S. W. BENSON AND G. R. HAUGEN
4404
though their “mobilities” are lower by nearly two orders of magnitude. Positive deviations occur for solute concentrations above 6 X M , as had been noted for the KI-I2 system12and are probably due to ion aggregates of higher charge or mass.
Acknowledgment. This study was supported in part by the Air Force Office of Scientific Research under Grant No. AF-AFOSR-624-64 with The University of Chicago and by the Advanced Research Projects Agency under Contract No. SD-89.
The Mechanism of the High-Temperature Reactions between C,H, and Hydrogen1
by S. FV. Benson and G. R. Haugen Department of Thermochemistry and Chemical Kinetics, Stanford Research Institute, Menlo Park, California 94086 (Received December 16, 1966)
The observed high-temperature rates of isotope exchange-betweenC2H2and D2 have been interpreted in terms of a radical mechanism. The chain propagation steps for the system C2Hz+ C2HD H and H D2 + D HD. The most probable initiaare D Dz -+ C2HzD D whileItermination is H (or D) C2H2D--t prodtion is C2H2 ucts. The lower temperature addition kinetics to form C2H4 are fitted very well by a related chain with the same initiation and termination but a different propagation, M H C2H2% CzH3 M and CzH3 H2 -+ C2H4 8. The theoretical steady-state rate expression, derived from the radical mechanism, adequately predicts the observed rates at temperatures greater than 1400°K. The problem of attainment of steady state during the short time interval of the experiment and the catalytic effect, of traces of oxygen and organic impurities on the induction period are discussed.
+
+
+
+
+
Introduction It is the purpose of the present paper to propose a plausible radical chain mechanism which gives a reasonable representation of the kinetic data on the hydrogenation of acetylene. The creditability of a mechanism can be tested by comparing the predicted rate with the observed kinetic behavior. This comparison relies on a better than order-of-magnitude precision in assessing the magnitude of the rate constants associated with the mechanism. This assessment is now attainable because of the similarities that exist between the A factors and activation energies of homologous reactions.2 It is a stringent requirement that the mechanism not The Journal of Physical Chemistry
+
+
+
+
+
+
+
only be consistent with the rate of hydrogenation of acetylene under diverse experimental conditions (lowtemperature static measurements3 and high-temperature shock measurements4), but also with the kinetics
(1) (a) The authors are indebted to the Department of Health, Education, and Welfare, U. S. Public Health Service, for support of this study through Research Grant No. AP-00353-02 from the Division of Air Pollution. (b) This paper and the following one involve different interpretations of the same data. The reader is, accordingly, advised to consider both of them together. (2) S. W. Benson and W. B. DeMore, Ann. Rev. Phys. Chem., 16, 397 (1965); S. W. Benson, Ind. Eng. Chem., 56, 18 (1964). (3) H. A. Taylor and A. Van Hook, J. Phys. Chem., 39, 811 (1935). (4) G. B. Skinner and E. M. Sokoloski, aid.,64, 1028 (1960).
HIGH-TEMPERATURE REACTIONS BETWEEN CzH2AND HYDROGEN
of the high-temperature exchange occuring between acetylene and d e ~ t e r i u m . ~ The Radical Chain Mechanism: Hydrogenation. The low-temperature (-750°K) hydrogenation of CzHz, observed by Taylor and Van Hook,3 proceeds by a chain with an apparent second-order rate constant of k = 1011.0-42’el./mole sec. We can see from Table I that this is compatible with the exchange rate, giving an average discrepancy of less than a factor of three. In fact, if we could increase the chain rate by a factor of three, it would be in reasonable agreement with the exchange data over the entire range. This suggests that a chain mechanism could provide a good representation of the data. A mechanism has been described6 that satisfactorily represents the kinetic behavior of the hydrogenation in the environment of a high-temperature shock. I n this article we will examine the applicability of the mechanism to the lowtemperature hydrogenation of C2H2,reported by Taylor and Van Hook, and the high-temperature exchange with D2.
