Equilibrium of the CF3CH3 il2 Reaction
(17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29)
(30) (31) (32)
2315
activation energies for c-C&T and c-C&T were assumed to be the same as for c-C& and c-C& R. C. Lord and I. Nakagawa, J. Chem. Phys., 39,2951 (1963). E. B. Wilson. Jr., J. C. Decius, and P. C. Cross, "Molecular Vibrations," McOraw-Hill, New York, N.Y., 1955, p 182. S. C. Chan, B. S.Ravinovitch, J. T. Bryant, L. D. Spicer, T. Fujimoto. Y. N. Lin. and S. P. Pavlou, J. phys. Chem., 74,3160 (1970). J. D.Rynbrandt and 6. S. Rabmvttch,J. Phys. Chem., 74, 1679 (1970). D.W. Setser and E. E. Sitfed, J. Chem. Phys., 57,3623 (1972). H. W. Chang, N. L. Craig, and D. W. Setser, J. Phys. Chem., 76, 954 (1972). Reference 9, p 315. W. Forst. "Theory of Unimolecubr Reactms," Academic Press, New York, N.Y.. 1973, p 225. H. vanweyssenhoffand E. W. Schhg, J. Chem. phys., 50, 729 (1973). A. M. Halpern and W. R. Ware, J. Chem. Phys., 53, 1969 (1970). C. J. Sneed and H. H. Harris, J. Chem. phys., 60, 1355 (1974). The small difference arises from the fact that the previous calculation dd not quite match the experimental points at D/S = 1, ref 2b. T. Valencich and D. L. Bunker, Chem. H y s . Left.,20, 50 (1973); T. Valencich and D. L. Bunker, J. Chem. phys., 61, 21 (1974); T. Vabncich, Ph.D. Thesis, University of California, Irvine. Calif., 1974 (university Microfilms, Ann Arbor, M i . ) . L. M. Raff, J. Ctym. Phys., 60, 2220 (1974). The threshold for T-fora substitution in CD, is also 35 kcal/mol; C. C. Chou and F. S. Rowbnd, J. Chem. Phys., 50,2763 (1969). P. J. Estrup and R. Wolfgang, J. Amer. Chem. Soc.,82, 2665 (1960); R. Wolfgang, J. Chem. Phys., 39, 2983 (1963).
(33) See the trajectuy resub of ref 29 and 30. (34) R. N. Porter, J. Chem. Phys., 45, 2284 (1966): R. N. Porter and Sinan Kunt. bid., 52,3240 (1970). (35) The experimental results with w h i i we are primarily interested are the values of D/S for c-C&T and c-C&T measured for samples simultaneously containing c-C4H8 and c-CP8.4 In these mixtwes both mdecules are e x w to the same tritlum atom flux and the DIS values have been measured for equivalent experimental conditions. However, the D/S values for C-CIH~T in pwe c-C4Hs3 and in C-CIH~-C-C& mixtures" are the same, M i t i n g the T atom flux and the deactivation processes of c-C"!+T do not differ appreciably in the two systems. (36) The distance of the H or D atom from the cyclobutane center of mass is 2 A. (37) T. Valencich and D. L. Bunker, ref 29, find at a T-atom energy of 200 kcallmol Walden inversion substlutions resuits in the ejected atoms canyirig an average fractiin of 0.20 of the incident energy with a largest fraction of 0.48.For substiution with retention the fractions are 0.25 and 0.62, respectively. These fractions change very little over a 500 kcal/mol range of T-atom energies: e.& for retained substitutions the smallest average fraction of energy carried by the ejected atom is at 130 kcallmol and equals 0.22, with a largest average fraction at 400 kcal/md equal to 0.36. (38) P. J. Kunb. E. M. Nemeth. J. C. Polanyi, and W. H. Wong, J. Chem. phys., 52, 4654 (1970); f que+ 0.57, 0.26, 0.42, and 0.38 at 46, 92, 138, and 277 kcal/mol, respectively. (39) E. K. C. Lee and F. S.Rowland, J. Amer. Chem. Soc., 85, 2907 (1963): E. K. C. Lee, G. Miller, and F. S.Rowland, ibid., 87, 190 (1965): J. W Root and F. S.Rowland, J. Phys. Chem., 74,451 (1970).
