THEPHOTOLYSIs
OF
3109
4-METHYL-1-PYRAZOLINE
Energy Partitioning in Photochemical Reactions. The Photolysis of 4-Methyl-l-pyrazoline by F. H. Dorer Department of Chemistry, California State College, Fullerton, Fullerton, Cal.ifornia 986’691
(Received February 17, 1963)
Methylcyclopropane produced by the 3130-A photolysis of 4-methyl-l-pyrazoline contains enough of the light energy absorbed by the reactant and the exothermicity of the reaction to undergo subsequent isomerization to the butene isomers. The pressure dependence of the magnitude of the experimental unimolecular rate constant for the isomerization of the vibrationally excited methylcyclopropaneformed in the primary process is compared to theoretical rate constants calculated for this reaction using the RRKM formulation. The results indicate that, although the hydrocarbon fragment contains a broad distribution of internal energies, the fraction of the available energy that it receives is less than would be predicted by a statistical model for energy partitioning. Consideration of the structural changes that occur when l-pyrazoline decomposes to a trimethylene intermediate and nitrogen offers a qualitative explanation of the partitioning of energy between these two products of this photodecomposition reaction.
Introduction The experimental characterization of how energy is distributed among the primary products of the photochemical decomposition of a relatively complex molecule has been possible for several types of systems. Recent studies of the photolysis of cyclic ketones, l I D a cyclic ether,3 and a bicyclic azo compound4 have demonstrated that the hydrocarbon fragments produced in the primary decomposition step can contain enough of the photolysis energy to cause them to undergo subsequent unimolecular reactions characteristic of vibrationally “hot” molecules. These studies have shown that even though the incident light energy may be monoenergetic, the hydrocarbon fragments are produced with a relatively broad distribution of internal energies; however, the energy is not necessarily statistically distributed among the available degrees of freedom of the reaction p r o d ~ c t s . ~ ~ ~ I n order to extend these studies to new systems for which the necessary kinetic parameters are known, we have characterized the photochemical decomposition of a cyclic azo compound, 4methyl-l-pyrazoline, over a wide range of pressures. On photolysis by 3100-A radiation this molecule produces methylcyclopropane, isobutene, propene, and nitrogen.6 At lower pressures the methylcyclopropane yield decreases with a corresponding appearance of the butene isomers in a stoichiometry characteristic of vibrationally “hot” methylcyclopropane isomerization.6-s Measurement of the product distribution as a function of pressure has yielded the unimolecular rate constants for isomerization to butenes of the vibrationally excited methylcyclopropane formed in the primary photodecomposition reaction. By comparison of the magnitude of these experimental rate constants as a function of pressure to rate constants calculated for the isomerization reaction
by using RRKM unimolecular rate theory9~’Oand an appropriate energy distribution function, we obtain the fraction of the total energy of the primary photodecomposition step partitioned to the internal degrees of freedom of the methylcyclopropane. Moreover, the pressure dependence of the experimental rate constant reflects the breadth of the internal-energy distribution function of the formed methylcyclopropane.
Experimental Section The 4-methyl-l-pyrazoline was synthesized by a procedure outlined by Crawford, et al.ll First, 4-methyl2-pyrazoline was prepared by the reaction of hydrazine with methacrolein. The 4-methyl-2-pyrazoline was subsequently reduced to 4-methylpyrazolidine on a Parr hydrogenation apparatus. The pyrazolidine was then oxidized by mercuric oxide to 4-methyl-l-pyrazoline. The final product was purified by gas chro(1) R. F. Klemm, D. N. Morrison, P. Gilderson, and A. T. Blades, Can. J. Chsm., 43,1934(1965). (2) R. J. Campbell and E. W. Schlag, J. Amer. Chem. Soc., 89,5103 (1987). (3) B. C . Roquitte, J.Phys. Chem., 70,1334 (1986). (4) T.F.Thomas, C. I. Sutin, and C. Steel, J . Amer. Chem. Soc., 89, 5107 (1967). (5) R. Moore, A. Mishra, and R. J. Crawford, Can. J . Chem., 46,3305 (1968). (6) J. N.Butler and G. B. Kistiakowsky, J. Amer. Chem. SOC.,82,759 (1960). (7) F. H.Dorer and B. 8. Rabinovitch, J. Phys. Chem., 69, 1952, 1964 (1965). (8) D. W.Setser and B. 8. Rabinovitch, J . Amer. Chem. SOC.,86, 564 (1954); J. P.Chesick, ibdd., 82,3277 (1960). (9) R. A. Marcus and 0. K. Rice, J . Phys. Colloid Chem., 55, 894 (1951); R.A.Marcus, J . Chem. Phys., 20,359 (1952). (10) F. H.Dorer and B. S. Rabinovitch, J . Phys. Chem., 69, 1973 (1965). (11) R. J. Crawford, A. Mishra, and R. J. Dummel, J . Amer. Chem. SOC.,88,3959(1986). Volume 769, Number 9 September lQG9