4405
2
M
+ CZH3 J_ H + CZHZ+ M -2
2C2H3t’_ C4HB At steady state we find (neglecting steps -1 and +2) (CzH3)/ (H) =
k-2
(C2Hz) (W/hi (Hz)
(1)
Using reasonable values for the rate constants k-2 and kl at 750°K with (H2)/(CzHz)= 5, we find that = 1, so that one expects termination (C&)/(&) principally by step t. However, it is quite likely that &Ha recombination can contribute. This C2H3 would be likely at lower (Hz)/(CzH2) ratios and more efficient quenching. The steady-state rate, using both terminations is
+
+
For very high (H2)/(C2Hz) ratios when only H C2H3 terminations are important, the limiting rate becomes
Table I : Comparison of the Observed Exchange and Hydrogenation Rates of Acetylene
The limiting rate for predominantly 2C2H3termination is 1200 1245 1390 1410 1545 1665 1680 1695 1700
-3.47 -3.11 -3.23 -2.75 -2.72 -3.00 -3.06 -2.99 -3.42
-2.94 -2.80 -3.23 -3.05 -2.72 -3.00 -2.76 -3.29 -2.90
-1.10 -0.77 -0.67 -0.25 -0.10 -0.19 -0.25 -0.20 -0.58
Concentration units: mole 1.-1. Rate units: mole L-1 sec-1. rate of hydrogenation of acetylene extrapolated from ref 3; &’ED, rate of exchange of acetylene and deuterium, reported in ref 5.
I n comparing the radical chain mechanism for the hydrogenation of CzH2a t 750°K with the Dz exchange at 1200”K, it can be seen that the difference in paths is determined by the relative stability of the vinyl radical. Let us consider the hydrogenation mechanism first
The apparent second-order rate constant under these conditions would be (5)
The rate data of Taylor and Van Hooka are not sufficiently precise to distinguish these two limiting expressions. Using reasonable values for the various rate constants,? we find that k,,, = 109.6-371e [(H2)/(C2H2)I1”1. mole-’ sec-’. The apparent rate con1. mole-’ stant for eq 3 is estimated as 10g~o-30’e(M)1/2 sec-1. At 750°K in the middle of the experimental range (495-535”), these rate constants have a value of 10-0.9 1. mole-’ sec-’, which is in agreement with the experimental value of lo-’.’ 1. mole-’ sec-’. It ap(5) K. Kuratani and S. H. Bauer, J . Am. Chem. SOC.,87, 150 (1965). (6) 5. W. Benson and G. R. Haugen, J . Phys. Chem., 71, 1735 (1967).
(7) Value of the rate constants used in this calculation are: ki = 109*&60.5/e 1. mole-’ sec-1; kt = 10gJ 1. mole-’ sec-1; kl = 109.5-6.4/8 mole-1 sec-1; and k--2 = 108.2+6.8/8 1.2 mole-2
sec -1.
Volume 7 1 , Number 13 December 1967
S. W. BENSON AND G. R. HAUGEN
4406
pears that the apparent second-order rate constant reported in the low-temperature measurements of Taylor and Van Hooka are in conflict with the high-temperature measurements of Skinner and Sok~loski.~However, the absolute rates for both studies are reasonably consistent with the hydrogenation mechanism proposed in ref 6 and discussed here. The narrow temperature range (40°K) employed in the low-temperature (-750°K) hydrogenation study casts uncertainty on the accuracy of the activation energy (the lower limit on the uncertainty in the activation energy is =!=4 kcal/mole). Radical Mechanism: Exchange. The homogeneous gas-phase exchange between C2H2 and D2 behind an incident shock wave has been studied with the use of spectrophotonietric techniques? In part, because the rate did not appear to follow simple second-order mixed kinetics, the authors ruled out a direct bimolecular exchange. On the basis of what appeared to them an anomalously low activation energy, -33 kcal/mole, they ruled out a radical mechanism. Proceeding from this point, they suggested a molecular mechanism involving a t least two unusual forms of a molecular complex between C2H2and D2 with special kinetic properties, which permitted the rationalization of their data. It has been showns that this molecular mechanism does not yield the proposed rate law and that the simple radical chain is in reasonable agreement with the reported data. The exchange reaction includes the propagation chain
D
+ CzHz H + D2
3
+ CzHD HD + D
A
-3
-
neglect the CzHd synthesis chain compared to the exchange chain, then (c2H3) = (H) (D),9and using mixed terminations1° we find
+
so that
The form of the rate law in eq 10 is already reasonably close to the observed rate expression in regard to the apparent order of 1 and '/4 with respect to D2 and C2H2 since we expect the denominator term k4(D2)/kS(C2H2) to be less than unity over the whole range of conditions. I n fact, the absolute rate calculated by the detailed eq (8) S. W. Benson and G. R. Haugen, Comments on Paper No. 10, "Transient Species Generated during the Pyrolysis of Hydrocarbons," presented by S. H. Bauer a t the 11th International Symposium on Combustion, San Francisco, Calif. I n the molecular complex mechanism i t is essential that acetylene be an efficient quencher of the complex (intermediate). The steps for formation of the complex (no matter how complicated) must be represented by the over-all chemical equilibrium
