A. Lifshitz, M. Frenklach, and A.
i 140
The Structural Isomerization CH2=C=CH2 Shock Tube
$
Burcat
CH~-CE=CH, Studies with a Single Pulse
Assa Lifshltz,* Michael Frenklach,’ Department of Physical Chemistry, The Hebrew University, Jerusalem, lsrael
and Alexander Burcat Department of Aeronautical Engineering, Technion, lsrael lnstltute of Technology,Haifa, lsrael (Received November 5, 1974)
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The allene propyne isomerization highly diluted in an inert gas was studied behind reflected shocks in a single-pulse shock tube. The temperature range covered was 1030-1220’K and pressures (Pj) varied between 1.2 and 6 atm. Under these experimental conditions the isomerization is very “clean”. Only 0.17% of the decomposition products was found after 30% of the allene had isomerized. The isomerization is first order with respect to allene and very slightly dependent on the total pressure under the above-mentioned experimental conditions. Around 5 atm the first-order rate constant is Kuni = 1013.17*0.60exp(-(60.4 f 3.1) X 103/RT] sec-’, with an overall power dependence of 0.2 on the total density. All the data points fit an equation kuni = 10“ exp(-E/RT)pfl with a = 14.17 f 0.66, E = 61.2 f 2.5 kcal/mol, and fl = 0.20 f 0.09 where p is the total density in units of mole/cc and 10“ is in sec-l. Several shocks run in the propyne allene direction gave rate constants which were by a factor of -2.3 smaller than those of the allene propyne direction. This value of 2.3 is smaller than the equilibrium constant calculated from the difference in AFf’ of the two isomers a t 1100’K. Shocks which were run with mixtures of 1% CDz=C=CDs and 1% CHz=C=CH2 and the analysis of the isotope distribution in the products proved the reaction to be pure unimolecular.
--
two double bonds. This process can take place by a unimolecular migration of the hydrogen atom from one end of the molecule to the other. It may also proceed via the formation of four-center dimers or by some free-radical mechanism. By the study of the kinetics of the reaction, the decomposition that accompanies the isomerization, and the isotope distribution of the product when labeled reactant is being used, the mechanism of the isomerization can be clarified. Although this isomerization is rather straightforward, very little attention has been devoted to its study. Only one kinetic investigation has come to our attentiona2This investigation presents the isomerization as one out of a number of reactions that take place when allene or propyne is heated to high temperatures. Using a flow system, Levush et aL2 determined the first-order rate constants of the isomerization over the temperature range 900-1150’. With mixtures of 1.23 and 2.26% propyne and 1.10% allene in nitrogen at an overall pressure of l atm the following rate constants were obtained k ~ - . p = 4.4 X 10l1 e x p ( 4 4 . 7 X 103/RT) sec-l and kp-A = 2.0 X 10l1 exp(-55.2 X 103/RT) sec-l. The fact that the two propyne mixtures gave the same profiles of conversion vs. time led the authors to the conclusion that the reaction was first order with respect to the isomerized molecule. They did not look, however, a t the effect of the total pressure on the isomerization nor did they try to study the mechanism of the reaction. The allene propyne isomerization was also mentioned in a series of papers by Sakakibara3y4 who demonstrated that the structural isomerization was considerably faster -+
The Journal of Physical Chemistry, Voi. 79, No. 12, 1975
