3006
J. Phys. Chem. 1983, 87,3906-3911
Multistep Collisional Deactivation of Highly Vibrationally Excited 1,1,2,2-Tetrafluorocyclopropane 6. Arbllla, J. C. Ferrero;
and E. H. Starlcco
Departamento de Flslco Quimlca, Facultad de Cienclas Quimicas, UniversMad Nacional de Ckdoba, Sucursal 16, Casiiia Correo 6 1, 50 16 Ckdoba, Argentina (Received: December 7, 1982)
The reaction of CH2('A1)with C2F4 was investigated at 298 K and pressures between 66 and 1837 torr. Chemically activated l,l,Z,Z-tetrafluorocyclopropanewas formed with an energy of about 41 kcal/mol above the threshold energy for decomposition to CF2 and CF2CH2. A significant dependence of the experimental specific rate constant for unimolecular decomposition with pressure was observed and is indicative of a multistep collisional deactivation process. The data could be fitted to a stepladder model, with down-energy loss of about 9 kcal/mol and with a minimum energy for the activated molecule of 85 f 2 kcal/mol. In these experiments C2F, is the major collision partner and the limiting high-pressure region could not be reached. With this value and the known heats of formation of CH2('Al) and C2F4,the heat of formation of tetrafluorocyclopropane was estimated to be Nf0 = -140 kcal/mol.
Introduction Chemical activation has proved to be a powerful tool in the study of unimolecular reactions and energy-transfer processes. Activated species have been obtained by a variety of methods' and, in particular, the addition of CH2 to olefins has been used to produce molecules with more than 40 kcal/mol above the critical energy for unimolecular decomposition or isomerization.2 Concomitant with the chemical process, the activated molecules experience collisions with the bath gas which removes the excess energy and stabilizes the activated molecules. At the high energies reached with chemical activation, several of these collisions are necessary to completely deactivate the hot molecule, even when the partner is polyatomic. This inefficiency in collisional energy transfer results in an increase of the specific rate constant as the total pressure is reduced, while a t high pressures no variations are detected within the experimental error. When experimental data are obtained in this high-pressure region only, application of unimolecular rate theory can lead t~ an equally good fit assuming either strong collisions or a less efficient energy-transfer model. The result is a different estimation of the average excess energy, ( E ) ,of the activated moleculea3 This is a crucial point, as the thermochemistry of the reaction is usually uncertain and a priori knowledge of the energy in excess is not possible. If the variation of pressure is not large enough, only a relatively small dependence of the specific rate constant, k,, is observed. In this case, a good fit can also be obtained with a variety of combinations of excess energy and average energy transferred by collision ( AE),but, if the pressure range is extended as to observe a large variation of k,, the uncertainties are reduced. This is a consequence of the fact that it is not possible to fit simultaneously both the low- and high-pressure region with any set of ( E )and ( AE): From the experimental point of view it is necessary to observe a dependence of the decomposition to stabilization ratio (or the apparent rate constant) in a range of pressure such that D / S varies at least a factor of 100. Then this apparent rate constant can be fitted by calculation using some (1) Tardy, D. C.; Rabinovitch, B. S. Chem. Reu. 1977, 77, 369. (2) McCluskey, R. J. Carr, R. W. J . Phys. Chem. 1978, 82, 2637. (3) (a) Setser, D. W. Phys. Chem., Ser. One, 1972-1973 1972,9, 1. (b) Carr, R. W.; Topor, M. G. J . Chem. Phys. 1973, 58, 757. (4) McCluskey, R. J.; Carr, R. W. J . Phys. Chem. 1976, 80, 1393.