C2Hz
+ Dz
kl
k -1
CzHz.Dz*(structure of the molecular complex unspecified in this discussion)
and
The catalytic destruction of the molecular complex by acetylene is represented by the over-all chemical equilibrium (no matter the complexity of the stepwise quenching)
+ C2H2
k1
2CzHz
CzH2.Dz*
+ Dz* (state of the deuterium unspecified in this discussion)
k -1
Neglecting the back reactions of the products (steps -3 and -4), the steady-state ratio of (H)/(D) is given by (HI/ (D) = lca(CzHz)/k4(Dz) [(HI
+ (D)J/(D)
=
1
+ ks.(CzHz)/k4(Dz)
(6)
(7)
and
The inequality, kz[CzH~] > k-1 expresses the efficient quenching ability of acetylene. However, the equilibrium constants for the uncatalyzed, ki/k-1, and catalyzed, ke/k-z, processes are related by
The steady-state exchange rate is given by Rearranging
The over-all rate is now determined by the termination processes in the system, which in turn depend on the fate of the vinyl radical (C2H3). At the high temperatures employed in the exchange measurements, the addition of H atoms to C B 2 is pressure dependent so that the ratio (CZH3)/(k> is small. If, in fact, we The Journal of Phyeical Chemistry
Hence, if kn[CzHz]/k~ > 1, then k-z[Dz*I[C~H~l/kt[Dz] > 1and the trimolecular step of the over-all chemical reaction is the most important process for forming the complex. (9) The C2Hs and D are produced in equal amounts by the initiation and the exchange affects only the (H)/(D) ratio. (10) Mixed termination by dzHs & (or fi) need not be the inverse of initiation; addition can lead to C2H4.
+
HIGH-TEMPERATURE REACTIONS BETWEEN CzHzAND HYDROGEN
14 is consistent with the observed acetylene, deuterium, and M dependence (Table 111) over the reported experimental range of these quantities, which is a sixfold variation in acetylene concentration, a fourfold variation in deuterium concentration, and a threefold variation in Ail conckntration. Using known rate constants for kg, and the ones already used for ki/kt, and neglecting the denominator, we find an apparent activation energy of 37.8 kcal/mole and an apparent A factor of 1010.91. mole-' sec-l. As can be seen from Table 11, this gives a good fit to the published data over most of the range. However, at the highest temperatures ( T > 1400"K), it is very unlikely that the vinyl radical remains undecomposed in the system, and so we must add to the scheme the steps 2 and -2, which will now be in the low-pressure region
4407
+v+
t
29 t'_ where represents any of the vinyl radicals. At steady state the radical concentrations are given by
(H)
+ (D)
=
[ki(C2H2)(D2)11/2/ [k,t.(nir) ktcp
+
+ kt'cp'2]'/2
(11)
where
Table I1 : The Rate of Exchange Estimated by the Simplified Eq 10
and -2.16 -1.52 -1.53 -0.92 +o. 09 -0.09 +0.29 -0.44
1200 1245 1390 1410 1545 1665 1680 1685 1700
-0.04
-1.95 -1.51 -1.37 -1.05 -0.26 -0.31 -0.01 -0.48 -0.12
0.6 1.0 0.7 1.4 2.2 1.7 2.0 1.1 1.2
(H)/(D) G ka(CzHz)/h(Dz) (12) The steady-state rate of exchange is obtained by substituting eq 11 and 12 into eq 8; thus
Re =
(
d(C2HD) dt k4(D2)'/2(C2H2)1/2 k4(D2)
2)ll2
[l+
and hence M dependent. The elementary steps 2 and - 2 involve thermalized vinyl radicals; while in step 3, our attention is focused on the fate of a ('hot" vinyl radical. A quantitative comparison of the kinetic behavior of "hot" and thermalized vinyl radicals is given in the next section. The entire scheme becomes
CzH2+ D2& & H D
+D
+ CzH2 -% CZHD+ H H + D~4_ HD + D D
WI
[a(M)+ cp
+
(13) p j 1 / 2
where a = kttt/kt and p = ktf/kt. This differs from the previous expression, eq 10, by the inclusion of the square-root term in the denominator involving the auxiliary terminations. This derivation assumes that the chain length is long. Introducing reasonable values of the rate constants into eq 13 allows the calculation of the absolute rate of exchange for the typical experimental conditions reported in ref 5 from the following expression 10io.~-37.s/e
(initiation)"
t
+
(chain)
+
(11) The elementary step CZHZ D2 + C Z H ~ D D was found to be the fastest initiation process involving the formation of two radicals available for this system. Although a biradical initiation process has a much lower activation energy, its total rate was found to be an order of magnitude slower.
