DORKO, MCGHEE,PAINTER, CAPONECCHI, AND CROSSLEY
2526
Shock Tube Isomerization of Cyclopropane by E. A. Dorko,* D. B. McGhee, C. E. Painter, A. J. Caponecchi, and R. W. Crossley Department of Aero-Mechanical Engineering, Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio &i.(85 (Received June $2, 1970) Publication costs assisted by the Air Force Institute of Technology
The shock tube isomerization of cyclopropane to propylene has been studied as a possible model system for shock tube isomerizations of small-ring compounds. At low (O.l-l%) concentrations of cyclopropane in helium-argon matrix the reaction is unimolecular with a high-pressure first-order rate k , = 1014J0*0.14 e-s5100*800/RTsec-1 in the temperature range 935-1397°K. The rate constants are smaller than the extrapolated low-temperature results. This difference is expressed in a smaller value for the frequency factor. A discussion of reasons for this difference is given. When the substrate concentration was increased to 5% it was found that the Arrhenius parameters are no longer in agreement with the values obtained at low substrate concentration. At this concentration the exothermicity of the reaction and other effects so seriously affect the ideality of the shock wave that the model cannot be relied upon for kinetic analysis.
Introduction The single pulse shock tube’ isomerization of cyclopropane to propylene has been studied as a possible model system for shock tube isomerizations of smallring compounds. We wish to report that a kinetic analysis of this reaction in the shock tube gave values for the Arrhenius parameters for infinite pressure which allow the extension of the kinetic analysis2 to a higher temperature regime. The Arrhenius parameters obtained from a least squares fit of the data for the temperature range 935-1397’K are given in eq 1.
IC, = 1014.50?=0.14e-f35,100*800/RT
(1)
These parameters were obtained at a substrate concentration of O.l-l% in a helium-argon matrix. When the substrate concentration was increased to 5% it was found that the Arrhenius parameters were no longer in agreement with the values obtained at low substrate concentration. The parameters are given in eq 2. IC = 107.6661tO.15e --30,20Of400/RT m (2) Graphs of data to support eq 1 and 2 are shown in Figures 1 and 2, respectively.
tank and driver section were evacuated t o 400 p pressure. Diaphragm material was 0.020-in. aluminum (5052H32) scored to 0.010 in. Velocity measurements were made by means of ‘/le in. wide thin-film platinum heat gauges which were placed 12.000 in. apart. The signal from the heat gauges was fed into an electronic counter (Hewlett-Packard Universal Counter, 53258) which counted to 0.1 psec. Pressure in the driven section was measured with a Wallace and Tiernan gauge (Model No. FA145) accurate to f0.1 psia. Initial driven pressures varied from 2.0 to 5.0 psia. Dwell time was obtained either from the appropriate wave diagram for ideal flow based on the n!Iach number of the shock wave and on the gas properties4 or according to the method described by Lifshitz, Bauer, and Resler.5 The pressure trace necessary for the second method was obtained with a Kistler pressure transducer (Model No. 603A) imbedded in the end plate of the shock tube. A slight modification of the latter method was necessary since the isolation valve was in the end plate rather than upstream of the test section. When the isolation valve was opened immediateIy after the
Experimental Section Procedure. The shock tube was fabricated in the
school machine shop and was of the double diaphragm type described by Glick, Squire, and H e r t ~ b e r g . ~It was fabricated of 2.5411. stainless steel with a 5-ft driver and 10-ft driven section. The dump tank was 10 ft3in volume. The test section, comprising the last 4 f t of the driven section, was honed with a J-7 finished stone to a microfinish of 14 to 16 to ensure a smooth inner surface. The driven section of the shock tube was evacuated to 1 p pressure by means of an oil diffusion pump. The leak rate at this pressure was 1-2 p/hr. The dump The Journal of Physical Chemistry, Vol. 76, No. 16,1971
(1) S. H. Bauer, Science, 141, 867 (1963). (2) (a) B. R. Davis and D. 8. Scott, Ind. Eng. Chem., Fundam., 3, 20 (1964); (b) B. S. Rabinovitch, E. W. Schlag, and K. B. Wiberg, J . Chem. Phys., 28, 504 (1968); (c) H. 0. Pritohard, R. G. Sowden, and A. F. Trotman-Dickenson, Proc. Roy. Soc., Ser. A , 217, 563 (1953); (d) E. 5. Corner and R. N. Pease, J. Amer. Chem. Soc., 67, 2067 (1945); (e) T. 8 . Chambers and G. B. Kistiakowsky, ibid., 56, 399 (1934). (3) H. 8 . Glick, W. Squire, and A. Hertzberg, “A New Shock Tube Technique for the Study of Higher Temperature Gas Phase Reac-
tions,’’ in “Fifth Symposium (International) on Combustion,” Reinhold, New York, N . Y., 1955. (4) See A. J. Caponecchi, M.S. Thesis, Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, June 1967, for a development of the theory and for the necessary computer program. ( 5 ) A. Lifshitz, S. H. Bauer, and E. L, Resler, Jr., J. Chem. Phys,, 38, 2056 (1963).