3110
F. H. DORER
Table I : Variation of Product Yields with Total Pressure’ C4dSC4,
c
0
Pressure, Torr
Mixture ratiob
0.032 0.041 0.071 0.090 0.095 0.10c 0.21 0.29 0.54 0.97 2.0 2.0d 2.3d 3.2 4.5 6.2 6.5 16.4 18.4 20.40 27.9. 29.Oc 51.6 55 73.5 210
9.2 9.2 9.2 9.2 9.2 9.2 9.2 9.2 9.2 9.2 20
i-1
(Ni)/(Cs 4- CA)
1.1 1.1 9.2 20 20 20 25 25 25 25 25 25 25
25 50
1.1 0.96 1.1
1.1 1.0 0.92 0.93 1.1
MCP
i-CtHs
trans-C4Ha-2
cis-C1Hs-2
CtHa-1
0.31 0.26 0.39 0.46 0.43 0.43 0.54 0.52 0.53 0.57 0.65 0.67 0.66 0.66 0.66 0.69 0.690 0.72 0.69 0.70 0.66 0.74 0.76 0.72 0.74 0.77
0.15 0.11 0.16 0.16 0.17 0.19 0.16 0.16 0.20 0.18 0.19 0.17 0.18 0.18 0.20 0.19 0.20 0.20 0.22 0.22 0.27 0.22 0.22 0.24 0.23 0.23
0.17 0.17 0.12 0.11 0.094 0.10 0.068 0.081 0.070 0.084 0.028 0.042 0.038 0.042 0.033 0.023 0.019 0.019 0.018 0.015 0.008
0.11 0.20 0.10 0.09 0.094 0.089 0.073
0.27 0.26 0.24 0.20 0.21 0.19 0.16 0.15 0.14 0.11 0.086 0.070 0.070 0 072 0.070 0.062 0.065 0.041 0.043 0.039 0.039 0.029
Photolysis of 4-methyl-l-pyrazoline by 3130-Aradiation.
b
0.081
0.068 0.058 0.051 0.051 0.046 0.041 0.042 0.036 0.037 0.024 0.025 0.026 0.022 0.016
I
Trace
Trace
Trace
0.009 0 006
0.016 0.008
0.025 0.016
I
Propane:4-methyl-l-pyraaolineratio.
c
(Ca)/(Ca
+ Ct)
0.14 0.12 0.14 0.13 0.16 0.15 0.12 0.12 0.12 0.11 0.10 0.10 0.11 0.11 0.098 0.11 0 094 0.093 0.10 0.11 0.13 0.12 0.090 0.098 0.11 0.088 I
Reactor contained Pyrex wool.
No propane diluent added.
matography using a 6-ft silicone gum rubber (SE-54) on diatoport column. The gas-phase ultraviolet spectra taken on a Cary 15 instrument showed the characteristic n-r* absorption band with a maximum at 319 mp.6J1 The infrared spectra displayed the -N=Nstretching frequency at 1545 cm-l.ll Matheson instrument grade propane was used as a diluent in the photolysis runs. The small amount of hydrocarbon impurities in the propane did not interfere with the product analysis. The products were analyzed on a Hewlett-Packard Model 5750 research chromatograph fitted with a vacuum inlet system for gas analysis. The gaseous products were expanded directly from the reactor into the inlet sample loop which had first been evacuated. The helium flow was then routed through the sample loop for injection of the sample onto the column. This technique allowed the simultaneous measurement of the nitrogen and the hydrocarbons produced in the reaction. For analysis of the lower pressure runs, where there are small amounts of material, the entire contents were pumped out of the reactor and into the sample loop, which was kept a t liquid nitrogen temperature. This technique, of course, prohibited an analysis for nitrogen. An adequate separation of the products was achieved The Journal of Physical Chmistry
on a 40-ft column packed with 60-80 mesh Chromosorb P coated with 20% by weight of AgNOs-saturated l,&propanediol. The higher pressure runs were analyzed using the thermal conductivity cell. For the low-pressure runs it was necessary to use the flame ionization detector. All products were identified and their relative detector sensitivities were measured by using calibration mixtures made up of known samples. A Hanovia 550-W medium-pressure mercury-arc lamp enclosed in a water-cooled hotsing was the radiation source. Isolation of the 3130-A region of the lamp output was achieved by use of a three-compartment quartz-jacketed solution filter and a Corning CS-7-54 filter. The solutions used, their path lengths, and the transmission of this filter using the above lamp can be found in ref 12. The photolysis runs were carried out by first making mixtures of 4-methyl-l-pyrazoline and propane in concentration ratios of 1:9.2, 1:20, 1:25, and 1:40. A known amount of the stored gaseous mixtures would be measured out and then frozen into either a 500- or lOOO-cm3 spherical Vycor 791 reactor at liquid nitrogen temperature. The reactor with the frozen gases would (12) J. G. Calvert and J. N. Pitts,, Jr., “Photochemistry,” John Wiley & Sons, Inc., New York, N. Y., 1966,p 732.