+
+
Thermochemistry of Gas-Phase Equilibrium CF3CH3 l2 = CF3CH21 HI. The Carbon-Hydrogen Bond Dissociation Energy in 1,l ,I-Trifluoroethane and the Heat of Formation of the 2,2,2-Trifluoroethyl Radical E-Chung Wu and Alan S. Rodgers' Thermodynamics Research Center, Department of Chemistry, Texas A 8 M University, Coliege Station, Texas 77843 (ReceivedApri7 7. 1974)
+
The equilibrium constants for the gas-phase reaction CF3CH3 I2 = CFsCH2I+ HI have been determined spectroscopically over the temperature range 730-775 K. The entropy of CF3CHzI was estimated and combined with known entropies for the other reagents and the experimental equilibrium constants to yield M r 0 ( 7 5 0 ) = 16.0 f 0.5 and f l r 0 ( 2 9 8 )= 15.3 f 0.5 kcal mol-'. This result yields DH02g8(CF3CHpH) = 106.7 f 1.1kcal mol-', indicating a marked strengthening of the C(sp3)-H bond dissociation energy with 6 fluorine substitution. This value for the C-H bond dissociation energy was combined with known thermochemistry to yield the heat of formation of the 2,2,2-trifluoroethyl radical, .Wfo(CF&H2, g, 298) = -123.6 f 1.2 kcal mol-'.
Introduction In a recent analysis of the kinetic data (both thermal and chemically activated) on the unimolecular decomposition of l,l,l-trifluoroethane to HF and 1,l-difluoroethenel the enthalpy of formation of l,l,l-trifluoroethane was derived as -178.2 f 1.6 kcal mol-l in excellent agreement with calorimetric data' corrected to the most recent values for ,lHfo(HF, aq, 298).3 Also, the study of the kinetics of the reaction of 2,2,2-trifluoroethyl iodide with HI4 has resulted in DHD29s(CF3CHpI)= 56.3 f 1 kcal mol-'. Consequently, this study of the equilibrium CFSCHS + 1, = CFSCH2I
+
HI
(1)
was undertaken to determine not only AHfo(CF3CH21, g,
Experimental Section l,l,l-Trifluoroethane and 2,2,2-trifuoroethyl iodide were obtained from PCR Inc. and hydrogen iodide was obtained from Matheson Co. All of these materials were purified by vacuum distillation. Iodine was purified before use by vacuum sublimation. The experimental apparatus and procedure were the same as described in our previous work,* except that the formation of CF3CHzI and HI were followed spectrophotometrically at 2600 A. Preliminary experiments indicated that the equilibrium was far to the left (reaction 1) so that The Journalof Physical Chemistry. Voi. 78. No. 23 1974
E-Chung Wu and Alan S.Rodgers
2316
TABLE I: Data for Equilibrium Studies of t h e Reaction CFsCH, IS = CFICHSI HI
+
+
PO P" P Temp, ( I 2 ) , (RH),(HI), O K Torr Torr Torr 776
752
732
24.7 24.4 24.1 23.6 19.6 15.5 14.8 10.1 24.3 23.9 19.9 19.7 19.5 10.3 25.4 21.2 20.7 20.7 20.7 20.5 20.1 10.4 9.9 5.1
305.3 182.6 120.4 396.4 328.4 308.5 348.6 393.4 419.2 109.6 173.6 354.8 41.2 334.7 251.2 320.8 109.3 127.3 261.5 131.5 119.4 263.1 148.6 238.4
0.76 0.58 0.45 0.83 0.72 0.55 0.68 0.61 0.83 0.51 0.52 0.62 0.30 0.58 0.68 0.59 0.33 0.50 0.61 0.50 0.39 0.55 0.48 0:37
In Kea
AHo, Atliz, sec kcal,' mol Calcd Obsd
16.64 1 3 . 3 -9.48 -9.50 16.68 17 -9.56 16.76 21 -9.52 16.70 11.7 -9.43 16.55 1 2 . 8 -9.67 16.93 1 3 . 2 -9.31 16.37 1 2 . 5 -9.29 16.35 1 1 . 7 -9.60 16.27 32 -9.24 15.74 63 16.04 50 -9.44 -9.82 16.61 35 - 9 . 1 1 15.54 103 -9.24 15.74 3 6 . 3 -9.53 15.72 96 16.24 84 -9.89 -9.94 16.32 144 -9.28 15.36 134 -9.60 15.82 94 - 9 . 3 1 15.40 132 -9.69 15.96 138.6 -9.11 15.11 9 3 . 4 -8.77 14.61 124 -9.10 15.10 98 Av 16.0 i. 0 . 5
12 15 12 13 12 12 12 12 33 60 48 36 120 36 105 84 140 80 90 150 190 96 144 84