SHOCK TUBEISOMERIZATION
OF
2527
CYCLOPROPANE
gas mixture had been shocked, a sample of the shocked gas was withdrawn into an evacuated sample chamber of known volume. The assumption was made that the volume of gas that flows from the shock tube exactly equals the volume of the sample chamber. The appropriate expressions for the calculation of the space-averaged dwell time are given in eq 3 and 4. tav
=
tmeaa
b
-I- (1
+ 1/M~)b/a5
(3)
-V/2A
(4) M R is the Mach number of the reflected shock wave, a5 is the sonic velocity behind the reflected shock wave, V is the volume of the sample chamber, and A is the cross-
lo3/ K
Figure 1. Arrhenius plot of the first-order rate constants for the unimolecular isomerization of cyclopropane: 0, low-temperature work;2 0, O.l’%o cyclopropane; 1.0% cyclopropane.
+,
3
2 -L
0
3
1
=
sectional area of the shock tube. Both methods gave identical results for dwell time. In order to maximize dwell time, the shocks were “tailored.” Impedance matching was achieved for the various pressure ratios by varying the ratio of helium and argon in the driven section from a He/Ar ratio of 3.5 to a ratio of 1.5.4 With this technique, dwell times of the order of 2.1 msec were achieved. Analysis of the gas in the sample chamber was done by gas chromatography. Immediate isolation of a gas sample after the shock prevented diffusion of cold gas mixture from the upstream section of the driven section.6 This procedure ensured that the gas sample used for analysis came from the test section of the shock tube. The gas mixture was analyzed on a 20 ft X in. columm packed with 15% triacetin on 60-80 mesh Chromosorb P which was operated at room temperature. For the higher gas concentrations thermister detectors were used. For 0.1% substrate concentration flame ionization detection was used. Retention times were 8.0 min for cyclopropane and 6.0 min for propylene. Extent of reaction was based on the amount of propylene formed. Side products were detected only in the 5% samples shocked at high temperatures (1300-14OO0K). The major side product was separated with a 10 ft X 1/4 in. 5A molecular sieve column and was identified as methane. The amount of methane accounted for no more than 2% of the final gas mixture. Other side products were present in much lesser amounts and no attempt was made to identify them. The shock temperature calculated from the initial shock velocity4 was corrected for the temperature increase due to the heat of reaction according to eq 5.
T
+ 23 Cp
= TSHOCK -
AHreaotion
X
gas mixture
(yosubstrate) (% reaction) 0
I
0.8
I
0.9
I 1.0
(5)
Heat capacity values for argon and helium were obtained from the JANAF Tables and the values for cyclopropane were calculated from spectroscopic data.’
lo3#0 K
Figure 2. Arrhenius plot of the first-order rate constants for unimolecular isomerization of cyclopropane (;yoCaHs).
(6) A. Bar-Nun and A. Lifshita, J. Chem. Phys., 47, 2878 (1967). (7) H. P. Nielsen, h l . S , Thesis, Air Force Institute of Technology,
Wright-Patterson Air Force Base, Ohio, June 1969. The Journal of Physical Chemistry, Vol. 76, N o . 16, 1971
2528 The temperature correction is necessary since release of the heat of reaction will cause a temperature increase during the course of the reaction. The factor of is used instead of the more obvious factor of ‘/zto take into account the nonlinearity of the temperature-rate relationship. For small temperature changes which do not affect the ideality of the shock wave, the correction serves as a refinement to the temperature determination. However, as the temperature increase becomes large the correction can only be taken as approximate (see below). In order to test the shock tube and the shock procedure, tert-butyl alcohol was converted into isobutylene in the shock tube. The analysis procedure followed was that described by Tsang.8 The Arrhenius parameters obtained are given in eq 6.