THEPHOTOLYSIS
OF
3111
4-METHYL-1-PYRAZOLINE
Figure 1. The experimental and calculated values of k. as a function of w . The filled point is a run in which the reactor contained Pyrex wool; €3 are runs with no propane diluent added. The solid line is a calculated curve with Em, = 82 kcal mol-' and u = 14 kcal mol-'. The broken line was calculated with E,, = 82 koa1 mol-' and u = 17 kcal mol-'.
then by pumped to a t least Torr before flashing its contents by immersing it in hot water. The contents were then irradiated a t room temperature from 2 to 4 hr.
hv *
k 4 CH3-c.C,HJ
Results The pressure dependence of the relative amounts of hydrocarbons and nitrogen produced by the 3130-A photolysis of 4-methyl-1-pyrazoline at -25" are given in Table I. The measurements range between 0.032 and 210 Torr. At higher pressures ( 2 2 Torr) propylene constitutes about 10% of the hydrocarbon product^.^ However, we find that the relative amount of propylene increases to 14% of the hydrocarbons at our lowest pressures (0.032 Torr). This interesting cleavage reaction is characteristic of 1-pyrazoline decomp~sition,~J~ but it is of no consequence to the present work, except that it may also produce rneth~lene.~I n this work, if small amounts of methylene were produced, it would for the great part be scavenged by the propane diluent, and, consequently, it would not substantially affect the relative yield of Cd products. Unfortunately, for these experiments small amounts of butanes in the products would have gone undetected. The formation of methylcyclopropane (MCP) and the Cq olefins can be described by the scheme
+
k
A (CH&C=CHz CH,-~-C,HJ
%
N2
+
N2
(4
CH~CH~CH=CH,
(4
-+
CH,CH= CHCH,
(e)
k
(CH,),C =CH2
(f)
CH3-c-C,H,
(d
ka z
The rate constant for the structural isomerization of the vibrationally excited methylcyclopropane (MCP*) is i-3
k, =
c
kad
i-1
and w is the collisional deactivation rate of MCP*. Evidence that reactions a-g and propene formation account for all of the hydrocarbon products of 4-methyl-1-pyrazoline decomposition is provided by the Nz :hydrocarbon ratio. Within the experimental error this ratio is equal to unity to pressures as low as 2 Torr (Ta(13) R. J. Crawford and A. Mishra, J. Amer. Chem. Soc., 88, 3963 (1966).
Volume '73,Number Q September 1060
3112
F. H. DORER
ble I). After a period of several runs the reactor walls did appear cloudy, but the data of Table I, including the packed reactor run, indicate that loss of hydrocarbons due to polymer formation is very little. The runs with Pyrex wool in the reactor did not affect the relative amounts of hydrocarbons produced. Some minor complication evidently exists with the suggested scheme since, even though the relative amounts of butene-2 and butene-1 formed are consistent with those produced by '(hot" methylcyclopropane isomerization,s-8 there is no increase in the amount of isobutene a t lower pressures. Isobutene, produced in reaction f, could constitute as much as 16% of the isomerization products of n/lCP*.* A likely explanation is that the rate ratio of the primary photodecomposition processes, kl/k2, is pressure dependent, and the formation of MCP" is favored by lower pressures. Although the average energy of the MCP* formed in this photolysis system is somewhat less than that formed by chemical activationlo (see Discussion) , the data for both the chemical activationaJ and the pyrolysis systems* indicate that a reasonable estimate of the contribution to the amount of isobutene due to reaction f is that it should constitute -10% of the isomerization olefins. If ICa is then defined as o ( D / S ) where D is the total amount of the isomerization olefins, and S is the amount of collisionally stabilized MCP, k, can be calculated from the expression
ka = l.lo(butene-1
+ butene-2)/(MCP)
(1)
The specific collision frequency of the MCPX with the bath molecules was calculated by using collision diameters of 5.6 A for MCP, 4.8 for propane, and 6.0 Bfor 4-methyl-1-pyrazoline. The resulting ka values are illustrated as a function of w in Figure 1.
