THERMAL DECOMPOSITION OF CYCLOBUTANE
Xov. 5,1963
Two other factors which could cause a n apparent leveling-out of the rate a t low pressures can probably be discounted. T h e diameter of the connecting tubing was large enough t h a t thermal transpiration corrections were small, and these corrections were made where necessary. Another possible factor could be inhomogeneous sampling. Because cyclobutane has twice the molecular weight of ethylene, i t would diffuse less rapidly, and a sample obtained a t low pressures might be expected to be richer in ethylene than the mixture in the reactor. T o test this idea, the time of sampling a t 10P3mm. pressure was varied from 20 sec. to 10 min., without any systematic variation being observed in the measured rate constant. In another series of tests a t mm. pressure, the reactor was filled with pre-purified nitrogen, just before sampling, to a pressure of about I O mm. These points are indicated by triangles on Fig. 1. The rate constant was the same within experimental error as when no nitrogen was used. T h u s the sampling procedure could not account for the low-pressure limiting rate.
[COSTRIBCTION F R O M THE
DEPARTMEST OF
3349
Thus, the low-pressure limiting rate does not seem to have a simple explanation. I t may merely be that under such conditions, the classical theory of unimolecular reactions no longer applies. T h e reactions forming propylene and 1-butene are probably wall reactions, as indicated by the fact that they are zero order. m'ithin experimental errors the rate constant in the 100-ml. vessel could be 10 times the rate constant in the 5-1. vessel (see Table 11). If a homogeneous first-order reaction forming propylene or 1-butene occurs, its high pressure limiting rate is less than 5 X 1OF4 times the rate of the reaction forming ethylene. Study of such a reaction would be very difficult because in any reactor of reasonable size, the surface reactions are more rapid than the homogeneous reaction. I t is probable that no homogeneous reaction forming propylene or 1-butene occurs. Acknowledgments.-The authors wish to thank the National Research Council of Canada and the University of British Columbia President s Research Fund for financial support of this work. Thanks are also due to Professors B. S. Rabinovitch, LV. *A. Bryce, and G. B. Porter for valuable discussions relating to this work.
CHEMISTRY AT THE U S I V E R S I T P O F ORECOX,
EUGENE, OREGON]
A Mass Spectometric Investigation of the Thermal Decomposition of Cyclobutane at Low Pressured BY ROBERTW. VREELAXD AND D. F. SWINE HART^ RECEIVEDDECEMBER 26, 1962 T h e decomposition of cyclobutane has been investigated over the temperature range 410 t o 500' and a pressure range of 0 . 5 p t o 20 m m . by a mass spectrometric technique. T h e reaction is accurately first order over the whole range of pressures and temperatures. T h e experimental d a t a are fit by the Kassel integral using Eo = 63,200 cal./mole and a n effective 18 oscillational modes. The d a t a show a n anomalous departure from curves calculated from t h e Kassel integral below 20 p , the rate constants being too large. This is not a surface effect as judged from packed flask measurements and it is suggested t h a t cyclobutane decomposes ttia two competing mechanisms.
Introduction T h e bulk of the data in the literature on unimolecular decompositions has been obtained simply by following the total pressure change with time. If the stoichiometry of the reaction is simple and unique, data obtained by this method may be an accurate and reliable measure of the actual rate of decomposition of the parent molecule. However, if the reaction is, in fact, complicated by successive or parallel reactions among the products and.'or the products and parent molecule, simply following the total pressure with time may be misleading and not be a measure of the actual decomposition rate a t all. What is needed is a method of measuring the partial pressure of the parent molecule irrespective of processes which occur after the initial decomposition. l l o s t data exist in the pressure range approximately from 1 m m .to 1 atm. Data are seriously needed over a much wider pressure range and particularly a t lower pressures. Consider the following experimental technique designed to provide data satisfying these requirements. Suppose the molecular leak conventionally used to introduce gas samples into a mass spectrometer is removed from the spectrometer ion source and is sealed directly into a reaction vessel and connected to the ion source of a mass spectrometer by a longer p a t h than is usually used. Suppose a decomposition reaction occurs in the reaction vessel. All products will have (1) Supported by Atomic Energy Commission Contract AT(45.1)-432. ( 2 ) To whom inquiries should be addressed.