The parameters are comparable, within experimental error, to those obtained by TsangS8 Error Estimate. The Arrhenius parameters, A and E , were calculated using program ACT EN,^ a program which calculates least squares with both the logarithmic (linear) and the exponential (nonlinear) forms of the Arrhenius equation. The values reported are those which yield the minimum sum of squares for the conventional linear form. The tolerances reported for the parameters also were obtained from the results of program ACTEX. The program displays sums of squares corresponding to selected confidence IevelslO as well as sums of squares over any desired range of (A,E). Thus, loci of the selected confidence levels can be plotted on the A ,E plane. The tolerance reported for each parameter was determined from the intersection of the reported value of the other parameter with the 99% confidence level. The deviations from ideality of the shock wave and the various other sources of random error present in a kinetic analysis by a single-pulse shock tube technique have been discussed at length by Lifshitz, Bauer, and Resler5 and by Tsang8 among others. The procedure employed by the present authors was checked out using the tert-butyl alcohol system studied by Tsang.8 To preclude the possibility of invalid results due to systematic errors, the low concentration analysis was performed at 0.1% and 1.0% substrate concentration. The plot of Figure 1 shows that the kinetic analysis is independent of concentration in this range.
DORKO, MCGHEE,PAINTER, CAPONECCHI, AND CROSSLEY A first-order mechanism was assumed and the data were reduced according to eq 7 where Co and Cr are the IC1
(7)
= In ( C O / C ~ / L
Table I : Summary of Data for the Unimolecular Isomerization of Cyclopropane a t Low (0.1-1 yo)Concentrations Temp, OK
Pa,a mm
Pi,b mm
Dwell time, msec
Extent of reaction
kuni, sec-1
1% Cyclopropane 1042.3 1055.3 1096.1 1103.6 1125.9 1127.8 1146.2 1158.6 1168.0 1169.6 1172.8 1191.7 1214.2 1264.5 1281.6
1767 2698 2875 2892 2996 2024 3128 2621 2123 3297 2123 3274 3380 3638 2479
103 155 155 155 155 103 155 129 103 160 103 155 155 155 103
2.005 2.055 2.216 1.756 2.197 2.007 2.167 2.058 2.408 2.188 2.158 2.228 2.209 2.210 2.210
0.010 0.008 0.062 0.021 0.266 0.116 0.105 0.147 0.333 0.345 0.644 0.603 0.634 0.707 0.916
4.8 4.5 28.8 11.9 140.7 61.3 51.2 77.3 168.4 193.5 478.3 414.4 455.7 556.3 1121.9
7.6 6.7 44.6 18.9 222.8 106.4 83.0 134.3 306.2 321.4 891.3 687.1 792.5 988.6 2239.0
1.5 2.4 2.6 4.9 3.8 4.4 11.1 14.9 123.4 94.0 39.4 387.9 412.3 474.8 747.5
2.1 3.3 3.6 7. I 6.6 8.0 15.7 23.6 208.9 163.3 68.6 706.3 841.4 993.1 1107.0
0 . 1yo Cyclopropane 998.7 1003.8 1017.5 1057.4 1060.3 1062.9 1081.0 1095.4 1156.6 1166.4 1170.2 1215.6 1231.2 1233.7 1250.9 5
2362 3187 3255 3481 1729 3524 4535 2792 3070 3105 3113 3352 2250 2257 3482
155 207 207 207 103 207 259 155 155 155 155 155 103 103 155
1.254 1.304 1.404 1.555 1.955 1.355 1.456 1.266 2.108 2.258 2.208 2.109 2.259 2.259 2.259
Reflected shock pressure.
b
0.002 0.003 0.004 0.008 0.007 0.006 0.016 0.019 0.229 0.191 0.083 0.559 0.606 0.658 0.815
Initial driven section pressure.
Discussion
initial and final concentrations of cyclopropane and t,, is the dwell time of the extracted gas sample. The rate constants were corrected for infinite pressure in the following manner. The total pressure in the reflected shock (Ps) was split into the partial pressures of the component gases. The inert portion of the gas mixture was assumed to be 30% argon and 70% helium. The pressure efficiencies of argon and helium were taken to be 0.06 and 0.053, respectively, that of cyclopropane.2c
Figures 1 and 2 are Arrhenius plots of the shock data for the concentrations listed. I n addition, Figure 1 shows the Arrhenius curve extrapolated from low-temperature results. The data on which the plots are based are listed in Tables I and 11.
