472
M. V. C. Sekhar and E. Tschuikow-Roux
A similar equation can be written for Rn but Dz is small and the spacial term is considered negligible.
dRn/at = 0 -kz(Rn),n, ikin, (20) Thus, eq 19 reduces to eq 11 and the solution is eq 12 with k replaced by 2k. Equation 20 shows that (Rn), is constant and exhibits no spacial distribution even though n , might (eq 12). The development of the equations, for time-dependent solutions with the assumption of small diffusion coefficients for secondary active species, is obvious even though the solutions may not be possible in closed form. The important point to realize is that these considerations with regard to the approach to steady state, in the steady state, and the decay from steady state can be experimentally minimized if the spacial distribution of the initially formed species is eliminated. This can be accomplished in three ways: poisoning the walls, working at low pressure (high diffusion coefficients), or working at high reactant concentrations so that the volume termination always dominates the diffusional term. The first two are designed to eliminate the effect through minimization of h, and the last, through maximization of k/D. Acknowledgment. The authors acknowledge the support of the Atomic Energy Commission under Contract No. AT(ll-1)-3242for this work.
(3) R. M. Noyes, J. Amer. Chem. SOC.,73, 3039 (1951). (4) D. A . Frank-Kamenetskii, "Diffusion and Heat Exchange in Chemical Kinetics," Princeton University Press, Princeton, N. J., 1955. (5) The mathematics required for this model is discussed in detail in (a), H. S. Carslaw and J. C. Jaeger. "Conduction of Heat in Solids, Oxford University Press, London, 1959; (b) J. Crank, "The Mathematics of Diffusion," Oxford University Press, London, 1956; (c) N. W. McLachlan. "Bessel Functions for Enaineers." Oxford Universitv Press, London, 1955. H. Motz and H. Wise, J. Chem. Phys., 32, 1893 (1960). J. V. Michael and D. T. Osborne, Chem. Phys. Lett., 3, 402 (1969). W. Braun and M. Lenzi, Discuss. Faraday Soc., 44,252 (1967). F. Stuhl and H. Niki, J. Chem. Phys., 57, 3671 (1972). J. A. Eyre, T. Hikida, and L. M. Dorfman, J. Chem. Phys., 53, 1281 (1970), J. A. Cowfer, D. G. Keil, J. V. Michael, and C. Yeh, J. Phys. Chem., 75, 1584 (1971). J.-H. Hong, Ph.D. Thesis, University of Detroit, 1972. J. R. Barker, D. G. Keil, J. V. Michael, and D. T. Osborne, J. Chem. Phys., 52, 2079 (1970). J. R. Barker and J. V. Michael. J. Opt. SOC. Amer., 58, 1615 (1968). D. Davisand W. Braun, Appl. Opt., 7, 2071 (1968). M. J. Kuryio, N. C. Peterson, and W. Braun. J. Chem. Phys., 53, 2776 (1970). W. Braun, A. M. Bass, and D. D. Davis, J. Opt. SOC.Amer., 60, 166 (1970). B. Khouw, J. E. Morgan, and H. I. Schiff, J. Chem. Phys., 50, 66 (1969). Dah Yu Cheng and P. L. Blackshear, Jr., J. Chem. Phys., 56, 213 (1972). A. Geib and S. K. Kim, J. Chem. Phys., 55,4935 (1971). B. J. Wood and H. Wise, J. Phys. Chem., 66, 1049 (1962). K. J. Laidler, "Chemicai Kinetics, McGraw-Hill, New York, N. Y., 1965, Chapter 6. D. 0. Ham, D. W. Trainor, and F. Kaufman, J. Chem. Phys., 53, 4395 (1970). -, S:-Dushman and J. M. Lafferty, Ed., "Scientific Foundations of Vacuum Technique," Wiley, New York, N. Y., 1962, Chapter 6. J. 0. Hirschfelder, C. F. Curtiss, and R. 8. Byrd, "Molecular Theory of Gases and Liquids," Wiley, New York, N. Y., 1954. \
References and Notes (1) N N Semenoff, Acta Physrcochim , URSS, 28, 93 (1943) (2) T L Hill, J Chem Phys, 17, 1125 (1949)
~
Kinetics of the Shock-I nduced Competitive Dehydrofluorinations of 1, I ,2-Trifl~oroethane'~ M. V. C. Sekharlb and E. Tschuikow-Roux* Department of Chemistry, University of Calgary, Calgary, Alberta, Canada, T2N 7N4
(Received August 23, 7973)
The thermal decomposition of 1,1,2-trifluoroethane between 1100 and 1250°K gives three isomeric difluoroet hylenes as the major carbon-containing products. The rate constants for the three molecular eliminaCHzCF2 HF (kl), CHzFCHFz trans-CHFCHF HF ( k z ) , and tion processes CHzFCHFz cis-CHFCHF HF (k3) have been evaluated to be log (kllsec-l) = 13.0 f 0.5 - (65.4 f CHzFCHFz 2.6)/2.303RT, log (kzlsec-1) = 14.1 f 0.5 - (69.1 f 2.9)/2.303RT, and log (k,/sec-1) = 13.5 f 0.5 (64.5 2.6)/2.303RT where R is in kcal mol-I. The experimental Arrhenius parameters were found to be in good agreement with those predicted theoretically using a modified semiion pair model. The observed differences in the three rate constants can be explained in terms of intramolecular interactions of the fluorine atoms.