molecular weights less than that of the product molecule and the peak intensity of the parent peak of the parent molecule will be a unique measure of the partial pressure of the parent molecule irrespective of the subsequent reactions among the products, providing only that two conditions are met. First, the products must not isomerize or polymerize to yield molecules of equal or larger molecular weight than the parent substance and, second, flow through the leak must be molecular flow and not viscous flow. Then the peak intensity of the parent peak will be directly proportional to the partial pressure of the parent substance. This paper is written to report the application of this technique to the decomposition of cyclobutane in the pressure range from 0.5 p to 20 mm. Future reports will be made on the investigation of more complex systems. This reaction has been investigated by the pressure change method by Genaux and IValters3and by Genaux, Kern, and \Valters4 in the pressure range 1 to 996 m m . and over the temperature range 42U to 46s'. They found that the reaction is homogeneous and yields ethylene stoichiometrically. They report that the rate constant a t 1 mm. is approximately two-thirds of the value obtained a t pressures above 100 mm. Pritchard, Sowden, and Trotman-Dickenson" have studied t h e composition a t one temperature (44S.4') down to 57 p ( 3 ) C. (4) C. (.5) H Roy. Soc
T. Genaux a n d W I) Walteri. J Ai!? r h e i n S o c , 7 3 , 4 4 ! l i ( l ! l . i l ) T Genaux, F Kern. and W I ) U'alters, i b i i t 7 5 , Cil!)ci (l%i.31 0. Pritchard. I< G Suwden. and A r) Trotman-llickeniiin Pi.oc. ( L o n d o n ) , 8 2 1 8 , 416 (19%)
L
A
/
n
I
I 1
I
I
I
lox
1
3
2
P,
I
I 4
I
ri ,
ir
Fig. 2 ---Pressure dependeiicc of tlie rate constant Solid curves calculated from the Kassel integral: V, added gas runs, 0,packed flask runs; X , data of &'alters, et a1 , 3 , 4 measured a t 449". These data were not corrected t o I 5 0 1
0
2
-1
li
8
in
12
T i m e , min
Fig. l.--~Representative kinetic run : T , 500.1"; k , 5.66 X sec - l . half-lives.
p;
Initial prrssure, 1:350 Time covers about six
pressure and have studied the collisional activation efficiency of a considerable variety of added gases.
Experimental The cyclobutane was purchased from the Fabian Chemical C o . , hlontreal. Mass spectrometric and gas chromatographic analysis showed t h e material to contain 3 ' ; of n-butane a s the only detectable impurity. The n-butane was removed gas chromatographically using a large column 2 in. in diameter and 12 f t . long packed with the detergent "Tide." The mass spectrometer was a conventional Sier-type 60' deflection mass spectrometer constructed in this Laboratory. The spectrometer tube was mounted in a separate chassis with minimum equipment around it so t h a t the thermostat containing the reaction vessel could he positioned as closely a s possible to the spectrorneter t u b e . The accelerating voltage (2500 v . ) and magnet supplies were electronically regulated to 1 part in IO4and the room was thermostated t o better than 1' by a n air conditioning unit t o improve the regulation and stability of the supplies. The filament emission in the ion source was regulated to about 0.1";. The electrometer was a very nearly 100';; feedback amplifier with a n input impedance of 10i2 ohms arid a n output impedance of ahout 3 X lo1 ohms providing a voltage gain of unity hut a power gain nf 3 X 10'. The amplifier was as linear a s the resistors and had a sensitivity of about 3 or 4 X amp. per scale division of the Leeds and S o r t h r u p Micromax recorder driven b y t h e o u t p u t . The leaks were all Pyrex and were constructed in this Laboratory. No metal surfaces were exposed t o the reacting system. All leaks were tested over the pressure range for which they were used to enstire linearity of response of the spectrometer, ;.e., that the flow through them was molecular. Several reaction flasks with corresponding leaks were used to cover various pressure ranges. In the highest range a 1-1. flask was used. T w o 2-1. flasks were used in the intermediate and lower ranges and three 13-1. flasks were used for the measurements a t the lowest prcssures. Loss of gas t'ia leak-out to the spectrometer was entirely negligible a t the higher pressures. It became significant, however, a t the lower pressures. Leak-out was first order a n d is represented by the equation from kinetic theory (eq. 1)