collisional transition probability model, usually the stepladder model when the collider is a polyatomic molecule. In addition, it is also necessary to compute the microscopic rate constants for decomposition and this needs the Arrhenius parameters for the reaction, A and E,, as obtained from a conventional kinetic study or estimated values based on related reaction^.^ The most serious experimental problem is a clean reaction system. CH2 is usually obtained from the photolysis of ketene and it yields a mixture of CH2('A1) and CH2(3B,), the latter being easily removed by the addition of small amounts of oxygen.6 Care has to be taken in order to avoid side reactions and heterogeneous processes on the walls. This can be accomplished by carefully selecting the experimental conditions and using aged reaction vessels. When the above conditions are fulfilled, chemical activation provides a method to obtain average excitation energy, information on collisional energy-transfer processes, and, sometimes, an estimation of Arrhenius parameters when they are not known. The average excitation energy with which the activated molecule is formed is directly related to the enthalpy change of the activation reaction and, hence, the heat of formation of the excited species can be obtained.' It is not possible to obtain all of this information simultaneously from a single study and previous knowledge of the Arrhenius parameters is highly desirable and permits a better use of the unimolecular reaction theory. The kinetics of the gas-phase thermal reaction of tetrafluorocyclopropane has been reported.8 The reaction is cleanly first order and was studied following the disappearance of reactant. Products polymerized extensively and were not identified. The reaction of CH2 with C2F4 was also studied, without added oxygen, in the high-pressure r e g i ~ n .The ~ reaction products were tentatively identified as tetrafluoropropene and tetrafluorocyclopropane. It is a t present well documented that gem-difluorocyclopropanes undergo decom(5) Forst, W. 'Theory of Unimolecular Reactions"; Academic Press: New York. 1973. (6) Russell, R. L.; Rowland, F. S. J . Am. Chem. SOC.1968, 90, 1671. (7) Eichler, K.; Heydtmann, H. Int. J. Chem. Kinet. 1981, 13, 1107. (8) Herbert, F. P.; Kerr, J. A,; Trotman-Dickenson, A. F. J . Chem. SOC. 1965. 5710. (9) Grzybowska, B. A.; Knox, J. H.; Trotman-Dickenson, A. F. J . Chem. SOC.1963, 746.
0022-3654/83/2087-3906$01.50/00 1983 American Chemical Society
Deactivation of Highly Vibrationally Excited TFC
position reactions with elimination of CF2, when they are produced by chemical activationlo or react thermally," with a few exceptions.12 The heats of formation of fluorinated cyclopropanes are unknown. This lack of information affects the interpretation of conventional kinetic studies and the only resource is the use of Benson's additivity rules.13 However, these rules seem to fail for highly polar compounds.'J4 According to the above consideration, we undertook a study of chemically activated tetrafluorocyclopropane over a wide pressure range in order to characterize the collisional energy-transfer process and calculate its heat of formation based on the calculated average excess energy.
Experimental Section Materials. Ketene was prepared by the pyrolysis of acetic anhydride according to the method of Jenkins.15 The product obtained was purified by trap-to-trap distillation and stored at 77 K. No impurities were found by IR and gas-chromatographic analysis. Tetrafluoroethene was obtained by the pyrolysis of polymeric C2F4 (Teflon) and purified by careful trap-to-trap distillation and by gas chromatography.16 Its purity was verified by gas chromatography on several different columns. Oxygen was obtained from a tank and condensed at the temperature of liquid nitrogen. The first fraction was pumped off and the middle fraction was expanded into an evacuated bulb and stored. Apparatus and Procedure. All gas handling was done on a greaseless standard high-vacuum system. Pressure measurements were done with a MKS Baratron 220 B manometer. In all the experiments a constant number of moles of each reactant was used excepting at pressures higher than lo00 torr. The desired pressures of ketene and CzF4 were measured a t room temperature in a calibrated volume of 16.43 cm3 and were then transferred to the reaction vessels by condensation at 77 K. The partial pressure of O2was obtained by expansion from a reservoir into the reaction vessels that already contained the other compounds. The reactant ratios for this study were CH,CO:C2F4:02 = 1:16:1.3. Several Pyrex reaction vessels were used with volumes from 1.007 to 17.32 cm3. It was necessary to season all the vessels before use in order to obtain reproducible results. The samples were photolized at room temperature by using an OSRAM HBO 500-W high-pressure mercury lamp. The effective wavelength for ketene photolysis in these conditions is 3200 f 200 A. Photolysis times varied from 0.5 to 80 min and were as short as possible. The minimum irradiation time was dependent on the conditions of the experiment and as long as necessary to obtain a sufficient amount of reaction products for analysis. Typically, the conversion was estimated to be less than 2%. After irradiation, the samples were condensed at 77 K, and the volatile components were pumped off, (CO, 0,) and then separated into two fractions for gas-chromatographic analysis. One fraction was analyzed on a 2.95-m alumina column coated with 1%dinonyl phthalate at 4 "C and the other fraction on a 6-m silica gel column at 50 "C, with a (10) (a) Craig, N. C.; Hu, T.; Martyn, P. H. J. Phys. Chem. 1968, 72, 2234. (b) Meagher, J. F.; Chao, K. J.; Rabinovitch, B. S. Zbid. 1974, 78, 2535. (11) (a) Quero, E. D.; Ferrero, J. C.; Staricco, E. H. Int. J . Chem. Kinet. 1977,9,339. (b) Ferrero, J. C.; Staricco, E. H. Zbid. 1979,11,1287. (12) Ferrero, J. C.; R. de Staricco, E. A.; Staricco, E. H. J. Phys. Chem. 1975, 79, 1242. (13) Benson, S. W. "Thermochemical Kinetics", 2nd ed.; Wiley: New York, 1976. (14) Benson, S. W. J . Phys. Chem. 1981, 85, 3375. (15) Jenkins, A. D. J . Chem. SOC.1952, 2563. (16) Atkinson, B. J . Chem. SOC.1952, 2684.