-
-+
+
Introduction In recent years the shock-tube technique has been SUCcessfully employed for studying the thermal decompositions of several fluorinated hydrocarbons.2-4 In these studies, it has been shown that the molecular elimination of hydrogen fluoride is the predominant reaction, the side reactions involving C-C bond rupture becoming more imThe Journalof Physical Chemistry, Voi. 78, No. 5, 1974
-
+
portant with increase in temperature. Molecular dehydrofluorination in several fluoroethanes has also been observed in chemical activation ~ t u d i e s . ~ - ~ Among the fluoroethanes, 1,1,2-trifluoroethane is unique in that it is the only member of the series that undergoes dehydrofluorination giving more than one olefin. This was confirmed in two independent chemical acti-
473
Dehydrofluor'inationsof 1,1,2-TrifIuoroethane vation s t u d i e ~ 7 3on ~ CH2FCHF2 which decomposed to three isomeric difluoroethylenes: 1,l-difluoroethylene and Of these the two geocis- and trans-1,2-difluoroethylenes. metric isomers, cis- and trans-CHFCHF are formed through transition states that are diasterioisomers and hence provide the advantage of making a comparison of two reactions in which the same bonds are made and broken. The 1,l-difluoroethylene, CF2CH2, is also formed in the decomposition of l,l,l-trifluoroethane.9 Thus the isomeric trifluoroethanes CH3CF3 and CHzFCHFz constitute an interesting pair to study the influence of the position of the fluorine atom on the dehydrofluorination reaction. The present work deals with the hitherto unreported pyrolitic decomposition of 1,1,2-trifluoroethane.
cluded that the following reactions represent the principal mechanism of decomposition of CHzFCHFz below 1250°K.
+
CH&F, HF trans-CHqCHF c~sCHFCHF Using the theoretical mass balance CH,FCHF,
+ HF
+ FF
+
(1) (2)
(3)
+
[CHZFCHF,], = [CHZFCHFZJ [CH,,CFzI, [t-CHFCHF], [c-CHFCHF], (I)
+
the three first-order rate constants are given as
+
h, = [R,/(tZR,)I In [1 Z R J h z = [R2/(tZR,)]In [l Z R J h, = [R,/(tZR,)] In [I ZR,1 are product/reactant ratios at time t
+ +
Experimental Section
The reactant CH2FCHF2 (Phillips Petroleum Co.) and t h e product gases, CH2CF2, and cis- and trans-CHFCHF (Peninsular Chem Research Inc.) were purified by bulbto-bulb distillation using methanol and n-pentane slush baths. The purity of these gases was determined by gc analysis to be better than 99.5%. Reaction mixtures of -0.5 and -1% trifluoroethane in argon (Matheson, 99.998% stated purity) were used for quantitative kinetic data runs. In the case of exploratory runs above 1300°K a 5% CH2FCHFz-Ar mixture was used for total product analysis. The reaction mixtures were prepared in large stainless steel tanks and were allowed to mix thoroughly before use. The modified single pulse shock tube, the recording devices, and the operating procedure were the same as described in previous communications.lOJ1 After initiation of the shock, the ball valve was closed, isolating the reaction mixture in the end section. Samples of the fully mixed gases were then withdrawn and analyzed in two ways: qualitative product identification was carried out by means of a gc-coupled mass spectrometer (Finnigan Model 3000) and the results were verified using authentic samples; quantitative analyses by means of a Varian 1740 gas chromatograph equipped with a flame ionization detector were carried out using a 12-ft Porapak Q column and temperature programming (45-150'). Standard calibration mixtures were used to correct for the sensitivity of the flame ionization detector. Hydrogen fluoride was not identified quantitatively because of its reactivity with the shock tube walls. Data Reduction and Results. The reflected shock conditions were calculated from measured incident and reflected shock velocities.12 The reaction dwell time and the cooling corrections were evaluated by a previously described rnethod.l0v13 Between 1100 and 1250°K the three isomeric difluoroethylenes were the major reaction products. However, above 1300"K, as many as 15 products were formed. Some of these were identified as CH3F, CH2F2, CHF3, CHzCHF, CFzCHF, CHzFCHzF, CHF2CHF2, CH3CHF2, and C F ~ C H Z FUnfortunately, . the formation of these compounds could not be studied in detail but it does indicate the presence of a reaction channel involving C-C bond scission (see Discussion). Below 1250"K, the three difluoroethylenes constitute nearly 93% of the total products formed. The rest of the reacted mixture consisted primarily of vinyl fluoride and trifluoroethylene. By analogy with the behavior of the rest of the fluoroethanes and coupled with the fact that the difluoroethylenes were the predominant products, it is con-