where A' is the number of rnolecules in the flask, 7 is their average theriiial velocity, .4 is the area of the leak, and T~' is the voluiiie of the vessel. Since A was never known with a n y accuracy, the value of k ' was measured directly using n-butane as the gas a t temperatures rvhere its own decomposition was negligible. The values of k ' n-ere corrected to the inolecular weight of cyclohut;ine and the temperatures used for the decompositions using the parameters in the above equation. Leak-out constants so determined varied frorn 0.1 X 1 0 - b sec. - 1 to :3.(1 x 10 S C C . ' and were applied :is corrections wherever significant. T h e largest corrections never comprised over 30' of the inensured rate constants a t the very lowest pressures and in nearly all c were much smaller thaii this. Initial pressures for each run were calculated h y e\paiiiioti between known volumes, making correction for the difference i n temperatures and requiring material balance. The volume ratios used were large enough t h a t a n y errors due to thermal tranipiration were reduced to negligible amounts. Initial pressures iiutside the reaction vessel before expansion were measured dircctly by a mercury manometer for higher pressures or by a micromanoineter, manufactured by Consolidated Electrodynainics Corp., for lower pressures. The kinetic measurements were made by focusing the sprctroiiieter on the 56 peak and plotting its intensity continuously ;is a function of time directly on a Leeds and S o r t h r u p Slicroinas, recorder. The dead space did not exceed 15 cc. and resulted i n :I iiegligible correction for all the flasks used. The thermostat was an air bath so designed tliat the ticaters were not in the same compartment with the reaction flask. The air was stirred rapidly b y a fan, recirculating the air over the heaters and hack over the reaction vessel. The hulk of the power necessary to maintain the operating temperature \vas supplied directly from the power lines E I Z O a I'ariac. T h e remainder of the power was frti to hand-wound heatrrs of lo\v heat capacity b y a GL-5R57 thyratron. The sensing element in the therrnnstat was a nickel wire resistance thermometer which \vas wired a s one arm of ;t resistance britlgr. A 60-cycle sigiial was frti to the bridge and the output signal \vas amplified, ztnd its phase shiftrd 90" by a suitable capacitance circuit. This signal ciintrollrd the firing cycle of the thyratron so t h a t power \vas fed tn tlie ciiiitrol heaters in proportion t o the error of the temperature froiii the mean temperature. By this means, the temperature a t one poitit in the thermostat could he controlled to ~ t 0 . 0 as 5 ~measured by a Leeds and S o r t h r u p platinum resistance therniotneter, Calibrated by the Sational Bureau of Standards, and a Mueller bridge. Gradients across the effective working volume of the thermostat were several times larger than this b u t were not larger than 0.3". Presurnably gradients across the flask (iiisitle) were less t h a n this. Temperatures were also measured by a n alumel-cl~ro~nel thermocouple in a thermocouple well sealed into the reaction flask close to the molecular leak. The thermocouple was callbrated a t 0 , loo", and a t the boiling point of mercury. Sitice the thermocouple and platinuin resistance thermometer ithe latter outside the flask) always agreed to better than 0.05', during most of the measurements the use of the thermocouple was discontinued.