The Journal of Physical Chemistry, Vol. 87,
No. 20, 1983 3907
Varian 3700 gas chromatograph with flame ionization detector. The detector response was calibrated by using prepared mixtures approximating the composition of the actual samples. Even though a good resolution was achieved on the alumina column for all the components of interest, we soon realized that tetrafluorocyclopropane was mostly irreversibly absorbed. Thus, this column was used to measure the decomposition product (C2HzF2)only and tetrafluorocyclopropane was analyzed on the silica gel column. The identity of the peaks was determined by comparison of the reaction times with authentic samples on several different columns.
Experimental Results The reaction products of interest observed from the photolysis of ketene in the presence of C2F, and 0, were CHz=CFz and 1,1,2,2-tetrafluorocyclopropane. The products are well explained by the following mechanism, which is based on the behavior of methylene as currently understood: CHzCO + hv CH2 + CO
-
CHZ(lA1) + C2F4
-+ + + -
TFC*
-
CH2=CFz
TFC*
+ CFz
M TFC + M CzF4 c-C~FG
TFC* CF2
2CFz
CH2(3Bl) 0,
CzF4
CO, CO,, H,, HzO, ...
TFC stands for 1,1,2,2-tetrafluorocyclopropaneand the asterisk denotes a chemically activated species. Some other minor reaction paths could be included but they are not of interest for the present purpose. The chemically activated tetrafluorocyclopropane may either decompose to yield CHz=CF, or be deactivated by collision with another molecule, mainly CzF,. This last process is represented as taking place in one step although it is actually a multistep process (see below). When the experiments were performed in clean vessels, an increase in the decomposition/stabilization ratio (abbreviated D / S from here on) was observed. The D / S value in these conditions was higher by a factor of 2 than in well-seasoned vessels, indicating the presence of a heterogeneous component, as is usually observed in these kinds of r e a ~ t i 0 n s . l ~As a consequence, care had to be taken of aging all the vessels in order to obtain reproducible results. Although the above mechanism predicts D / S to be independent of the extent of reaction, a variation with time was actually found, which resulted in a decrease of D / S with time. This is not a surprising fact as it was also found to occur in the decomposition of chemically activated methylcyclobutane.l* To account for this dependence an additional path leading to the destruction of CH2=CF2 and/or the production of tetrafluorocyclopropane must be considered. The reaction of CHz=CFz with either CH, or CF, would result in a relative decrease of CH2=CF2 concentration as well as an increase in tetrafluorocyclopropane from the reaction of CH2=CFz with CFz. A direct reaction of olefins with photoexcited ketene has also been proposed.18 In order to achieve a better understanding of this complication the use of an internal monitor would be necessary. We did not investigate this question further but care was taken to use the shortest reaction times possible. The time limit to (17) Setser, D. W.; Rabinovitch, B. S. Can. J . Chem. 1962, 40, 1425. (18) Kolln, W. S.; Johnson, M.; Peebles, D. E.; Simons, J. W. Chem. Phys. Lett. 1979, 65, 85.
3908
The Journal
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of Physical Chemistry, Vol. 87, No. 20, 1983
Arbilla et al.
c 15C m
-
0
-
D/S
\
-
i L
c 0
c'
z
40 -
100
Q c
m
z
0 0
w 1
2
I
50
[L
500
65.9
77.2 87.9 13fi.6 166.8 173.9 177.2 217 1 251.2 348.7 422.6 191.1 680.9 772.3 916.8 1301.4 1418.2 1493.1 1837.9
0.015 1 7 0.012 9 5 0.011 3 8 0 . 0 0 7 32 0.005 99 0.005 75 0 . 0 0 5 64 0.00405 0.003 98 0.002 87 0.002 37 0.002 0 4 0.001 47 0.001 29 0.001 0 9 0.000 77 0.000 70 0.000 67 0.000 54
2594.50 2136.36 1199.68 620.69 424.00 290.69 324.47 153.12 111.26 60.85 44.90 27.91 23.50 14.65 10.81 6.46 5.85 5.54 A.46
170.977 165.995 105.140 84.786 70.723 50.551 57.496 37.836 35.484 21.218 18.975 13.707 16.001 11.313 9.9 11 8.407 8.296 8.272 8.197
a T h e Least-squares fitting t o e q 1 was done in pressure units o f mmHg. I n these units t h e least-squares polynomial was li,= 0 . 5 8 8 1 2 5 6 X l o 4 T ( 0 . 1 8 9 1 1 6 x IO' 1 0 7 ) p - ' t ( 0 . 2 0 1 6 2 0 6 x 1010)P-2 - (0.1676617 x 10")P i ( 0 . 4 2 8 0 4 4 6 X 1013)P-4,
(19) Marcoux, P. J.; Setser, D. W. J . Phys. Chem. 1978, 82, 97.