Discussion The total amount of energy to be distributed among the degrees of freedom of the products of reaction b is the sum of the absorbed light energy, the exothermicity of b, and the thermal energy of the reactants. An estimate of the heat of formation of Pmethyl-1-pyrazoline can be made by noting that the heat of combustion of azoi~opropanel~ indicates one should add about 45 kcal mol-l to the heat of formation of 4-methylcyclopentene when an -N=N- group is substituted for a -CH=CH- group.16 This value is only 6 kcal mol-' greater than the value one would deduce from the difference in the heats of formation of ethylene and diimide.16 Using its heat of hydrogenation" and the heat of formation of methylcyclopentanels to obtain the heat of formation of gaseous 4-methylcyclopentene, we estimate the heat of formation of gaseous 4-methyl-lpyrazoline to be 49 kcal mol-1 a t 25'. The heat of formation of MCP has been estimated to be 13.6 kcal mol-' at O O K . 7 Comparison of the difference in the The Journal of Phylskal Chemistry
heat of formation between 298 and OOK for similar molecules181eadsto an estimate of 8.1 kcal mol-1 for the heat of formation of MCP a t 25". Therefore, reaction b is about 41 kcal mol-' exothermic a t 25". However, reflection on this method of obtaining the heat of reaction indicates that the value could be as low as 35 kcal mol-'. The result of the superposition of the frequency distribution from the lamp and filter12 and the gas-phase absorption spectrum of 4-methyl-1-pyrazoline (taken on the Cary 15 instrument) is illustrated in Figure 2. The maximum in this curve occurs at 90.6 kcal mol-l, and, therefore, there is -132 kcal mol-' to be distributed among the degrees of freedom of the MCP and nitrogen formed by the photolysis of 4-methyl-l-p~raaoline in these experiments. The experimental unimolecular rate constant, k,, is related to the microscopic unimolecular rate constant for isomerization of MCP' with energy E, k E ,by
t -
EkE+W
In eq 2 f ( E ) is the distribution function for the internal energy of MCP*. The microscopic unimolecular rate constants, k,, were calculated using the RRKM unimolecular rate f o r m ~ l a t i o n . ~The approximation of Whitten and R a b i n o ~ i t c h was ' ~ employed for calculating the necessary densities and sums of energy eigenstates of the molecule and the activated complex. The vibrational frequency assignments for the molecule and the activated complex are those previously used for the chemical activation system.'O The criticaI energy for the isomerization of MCP is 61.4 kcal mol-'.lo I n order to characterize its width, we assumed f ( E ) to have the form of a Gaussian distribution4
The upper limit of the sums in eq 2 and 3 is the total amount of energy available to the products; the lower limit is zero. Calculations of k , as a function of w were done by summing eq 2 over the energy range in 5-kcal (14) G.E.Coates and L. E. Sutton, J . Chem. Soc., 1187 (1948). (16) R. J. Crawford and D. M. Cameron, Can. J. Chem., 45, 691 (1967). (16) Reference 12,p 823. (17) A.Lahbauf and F. D. Rossini, J . Phys. Chem., 65,479 (1961). (18) F.D.Rossini, "Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds," American Petroleum Institute, Carnegie, Press, Pittsburgh, Pa., 1953. (19) G. 2. Whitten and B. 8.Rabinovitch, J . Chem. Phys., 38, 2466 (1963).
THEPHOTOLYSIS
OF
3113
4-n/IETHYL-1-PYRAZOLINE 0
P
B
W
7
-
0)
0
6
5
1
€ ( k c a t mote")
Figure 2. The distribution function, f ( E ) , that best fits the data for o 5 108 sec-1 and k~ as a function of energy. For comparison, the broken line represents, in arbitrary units, the distribution of light energy absorbed by the 4-methyl-1-pyrazoline.