THERMAL DECOMPOSITION OF CYCLOBUTAKE
Nov. 5 , 1963
3351
TABLE I FIRST-ORDERRATE COSSTANTS FOR CVCLORUTASE DECOMPOSITIOSS k P P
k X 105
X 105
sec
Flask
sec
1380 636 330
B
160
B
3 2 2 1 1
P P
-1
--I
k X IO., P P
Flask
505()
39 49
66
14 63 L 98 3 54
3780 3310 2700 "X30
B B
87 2 41 I
B
B
12 76 44 95
57 1 41
703 L ° K
13 13 13 13 11 12 12 11 10 8
15900 8150 5200 3760 2820 2550 2040 12:30 703 337
1 8
5 3 8 8 0 8 7 93
143 98 40 20 11
B
5 0 4 4
5 00 2 36 1 23 0 71
B B B C C C C C
7 6 4 3 2 2 1 1 1
29 08 41 32 45 21 63 53 32
723 3 ° K 20 100 16300 7860 5160 4090 3700 2540 2060 1075 695 509 273
44 6
45 45 45 43 44 41 43 36 33 31 25
P P
-1
7448'K
683 3'K 3 3 3 4 3
15800 7740
sec
7 3 1 5 9 3 5 8 5
B
163 160 137
4 2
72 38 19 19 10 5 2 1 0
0 0
8 1 0 05 48 21 72
.A B B B C B C C C
C C
23 22 21 17 14 9 10
8 6 5 4 4
3 8 9 2 3 62 6 28 42 31 66 32
744 8'K
2000 1210 636
257 194 119 77 9 40 5 20 2 18 0
A B
B B B
B B B C B
Flask
k X 105, sec 1
(contd )
141 128 112 84 6 7; 0 65 6 57 8 31 5 32 2 31 7
3 01 2 34 2 00" 1 90 1 19 1 04d 0 99 (1 66 0 52 0 47
D C E
I> C E D
C D E
17 17 18 16 13 13 12 13 11 13
7 0 7 3 9
0 2 0 9 9
763 3'K 16100 7600 4870 3640 3000 2970 2460 1350 6\53 337 153
85 7 41 0 22 8
.I A A
x -I B A
B B B
B B
B
B
452 435 420 397 394 370 389 343 29 1 240 183 I48 109 83 2
4 2 0 1 82 02 78 54 02 25 0 97 81 50
20 20 15 10 8 5 3 2 2 1
D C
D C D C D C D C D C D
87 3 70 2 75 3 60 4 51 9 43 9 42 0 39 8 34 3 32 4 29 4 30 3 16 7
773 3'K 16200 8140 5140 3720 3070 2680 2420 1350 669 334 168
A A A ;z
.I
86 50 20 19 10 5 2 1 1 0
774 736 715 671 643 611 644 566 454 374 292
6 2 8 8 1
B B C B C C C C C C
233 176 114 127 89 6
D B 05 32 8 68 6 24 0 x C 50 53 0 E 22 0 B 30 49 5 D B 23 23 0 47 0 130 C 20 6 B 74 45 7 E 20 7 B 140 Sominal flask sizes: A, 1 1 . ; B, 2 1.; C, 2 1. (different flask and different leak than B ) ; D , 13 I . : E, new 13-1. flask and ne!\- leak. 2nd run in new flask, E . 1st run after seasoning flask E in C.H4. '' 2nd run after seasoning flask E 1st run in ne\v flask, E. in CIH4. ' :3rd run after seasoning flask E in C2Hi. 16200 8240 4040 3680 275i) 2330
13 2 9 40 8 03h 6 18 5 56 4 96'
156 158 148 154
(1
Results Figure 1 shows a plot of the logarithm of the peak height of the 36 peak as a function of the time for a representative run. I t is seen t h a t the plot is accurately linear over at least six half-lives and has been found t o be so over three more half-lives, showing that the actual rate of disappearance of cyclobutane was accurately first order over the whole course of the decomposition. This was true a t all pressures. The standard deviations of the slopes for the faster runs were generally lC; or less. For the slower runs the scatter was greater, generally not greater than 2 or 3";. Reproducibility of duplicate runs was poorer b y about a factor of two and a few deviations of 10Tc were observed. Table I shows the results of 13G runs made at six temperatures in the range 410 to 300". Table I1 shows the results of 15 runs made either in a flask packed with enough Pyrex glass wool to increase the surface area a t least 20-fold or with certain foreign gases added. The data are represented in Fig. 2 in the form of a plot of 5 log k t's. log p , where p is the initial
+
pressure in microns. In plotting the points for the added gas runs, the total pressure was used. Mass spectrometric and gas chromatographic measurements indicated that the product was about !%.Byc ethylene. The gas chromatograms using a silicone column showed two very small additional peaks whose retention times corresponded to propane and 72-butane, although no certain identification was made. T h e peak area corresponding to propane was about three times t h a t of the other peak and the sum of the two was estimated to be about 0.2Tc of the ethylene peak. .in average oi several measurements showed t h a t not niore than 0.0:3('> of the gas remaining after ten or more half-lives was left aiter condensation in liquid air. Thus, no appreciable amount of H, was produced, The peak intensity at the 36-peak dropped to zero after 10-lq5 half-lives. There was no evidence of isomerization to 1-butene at any pressure. Discussion The experimental data were fit by the Kassel integralfi (eq. %) ( 6 ) 1.