1500 Torr
Flgure 2. Experimental rate constant (k, = pressure (CF,CH,/TFC)) vs. pressure for 1,1,2,2-tetrafluorocyclopropane. The curve is the least-squares fit from eq 1.
From this equation, Po equals the limiting high-pressure rate constant, k,", the value obtained being k , = 5.88 x lo3 torr-' on the basis of a fourth-order fit. A plot of k , vs. 1/Pis not a convenient way to display the data due to the compressed nature of the abscissa. Instead, a plot of k , vs. P was preferred and in Figure 2 are shown the experimental points together with the fit from eq 1. A t pressures above 1000 torr a small variation of k , with P is observed, and k , seems to be constant within experimental error. However, at that pressure D / S = 9, a clear indication that the high-pressure region has not been reached. From eq 1, it can be estimated that D / S = 1 at about 5900 torr, a pressure far above the highest pressure used in this work. Conversion of k , from pressure units to s-l requires estimation of the collision number. The collision number, kM, is computed from the following relations: 2o kM =
S A M ' ( ~ X ~ T / ~ A M ) ~ / SAM ' =
GAM
assure the absence of side complications was obtained from plots of D / S vs. time for various conditions. One such plot is shown in Figure 1. From the gas-chromatographic analysis the ratio D / S was calculated. It was then converted to the apparent unimolecular rate constant for decomposition in pressure units by multiplication by the pressure, k , = ( D / S ) P . Considering all of the experimental uncertainties, higher limits to the error in k , were estimated to be about 15% at the higher pressures and 20% a t the lowest pressures used. The experimental results are given in Table I. It is evident that at all the pressures studied multistep collisional deactivation occurs, Le., the experimental rate constants increase with decreasing pressure. Data points in the true high-pressure region (such that k , = constant = k,") could not be obtained and the limiting high-pressure rate constant had to be calculated by regression analysis. The procedure was similar to that employed by Setser et al.19 and consisted of fitting the experimental values to a polynomial by a least-squares procedure. k a = Bo + Pl(l/'P) + Bz(l/P)' + ... + Pn(1/pIn (1)
1000 PRESSURE
=
(UA
+UM)/~
cAM/k
UAM[~"~"(T*)]~''
= (tA/k)(cM/k)"2
M and A stand for the bath gas and the activated molecule, respectively. The selection of the values of u and t / k presents some difficulty. For CzF4,the bath gas in this study, the values u = 4.14 A and t / k = 157 K used by Rabinovitch et al. were adopted.2n On the basis of experimental data, Ireton and Rabinovitch found an empirical correlation between t / k and the boiling point Tb, given by t / k = 72 0.43 Tb, which results in a consistent set of c / k for perfluoroalkane molecules.21 From this expression, t / k = 187 K is obtained for tetrafluorocyclopropane. The molecular diameter for this compound was estimated as u = 4.74 A by comparison of the existing data on a series of hydrogenated and perfluorinated molecules, including alkanes, olefins, and cyclic compounds.22 It is worth noting that an error in the selection of these parameters will have a systematic effect
+
(20) Ireton, R. C.; An-NanKO;Rabinovitch, B. S. J . Phys. Chem. 1974, 78, 1984. (21) Ireton, R. C.; Rabinovitch, B. S. J . Phys. Chem. 1974, 78, 1984. (22) (a) Chan, S. C.; Rabinovitch, B. S.; Bryant, J. T.; Spicer, L. D.; Fujimoto, T.; Lin, Y. N.; Pavlou, S. P. J. Phys. Chem. 1970, 74,3160. (b) Hirshfelder, J. 0.;Curtis, C. F.; Bird, R. B. "Molecular Theory of Gases and Liquids"; Wiley: New York, 1964.
