S.BAUER,P. JEFFERS, AND N. ZEVOS
4412
On the Mechanism of H-D Exchange in Acetylene at Intermediate Temperatures: a Response'
by S. H. Bauer, Peter Jeffers, and Nicholas Zevos Department of Chemistry, Cornell University, Ithaca, New York 14850 (Received June 12, 1967)
Data on the rates of substitution of D for H during shock heating of deuterium-acetylene mixtures are briefly summarized. For the strictly homogeneous reaction (ambient gas 90-98% Ar) over the approximate temperature range 110O-15OO0K, the empirical power rate expression, the observed activation energy, ratios of the products generated, and study of the rates as they are affected by admixing a variety of selected reagents all favor a mechanism which involves a molecular complex intermediate, rather than a freeradical chain. Several experiments expressly designed to provide tests for these alternate mechanisms are described; those which have been completed support the molecular complex route.
A reaction mechanism is a fragile commodity, in that although a proposed sequence of steps may be in agreement with many observations, when a single contradictory fact is uncovered the mechanism becomes unacceptable. Differences of opinion regarding mechanisms arise because of disagreement as to what constitute umambiguous contradictory facts. Herein we differ with Benson and Haugen.'& After a brief summary of pertinent observations we made during the shock-tube investigation of H-D exchange between acetylene and deuterium12the molecular-complex and the free-radical chain mechanisms will be scrutinized for such critical facts; aspects which provide supporting arguments will then be listed and the rebuttal will be concluded with a discussion of predictions. On shock heating a dilute mixture of acetylene and hydrogen to temperatures up to 1600"K, the characteristic infrared emission from acetylene at 3195 cm-' rose very rapidly to a value which was dependent on the temperature and the concentration and remained at that level for the duration of the test time of the experiment (up to 400 psec). However, when acetylene and deuterium were treated in the same way, the emission at 3195 cm-' rose rapidly and then linearly declined, indicating the disappearance of CzH2. The total order for the (CzH2 D2) reaction was found to be approximately 5/4. Two independent sets of data were obtained; the inital rate of disappearance of acetylene
+
The Journal of Physical Chemistry
(emission at 3195 cm-l), which showed no induction period (time resolution of the order of 5 psec), and the initial rate of appearance of C2HD (emission at 2555 cm-') were analyzed independently. Both sets of data were well represented by the expression = a(T) + b(T)[CzHz] (1) Q(T)= [C2Hz10[Dz10 P!
where -dI(3195)/dt or dI(2555)ldt. Both a and b were found to depend on the temperature, but CY = b/a was independent of T (ref 2, Figure 7a, b, c). The value for CY deduced from the 3195-cm-' data was 4 X lo3 mole/l. A plot of log (l/b) us. 1/T gave an activation energy of 33.0 kcal/mole. Note (ref 2, Figure 8) that there are no significant departures of the lowtemperature points from the Arrhenius line. The above value for CY was determined from the 3195cm-' set which comprised 46 points. ,4n additional 17 points, obtained from the emission at 2555 cm-l, were reduced with the same value for C Y ; these also fell on a straight line with a slope corresponding to an activation energy of 31.2 kcal/mole. Furthermore, quantitative comparison of the rate of intensity decrease at (1) (a) Refer to preceding paper by S. W. Benson and G. R. Haugen, J . Phys. Chem., 71, 4404 (1967). (b) This paper and the preceding one involve different interpretations of the same data. The reader is, accordingly, advised to consider both of them together. (2) K. Kuratani and S. H. Bauer, J. .4m. Chem. SOC.,87, 150 (1965).