S Kassel,
J P h r s Chriii
,
33, 22: (1928).
ROBERTI&:. VREELANDA N D D. F. SWINEHART
3352
Eo s
where z = E - En) the energy in excess of the activation energy. Eo is the activation energy, .I = k,e+"nIRT, s is the effective number of vibrational modes contributing to the decomposition, n = 4 u 2 ( a k T m)'/V,u being the collision diameter, and p is the pressure. TABLE I1 PACKEDFLASK ASD ADDEDGAS RUNS k X 105,
Temp, Flask"
OK
3 3 8 8 2 763 2 773 1 773 1 724 724 744 744 763
703 723 744 744
2 3 8 8
723 3
sec
P r
-1
Packed flask runs F 5 04 F 2 03 F 3 75 F 1 06 F 5 03 F 2 36 F 6 10 F 1 98
7 53 ,5 86 21 9 15 7 55 7 46 7 89 2 64 9
Nitric oxide (50 mole %) x 5150 C 10 4 A 5180 C 5 25
13 8 7 50 154 17 6
Propylene (50 mole A 4910
'4) 49 2
Air (10 mole [ & ) 744 8
744 8
C
8 51
Water vapor (20 mole ' c ) C 14 1
19 9 28 5
Flask F, 13 I., packed with Pyrex glass wool to increase surface 20-fold
I B M 704 computers a t Los Alamos, New Mexico, a n d later a n I B M 1620 a t the University of Oregon, were coded to compute values of this integral by numerical integration. Using initial estimates of Eo and .-I from the data a t our highest pressures, values of the integral were computed for a series of values of s and u a t one temperature. Fits were made visually on large-scale plots. An excellent fit a t one temperature was obtained using With all the parameters thus s = 18 a n d u = 6 assigned, calculation at the other temperatures revealed that the calculated curves were closer together throughout the whole pressure range than were the experimental curves. This indicated that the initially chosen value of Eo was too small as might have been expected. New integrals with larger values of Eo were computed and excellent fits were obtained a t all temperatures in the pressure range 16 mm. to 20 I.L. These computed integrals are shown as the solid curves in Fig. 2. T h e final values of the parameters and the computed values of the integrals are tabulated in Table I I I. Attempts to extrapolate k to infinite pressure via a plot of I l k ZJS. 1 ! p yielded too low a value of Eo also. I t appears that there are inherent errors in this extrapolation a n d it seems far better to adopt a value of & which will yield a good theoretical fit over as wide a pressure range as possible. Thus, we choose Eo = G3,200 cal./mole as a much more reliable value. This value is to be compared to t h a t reported by Walters a n d co-workers,3 , 4 obtained by measurements a t higher pressures by the pressure change method. They obtaine-d Eo = 62,500 cal. 'mole.