even with high temperatures and partial pressures of the reactants, the optical density (OD) of the products at 2600 was 0.1 OD units or less. Furthermore, 2,2,2-trifluoroethyl iodide decomposed at the high temperatures used, consequently its extinction coefficient was determined at lower temperatures and extrapolated into the experimental temperature range by assuming that the molar extinction coefficient at the maximum (2600 A) would be temperature independent. The decomposition of 2,2,2-trifluoroethyl iodide was greatly inhibited in the presence of I2 so in an experiment at, e.g. 750 K, one would observe an initial, and fairly rapid, increase in OD in the first 5-10 min of reaction, followed by a very much slower, but steady, increase in OD. The former was presumed due to reaction 1 while the latter was attributed to the decomposition of the CFSCH~Iformed. The data were interpreted as follows. An approximate half-life of the initial OD increase was estimated and five half-lives were marked off. The value of the OD at five half-lives was taken as the equilibrium value for reaction 1 and recorded. Then the half-life of the reaction based on (OD) equilibrium was determined and recorded. Equilibrium partial pressures were calculated from the absorption coefficients and the assumption that the partial pressures of HI and CF3CH21 were equal. This, and the initial partial pressures of 12 and CF3CH3, permitted the calculation of the equilibrium constants for reaction 1.
Results The experimental results obtained for reaction 1 are summarized in Table I. The observed change in OD at equilibrium was of the order of 0.05-0.10 OD units, measured to a precision of f0.01 OD units. Thus, the partial pressures of HI have a precision of f10-20% and the equilibrium constants, which depend upon the square of HI CPHI), H ~ I have a precision of partial pressure (since P _ C F ~= f20-40%. Data with such a large variance can still yield The Journal o f Physical Chemistry, Vol. 78. NO. 23. 1974
free energy changes with a precision of fl kcal mol-', but cannot be used in a Van't Hoff plot to determine both AS," and AH,'. Thus, entropy data for reactants and products are needed to yield the desired AH,". The thermodynamic functions of HI and Ip are well known5 and those for C F ~ C Hhave B been evaluated using the same procedures as in the recent calculations for chloroethanes.6 The entropy at 298 K and heat capacity at various temperatures for C F B C H ~has I been estimated by group additivity methods? The relevant thermodynamic data are summarized in Table I1 and lead to hS,O(l,T) = 1.2 + 1 , 5 h ( T / 3 0 0 ) 300 5 T 9 800 (2) Equation 2 may be combined with the experimental values of AG,"(l, T ) to yield AH,"(l, T ) , given in the sixth column of Table I. The mean of these results and its standard deviation is AH,"(l, 750) = 16.0 f 0.5 kcal mol-'. From Table 11, one can calculate A C , O = 1.5 f 1 cal mol-' K-1 from 750 to 298 K, so that AH,"(l, 298) = 15.3 f 0.5 cal mol-'. The equilibrium constant for reaction 1 at the mean temperature, 750 K, is given by K , = 10°'56-16'oi8 (0 = 2.3RTkcalmol") (3) It is not possible to verify that the system is at equilibrium by a study of the reverse reaction. However, the kinetics of the reverse reaction have been determined4 so it is possible to check the validity of the equilibrium constant by comparing the observed and calculated times required for HI and CF3CHzI to reach 50% of their equilibrium values (Atllz). It is to be noted, that while the experimental equilibrium constants show a barely discernable trend in this temperature range, the values for At 112 (column 8, Table I) increase by a factor of 10 with increasing temperature. The mechanism for this reaction has been shown to be4 12 + M + 21 + M KIZ CF,CH,
+
I
CF$H,
+
I,
+ CF,CH~ + +
HI
(a, b)
CF,CH~I + I
(c, 4
and K - - - - 100.56-16-0/8(T) = 750K I - Kbk, From previous work4 k , = 10'1.