11. Experimental Section A. Apparatus. The isomerization reaction was studied in a 2-in. i.d. single-pulse shock tube. The driven section was 13 ft long made of “double tough” Pyrex tubing including an 11-in. stainless steel test section. The driver section was constructed from brass and its length could be adjusted in small steps in order to achieve the best cooling conditions. A 36-1. dump tank was connected to the driven section near the diaphragm area to prevent reheating of the gas by doubly reflected shock waves. The driver section was separated from the driven section by Mylar polyester films of various thickness. A full description of the shock tube and the details of its operation has already been discussed in previous pub1ications.j Before each test run, the tube was pumped down to several hundredths of a micron. The leak and/or degassing rate was approximately 2 X 10-5 Torr/min. The vacuum in the tube was measured with a cold cathode gauge located near the end plate of the driven section. Incident shock velocities were measured from which the reflected shock parameters were calculated. This was done with two miniature high-frequency pressure transducers (Vibrometer Model 6QP500) the output of which was fed into a home-built period meter, accurate to 0.1 Msec. Dwell times corresponding to the location of one of the transducers were recorded on the oscilloscope and could be determined from the pictures to &lo%. These dwell times were later corrected and averaged as has been discussed in a previous publication.6
1149
Allene-Propyne Isomerization
TABLE I: Test Mixtures and Experimental Conditions of the Seven Groups of Experiments
Group 1A 2A 3A 4D 5P 6P 7p
Com position
range, Torr
Sym bo1 used No. of in T, shocks figrange,"K run ures
0.25% allene 1% allene 1% allene 1% allene-d4 0.25% ProPYne 1% ProPYne 1% ProPYne
178-224
1060-1200
29
169-223
1052-1198
20
0
4658
1040-1217
19
0
198-218
1027-1212
15
+
190-210
1083-1151
7
A
194-198
1039-1109
6
49-55
1051-1160
9
PI
65' to increase the separation. Runs at high extent of reaction were analyzed also for decomposition products. This was done a t an initial temperature of 40' which was gradually raised to 85' with a Packard Model 846 temperature programmer. At the highest temperature (1217'K) tested, the following decomposition products were observed: CH4, 0.067%; C2H4, 0.071%; and C2H2, 0.16%. In this run 27.6% conversion to propyne has occurred. The mass spectral analysis of the pure C3D4 was performed on a Varian-MAT Model 311 mass spectrometer. Mixtures of 1%C3D4 1%C3H4 (allene), shocked and unshocked, were analyzed on the GNOM, Varian-MAT Model 111 GC-MS, using Porapak N column at 85'. The mass spectrum of each substance was recorded photographically when reaching the peak on the gas chromatograph detector (total ionization detector).
+
4
B. Materials. Seven reaction mixtures, three containing allene, one containing allene-d4, and three containing propyne (all diluted in argon), were prepared on a high-pressure stainless steel line and were stored in stainless steel cylinders at approximately 100 psi. The cylinders were baked prior to their use and were later pumped down to 2 X Torr. The seven reaction mixtures and some additional information are presented in Table I. A number of tests were also run with a mixture of 1% allene and l% perdeuterioallene for isotope distribution studies. The allene and the propyne used were obtained from the Matheson Gas Co. Before the preparation of the mixtures, a portion of the allene was transferred into a glass bulb for removal of impurities. It was frozen in liquid N2, pumped on, and then thawed out. This was repeated several times. It was later frozen in a methylcyclohexane-liquid N2 bath and pumped on for some time. The final analysis of the allene showed 0.00022% CH4, no traces of C2H4 or C ~ H G , 0.001% C2H2, and 0.10% propyne. Following the same procedure, the propyne showed in the final analysis 0.0003% CH4, no traces of CzH4 or C ~ H G3.9% , CzH2, and 0.425% allene. The cleaning procedure in the propyne increased slightly the acetylene from 3.6 to 3.9%, but decreased the allene contamination from 2.1 to 0.425%. We could not decrease the percentage of acetylene in the propyne. The perdeuterioallene was purchased from Merck Sharp and Dohme of Canada, Ltd. A mass spectrometric analysis showed approximately 9% C3D3H and 91% C3D4. A gas chromatographic analysis showed 0.024% propyne and almost undetectable quantities of the other hydrocarbons mentioned above. The argon used was Matheson Grade listed as 99.9995% pure. The driver gas was helium prepurified grade. C. Analysis. Samples were taken from the end block of the driven section in 50-cc glass bulbs and were analyzed for allene and propyne on a Packard 800 series gas chromatograph using a flame ionization detector. A Porapak N column at 85' separated the allene from the propyne. At very low extents of reaction where the ratio [propyne]:[allene] did not exceed 1:100, the analyses were carried out at