A.
u
A
T.4BLE 111 63,200 (kt300) cal./mole 18
= =
5.8 A
=
=
7.02 ( 1 0 . 1 0 ) X 10';
~ _ - (_ i + log k) a t P,
1 3 10 31 100 316 1000 3160 10000 m
683 3'
P
00 16 0 6
703 25
+o
-0 476 252 - 053 119 265 3 83 174 539 d82 632
7'28 :3'
0 476 ,717 4.i5 ,935 698 1 127 793 1 . 2 9 3 92 1 1 ,430 1 020 1 . 5 3 9 1 094 1 620 1 143 1 67; 1 204 1 750
+
From the value lation'
.I A
014 216
= 7.02 =
T3K.-----744 83 76:i io
0.937 1.188 1 115 1 617 1.793 1 940 2 059 2.149 2 213 2.301
1 037 1 Xi5 1 ,800 2 011 2 l9,5 2 .:350 2 177 2 575 2 (Mi 2 748
X 101jsec.-' and the re-
E(kT/h)e+-\'*/R
a value of A S * of 10.2 cal. deg. a t 450' is calculated. From the variation of the fits with change in EO we estimate the precision in this parameter to be +300 cal. and the precision in .3 to be about +O.lO X lO',' sec. -I. I t is significant to note that the data of Pritchard, Sowden, a n d Trotman-Dickensonj a t one temperature show a faster fall-off of k with pressure than do the present data and they would require an anomalously small value of the parameter s to fit their data. I t is inherent in the derivation of the Kassel integral t h a t the assumption is made that all activated molecules are deactivated a t the first subsequent collision (unless decomposition intervenes). I t is not a t all clear that this assumption is valid. On the one hand, evidence from ultrasonic measurementsL: indicate that many collisions are required to de-excite vibrationally excited molecules. On the other hand, for kinetic purposes in decomposition reactions, deactivation need mean the loss of only a relatively small fraction of the vibrational energy for the molecule to be deactivated, ;.e., unreactive. This observation tends to support o deactivation by collision. the idea of 1 0 0 ~ efficient To find out if the Kassel theory could throw any light on this question, new values of the integral were calculated for s = 30, the total number of modes possible for cyclobutane. T h e value of u was then decreased to obtain the best possible fit to the experimental data. A value u = 0.43 was finally chosen. The values of the Kassel integral calculated with these parameters are shown in Table IV. Comparisons with values in Table I11 shows that these values also fit the experimental data down to about 20 p within the limits of the scatter an$ do so as well as the values with s = 18 and u = 5.8 A. T h e ratio (5.8:0.43)? = 166 can be interpreted as meaning that nearly 200 collisions are needed to deactivate a molecule a n d t h a t all modes are involved in the decomposition. This assumption fits the data just as well as the assumption of 1 0 0 ~ odeactivation efficiency and a lesser number of modes being effective. I t is apparent t h a t direct measurements of rate constants cannot distinguish between these two extremes, a t least in the available pressure range. The
A.
( 7 ) S Glasstone, K J Laidler, a n d H Eyring, "Theory of R a t e P r o c ~ csses," McGraw-Hill Bonk Co , Inc , Xew Y o r k , N Y , 1941 (8) M a n y investigators have found collision numbers in t h e range I O 4 t o 105 f o r decay of vibrationally excited C O L F o r a n extensive review. see T I,. Cnttrell a n d J C. McCoubrey, "Molecular Energy T r a n s f e r in Gases," Butterworth a n d Co (Publishers) L t d . , London, 1961 Also see F w Schneider a n d B S . Rabinovitch, J . A m . Chem S o c . , 8 4 , 421.5 (1962), f o r a n Pxtrnsive rliscusqinn of energy transfer
THERMAL DECOMPOSITION O F CYCLOBUTANE
Nov. 5, 1963 TABLE IV Eo s
63,200 cal./rnole = 30 u = 0.45 A. A = 7 02 X 10'5 sec.-1 =
~
P,
1 3 10 31 100 316 1000 3160 10000 m
683 3'
P
00 16 0
6
-0 343 - 148 025 175 301 404 484 542 581 632
+
__(5 703 2 O
+ log k) 728
:3O
+ 0 125 0 564 333 5 83 518 9 80 6 80 1 15.5 819 1 305 933 1 432 1 023 1 533 1 091 1 611 1 139 1 667 1 204 1 750
-
a t 5'K - __--
744 8 '
763 2'
773 30
0 1 1 1 1 1 2 2
1 344 1 588 1 805 2 002 2 177 2 326 2 450 2 549 2 623 2 750
1 1 1 2 2 2 2 2 2 2
999 229 439 626 790 928 042 131 2 i9i 2 301
524 770 996 199 379 534 664 768 847 985