5 ki
where the Rl
RI
(111 (111)
(N)
= CCH,CF,I,/[CH,FCHF,lt
R, = [trans-CHFCHF],/[CH,FCHF,I, R3 = [c~s-CHFCHF],/[CH~FCHF,~, The rate constants and various shock parameters are listed in Table I. Discussion
The unimolecular character of the hydrogen fluoride eliminations from fluoroethanes has been demonstrated by several workers.14J5 Among the other possible primary processes, the homolytic bond scissions of the CF and CH bonds are energetically unfavorable. By analogy to the thermochemical data on other fluoroethanes16J7 the bond energies of the C-F and C-H bonds in CHzFCHFz are estimated to be 110 and 103 kcal mol-l, respectively. Homolytic initiation followed by radical chain reactions could, of course, lead to a n apparent overall activation energy considerably lower than the bond dissociation energies. However, the presence of such chain reactions would be indicated by the formation of other fluorohydrocarbon products in addition to the fluoroethylenes, and these were not observed at temperatures below 1250°K. As for the C-C bond scission reaction channel, it has been s h 0 w n ~ 3 ~ 8 Jthat Q this reaction becomes competitive with H F eliminations only at temperatures above 1300°K. The presence of small amounts of vinyl fluoride and trifluoroethylene below 1300°K indicates the onset of this process and as expected at higher temperatures the C-C bond rupture does become important as evidenced by the large number of products. The radical chain reaction can therefore be excluded in the temperature range below -1250°K and the formation of the CzHzF2 isomers explained through reactions 1-3. The rate constants listed in Table I were obtained by neglecting the two side products C2H3F and C Z F ~ HIn. order to test whether this exclusion would affect the results, the calculations were repeated using a new mass balance equation
and it was found that the rate constants were affected only in their last digits. Another possible side reaction that need be considered is the consecutive HF elimination from the product difluoroethylenes. However, earlier studies on fluoroethylenes20.21and specifically 1,l-difluoroethylene20have shown that these reactions require much higher activation enerThe Journal of Physical Chemistry, Vol. 78, No. 5, 1974
474
M. V. C. Sekhar and E. Tschuikow-Roux
Table I: Experimental Results Mach no.a
Wll
2 .'lo 2.13 2.13 2.16 2.15 2.20 2.18 2.19 2.19 2.20 2.20 2.20 2.20 2.20 2.22 2.22 2.20 2.21 2.20 2.21 2.22 2.23 2.23 2.23 2.23 2.23 2.25 2.24 2.25 2.24 2.25 2.27
Product ratiosb
W Z I p6,a Torr
1.24 1.25 1.26 1.25 1.26 1.24 1.26 1.27 1.26 1.28 1.26 1.26 1.27 1.29 1.27 1.27 1.27 1.28 1.28 1.27 1.28 1.28 1.29 1.30 1.28 1.28 1.27 1.28 1.29 1.30 1.30 1.29
3321 4318 4370 2715 4465 2772 2779 2822 2796 2862 2853 2837 2856 2884 2931 2907 2871 2911 2881 2897 2941 2978 2705 3022 2995 2992 3022 2820 3075 3052 3095 2820
T6,a OK
1101
1127 1130 1139 1157 1163 1167 1169 1172 1179 1182 1182 1182 1188 1189 1190 1190 1192 1192 1196 1199 1202 1214 1218 1219 1220 1220 1223 1228 1234 1236 1246
t,
R1
Rz
Ra
k,Csec-1
k], sec-1
kz, sec-
0 .009Bd
0 .00230 0.00195 0 .00254 0.0126 0 ,00609 0.00554 0.0105 0.0210 0.00835 0.0149 0.00696 0.0120 0 .0144 0 .0109 0 ,0390 0.0315 0.0156 0.0457
0 .00461 0 .00451
9.98 12.8 15.7 31.9 30.5 44.4 49.8 64.0 68.9 67.7 69.1 82.8 63.7 98 . O 109 94.9 103 128 85.3 81.8 134
1.24
2.98 3.58 4.64 10.4 9.17 12.5 15.2 20 .o 21.4 19.9 20.9 26.7 19.9 31.6 34.2 31.7 33.9 41.9 25.9 26.7 43.8 36.2 56.6 64.7 47.4 51.3 52 .0 69.8 55.4 62.4 76.6