Volume 71, Number 13 December 1967
S. W. BENSON AND G. R. HAUGEN
4408
Table I11 : The R a t e of Exchange Estimated by Eq 14”
1200 1245 1390 1410 1545 1665 1680 1695 1700
-2.94 -2.80 -3.23 -3.05 -2.72 -3.00 -2.76 -3.29 -2.90
-3.47 -3.11 -3.23 -2.75 -2.72 -3.00 -3.06 -2.99 -3.42
-2.00 -1.88 -2.32 -1.82 -1.82 -2.10 -1.83 -2.06 -1.98
where
a=
10-3.80+46.7/e(C2Hz) 1 + 10-2.15+24.1/0__ (D2)
(M) Comparison of the absolute rate of exchange calculated by eq 14 with the experimentally observed values6 is shown in Table 111. The steady-state chain mechanism is in reasonable agreement wit,h the data over most of the experimental range. A secondary point of interest, is the relative ratios of ethylene formation t o exchange. This is given by
RCP5 - klOr) = k’m[l+ Re k4(H) k4
-1
kd (Dz) ka(C2Hz)
0.2 0.3 0.7 0.6 2.0 3.2 3.1 2.3 2.0
0.25 0.35 0.06 0.23 0.07 0.02 0.02 0.02 0.01
M. Once thermally equilibrated, the vinyl radical proceeds to ethylene. The relative amounts of exchange and ethylene formations is determined by the competition between dissociation and deactivation of the ‘(hot” vinyl radical
+H C2H2D + M
@2H2D)* f_ C2HD (C2H2D)*
+M
The classical Rice-Ramsperger-Kassel theory of unimolecular reactions can be used to estimate the ratio of deactivation to fragmentation, ka(M)/lct l 2
(15)
Introducing into eq 15 the appropriate value for the rate constants, results in the following expression
This ratio, Rc,EI,/R,,is tabulated in the last column of Table 111,where it is seen that the formation of ethylene is only negligible at high temperatures. I n ref 6, the radical mechanism was shown to be consist.ent with the observed high-temperature hydrogenation of acetylene. Also, evidence was offered that demonstrated that the rate of formation of 1,3-butadiene is not larger than the rate of formation of ethylene under the conditions of the exchange experiments. The Exchange vs. the Thermal Stabilization of Vinyl Radical. “Hot” vinyl radical can either dissociate or be thermally equilibrated by collisions with The Journal of Physical Chemistry
-2.60 -2.06 -1.52 -1.30 so.05 +0.20 $0.48 -0.11 +o. 19
where X represents the probability of “complete” deactivation on collisions, 2 is the number of collisions per second per unit pressure, At is the frequency factor for the unimolecular fragmentation, E * and E represent the critical energy necessary for fragmentation and the internal energy of the molecule, respectively, and S is the number of effective oscillators. Now E can be evaluated from the C-H bond energy in the vinyl radical, the activation energy of hydrogen atom addition to acetylene, and the thermal energy in the vinyl radica112
E
=
BE
= 42
+
Eact
+ Evib(C2H2) + RT
+ 5 + RT +
LTCvibT
dT
(18)
where CvibT is the mean vibrational heat capacity for acetylene a t temperature T’K. We have tabulated the value of E at different temperatures in Table IV. (12) S. W. Benson and G. R. Haugen, J . Phya. Chem., 69, 3898 (1965).