Deactivation of Highly Vibrationally Excited TFC
The Journal of Physical Chemistry, Vol. 87,
TABLE 11: Summary of Molecular and Transition-State Models for 1,1,2,2-Tetrafluorocyclopropane molecule vibrational frequencies (degeneracies), c m - ’
3100 ( 2 ) 1412 (3) 1230 (2) 1005 (3) 772 ( 4 ) 424 ( 5 ) 186 ( 2 )
calcd preexponential factor, s-’ exptl preexponential factor,a s-’ calcd E,, kcalimol exptl E,,a kcalimol
See ref 8.
3100 ( 2 ) 1 6 0 0 (1) 1290 (4) 762 (5) 418 ( 3 ) 265 (2) 128 ( 3 ) 1.85 x 1015 1.86 x
10’5
46.31 48.48 4.9406 0.8524 X 10’
SAM,’ a k M , c s-’ torr-’ a
transition state
Collision diameter.
Collision n u m b e r .
upon k, when expressed in s-l. Calculated RRKM Rate Constants. The RRKM rate constant, kE, at specific energy E is given by
where CP(E+)is the total number of vibrational quantum states of the transition state, N*(E*) is the density of vibrational states of the molecule a t energy E*, u is the reaction path degeneracy, and I+/Z* is the ratio of moments of inertia of the activated complex and the mole~ u l e . 2 ~For the evaluation of CP(E+)and N*(E*) the vibrational frequencies of the activated complex and the molecule are also needed. Normal-mode frequencies for tetrafluorocyclopropane have been reported.24 The vibrational frequencies of the activated complex were selected to give an Arrhenius A factor equal to that reported for the thermal decomposition of tetrafluorocyclopropane, i.e., log A = 15.28. The critical energy for the reaction, E,, was also calculated from the experimental activation energy (E, = 48.48 kcal/mol) to be E, = 46.3 kcal/mol.s The evaluation of kE was performed with an IBM computer, as were all the other calculations. Computations were done by direct count up to 20 kcal/mol and then by the Haarhoff approximation, using a seven-frequency grouped model and a grain size of 350 cm-l. All the parameters relevant to these calculations are presented in Table 11. The method given by Schlag and Haller was adopted for the assignment of the reaction path d e g e n e r a ~ y . ~ ~ The ratio D / S was computed from the matrix formulationZ6 D / S = ( l / w ) C [ k ( I - P + k/w)-lF]i i
where k is a diagonal matrix with elements kE, I is the unit matrix, P is a matrix with elements Pi;, and f is a vector with elements f ( E ) ,the energy distribution function of TFC*. The collisional transition probabilities, Pi;, from state j to i, depend on the model selected. In this work only the stepladder model was used, and the down-transition elements Pi;are defined as follows: Pi; = 1.0 - p;i for i - j = ( m ) d
pij = 0
for i - j # ( h E ) d
(23) Robinson, P. J.; Holbrook, K. A. “Unimolecular Reactions”; Wiley: New York, 1972. (24) Craig, N. C.; Anderson, G. J.; Cueller-Ferreira, E.; Koepke, J. W.; Martyn,P. H. Spectrochim. Acta, Part A 1972, 28, 1175. (25) Schlag, E. W.; Haller, G. L. J. Chem. Phys. 1965, 42, 584. (26) Hoare, M. J. Chem. Phys. 1963, 38, 1630.