~SEC
409 377 379 544 402 141 457 552 188 511 130 309 405 183 571 555 220 655 185 572 589 554 562 549 456 479 565 564 547 555 555 473
0 ,0O06Od
0 .00105d 0.00422 0 .00229 0.00233 0 .00330d 0.00675 0 .00281d 0.00684 0 . 00262d 0 .00412d 0 .005Ed 0 .00365d 0.0131 0.00918 0 ,00534d 0.0137 0 , 00422d 0.00890d 0 ,0143 0.0130 0.0151 0.0194 0 .0142d 0 .0176d 0.0176 0.0174 0.0162 0 .0182d 0.0218 0 10234
0.0117
0,0226 0.0449 0.0341 0.0533 0.0601 0 ,0397 0.0524 0.0548 0.0580 0.0475 0,0510 0 .0665 0 ,0761
0.00517 0 ,0229
0.0123 0.0125 0.0212 0.0408 0.0164 0.0299 0.0142 0.0216 0.0275 0.0201 0.0747 0.0555 0 ,0278 0.0833 0 ,0239 0 ,0406 0.0812 0 ,0595 0.0950 0.1071 0.0692 0.0957 0.0957
111
170 197 144 158 156 209 168 192 225 300
0,100 0 ,0828 0 .0903 0.110
0.132
1.OB 1.88
3.37 3.36 5.05 4.68 6.27 7 .OO 8.93 7.59 9.04 6.95 10.3 11.2 9.01 11
12.3 9 .oo 10.1
13.7 13.5 15.7 20.4 16.6 16.7 16.3 20.6 18.5 21.9 24.7 30.2
100
k3,
sec-
5.76 8.10 9.21 18.1 18 . O 26.8 29.9 37.7 40.5 38.9 40.7 47 . O 36.8 56.1 63.2 54.1 58.1 74.3 50.5 45.6 76.8 61.3 98.2 112 79.9 90.2 87.9 118 94.2 108 124 169
Wil and W?Idenote, respectively, incident and reflectedshock Mach numbers relative to laboratory coordinates (reference speed of sound: argon at 298'Kj. R3 = [cisPIand 2'6 refer to pressure and temperature in the reflected shock zone. Ri = [CHzCFrl/[CH2FCHFzl; Rz = [truns-CHFCHFI/[CHzFCHFzI; kz k3. I -1% CH?FCHF?in Ar. Rest of the runs were made with -0.5% CH?FCHF?in Ar. CHFCHF]/[CH?FCHF?]. Overall rate constant, k = ki a
+ +
gies than their saturated analogs and occur only at temperatures above the range of this study. Yet another possible side reaction is the cis-trans isomerization of the 1,Z-difluoroethylenes. The rate constants228 and the activation energies for these reactions are of the same order of magnitude as those of reactions 1-3. However, when the rate constants k l , k2, and k3 were recalculated taking into account the cis-trans isomerization reactions, it was found again that this affected the k values only in their last digits.22b Thus the three reactions 1-3 represent the only main processes that occur in the decomposition of 1,1,2trifluoroethane below 1250°K. The temperature dependence of the three rate constants is shown in Figure 1 and a least-squares analysis of the data gives log (kllsec-l) = 13.0 f 0.5 - (65.4 f 2.6)/ 2.303RT, log (kZ/sec-l) = 14.1 f 0.5 - (69.1 f 2.9)/ 2.303RT, and log (kS/sec-l) = 13.5 A 0.5 - (64.5 A 2.6)/ 2.303RT where R is in kcal mol-l and the error limits are standard deviations. a,p us. a,a Eliminations. Recent experiments on vibrationally excited haloethanes produced by chemical activation have i n d i ~ a t e d 2 3 . the ~ ~ occurence of three-center (a,a)HX eliminations in competition with the more common four-center (01,a)eliminations. This type of threecenter elimination is, in principle, possible with CHzFCHFz CH,FCF
+ HF +
(4)
.. CHCHFz HF (5) The a,a elimination is followed by rapid rearrangement of t h e carbene to give the olefin. CH2FCHF2
The Journal of Physical Chemistry, Vol. 78, No. 5 , 1974
TABLE 11: Ratios of C Z H Z X Isomers ~ Produced in the Decompositions of CHzXCHXzMolecules X
Temp, OK
F F F F
393-597 293 1100-1250
c1
298
Asym:trans:cis
1:1.06:3.12 1:3.8:6 1:2.7:4.6 1:2:6 1:2.1:3.2
Ref
8 7 This work Free rotation5
24
a Based on the assumption that the three conformers d, e, and f have equal probability of decomposition which implies roughly equal energies for H F elimination and free rotation about the C-C bond, the probability of decomposition of anyone conformer is 1/3. Since trans-CHFCHF can only he formed from the e form, and since two of the three ways in which this conformer eliminates lead to trans-CHFCHF the probability of its formation (2/3j (1/3j = Z/Q. Similarly the probability of formation of CHsCFz which can be formed only from the e conformer is l / g . Finally, since the d and f conformers can decompose in only one way giving rise to cis-CHFCHF, the cis isomer has a probability of formation of 2(1/3) = 2/3. Hence the ratio asym:trans:cis = 1:2:6.
