
1.33 (1.60) 1.77
1.70 1.76
1.64
c-c=
d
1.52
1.98
1.74
( N O . 8)
4.33
4.28
C'
c=c C '
/
z
2@ z
O
8
> a