50-19
k,/kb =
q/8
&)f-1sec-1
10O.fl5*i.O/S
(3)
(4)
(5)
so that k
-
a -
1011-4-36.9/8
;21-lsec-l
(6)
From a steady-state treatment of the reaction mechanism, one has
(CF CH,I)(HI)
-
mhlmll
(7)
Because of the small extent of reaction (see Table I) equilibrium concentrations of CF3CH3 and 1 2 are essentially equal to their initial concentrations; and, if one lets X = (HI) = (CF3CHzI) then eq 7 becomes
Equilibrium of the CF3CH3
+
12
Reaction
2317
TABLE 11: Thermodynamic Data for the Reaction CF3CHs
+ Iz
=
AHi O (298),
S" (298),
Compd
kea1 mol - 1
cal K -1 mol - 1
CF;CH3.
-178.2 & 0 . 4 14.9 6.3
68.7 62.3 49.4
Izb
HIb CF~CH~IC
+ HI
CFaCH21
C,"(298),
cal K
mol - 1
C,' (800) , cal K-l mol-'
18.8
32 .0 9 .0 7.6 35.1
8.8 7.0 21.9
82.8
a B. J. Zwolinski, private communication, Thermodynamic Research Center, Department of Chemistry, Texas -4 8: M University. * Reference 5 . c Estimated, S. W. Benson, et al., Chem. Rev., 64, 279 (1969).
+
Equation 8 may be integrated from X = 0 a t t = 0 to X = O.5Xe, at t = At112 to yield A t l 1 ? = (Xm In 3) '(2kaK121'2(I?)il' '?(CF3CH,),) (9)
Finally, one may substitute -Y, (Ki(I?),(CF,CH,),)'" so that Atl,, = (Ki"21n3)/ (2k,K,,*'2(CF,CH,),"2)
(10)
The values of At112 were calculated from eq 10 and are given in column 'iof Table I (KI~''*was taken from ref 5). The good agreement between the observed and calculated values confirms the fact that the experimental data of Table I do, indeed, correspond to equilibrium conditions for reaction 1.