CH,FCF (6)
CHCHF~
It has been argued24 that carbenes such as CH2FCF are thermodynamically more stable than CHFzeH due to A bonding between the halogen and the vacant p orbital of the carbene,25 and hence reaction 4 is more likely to occur than reaction 5. Thus with CD3CH2F only four-center eliminations have been observed.26 In the present case, it is not possible to distinguish between three- and four-center eliminations. However, Kim, et a1.,26 have shown that
475
Dehydrofluorinations of 1,1,2-Trifluoroethane the three-center process in the case of CDaCHF2 is 18%of the total rate. After correction for the intramolecular isotope effects, a n estimate for the a,a contribution of 10% was obtained in the case of CHsCHF2. By inference, we therefore conclude that the experimental Arrhenius parameters for CHzFCHF2 obtained in this study are a close estimate for the a,@process. T h e E f f e c t of Rotational Isomerism. The product distribution observed in this investigation is compared with other related systems in Table 11. Unlike the rest of the fluoroethanes, CH2FCHF2 undergoes HF elimination to give three different products depending upon the rotational conformation of the reacting molecule. Microwave spectral studies2' on CH2FCHF2 indicate that there are three stable forms of the molecule represented by the following Newman projection formulae. H
H
H
I
I
I
-
7
1.5 -
0D 7 N
.x
b
-
2 1.0-
CY
s 0.5 .
F H a b C Based on calculations the two conformations a and c which are enantiomorphic are suggested to be more stable that the form b in contrast to the 1,2-difluoroethane rotational isomers. The three conformations d, e, and f correspond to the three maxima in the potential for internal rotation with the lower maximum corresponding to the e form. The planar four-center cyclic transition state requires that the H and F atoms forming hydrogen fluoride depart from the same side of the incipient double bond and such a transition state can be formed only with the three conformations d, e, and f. Of these the optically acH
2.0-
80
8 5
(io4
Temperature dependence of the rate constants for H F elimination from CH2FCHF2: squares, k l ; triangles, k3; circles, k3. Filled symbols refer to runs with 1% reactant in Ar; open symbols refer to r u n s with 0.5% reactant in Ar. Figure 1.
TABLE 111: Evaluation of Entropies of Activation, A S * (gibbs mol-') at 1200'K HF elimination products from CHzFCHFz
C-C torsional frequency, cm-1 Shir
165' 5.2 7.5
248b 4.4 7.5
AS,,t*
N O
N O
N O
ASaym*'
0 -3.8
Log Aoaiod, sec-l Log Aexpt, sec-1
f
tive d and f forms eliminate HF to give cis-1,2-difluoroethylene, whereas the conformer e dehydrofluorinates to give either trans-1,2-difluoroethyleneor 1,l-difluoroethylene. However, since the activation energies for the elimination reactions are large compared to the potential barrier for internal rotation, the relative populations of the ground state conformations are not reflected in the proportion of the final products.28 If there were free rotation about the C-C bond and if the activation energies for the eliminations were about equal, then one would expect a product ratio of asymmetric:trans:cis equals 1:2:6. The experimental ratio is 1:2.7:4.6and shows the effects of the hindered rotation and the small differences in the activation energies for the three eliminations. As seen from Table 11, the agreement between the three studies on the observed product ratios is only qualitative which is probably due to the wide difference in the temperature ranges of these studies. A Factor Calculations. The preexponential factor A is related to the entropy of activation A S * by the relation
A
=
(ekT/h) exp(AS*/R)
(VI)
and a rigorous evaluation of A S * would require a normal coordinate analysis on the transition state and the reac-
cis-
CHFCHF
357a 3.7 7.5
Astotal*
e
transCHFCHF
CHzCFz
Stors*
d
3.0
T ~, O) K - '
2.8 0.5 13.9 14.1
13 . O
1.4 -1.7 13.5 13.5
a S. Brodersen and A. Langseth, J . Mol. Spectmsc., 3, 114 (1959). N. C. Craig and J. Overend, J. Chem. Phys., 51,1127 (1969). The transition state leading to CHzCFz does not have any optical isomers, n* = n = 1 and also (./a*) = 1. For the formation of trans-CHFCHF, n* = 2, n = 1,and ( u / u * ) = 2, while the cis-CHFCHF, n* = n = 2 and (u/u*) = 2.