HIGH-TEMPERATURE REACTIONS BETWEEN C2H2AND HYDROGEN
4409
Table IV: Value of E at Different Temperatures
6
-9\ - \ s = ?I
I
1
I
I
I
-
\ \
E, kcal/mole
Temp, OK
298 750 1200 1400 1700
48.4 51.6 56.4 58.8 62.8
\
Eflective no. of oscillators, Cvib(C2Hd/R
1.3 4.5 6.2 6.8 7.7
7
-z
2
.-5 ...
-
\,
\\,
‘
s
’Q\\
\
3
< 9 2
-
,
2\\\ .‘\\.\’ ’.\ ‘Q., . Q. ’\ ‘.Q.. . ps .7 ‘a, -. . ‘.‘Q\....‘...‘.-. I ‘n.. a-%, -1 -.-.-. %o O\
0
-
Q\S.8
\\
5=6\\\ 4 \
-’\\
\
‘
\
\\\\
Q\
‘*
4\\\,
:
‘.-)I
\
0
The variation of the ratio k d / k t with temperature and the number of effective oscillators, S, is shown in Figure 1. The number of effectiveoscillators can be estimated from the vibrational heat capacity of C2H3 (see Table IV). The number of effective oscillators is dependent on the temperature and the most probable variation of k d l k t with temperature, represented by the solid line in Figure 1. I n the high-temperature exchange experiments,s the total concentration of quencher (R4) is about mole 1.-1. We see from Figure 1 that the collisional deactivation is about one order-of-magnitude slower than the fragmentation of the “hot” radical. This indicates that the formation of thermalized vinyl radicals from the addition of hydrogen atoms to acetylene is slow compared to exchange. Taylor and Van Hook’s3experiments were performed a t a total pressure between 0.5 and 1 atm and a mean temperature of 750°K [(AI) 10-2 moles I.-’]. The composition of the gas varied from a (H2)/(CzH2) ratio of 1 to 32. The quenching efficiency of H, is very similar to that of the rare gases (A 0.3), whereas acetylene is more efficient. Thus, we see from Figure 1 that the ratio of deactivations to fragmentations is nearly the same, under these conditions, as that found in the exchange studies. I n these systems the formation of vinyl radical is in its low-pressure limit. Induction Period. The comparison of the calculated steady-state rates with the observed values is meaningful only as long as the time for the attainment of the steady-state concentrations of the radicals is small com-
\\\
\\
-m In the case of the fragmentation, the activation energy is 47 kcal/mole and the frequency factor is generally about 1013.5sec-’.13 The collision frequency, 1. mole-’ sec-’, can be combined with the 2 = collison efficiency, A, to give the rate constant for colli-
-
\
9
l -
’T,
D--.
--0
0 -
Q--
Q---
-I
fl
I
I
\
I
I
l
I
‘I,
pared with the time interval of the experiment. The fraction of the steady-state concentrations attained by the predominant radical in a fixed time interval is shown in Table V. Evidently, a t temperatures below 1410OK the predominant radicals have not attained their steadystate concentrations within the experimental time interval. This demonstrates that for temperatures below 1400°K the simple bimolecular initiation processes are much too slow to reach the desired level of radicals. We are compelled to seek unimolecular initiation processes, or catalysis of the bimolecular initiations to obtain the required radical concentrations. The short-duration high-temperature shock measurements may be very sensitive to impurities. In fact, the most likely impurity in shock-tube studies, oxygen, has been shown to be a catalyst for the dissociation of H2. The extreme sensitivity of the kinetics of HZdissociation to traces of oxygen was satisfactorily demonstrated by the study on the resonance absorption of hydrogen atoms behind a shock wave.14,15 The measured rates of dissociation of hydrogen were found to be higher than the values calculated from collision theory, but by a factor which decreases with increasing temperature (300 at 1675°K to 10 at 2145°K). A much better correlation between the observed and cal~~~
~~
(13) B. S. Rabinovitch and D. W. Setser, “Advances in Photochemistry,” Vol. 3, Interscience Publishers, Inc., New York, N. Y . , 1964, p 1. (14) A. L. Meyerson, H. M. Thompson, and P. J. Joseph, Cornel1 Aeronautical Laboratory Report No. AD-1689--4-3, 1964. (15) A. L. Meyerson, H. M.Thompson, and P. J. Joseph, J . Chem. Phys., 42, 3331 (1965).