111. Computations A. Reflected Shock Parameters. The reflected shock parameters were calculated from the measured incident shock velocities using the three conservation equations and the ideal gas equation of state. The enthalpies of allene and propyne were taken from the America1 Petroleum Institute Project No. 447 and were presented as six-term polynomials. The polynomial coefficients were calculated by the least-squares method. The calculations were carried out on a C.D.C. 6600. B. Dwell Times. The reaction dwell times were recorded as the time interval between the arrival of the reflected shock wave and the expansion wave to the transducer located farthest from the end plate. The dwell time a t this point is considerably smaller than the average dwell time which must be introduced into the kinetic equations. The measured dwell time must be corrected for its variation along the test section of the driven section and for the change in the location of the gas during the expansion process. These two corrections require the knowledge of the shock.parameters and the final pressure in the shock tube, P7. The equation which relates the corrected dwell time t , with the measured one t , is6
where b, is the distance between the transducer which measures t , and the end plate, d f is the length of the sampling zone, p 5 / p 1 is the compression ratio behind the reflected shock, u5 is the reflected shock velocity, and a 5 is the speed of sound at Tg.
IV. Results and Discussion A. Rate Constants. In order to determine the reaction order, the rate constants and the activation energy of the reaction, seven groups of experiments were carried out. Four started from allene and three started from propyne. The seven groups and their experimental conditions are listed in Table I. In Table I1 three representative shocks from each one of the seven groups are listed in detail. Owing to the very high purity of the allene used, conversions as low as a few tenths of 1% could be accurately measured and a variation of almost 2 orders of magnitude in the isomerization rate constant could be covered, considerably below equilibrium. We have chosen the first three groups of experiments in such a way that both the effect of the total pressure and the concentration of the reacting molecule on the first-order The Journal of Physical Chemistry, Vol. 79,No. 12, 1975
1150
A. Lifshitz, M. Frenklach, and A. Burcat
TABLE 11: Details of Three Representative Tests from Each of the Seven Groups of Experiments Dwell time, msec
Pi, Group
Composition
1A
0.25% CHZ=C=CH,
2A
1%CH,=C=CH2
3A
1%CH,=C=CHz
4D
1%CDz=C=CD,
5P
0.25% CH,-C=CH
6P
1%CH,--C=CH
7P
1% CH,-C=CH
'
Torr
Tg,OK
tm
t,
P ~atm ,
207 204 179 217 200 186 56 52 57 198 200 215 195 194 197 197 197 195 55 54 55
1081 1126 1200 1052 1101 1151 1040 1111 1216 1027 1101 1212 1083 1116 1151 1039 1063 1109 1051 1086 1160
1.78 1.78 1.67 1.69 1.72 1.72 1.83 1.69 1.56 1.61 1.44 1.67 1.69 1.68 1.75 1.78 1.69 1.75 1.81 1.89 1.69
2.46 2.45 2.30 2.41 2.42 2.39 2.54 2.34 2.17 2.33 2.14 2.32 2.38 2.34 2.41 2.48 2.40 2.43 2.50 2.57 2.32
4.48 4.74 4.64 4.70 4.70 4.73 1.19 1.24 1.59 4.11 4.70 5.97 4.24 4.44 4.75 4.17 4.35 4.64 1.19 1.24 1.42
,,
\.
2.4,
t
2.1 6.7 30.4 1.0 3.4 11.5 0.5 3.2 27.1 0.46 2.4 33.2 1.2 2.0 4.6 0.4 0.6 2.1 0.5 0.7 4.5
8.5 28.7 168 4.2 14.4 52.4 2.0 13.9 154 2.0 16.2 188 5.4 9.0 21.5 1.6 2.5 9.3 1.8 2.8 22.0
I
i
1
c
-
0 6-
Conver sion ( t ) - conver sion ( O ) , % k,,,, sec"
.
1 'IoCH2=C = C H
LEVUSH et. el.