TABLE IV: Thermochemical Values5 (kcal mol -1) Fluoroethane
CHICHF CHICHFz CHzFCHzF CH3CF3 CH2FCHFz CHzFCF3 CHF~CHFZ
AHf"211
-62.5 -118.0 jz 1 - 103.7 i 2b -170.6 i 1" -158.9 jz 1 -211.8 jz 2 b -201.1 i 2'
Fluoroethylene
CzH4 CzH3F CHzCFz CHFCHF CzHFz HF
AHf
a 211
12.5d -31.6d -82.5 i 2.4 -75.26 -118.5 k 0 . 7 -64.Sd
All values taken from J. R. Lacher and H. A. Skinner, J. Chem. Soc. A , 1034 (1968), unleas specified otherwise. Derived from thermochemical calculations. Based on group additivity contributions derived from AHfom values for CzHe ( -20.2) and CzFe (-321.0 f 1). Reference 34. e Based on group additivity tables of Benson.34 a
'
tant. In view of the uncertain geometry of the activated complex, the much simpler group frequency method of Benson and O'NealZ9 was adopted to compute the entropies of activation. According to this method AS* is given by The Journal of Physical Chemistry, Vol. 78, No. 5, 1974
476
M. V. C.Sekhar and E. Tschuikow-Roux
TABLE V: Arrhenius P a r a m e t e r s f o r HF Eliminations f r o m Fluoroethanes Activation energy, kcal mol-1 Fluoroethane
CHgCHzF
C products
Edcd
CzH4
60.5
CHaCHFz
61.3
CHzFCHzF CHgCF3
CzHaF CHzCFz
CHzFCHFa
CzHzFzb CHzCFz ~~uTzs-CHFCHF cis-CHFCHF CzHF, CzHF,
CHBFCFI CHFzCHFz
56.9 67.7
67.5 69.1 73.0 77.9
Esxptl
62.6 58.2 59.9 61.9 65 .O 61.9 f 1.8 62.9 61.4 73.6 68.7 f 2 . 4 65.9 f 2 . 6 65.4 f2.6 69.1 f 2 . 9 64.5 f 2 . 6 7 0 . 7 i= 1 . 7 69.4 f 3.1
Log A , wc-1
MethodC
14.4 13.3 13.4 13.3 13.5 13.9 f 0 . 3 13.4 12.1 13.8 14.0 f0 . 4 14.0 f0 . 5 13.0 f0.5 14.1 f0 . 5 13.5 f 0 . 5 13.4 f 0 . 3 13.3 f 0 . 3
FS SP _ST FS ST SPST SP FS ST SPST SPST SPST SPST SPST SPST SPST
Ref
14
-
2
3 14 3 a 15 14 3 9 This This This This
work work work work
4 18
a E. Tschuikow-Roux, W. J. Quiring, and J. M. Simmie, J. Phys. Chem., 75,3195 (1971). Overall rate constant for the formation of CzHzFe isomers. FS = flow system; SP = static pyrolysis; ST = comparative shocktube; SPST = single pulse shock tube.
* - Shlr)+ ASint+ R In (n*r/n~*)(VII) where (Stor,* - S h i r ) is the entropy change in going from AS*
=
(S,,,,
the hindered internal rotation of the ground state to the torsional mode of the complex, AS,,,* is the intrinsic entropy change of the vibrational modes in going from the ground state t o the transition state, and the last term is the contribution due to symmetry changes. In the above equation, u and u* are the overall symmetry numbers and n and n* are the number of optical isomers of the ground and transition states, respectively. ASint*was calculated using the equation
1
i
where the vibrational frequency assignments were made by comparison with other fluoroethanes.lQ Stor,* was computed using torsion frequencies of 3/2-order bonds which were taken as half the torsion frequency of the corresponding olefin.29 The calculation of S h l r is involved due to the presence of more than one minimum in the potential function for internal rotation and hence an indirect method was adopted for its computation. Using the experimental entropy of activation for reaction 1 s h i , was evaluated from eq VI1 and VI11 to be 7.5 eu a t 1200°K. This value was then used in the subsequent calculations for reactions 2 and 3. The details of the calculations are given in Table 111. The predicted values for the preexponential factors agree very well with the experiment. Activation Energy Calculations. Maltman and Tschuikow-Roux30 have proposed a modification to the semiion pair model of Benson and Bose31 for the calculation of activation energies for addition reactions of olefins including halo-substituted polar olefins. The major aspect of this modification lies in the fact that the partial formal charge separation is treated as a variable of the system rather than being held constant and that true generalized bond order conservation is invoked. The necessary input parameters are the bond energies and bond lengths of the bonds undergoing change in the reaction. The partial formal charge separation was calculated from parameters related to these quantities. This method has been found to be very successful with the addition reactions of hydrogen halides to various olefins. According to the method, the activation energy for the The Journal of Physical Chemistry, Vol. 78, No. 5, 1974