No. 20, 1983 3909
where (AE)dis the mean down-energy loss. The up transitions were calculated from detailed balance:
Pi;/pji = gi/gj exp(-&
- Ej)/kT)
gi and E; are the degeneracies and energies of the ith element. Also, the condition of completeness = 1.0) was imposed on the transition probability matrix. The distribution of initial energies of the chemically activated tetrafluorocyclopropane was calculated by constructing a RRKM model for the reverse reaction of the chemical activation step, that is, the decomposition of tetrafluorocyclopropane in CH, + CzFbB This implies that all the reactants are in thermal equilibrium and is justified by the fact that photon energy a t 3200 A is close to the dissociation limit of ketene. Then excess energy of CH2 need not be considered. The distribution function is given by
k,E~~(~) d~ where K ( E ) is thermal Boltzmann distribution for the stabilized molecule and kE’the specific rate constant for the reverse process.23 In order to proceed with the calculation, E-, the critical energy for the reverse process, has to be known and is obtained from the heat of reaction plus the activation energy for the activation reaction. As the heat of formation of tetrafluorocyclopropane has not been reported, Eminwas used as an adjustable parameter, together with ( h E ) d . Exploratory calculations were initially performed with values of Emh from 80 to 100 kcal/mol and ( m ) d from 4 to 12 kcal/mol. Any value higher than 90 kcal/mol produced a rate constant unreasonably high and so the E ~ ,value , was constrained to variation in the range 80-87 kcal/ mol. Several computations were made with different pairs of Eminand ( m ) d . With Emin= 80-83 kcal/mol and ( m ) d values in the range 4-7 kcal/mol, a reasonable fit could be obtained in the intermediate-pressure region but the calculated k, was too high at low pressures and too low at the highest pressures used. Also, calculations with Emin = 87 kcal/mol required (m),= 10 kcal/mol and produced rate constants higher than the experimental values in the whole range. We concluded that Emincould be selected to be in the range 83-87 kcal/mol with ( m ) d between 7 and 10 kcal/mol, respectively. The preferred fit with the present set of effective collision diameters is Emin= 85 kcal/mol with ( m ) d = 9 kcal/mol. The experimental points together with some selected computed results are displayed in Figure 3. Either increasing or decreasing the collision number would result in higher or lower values of Emh,respectively. That this is so can be seen, for example, in Figure 3 with the computed curve for Emin= 87 kcal/mol and (AE)= 10 kcal/mol. It is evident that, although all the experimental points are below the calculated curve, some scaling would produce an acceptable fit. Considering all of these uncertainties we conclude that Emh= 85 f 2 kcal/mol and ( m ) d = 9 f 2 kcal/mol. Unfortunately, the limiting high-pressure region could not be reached in this study, and so a better estimation of the above parameters could not be achieved. The effect of reducing the grain size and the variation of the model for the reverse reaction were also investigated. None of them had a significant influence in the calculations, as expected from the results of other workers. The Arrhenius parameters for the decomposition reaction are very important in the calculations, any change on
The Journal of Physical Chemistry, Vol. 87,
3910
Arbilla et al.
No. 20, 1983 I
W
c Q
11
a 10
s/ D Figure 3. Comparison of experimental data with stepladder calculations for various pairs of E, and step sizes (Enr,/( A€ ),) in kcal/mol: (- -) 83/7, 85/9,(--) 86/10,(-.-) 87/10.
-
demonstrated'O that the decomposition product is in fact CF2CH2and is confirmed by our present results. The infrared spectrum of tetrafluorocyclopropane is at present well-known from a vibrational study of Craig et alez4The bands of the supposed tetrafluorocyclopropane in the chemical activation work do not agree with those reported in that study but seem to coincide with those for hexafluorocyclopropane.n The reason for this misidentification is that only an alumina column was used for analysis. When the first experiments in the present study were performed, we realized that tetrafluorocyclopropane was mostly irreversibly adsorbed on the column (see Experimental Section) and that c-C3F6has the same retention time. This is a frequent problem in gas-chromatographic analysis which emphasizes the need of using different types of columns. Our results clearly show a multistep deactivation process which could be satisfactorily explained with a stepladder model with mean down-energy loss of about 9 kcal/mol and Emh= 85 kcal/mol. With this value and the heat of formation of CH2('A1) and C2F4, AHf" for tetrafluorocyclopropane can be calculated:
(7)
them affecting both Eminand ( AE). Although there is no basis to suspect the Arrhenius parameters, as the reaction was certainly studied in the high-pressure region and over a wide range of temperatures, some computations were made considering the possible uncertainties in both the A factor and the activation energy. The activation energy is probably accurate to f 2 kcal/mol and log A to f0.6. Taking E , = 46.5 kcal/mol and log A (s-') = 14.6 a reasonable fit to the experimental data could be obtained with Emin5 95 kcal/mol and ( h E ) d I13 kcal/mol, whereas with E , = 49.5 kcal/mol and log A(s-') = 15.8 the experimental results could be reproduced with EminI 80 kcal/mol and ( h E ) d 2 5 kcal/mol. Therefore, it is rather unlikely that Emhand ( AE)d could be calculated to better than 85 f 10 and 9 f 4 kcal/mol, respectively. The average energy of the activated molecule, ( E ) ,can be calculated by the addition of E-, the threshold energy for the activation reaction, and the average thermal energy of the activated molecule. Assuming that no excess energy is carried by CH2, one can obtain the average thermal energy from the thermal energy distribution f(E) dE which was computed as indicated above, to yield ( E t h ) = 2.4 kcal/mol. The addition of CH2 to olefins, which is a very fast process, is generally accepted to occur with a very low activation energy and was not considered. Combining all these values, ( E ) = 85.0 + 2.4 = 87.4 kcal/mol; that is 41 kcal/mol above the threshold energy for decomposition of the activated tetrafluorocyclopropane with a probable error of f10 kcal/mol.