~IECHANISM OF H-D EXCHANGE IN ACETYLENE
4413
3195 cm-I with the rate of intensity increase at 2555 cm-' showed that the acetylene was disappearing at approximately 3/z the rate of appearance of the monodeuterioacetylene (to within 5%). Many subsequent single-pulse shock-tube experiments showed that considerable dideuterioacetylene and no other products were produced by heating acetylene and deuterium to the temperature range 1300-1600°K. We concluded that the rate of single to double exchange is 2: 1. This additional condition should be satisfied by any proposed mechanism. Finally, we found a strong similarity between the rate expressions for exchange in (CZHZ Dz) and in (CzH2 C2D2).3 For the latter (errorlimitson empirical powers, 0.1)
+
+
lation (l), whereas neglect of step - 2 leads to the omission of the second term in the right bracket and gives an expression which is identical with (1). Note that a selfquenching step is essential to a molecular-complex mechanism, in order that the power dependence on the CzHz concentration be depressed well below unity. Benson and Haugen correctly pointed out that for the combination of steps proposed k-z(CzH2) 3 kl. However, several alternate but reasonable assumptions can be made which in a formal manner rectify this difficulty. The most plausible one involves vibrational energy transfer, since it is established that the vibrational relaxation time for De is considerably longer than for CzHZ4v6
CzHz Kot only are the empirical forms of the two equations similar; but the magnitudes of the experimental rate constants are comparable, as are the activation energies (to within 4 kcal). The pertinent observations here are that the power dependence of the acetylene is clearly less than that of the dideuterioacetylene, and that the argon plays some role during the reaction. Molecular complexes were postulated as reaction intermediates in the mechanism proposed by Kuratani and Bauer.z The structures of these complexes can be formulated on the basis of currently accepted organic chemical principles and reasonable values for thermochemical parameters. We stress that this mechanism does not preempt the significant role of radicals in reacting mixtures of hydrocarbons under all circumstances. However, as shown below, we found no evidence that radicals were responsible for the major reactions which occur under strictly homogeneous conditions over the temperature range 1000-1500"K, over intervals of about 1 msec, when the reactants are present at densities of to mole/l. The criticism that, in developing the consequences of the molecular mechanism, we neglected to include the reverse of reaction 2 is valid.
+ CzHz z2CzHz + Dz 2
Inclusion of the inverse of the quenching reaction (termolecular) leads to the rate expression
a=
kz k-I
+
k3
(3)
which is not in agreement with the experimental re-
k --I
1
CzHz.Dz
CzHz
2
+ A1
-1
-2
+ CzHz
CzHz-Dz
CZHz'
kr
+ Dz
(CzHzDz)
+ CzHz + DzV CzHD.HD
The role of vibrational excitation as an initiating step is suggested by the similarities in the kinetics of H-D exchange in the (CzHZ Dz) and (CZHZ C2D2) systems and by the dependence of the exchange rate on the argon concentration in the latter case. Other possible mechanisms which lead to an adequate formal representation of the data can be written, wherein the quench step is replaced by one of the following sequences
+
+
-2
+
c z H 2 . D ~ ~ CzHz C,C4H4T
+
C4H4T AI
2
+ Dz
22CzHz + A I 5
or - 2'
+
c 2 H z - D ~ ~CzHz
+
cdH4.D~ M
-2
CzHz. Dz
GHz' CzHz-Dz
__ __ __
+M
7c4H4-D~ 2
z 2CzHz + Dz + M 5'
5'
Here CZH2.DzT denotes a carbene in its triplet state. These changes are significant not, only because they lead to the desired form for the rate law, but also because plausible structures may be written for the new (3) P. Jeffers and S. H. Bauer, Abstract 116. 150th National Meeting of the American Chemical Society, Atlantic City, N. J.. Sept 1965. (4) J. H. Kiefer and R. W. Lutz, J. Chem. Phys., 42, 1709 (1965). (5) J. L. Stretton, Trans. Faraday sot., 61, 35 (1965).
Volume 71,Number 13 December 1967
S. BAUER, P. JEFFERS, AND N. ZEVOS
4414
species postulated. A detailed analysis of these excitation and quenching steps as applied to the (C2H2 C2D2) exchange will be presented shortly for publi~ation.~ When the exchange data were first obtained2 the radical-chain mechanism was analyzed and discarded, for several reasons. The first is that it requires too high an activation energy and predicts significantly lower exchange rates at the lower temperatures (by a factor of 15) if the data are matched with the observed rates a t higher temperatures (ref 1, Table 111). The difficulty is further compounded by the requirement that at the lower temperatures (