addition reaction, Ead, is given by A
1 =1
where the El represent the bond energies of the four partial bonds and Edjp is the energy contribution due to the interaction of the two induced dipoles. The bond energies for the partial bonds were calculated using a bond-energybond-order relationship similar to that of Johnston.32 The dipole-dipole interaction was approximated to the interaction of two point dipoles of the same magnitude and orientation situated at the center of the two breaking bonds. The activation energy for the elimination reaction, Eel, was then calculated from Ead and the heat of reaction The heats of reaction for the elimination processes were calculated using either known values33 of heats of formation or values derived from the group additivity method of B e n ~ o n .The ~ ~ various AHfo values used are listed in Table IV and the calculated activation energies are given in Table V. Unfortunately the calculations could not be carried out for all the reactions in Table V, as reliable structural parameters for some of the fluoroethylenes are not available. The experimentally observed activation energy difference of 4.6 kcal mo1-I between trans- and cis-CHFCHF is a t first surprising. The two transition states are diastereoisomers and both reactions involve the breaking and the formation of the same bonds. However, the transition state for reaction 3 can be stabilized through p-p ineraction35 between the unshared electron pairs of the fluorine substituents, whereas such interaction is not possible with the transition state for reaction 2. Additional support that the reaction path leading to the cis olefin is one of lower energy is suggested by the fact that the cis-CHFCHF is more stable than the trans isomer. The increased stability of the cis isomer has been explained36 in terms of resonance contributions from the ionic forms
where the interaction between the two dipoles is energetically more favorable in the cis than in the trans isomer.
477
Dehydrofluorinations of 1 ,1,2-Trifluoroethane TABLE VI: Dehydrofluorination R a t e C o n s t a n t Ratios for 01- and /%Fluorine Substitutions at 1200°K
CHaCFa
CHaCHFz
CHzFCHFz
0.07
1
0.24
CHzFCFa
CHzFCHFz
CHFzCHFz
0.03
1
0.05
Comparison with Other Systems. Table V summarizes the rate constants for the thermal elimination reactions of fluoroethanes: As may be seen, the position of the fluorine atom does not significantly change the activation energy for HF elimination. Thus between the isomeric di- and tetrafluoroethanes the difference in the activation energies is only about 1 kcal mol-1, which is well within the experimental uncertainty. Between the isomeric trifluoroethanes, the difference is somewhat larger, -3 kcal mol-I. The effects of a- and p-fluoro substitutions are illustrated in Table VI, where the rate constant ratios correspond to a mean temperature of 1200°K. Unlike in the case of chloro- and bromoethanes, in fluoroethanes both a a n d p fluorinations decrease the rate of elimination. The following sequence shows the percentage increases in activation energy for a- and p-fluorine substitutions.
2 CH,CHF, 3 CH,FCHF,
CH3CF3
CHzFCFB2 CH,FCHF2 @+ CHF,CHF, The more pronounced effect with the first series can be attributed to the larger change in the atomic charge densities in the rearrangement of the fluorine atoms in CzH3F3 than in CzHzF4. Based on microwave spectra, the C-F bond length in CH3CF3 has been reported37 to be 1.335 f 0.005 A whereas in CHzFCHFz, the C-F bonds are 1.37 f 0.01 A and 1.35 f 0.01 in the CHzF and the CHFz groups, r e s p e c t i ~ e l y .In ~ ~ analogy with the fluorinated methanes, the shorter C-F bonds reflect an increase in the positive charge on the carbon atom and a strengthening of the C-F bond. Also the polarization along the C-C bond in CHzFCHFz is expected to be smaller than in CH3CF3 which would tend to lower the C-C bond dissociation energy.