Discussion Chemically activated 1,1,2,2-tetrafluorocyclopropane, obtained by the addition of CH2(.'A1) to C2F4, decomposes to yield CF2CH2+ CF,, or stabilizes by a multistep collisional process, as shown by the pronounced dependence of k , on the pressure. The reaction was first studied by Grzybowska, Knox, and Trotman-Dicken~on.~ The sole products found were thought to be tetrafluorocyclopropane and tetrafluoropropene. Also, a plot of D / S vs. 1/P was a straight line in the whole range of pressures studied. At that time, the infrared spectra of both compounds, as well as those of other fluorinated cyclopropanes, were not known, so that identification was tentative. The authors reported the wavenumbers of the main absorption bands. It was further
fifoo(~-C3H2F4)= mf",(CH,)
+ mfOo(CzF4) - Emin
The correct value of AHfoo(CH2, lA1) has been the subject of much controversy in the past and has finally been settled in favor of about 101 kcal/mol, in agreement with requirements of most chemical activation studies.28 Determinations of AHf"(CH2,'Al) with different techniques have yielded values of 101.7,29101.E1,~ and 1O1.g3Okcal/mol and a value of 102.6 kcal/mol has recently been obtained from the molecular beam photodissociation of ketene.31 An average value of 102 kcal/mol is within the experimental error of all these studies and was used for the calculations. For CzF4it is generally accepted that AHf' = -155 kcal/m01'~ and AHfoo= -154 kcal/mol. From the above values and Eminresults AHfoo(c-C3H,F4)= -138 kcal/mol, with an uncertainty of f l 0 kcal/mol, considering the probable error in the determination of Emh.Correction of this value to 298 K leads to AHH,' = -140 kcal/mol. Thus, AH? obtained is 14 kcal/mol higher than previously estimated from group additivity rules and considering an extra ring strain of 4 kcal/mol per fluorine atom on the ring. To be consistent with AHf" = -140 kcal/mol either the ring strain should be increased to about 8 kcal/mol per fluorine atom or the group additivity rules are not adequate for such strained polar compounds. In a chemical activation study of 1,l-dichlorocyclopropane a similar conclusion was attained with an estimated AHf" = 10 kcal/mol vs. AHf' = -3.4 kcal/mol from group additivity.; It must be noted that AH,"depends on the determination of Emin and the difficulty of obtaining this value by this technique has been well documentedS4 In spite of the uncertainties of the method, the experimental results for tetrafluorocyclopropane could not be fitted if Emin > 90 kcal/mol with any reasonable variation of the parameters involved if the Arrhenius parameters are used as reported.8 For instance, with Emin= 95 kcal/mol and ( S ) d = 10 kcal/mol the calculated rate constants at P = 1000 torr and P = 400 torr were 15 and 30 times higher than the experimental values, respectively. Then Emin= 90 kcal/ mol is to be considered as an upper limit giving AH,' = (27) Heicklen, J.; Wachi, F.; Knight, V. J . Phys. Chem. 1965,69, 693. (28) Holmes, B. E.; Setser, D. W. J . Phys. Chem. 1978, 82, 2450. (29) Lengel, R. K.; Zare, R. N. J . A m . Chem. SOC.1978, 100, 7495. (30) Feldmann, D.; Meier, K.; Zacharias, H.; Welge, K. H. Chem. Ph.ys. Lett. 1978, 59, 171. (31) Hayden, C. C.; Neumark, D. M.; Shobatake, K.; Sparks, R. K.; Lee, Y. T. J . Chem. Phys. 1982,76, 3607.
J. Phys. Chem. 1983, 87, 3911-3918
3911
-145 kcal/mol as a lower limit to the heat of formation of tetrafluorocyclopropane. However, if the uncertainties in the Arrhenius parameters are considered, higher and lower values of Emincan fit the experimental results yielding values of AHf0(c-C3H2F4) between -130 and -150 kcal/mol. Considering that the activation energy for the decomposition of tetrafluorocyclopropane is 48.5 f 2 kcal/mol and that E , for the addition of CF, to CH2=CF2 can be estimated as 10 f 2 kcal/m01,~,the heat of reaction of tetrafluorocyclopropane = 38.5 f 4 kcal/mol. With this value and AHfo(CF2) = -43.5 f 2.0 kcal/moP3 and AHfo(CH2=CF2) = 71.5 f 5 kcal/moP2 as estimated by
group additivity, AHfO(c-C3H2F4) = -153.5 f 11 kcal/mol is obtained. This value is 13.5 kcal/mol lower than that calculated from the chemical activation results in this work, although they are both within the error limits. However, it must be noted that the best agreement is obtained with the lower set of Arrhenius parameters. Unfortunately, the thermochemistry is so uncertain that it is difficult at present to make a decision about the best values. Also, if AHf0(CH2)were lower than 102 kcal/mol, a better agreement could be obtained.