Volume 71. Number IS
December 1967
4410
S.W. BENSON A N D G. R. HAUGEN
Table V: Fractions of t h e Steady-State Concentration of the Predominant Radical after a Fixed-Time Interval” Temp,
OK
1200 1245 1390 1410 1545 1665 1680 1695 1700
-Duration 100
0.07 0.2 0.5
0.7 1.0 1.0 1.0 1.0 1.0
of time interval, psec--
250
500
0.2 0.4 0.9 1.0 1.0 1.0
0.3
1.0
1.0 1.0 1.0
1.0 1.0
0.7 1.0
1.0 1.0 1.0
O S . W. Benson, “The Foundations of Chemical Kinetics,” McGraw-Hill Book Company, Inc., New York, N. Y., 1960, p 334.
culated rates was found when the participation of the reaction of the H2-02 system was included in the mechanism (the shock mixtures contained 2 p of oxygen). Investigation with a high-purity shock tube16 has reduced appreciably the catalytic effect of oxygen. This work has shown that the kinetic behavior of the hydrogen atoms in the temperature range 1675-2145°K appears to be abnormal when there are minute amounts of oxygen present. In other words, the hydrogen atom concentration reaches a higher value in a given time interval than would normally have been expected. The highest purity of acetylene available commercially contains 0.1-0.4% air, which is sufficient to produce the catalytic effect described above. If the total oxygen pressure is only 2-3 1, as asserted by Bauer, then the D2-02 branching chain mechanism cannot establish the necessary radical concentration within the short duration of the measurement. The uniniolecular decompositions of traces of an impurity could establish the steady-state concentration of radicals during the reaction interval. Let us assume that there is 0.05 mole % of an impurity in the acetylene mole 1.-’) that can establish a radical concentration of 10-8.amole 1.-’ in 100 psec at 1200°K. This requires that the unimolecular rate constant for fission of the impurity be approximately 1 O 2 a 0 sec-I. A plausible Arrhenius form would be 101e-5-80’esec-l. This rate constant approaches the kinetic characteristics of the splitting of almost any carbon-carbon single bond in an organic molecule, especially if the fission results in the formation of two large radicals. A similar sensitivity to impurities has been experimentally observed for the shock-tube pyrolysis of eth~1ene.l~ Four parts in 1000 of butene remaining in ethylene The Journal of Physzcal Chemistry
after vacuum distillation (one part in 10,000 of butene is present in the mixture being shocked) increased the observed rate by 65% at 1640°K. This enhancement of the rate increases with the lowering of the reaction temperature. These examples emphasize the sensitivity of these systems to contamination of the gas mixture residing in the shock tube either before or after filling, especially at the lowest temperatures. According to Beilstein,18 the use of a concentrated sulfuric acid scrubber for purifying acetylene is inadequate. Kistiako~sky’~ found that an ultraviolet absorption spectrum of acetylene that is free of impurities could only be obtained by careful execution of the elaborate purification procedure described by Beilstein. Keeping in mind the possible catalysis at the low temperatures, we see that the simple radical-chain mechanism which represents the low- and high-temperature hydrogenation of acetylene does give a reasonable representation of the exchange data. The invariance in the rate of exchange between undeuterated and deuterated acetylene, without and with toluene under similar conditions, *O demonstrates unequivocally the involvement of radicals. Toluene dissociates into radicals in the environment produced by the shock 5
CeH5CH3
CsHSCH2 -5
H 4- C6H.$H3
+A
CeH5CH2 f Ht
This represents a dissociation of toluene into benzyl radicals and hydrogen 2CsHSCH3
A 2CsHsCHz + Ht