steps. Reducing the step size to 1 kcal has no substantial effect on the fit of the theoretical curves to the experimental data. The calculated curve that best fits the experimental values of IC, for w 5 100 X lo6 sec-l corresponds to f ( E ) having E,, of 82 kcal mol-l and u = 14 kcal mol-l (Figure 1). Although the k , values are less reliable because of the relatively small amount of decomposition, the higher pressure results (W > 2 X los sec-') indicate that even a broader distribution function is necessary to fit the experimental data over the entire pressure range. However, it then appears that f(R)might not have the form of a Gaussian since a greater value of u gives a curve which is inconsistent with the lower pressure measurements (Figure 1). The most probable energy, 82 kcal mol-', is only 62% of the total energy available to be distributed between the MCP and nitrogen produced in reaction b. If a statistical model were appropriate for describing the energy distribution between the cychpropane and carbon monoxide produced by the 2537-A photolysis of cyclobutanone, Campbell and Schlag have calculated that the most probable energy of the formed cyclopropane would correspond to about 77% of the available
energy. Statistically, one then anticipates an even greater fraction of the energy to be partitioned to the hICP fragment when 4-methyl-1-pyrazoline decomposes. Like cyclobutanone2 and 2,3-diazabicyclo [2.2.llhept-2-ene photolysis,4 statistical theory then fails quantitatively to describe the distribution of energy between the reaction products. However, unlike cyclobutanone photolysis,2 there is in this system less energy in the vibrational degrees of freedom of the hydrocarbon fragment than would be predicted by statistical theory. Consideration of the structural changes that occur when 1-pyrazolines decompose to form cyclopropanes and nitrogen offers a qualitative explanation of why a relatively small amount of the total energy is partitioned to the hydrocarbon fragment. It has been proposed that an excited singlet trimethylene is an intermediate in the formation of cyclopropane on photolysis of 1-pyrazoline.5 If methyltrimethylene and nitrogen are the primary products of the decomposition of 4-methyl-l-pyrazoline, these results indicate that the most probable energy of the diradical intermediate would be only -21 kcal mol-' from a total of 71 kcal mol-' to be distributed between these two products. Volume 75, Number 9 September 1969
3114
Hoffmann’s calculations reveal that the potential energy surface of the excited trimethylene species has a broad minimum ranging over CCC bond angles of 100-130” with no barriers to internal rotationa20 The structure of l-pyrazolinel’ is similar to that of cyclopenteneZ1 which has a C G C 6 bond angle of 106’ 20’. The -N=N- bond distance in l-pyrazoline is 1.25 b.ll Therefore, there would be very little structural change in the hydrocarbon fragment on formation of a trimethylene intermediate, whereas the Na-N bond distance must decrease from 1.25 to 1.09 A upon forming nitrogen. It is then possible that the nitrogen fragment could be formed with more vibrational energy than expected from statistical considerations. Using a Morse potential-energy function, one can calculate that only 28 kcal mol-l isaneeded to increase the nitrogen bond length to 1.25 A.4,22 If this were the most probable internal-energy content of the nitrogen, there would yet remain 22 kcal mol-’ to be distributed among the translational and rotational degrees of freedom of the products. Even though energy partitioning is nonstatistical, the methylcyclopropanes formed in reaction b contain a much broader distribution of internal energies than the initially excited Imethyl-l-pyrazoline. If a Gaussian is a close approximation to the form of f(E), the results imply that a small fraction of the formed MCP contains insufficient energy for isomerization to the
The Journal of Physical Chemistry
F. H. DORER butene isomers. A broad internal-energy distribution of the vibrationally excited hydrocarbon product is also characteristic of cyclobutanone2 and 2,3-diazabicyclo [2.2.1Ihept-2-ene4 photolysis by monochromatic radiation. Some contribution to the width of f(E)is perhaps a consequence of the pressure dependence of the ratio of MCP to isobutene formed in the primary photodecomposition process. The formation of MCP becomes even more favored relative to isobutene at lower pressures. Pressure-induced dissociation has been observed in the photolysis of 2,3-diazabicyclo [2.2.l]he~t-2-ene.~~ It might be possible that pressure-induced dissociation of the excited pyraeoline would affect the relative amounts of MCP and isobutene, but it is difficult to understand why such a process would effectively increase the average energy of the MCP formed at higher pressures yet decrease its probability of formation.
Acknowledgment. This work is supported in part by grants from the National Science Foundation and the Research Corporation. (20) R . Hoffnmnn, J.Bmer. Chem. Soc., 90, 1475 (1968). (21) G. W. Rathjens, J . C‘hem.P h w , 36,2401 (1962). (22) G. Hereberg, “Molecular Spectra and Molecular Structure. I.
Spectra of Diatomic Molecules,” D. Van Nostrmd Co., Inc., Princeton, N. J., 1950. (23) B. S. Solomon, T. F. Thomas, and C. Steel, J . Amer. Chem. SOC., 90, 2249 (1968).