(32) Benson, S. W.; O’Neal, H. E. “Kinetic Data on Gas Phase Unimolecular Reactions”; National Bureau of Standards: Washington, DC, 1970. (33) Stull, D. R., Prophet, H., Eds. “JANAF Thermochemical Tables”, 2nd ed.; U.S. Department of Commerce: Washington, DC, 1971.
partial financial support through Programa de Investigacidn Fisicoquimica. Registry No. CH,, 2465-56-7; C2F4,116-14-3; 1,1,2,2-tetrafluorocyclopropane, 3899-71-6.
Acknowledgment. We express our appreciation to Dr. D. W. Setser for providing most of the programs used in the calculations and to the CONICET (R. Argentina) for
Square Wave Voltammetry and Other Pulse Techniques for the Determination of Kinetic Parameters. The Reduction of Zinc( I I ) at Mercury Electrodes John J. O’Dea, Janet Osteryoung,’ and Robert A. Osteryoung Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14214 (Received: December 14, 1982)
Square wave voltammetry was used to determine kinetic parameters for the couple Zn(II)/Zn(Hg). Rapid-scan square wave voltammograms for the reduction of Zn(I1) were analyzed numerically to yield estimates and confidence intervals for reversible half-wave potential (ET1,*), transfer coefficient ( a ) ,and electron-transfer rate constant (he,). Simplex optimization was used to minimize the difference between the experimental voltammogram and that calculated by using the boundary condition for a quasi-reversible reaction. As expected, the kinetic parameters which characterize this reaction were found to be independent of the step height and frequency of the excitation wave form. The utility of rapid-scan square wave voltammetry for kinetic studies at trace concentration levels (3.2 pM) was also demonstrated. The values of Er1/2,a , and hec at 25 “C in 1 M NaN03 (without double-layer correction) were found to be 0.998 f 0.003 V vs. SCE, 0.23 f 0.01, and (4.6 f 0.3) X cm/s, respectively.
Modern theories of electrode reactions predict relationships of kinetic parameters which can be tested experimentally.’ This has heightened interest in obtaining accurate values for these parameters. The range of values reported in the literature for nominally identical systems2B confirms the complexity and difficulty of this straightforward-seeming task. There are three different considerations which enter into the quality of the values of parameters derived from experiment. First, the experiment must be free of chemical artifact; that is, the rate determined experimentally must be characteristic of the electrochemical system as described. For example, reaction rates often depend strongly on trace quantities of surfactants which may be introduced inadvertently. This problem area is highly specific to the laboratory and the experimental system and will be addressed only inciden(1) Hush, N. S., Ed. “Reactions of Molecules at Electrodes”; WileyInterscience, New York; 1971. (2) Tamamushi, R. “Kinetic Parameters of Electrode Reactions of Metallic Compounds”; Butterworths: London, 1975. (3) Meites, L.; Zuman, P., Eds. “Handbook Series in Organic Electrochemistry”; CRC Press: Boca Raton, FL, 1976; Vol. 1, and succeeding volumes. 0022-3654/83/2087-39 1 1$01.50/0
tally here. Second, the mathematical description used to relate the rate of the reaction to the kinetic parameters must correspond to the actual experimental situation. Common problems in this regard include ignoring deviations from conditions of semiinfinite linear diffusion, lack of accurate potential control in transient techniques, and the intrinsic problem of subtracting “background” currents. Third, the data and the mathematical desccription must be brought together in some way to yield values of the kinetic parameters. Published procedures for doing this are uniformly inadequate in lacking a well-defined method for calculating the uncertainty associated with the derived values of parameters. In the following we describe the application of pulse voltammetric techniques, especially square wave voltammetry, for the determination of kinetic parameters. Square wave voltammetry as employed here is a largeamplitude technique carried out at fast scan rates. Thus, it is quite different from the steay-state technique employed by Tamamushi and M a t s ~ d a .Although ~ it can be (4) Tamamushi, R.; Matsuda, K. J. Electroanal. Chem. 1977, 80,
201-8.
0 1983 American Chemical Society