If reaction 5 reaches equilibrium, an undetectable amount of toluene would be dissociated (0.4% at 1400°K);21 however, a more than sufficient concentra(16) A. L. Meyerson and W. S. Walt, Paper No. 28 of the Division of Physical Chemistry, 151st Meeting of the American Chemical Society, Pittsburgh, Pa., March 22-31, 1966. (17) I. P. Gay, R. D. Kern, G. B. Kistiakowsky, and H. Niki, J . Chem. Phys., 45, 2371 (1966). (18) F. K. Beilstein, “Handbuch der Organischen Chemie,” Vol. I. (19) G. B. Kistiakowsky, Phys. Rev., 37, 276 (1931). (20) S. H. Bauer, “Transient Species Generated During the Pyrolysis of Hydrocarbons,” presented a t the 11th International Symposium on Combustion a t San Francisco, Calif. (21) The equilibrium constant for reaction 5 is ki/k_1(140o0K) = 105*’-85/e moles 1. -1. Thermochemical data were obtained from “Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds,” American Petroleum Institute, Carnegie Press, Pittsburgh, Pa., 1953; R. Walsh, D. M. Golden, and S. W. Benson, J . Am. Chem. Soc., 88, 650 (1966). The entropy and heat capacity of the benzyl radical were determined by estimating the change in these properties brought about by the
HIGH-TEMPERATURE REACTIONS BETWEEN CzH2AND HYDROGEN
tion of hydrogen atoms would be present to catalyze a chain mole I.-' a t 1400°K with an initial toluene concentration of mole I.-'). At these high temperatures, toluene is an immediate source of radicals. The unimolecular fission of toluene has a rate constant of 1015--85'esec-1.22 At 1400°K with a toluene concentration of mole reaction 5 generates 10-7*3 mole 1.-' of hydrogen atoms within 10 psec. This is sufficient to catalyze the exchange without a detectable induction period. Before the equilibrium is achieved, reactions 5 and 6 will establish a steady state. In this system the steady-state concentration of hydrogen atoms is independent of the toluene concentration and is determined by the relative rates of reactions 5 and 6
4411
of the steady-state concentration within the first 10 pse~.~~ necessary modifications of the structure of toluene: S0(C8HsCH~)= SO(CsHsCHs) - (CHs free rotor) (isobutene 3e torsion) - 2(H-CH) bends R In 2(spin) R In u (benzyl) - R In u (to!uene); Soimo~(C8HaCHz) = Soirwo~(C~HsCHa)2.6 eu; C,O(CKHSCHZ) = Cpo(CsHsCHa) - (CHa free rotor) j- (isobutene 3e torsion) 2(H-C-H) bends: and C,o~ro~o~(CsHsCHz) = C p o ~ ~ a o ~ ( C ~ H sCH3) 2.2 eu. (22) A typical rate constant for an unimolecular fission into radicals: S. W. Benson, Ann. Rev. Phys. Chem., 16, 397 (1965); S. J. Price, Can. J . Chem., 40, 1310 (1962). (23) IC5 = 10'5-85/e sec-1 and k6 = 1010*5-6/el. mole-' sec-1. The value of ks is typical of a rate constant for hydrogen abstraction: S. W. Benson and W. B. DeMore, Ann. Rev. Phys. Chem., 16, 397 (1965). (24) The insignificant production of CD3H a t temperatures below 1425OK in a mixture of 1% CD4 and 27& toluene was presented as a demonstration of the ineffectiveness of toluene in generating sufficient hydrogen atoms. However, in this system no fast chain mechanism for exchange exists, so that the minor rates of production of CDaH are in agreement with the calculation. This is different in principle from the CZHZ DZsystem, where a fast chain is possible. The same objections apply to the system CZDZ CHI. Even after a stationary concentration of atoms and radicals are produced, no rapid radical exchange will be observed because the system does not admit a rapid chain: H CZDZF? CzHD D; D CHI F! D H
+
+
+
-
+
A t 1400°K with a toluene concentration of mole L-l, the steady-state Concentration' of hydrogen atoms will be 10-7.9mole 1.-'. The system will establish 90%
+
+
0 --t
+
+
+
+
+
CH3; and CHI CZDI CHsD CzD. Any chain mechanism would have to include step c which is prohibitively slow with an activation energy in excess of 20 kcal.
Volume 71. Number 19 December 1967