Acknowledgments. We wish to thank K. R. Maltman of this laboratory for helpful discussions and theoretical calculations of activation energies, and Dr. K. H. Tung for help with the computer program. References and Notes (1) (a) Work supported by the National Research Council of Canada (b) Abstracted, in part, from Ph.D. Thesis of M. V C. Sekhar, University of Calgary, 1973. (2) D. C. Montagne and R. Walsh, Ann. Rep. A, Chem. SOC.(London), 175 (1971)
(3) P. Cadman, M. Day, A. W. Kirk, and A . F. Trotman-Dickenson, Chem. Commun., 203 (1970). (4) G. E. Millward and E. Tschuikow-Roux, J. Phys. Chem., 76, 292 ( 19 7 2). (5) J. A. Kerr, A. W. Kirk, 8. V. O'Grady, D. C. Phillips, and A. F. Trotman-Dickenson, Discuss. Faraday Soc., 44, 263 (1967). (6) H. W. Chang and D. W. Setser, J. Amer. Chem. Soc., 91, 7648 (1969). (7) (a) J. T. Bryant, B. Kirtman, and G. 0. Pritchard, J. Phys. Chem., 71, 1960 (1967); (b) G. 0. Pritchard and J. T. Bryant, ibid.. 72, 1603 (1968). (8) D. C. Phillips and A. F. Trotman-Dickenson, J. Chem. SOC. A, 1144 (1968). (9) E. Tschuikow-Roux and W. J. Quiring, J. Phys. Chem., 75, 295 (1971). (10) E. Tschuikow-Roux, Phys. Fluids, 8, 821 11965). (11) J. M. Simmie, W. J. Quirina, and E. Tschuikow-Roux, J. Phys. Chem., 73,3830 (1969). (12) E. Tschuikow-Roux, J. M. Simmie, and W. J. Quiring, Astronaut. Acta, 15, 511 (1970). (13) G. E. Millward and E. Tschuikow-Roux, Int. J. Chem. Kinet., 4, 559 (19721. (14) D. SGnesi, G. Nelli, and R. Fontanelli, Chem. lnd. (Milan), 50, 619 (1968). (15) J. A. Kerr and D. M. Timlin, int. J. Chem. Kinet., 3, 427 (1971). (16) B. de 6.Darwent, Nat. Stand. Ref. Data Ser., Nat. Bur. Stand., 31 (1970). (17) J. A. Kerr, Chem. Rev., 66, 465 (1966). (18) G. E. Millward, R. Hartiq, and E. Tschuikow-Roux, J. Phys. Chem., 75, 3195 (1971). (19) E. Tschuikow-Roux, G. E. Millward, and W. J. Quiring, J. Phys. Chem., 75,3493 (1971). (20) J. M. Simmie and E. Tschuikow-Roux, J. Phys. Chem., 74, 4075 119701 (21) .j -M;'Simmie, W. J. Quiring, and E. Tschuikow-Roux, J. Phys. Chem., 74, 992 (1970). (22) (a) P. M. Jeffers and W. Shaub, J. Amer: Chem. Soc., 91, 7706 (1969). (b) In this treatment we have not taken into account the possibility of HF-promoted isomerization of the 1,2-difiuoroethylenes, as noted by one of the reviewers. I t is felt that our mode of product analysis does not provide enough information to estimate this possible effect. (23) M. J. Perona, J. T. Bryant, and G. 0. Pritchard, J. Amer. Chem. SOC.,90, 4782 (1968). (24) K. C. Kim and D. W. Setser, J. Phys. Chem., 76, 283 (1972). (25) J. F. Harrison, J. Amer. Chem. Soc., 93, 4112 (1971). (26) K. C. Kim, D. W. Setser, and B. E. Holmes, J. Phys. Chem., 77, 725 (1973). (27) (a) I. A. Mukhtarov and R. I . Mukhtarov, Opt. Spectrosk., 19, 979 (1965); (b) I. A. Mukhtarov, ibid., 20, 352 (1966); (c) Doki. Akad. Nauk SSSR, 151, 1076 (1963); (d) I . A. Mukharov and R. I. Mukhtarov, ibid., 180, 150 (1968). (28) D. Y. Curtin. Rec. Chem. Progr., 15, 111 (1954). (29) H. E. O'Neal and S. W. Benson, J. Phys. Chem., 71,2903 (1967). (30) (a) K. R. Maltman and E. Tschuikow-Roux, to be submitted for publication; (b) K. R. Maltman, M S c . Thesis, University of Calgary, 1973. (31) S. W. Benson and A. N. Bose, J. Chem. Phys., 39, 3463 (1963). (32) H. S. Johnston, "Gas Phase Reaction Rate Theory," Ronald Press, New York, N. Y., 1966. (33) J. R. Lacher and H. A. Skinner, J. Chem. SOC.A, 1034 (1968). (34) S. W. Benson, "Thermochemical Kinetics," Wiiey, New York, N. Y., 1968. (35) W. A . Sheppard and C. M. Sharts, "Organic Fluorine Chemistry," W. A. Benjamin, New York, N . Y., 1969. (36) (a) N. C. Craig and E. A. Entemann, J. Amer. Chem. SOC., 63, 3047 (1961); (b) H. G. Viehe, J. Dale, and E. Franchlmont, Chem. Ber., 97, 244 (1964). (37) W. F. Edgell, G. B. Miller, and J. W. Amy, J. Amer. Chem. Soc., 79, 2391 (1957). (38) I. A. Mukhtarov, R. I. Mukhtarov, and E. I. Mukhtarov, izv. Akad. Nauk Azerb. SSR, Ser. Fiz.-Tekh. Mat. Nauk, 74 (1967).
The Journal of Physical Chemistry, Voi. 78, No. 5, 1974