(8) W. Tsang, J. Chem.Phys.,40, 1498 (1964). R.W. Crossley and E. A. Dorko, Program ACTEN, available from the Quantum Chemistry Program Exchange, Indiana University, Bloomington, Ind., No. QCPE 179. (10) R. S. Burington and D. C. May, “Handbook of Probability and Statistics,” Handbook Publishers, Sandusky, Ohio, 1958, p 158.
The Journal of Physical Chemistry,Vol. 76, N o . 16,1971
(9)
2529
SHOCK TUBEISOMERIZATION OF CYCLOPROPANE Table 11: Summary of Data for the Unimolecular Isomerization of Cyclopropane a t High ( 570) Concentrations
mm
Dwell time, msec
Extent of reaction
sec-1
155 168 155 155 155 181 155 155 169 156 130 129 155 155 146 155 142 103 130 116
2.231 2.435 2.397 2.258 2.083 I.880 2.208 2.108 2.141 1.992 1.407 2.351 2.411 2.412 2,069 1.409 1.785 2.554 2.311 2.352
0.015 0.022 0.017 0.020 0.036 0,035 0.048 0.039 0,057 0,095 0.061 0.240 0.348 0,470 0.448 0.609 0.563 0,765 0 688 0.513
6.7 8.9 7.0 8.8 17.4 18.8 22.1 19.1 27.7 50.1 44.8 116.8 177.4 263,l 287.3 667.2 463.2 567.4 503.6 305.6
Temp, OK
p6va mm
Pl,b
955.7 974.1 1006.2 1021.6 1031.8 1040.4 1044.0 1048.5 1060.7 1074.2 1140.0 1169.9 1192.6 1203.9 1240.7 1249.9 1296.8 1350.0 1361.2 1412.1
2404 2741 2641 2744 2763 3405 2836 2861 3224 3028 2809 2813 3448 3467 3556 3654 3614 2733 3542 3412
a
Reflected shock pressure.
I
kca,
Initial driven section pressure.
The rate constant was corrected for this effective pressure by utilizing the falloff curve determined at 491O.l’ In addition, the effect of temperature on the position of the plot of log (klk,) against log p was taken into account by utilization of eq 8.l’ The factor n was A log p = l/*nlog (T$l”1)
(8)
taken to be 14, the number of independent vibrations in cyclopropane.l 2 For comparison with present results the commonly accepted low-temperature rate equation for infinite pressure is showm. k , = 1015.17e-65,500/RT (9)
It can be seen that the activation energies agree but the frequency factors differ by a power of 0.67. The question must immediately be asked if the high-temperature shock tube results represent a direct extension of the low-temperature results. It is obvious from Figure 1 and from a comparison of eq 1 and 9 that this is not the case. The rate constants appear to be smaller than the extrapolated low-temperature results. This difference is expressed in a smaller value for the frequency factor. Tsang8 and others6have discussed some of the reasons why the rate constants determined in a single pulse shock tube tend to be smaller than expected from lowtemperature extrapolation. However, one effect which has not been considered in previous discussions is the large difference in residence time between shock tube
experiments and conventional heating techniques. Residence or dwell times in a single pulse shock tube are of the order of several hundreds of microseconds. I n comparison, residence times for the low-temperature experiments are much longer than this. In order to understand the significance of this difference, let us consider the mechanism postulated for cyclopropane isomerization. The process is usually represented as an initial second-order activation followed by a first-order decomp~sition~~ as shown in eq 10 and 11. V
+
M
hi
--L k-1
V*
+
M
v r -L A
(10) (11)
The rate expressions are given as eq 12 and 13.