1.2-
( r e f . 2)
0
: pl-200 t o r r
1/4010CH=C=CH :p,-200 t o r r
-
+
8.0
1 'lloCDpC=CD2:p1-200torr
8.5
io'/
9.0 T~O K
9.5
8.0
8.5
9.0
9.5
1 0 4 T5 "K
Flgure 1. A plot of log kunlvs. 11Tfor groups of experiments I A , 2A, and 4D (allene). The points of these three groups scatter along one line indicating first order with respect to allene.
Figure 2. A plot of log kunivs. 1 / T for experiments of group 3A (allene). These points are slightly below the ones shown in Figure l indicating a weak dependence on the total pressure. The line obtained by Levush et al. is shown for sake of comparison.
rate constant could be independently determined. In Figure 1, log K A is plotted vs. 1/T for groups of experiments lA, 2A, and 4D. The points of these three groups scatter along one line indicating no effect of the allene concentration on the first-order rate constant and no obvious isotope effects. A least-squares analysis of the lA, 2A, and 4D data points yields k A = 1013.17*0.6 exp{-(60.4 f 3.1) X 103/RT) sec-l. The data points of group 3A are slightly lower than those of the high-pressure runs. Since the difference is very small ( A log k 0.12) they are presented on a separate figure (Figure 2). This small difference indicates that under our experimental conditions the reaction does not lie in the
first-order limit but very close to it. The overall reaction order is
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The Journal of Physical Chemistry, Vol. 79,No. 12, 1975
The slopes of the lines in Figures 1 and 2 are almost identical although one would expect the slope in Figure 2 to be slightly smaller than that in Figure 1. A least-squares analysis which includes all the points of the four groups of experiments together, to fit an equation of the type k = lo* exp(-E/RT)po yields a = 14.17 f 0.66, E = 61.2 f 2.5, and /3 = 0.20 f 0.09 where p is the total density of the reaction mixture in units of mole/cc and IOa is in units of sec-l.
1151
Allene-Propyne Isomerization
0
+
1 OIoCH3-CmCH: pl-200tor
1°10CH3-C=CH: ~ ~ - 5tor 0
A ~/&I,C H,-c SCH
1
:
~ ~ - 2 0tor 0
4
j
TABLE 111: Cracking Pattern of Propynea (a) and the Mass Spectrum of Propgne(b) Obtained from a Shocked Mixture of 1% CDz=C=CDz and 1% CHz=C=CHz in Argon (Tn = 1190°K) a. Ion
Re1 in-
Parent -H 1 Ji=0.92
-2 H f2=0.36
-3H f3=0.28
tensity b. m / e Intensity
0
-1.2
a
-4H f4=
0.09
44 0
43 78
42 27
41 45
40 100
39 110
Reference 8.
L
0.81
-8.0
8.5
9.0
9.5
lo3/ T ~ O K
Figure 3. A plot of log kunlvs. 1/ T for groups of experiments 5P, 6P, and 7P (propyne). The line corresponding to the high-pressure allene points is also shown for comparison. The distance between the lines gives the value of Keq.