two sets of curves calculated with s = 18 a n d s = 30 are not identical, however, the latter having slightly less curvature. The two sets of curves would be increasingly farther apart a t still lower pressures, the one for s = 30 being above the one for s = 18 a t lower pressures. If measurements could be made to yet lower pressures, without trouble from surface effects, it might be possible to distinguish between these two points of view and to throw some light on the question of efficiency of collisional deactivation. Perhaps the most interesting point about the data is the departure of the data from theory below 20 p. .4t all temperatures the rate constants appear t o be too high. In fact, a close examination of Fig. 2 suggests t h a t the experimental data show a n inflection point a t approximately 10 p. Since a t this pressure i t is approximately true for a 1X-1. spherical flask t h a t half the collisions of each molecule are with the walls and half are intermolecular, one immediately suspects a surface reaction. flask was packed with enough washed Pyrex wool to increase the surface area by a t least 20-fold. T h e measurements in this flask are shown in Table I1 and as squares on Fig. 2. R a t e constants from half these runs fall within the limits of the scatter of the constants from the runs in unpacked flasks. The largest deviation observed was 2(iTc increase in k . This argues that. for the unpacked flasks, not more than lc/c of the reaction was a reaction on the wall. Further, it is not possible to distinguish data obtained a t low pressures in 2-1. and in 13-1. flasks. I t does not seem reasonable that so little wall reaction could account for the observed deviation of the experimental rate constants from the Kassel curves by more than a factor of two a t 0.5 p. T o find if the wall was conditionedg by previous re-
3353
actions in the flask, a factory-new flask (flask E) was prepared and two runs were made a t low pressures. Then the flask was conditioned by filling it with 15 mm. of cyclobutane and heating overnight a t 745OK. Then the next three runs were made a t low pressures. No significant differences were observed in the values of k obtained. These five runs are indicated in Table 1.
It has been suggested by RabinovitchIo t h a t a possible explanation of the low pressure behavior of k could be that cyclobutane decomposes via two paths. If one path involves a different number of oscillational modes than does the other, then one rate constant would decrease with pressure a t a different rate than the other. T h e two curves might cross a t about 10 1.1. The two paths might be (1) rupture of one bond and then rupture of the second a number of oscillational cycles later and (2) simultaneous rupture of two bonds, i.e., within about one vibrational cycle. T h e latter might be visualized as involving more oscillational modes and so k for this process should decrease more slowly than k for the first process. This implies that the higher pressure process would proceed via the tetramethylene free radical. Decompositions carried out with added gases, particularly XO, showed no inhibition of the reaction. T h e rate corresponded to the rates in pure cyclobutane if the constants were plotted using the total pressure instead of the partial pressure of cyclobutane. T h e effect of added water vapor was investigated due to the impossibility of removing the last traces of water vapor from glass vessels. Neither water vapor nor air changed the rate constants, compared on a total pressure basis. Lack of inhibition by N O does not argue for the absence of free radicals and so against the mechanism given earlier. I t only argues that the free radicals, if present, do not react with the parent molecule. The data suggest that the collisional efficiencies for activation of the parent molecule by all these added gases is quite high, nearly as high as for cyclobutane itself, If the decomposition does proceed via two competitive mechanisms, this would argue in favor of a high collisional deactivational efficiency and the participation of less than the maximum number of oscillational modes in the mechanism chiefly responsible for the decomposition above 20 p. Acknowledgment.-\Xre wish to thank the Atomic Energy Commission for support and Dr. LVilliam D. Clark and E. hl. Willbanks a t Los Alamos and M r . Terry Beyer a t the University of Oregon for coding the computers. (9) F. 0. Rice a n d K . F Herzfeld, J . P h y s Chem., titi, 97,5 (19,511, (10) B. S. Rabinovitch, private communication.