Equation 12 represents the general rate expression and eq 13 represents the rate expression for high pressure. These two equations can only be developed if it is assumed that after a relatively short initial period the concentration of reactive intermediate reaches its steady-state concentration (the steady-state assumption).14 The assumption maintains that this induction time is negligibly small compared t o the total time of the kinetic determination. As the total residence time decreases this assumption becomes more and more tenuous. Currently, research is being conducted with a view toward determining the time required for the build-up of the concentration of reactive intermediate. Preliminary experiments indicate that this induction time can be as high as 10% of the total dwell time.15 A subsequent report will deal with this effect in detail. The activation parameters obtained for the high (5%) substrate concentration vary significantly from the corresponding values obtained for the low-concentration reactions. The activation energy drops and the frequency factor value is no longer of the expected order of magnitude for a first-order reaction. It is quite likely that the deviation at the high concentration is caused by the substantial change from ideality in the shock tube due to the exothermicity of the isomerization. The average temperature change, as calculated by eq 5, for the 5% concentration can be as high as 60-70°K. A (11) N. B. Slater, Phil. Trans., A246, 57 (1953). (12) W. E. Falconer, T . F. Hunter, and A. F. Trotman-Diekenson, J. Chem. SOC.,609 (1961). (13) 8. W. Benson and H. E. O’Neal, “Kinetic Data on Gas Phase Unimolecular Reactions,” NSRDS-NBS-21, U. S. Government Printing Office, Washington, D. C. 20402, 1970, p 15. (14) W. 8 . Benson, J . Chem. Phys., 20, 1605 (1952). (15) E. A. Dorko, U. Grimm, G. Mueller, and R. W. Crossley, work in progress. The Journal of Physical Chemistry, Vol. 76, No. 16, 2971
2530 temperature change of this magnitude should have a significant effect on the shock wave, and most likely a simple analysis based on an ideal, one-dimensional wave is no longer adequate. At the high concentration the reacting mixture may be exothermic enough to cause the velocity to approach the Chapman-Jouget or detonation velocity.16 This effect would make the simple shock wave model invalid. In addition to the heat effects there may be a series of systematic errors such as boundary layer effects which become appreciable at the high concentration.” In addition there may be a significant change in kinetic mechanism. A discrepancy exists between the present high-concentration results and the results of a previous highconcentration isomerization performed by Miyama and Takeyama.17 Their work utilized 5 and 10% cgclopropane concentrations. Their analysis as a first-order reaction shows a bend in the curve at 1200°K. This bend was not observed in the present work, whether an Arrhenius plot was made assuming either a first- or second-order mechanism. However, a first-order plot of the present data and a plot of the previous work indicate that the present rate constants are lower by almost two orders of magnitude than the constants determined by the previous researchers. An Arrhenius plot of both sets of data leads to two parallel lines for the re-
NOTES gion below 1200°K. We feel that the temperature determination by Rliyama and Takeyama is too low. Apparently no correction was made for the heat given off by the reaction. At the 5% concentration this could lead to as much as a 60-70°K temperature difference and at the 10% concentration the difference could be as great as 120-140’. Another discrepancy could arise due to difference in shock velocity determination. Clearly additional work remains to be performed with the higher cyclopropane concentrations. The important consideration at this point is that only the low-concentration data can be reasonably compared with the low-temperature work,
Acknozuledgments. We wish to thank Dr. Ulrich Grimm and Dr. Gerhard Nueller for advice and assistance given during the fabrication of the shock tube. The technical assistance of Mr. John Parks and Mr. Ernest Pinti is gratefully acknowledged. The work was supported in part by the Air Force Office of Aerospace Research through the OAR/AFIT Research Support Fund. (16) R. L.Belford and R. A . Strehlow, Ann. Rev. Phys. Chem., 20, 247 (1969). (17) H.Miyama and T . Takeyama, Bull. Chem. SOC.Jap., 38, 2189 (1965).
NOTES Entropies of Vaporization for Fluorocarbons and Hydrocarbons from the Hildebrand Rule
the same saturated vapor volume, arbitrarily chosen to be 49.5 1. per mol.
Data Reduction by E. W. Funk and J. M. Prausnitz* Department of Chemical Engineering, University of California, Berkeley, California 94780 (Received October 6 , 1970) Publication costs borne completely by The Journal of Phzlsical Chemistry
The anomalous behavior of solutions containing saturated hydrocarbons and fluorocarbons, first noted by Hildebrand and Scott,’ continues to be incompletely understood. I n an effort to contribute toward a better understanding of such solutions we have calculated the entropies of vaporization of 12 saturated hydrocarbons and of the corresponding 12 fluorocarbons. For reasons given by Hildebrand many years ago,2 we have calculated these entropies not at the same temperature nor at the same reduced temperature but at T h e Journal of Physical Chemistry, Vol. 7 6 , N o . 16, 1971
The molar entropy of vaporization As is given by the Clapeyron equation AS
=
A(%)
where P is the saturat,ion (vapor) pressure at temperature T and Av is 49.5 1. minus the molar volume of the saturated liquid. The pressure and temperature corresponding to the selected saturated-vapor volume are found from simultaneous solution of two equations RT 49.5 = p B(T)
+
P
=
f(T)
(3)
(1) J. H . Hildebrand and R. L. Scott, “Solubility of Nonelectrolytes,” Reinhold, New York, N. Y . , 1950. (2) J. H. Hildebrand, J . Chem. Phys., 7, 233 (1939).