Our low-pressure experiments which were run at the same pressure as the ones described by Levush et aL2 lie 0.28 at above their corresponding points by A log k 1100°K. Also, our activation energy 60.4 f 3.1 is slightly higher than theirs, which is 54.7 kcal/mol. However, in view of the fact that the experimental techniques are completely different and that their temperature range is almost 200" higher than ours, the agreement between the results can be considered very good. The slightly lower activation energy obtained in the flow experiments might be a result of some catalytic effect of the very narrow flow tube used. B. T h e Equilibrium Constant. In order to evaluate the rate constant of the isomerization from the measured extent of reaction, the equilibrium constant must be known. The rate constant k A is given by
-
-
where the subscript A denotes the allene propyne direction, xo and x t are the initial concentration of propyne and its concentration a t time t , respectively, and a is the sum [allene] [propyne]. K is the equilibrium constant of the reaction. RT In K is given by the difference in A F f O of the two isomers. This is however a very small difference between two big numbers, and the error in the calculated K can be quite high. In fact, the ratio [propyne]/[allene] observed a t the high temperature shocks was not equal to the one calculated from the difference in A F f O of the two isomers although equilibrium has been attained in the shock tube. It was considerably smaller. The purpose in studying the propyne allene direction was the evaluation of the equilibrium constant from the ratio of the rate constants of the forward and backward reactions. In Figure 3 a plot of log h p ) vs. 1/T for groups of shocks 5P, 6P, and 7P is shown. It is hard to decide whether the low-pressure points are really below the high-pressure ones because of the relatively high scatter in the data. The best line which connects the high-pressure data points is clearly below the one which appears in Figure 1. From the vertical distance between the lines one can calculate the equilibrium constant of the allene e propyne conversion. The dis-
+
-
tance corresponds to a value of 2.3 for Keq. The heat of reaction is rather small (-2 kcal/mol) and it is impossible to isolate changes in K over the temperature range covered in this study because of the high activation energy (-60 kcal/mol). We therefore used the value of 2.3 for K,, in our eq I1 over the entire range. This is acceptable as the rate constant k is not very sensitive to the value of the equilibrium constant K if the conversions are not too high. The value of K calculated from the difference in A F f O of the two isomers at llOOOK is 3.45, considerably higher than the value of 2.3 observed experimentally. In fact, 2.3 is roughly the ratio of the two isomers observed in the gas chromatograph from high-temperature shocks where equilibrium has been attained in the shock tube. C. Studies with Perdeuterioallene. There are number of ways to investigate whether a reaction is unimolecular or whether it proceeds via another mechanism. The easiest one is the isotope labeling of the reactant and the examination of the isotopic distribution in the product. In the alpropyne isomerization, the unimolecularity of the lene reaction can be examined by shocking a 50-50 mixture of CHz=C=CHz and CDz=C=CDz. If the formed propynes are unscrambled, Le., only the CH3-C=CH and CD3CECD are present, the reaction is clearly unimolecular. On the other hand, if C3D3H and C3H3D are observed then either isotope exchange reaction has occurred or the reaction is not unimolecular. The temperature dependence of the extent of scrambling, if scrambling is indeed found, can help to distinguish between these two possibilities. The mass spectrum of the propyne formed in a mixture of 1%CDz=C=CD2 and 1%CHz=C=CHz in argon at Tb = 119O0K is shown in Table 111. The cracking pattern of the propyne* molecule is also shown for the interpretation of the spectrum. T o our great surprise, no peak at m / e 44 (CDB-CECD) above the COz background was observed, but a very intense peak a t m / e 43 (C3D3H) showed up, as if the isomerization is not unimolecular or a lot of isotope exchange has occurred (in fact, more than the symmetry would allow). On the other hand, very intense peaks a t m / e 40 and 39, which indicate the presence of large quantities of CH3-CaCH were observed as if the isomerization is unimolecular. The strange result was explained when 1% CDz=C=CDz (in the absence of undeuterated allene) was shocked and then analyzed in the GC-MS. Instead of the perdeuterated propyne which should have been formed and shown up at m / e = 44, there was none a t that mass but instead intense peaks appeared a t m l e 43 and 41. This behavior was interpreted in view of the acidity of the acetylenic hydrogen in the propyne. CD3--C=CD behaves as a monobasic acid and exchanges one deuterium atom with the water absorbed on the gas injection system of the GC-MS or on the walls of the ion source of the mass spectrometer. The absence of a peak a t m l e 44 and the appear-
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The Journal of Physical Chemistry, Vol. 79, No. 12, 1975
A. Lifshitz, M. Frenklach, and A. Burcat
1152
ance of one at mle 43 for propyne in the shocked mixture of 1%CHz=C=CHz and 1% CD2=C=CD2 is no indication of scrambling during the reaction. When this discrepancy has been cleared up, the mass spectrum was analyzed in order to isolate the peak heights of C3H4 and C3H3D from the contribution of the cracking pattern of the C3D3H and to examine the ratio of these two substances. In the analysis we have assumed that mle 42 arises only from the parent ion C3D3H by removal of the hydrogen and that no double scrambling has occurred. (This assumption is not critical but simplifies the analysis.) The ion which is produced by the removal of one hydrogen from the parent has an intensity of f l = 0.92 relative to the parent ion.s mle 42 is the ion produced by the removal of H, and 41 by the removal of D. One can readily see in Table I11 that the sum of the peak heights of the mle 42 and mle 41, namely, 72 (in arbitrary units), is equal to 78fl. Clearly, within the limit of the experimental accuracy all the contribution to mle 42 and 41 arise from the parent ion and there is no contribution from the original C3H3D or C3DzHz ions. I t is interesting to note that the ratio (mle 41):(mle42) is not 3, as has been expected, but considerably smaller. It seems that the removal of the acetylenic hydrogen (HCsC-) is easier than the removal of a hydrogen from the methyl group in the pyropyne ion. m/e 40 and 39 have very intense peaks; their major part is due to the existence of C3H4. From the evidence gathered here, namely, the absence of C3H3D and the presence of a high intensity of C3H4, one can conclude that the propyne formed in the isomerization reaction is unscrambled. D. The Mechanism of Isomerization. There are in principle three major reaction paths that can lead to isomerization: (1)a unimolecular reaction: U
/"\
The Journal of Physical Chemistry, Vol. 79, No. 12, 1975
(3) isomerization via free-radical reactions:
CH,=C=CH,
3
CH,=C=CH CH,-C=CH
+
RD
CH,=C=CH
-
-I- H
CHZ-CzCH
+
CH,D-C=CH
R'
The experimental results described in the previous section indicate that mechanism 1 is operative to the largest extent and that there is very little contribution, if any, from the reaction paths 2 and 3. Unit reaction order with respect to the allene (Figure l),clearly shows that the reaction is not bimolecular and that the isomerization does not proceed via the formation of a four-center dimer. In addition, mechanism 2 should have produced scrambled propynes in a shocked mixture of C3D4 and C3H4. As has been shown, only unscrambled products were observed. Mechanism 3 can also be ruled out on the basis of the extent of decomposition which accompanies the isomerization, in addition to the results of the isotope distribution studies. The production of free radicals in the system can lead to the production of othe: substances. The free radicals such as CHz=C=CH and CH2-C=CH can undergo unimolecular decomposition as many C3 free radicals d0,9 and thus produce a variety of decomposition products. It has been shown in the experimental section that even a t the highest temperatures, where close to 30% of the allene has isomerized, the overall extent of decomposition did not exceed 0.17% of the initial allene concentration. In addition, mechanism 3 should have produced scrambled propynes which were not observed. It is believed, therefore, that the allene propyne isomerization is a unimolecular reaction.
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References and Notes (1) in partial fulfillment of the requirements for a Ph.D. Thesis, to be submitted to the Senate of the Hebrew University of Jerusalem by M.F. (2) S. S. Levush, S. S. Abadzhev, and V. U. Shevchuk, Neftechimia, 8, 215 (1969). (3) Y. Sakakibara, Bull. Chem. SOC.Jpn., 37, 1262 (1964). (4) Y. Sakaklbara, Bull. Chern. SOC.Jpn., 37, 1268 (1964). (5) A. Bar-Nun and A. Lifshitz, J. Chern. Phys., 47, 2878 (1987). (6) A. Lifshitz and P. Schechner, lsr. J. Chem., 12, 729 (1974). (7) F. D. Rossini, et ai., Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds", Carnegie Press, Pittsburgh, Pa., 1953. (8) A. Cornu and R. Massot, "Compilation of Mass Spectral Data", Heyden & Son, Ltd., 1966. (9) S. W. Benson and H. E. O'Neal, Nat. Stand. Ref. Data Ser., NaN. Bur. Stand., No. 21'(1970).