Discussion The result, AHr0(1,298) = 15.3 f 0.5 kcal mol-', can be combined with the data of Table I1 to yield Wf0(CF3CH2I, g, 298) = -154.3 f 0.7 kcal mol-'. Also, the enthalpy change for reaction 1can be expressed as AH,O(l, 298) = DH"(CF3CHz-H) + DH' (I,)- DHO(CF,CH, -I) - DH" (H -I) (11) The values are DH0298(12) = 36.2,5 DH02g8(HI) = 71.3,j and DH0298(CF3CH2-I) = 56.3 f l 4 kcal mol-', thus DHo298(CF3CHpH) = 106.7 f 1.1 kcal mol-'. This latter value may be combined with lHfo(CF3CH3, g, 298) of Table I1 and l H f o ( H , g, 298) = 52.lj to yield lHf0(CF3CH2,g, 298) = -123.6 f 1.2 kcal mol-'. The value for the C-H bond dissociation energy (BDE) in l,l,l-trifluoroethane, DH0298(CF3CHeH) = 106.7 f 1.1 kcal mol-', i s unexpectedly high. This is, after all, a 3 substituted ethane and, it may be recalled, /3 substitution with methyl groups ( e g . , neopentane) leaves the C-H BDE nominally unchanged.8 Quite apparently, this is not the case for /3 fluorine substituents. This high value for the CH BDE is, however, in good agreement with data on the bromination of CF3CH3 obtained by Coomber and Whittle.9 Their results for reaction 12, which lead them to proCF3CH3 + Br ==+ CF,CH,
-
HBr
(12) pose that DHo298(CF3CH2-H) I 110 kcal mol-' are log (k 12/mol-' sec-') = 11.0 - 23.5/8 ( T ) = 650 K. Using the results of this work and l H f o ( B r )and (HBr) of ref 5 one obtains AHr0(12, 298 K) = 19.2 & 1.2 kcal mol-'. Taking ACp0(12) = +1 cal K-l,j one calculates AHro(12, 650) = 19.6 f 1.2 kcal mol-' and, therefore, E-12 = E12 1 H r o ( 1 2 , 650) = 3.8 f 1.3 kcal mol-'. This value is in line
with that obtained for CF3CF2 HBr ( E , = 3.1 f 1 kcal mol-l)lo by Whittle and coworkers at similar temperatures. It has already been noted that the C-C BDE in l,l,l-trifluoroethane was much larger than expected from group additivity considerations and that this added strength was attributed, primarily to attractive dipole-dipole interactions in the l,l,l-trifluoroethane molecule.1 It is interesting to speculate along similar lines in attempting to explain the unexpected strength of the C-H bond also. Certainly, calculations of the charge distribution in l,l,l-trifluoroethane a t the CNDO/2 level of approximation with standard geometryll yields the /3 carbon negative and the hydrogen positive. However, the charge on the hydrogen is small and the electrostatic attraction is approximately 1 kcal mol-'; this is in the right direction. but not nearly large enough. There are, however, other changes taking place in the dissociation reaction 13 which could CF3CH3
-
CF,bH, - H
(13)
contribute to the strengthening of the C-H bond ( i e . , to the enthalpy of reaction 13). If the carbon atom p to the fluorines becomes less negatively charged in changing from sp3 hybridization in the reactant to sp2 in the product, then the dipole-dipole energy (attractive) would be less in CF3CH2 than in CF$H3. This energy has been estimated at -6 kcal mol-' in CF3CH3' SO that a significant contribution to the enthalpy change of reaction 13 would be possible. While we hope to be able to quantify these speculations in the near future, we have at least shown that they are in the right direction and, taken together, could be of the correct size.
Acknowledgment. The authors wish to express their appreciation to the Robert A. Welch Foundation for support of this research.
References and Notes (1) A. S. Rodgersand W. G.F. Ford, Int. J. Chem. Kinet., 5, 965 (1973). (2) V. P. Kolesov. A . M. Martynov, and S. M. Skuratov, Russ. J. Phys. Chem.. 39, 223 (1965). (3) G. K. Johnson, P. N. Smith, and W. N. Hubbard, J. Chem. Tbermodyn., 5, 793 (1973). (4) E-Chung Wu and A . S. Rodgers, lnt. J. Chem. Kinet., 5, 1001 (1973). (5) D. Stull, Ed., "JANAF Thermochemical Tables," Dow Chemical Co., Midland, Mich. (6) J. Chao, A. S. Rodgers, R. C. Wilhoit. am3 B. J. Zwolinski, J. Phys. Chem. Ref. Data, in press. (7) S. W. Benson, "Thermochemical Kinetics." Wiley, New York, N.Y., 1969. (8) D. M. Golden and S.W. Benson, Chern. Rev.. 69, 125 (1969). (9) (a) J. W. Coomber and E. Whittle, Trans. Faraday SOC., 62, 1553 (1966): (b) J. C. Amphlett and E. Whittle, Trans. Faraday SOC., 64, 2130 (1963).
(10) K. C. Ferguson and E. Whittle, J. Chem. SOC.,Faraday Trans. 7, 68, 295 (1972). (11) J. A. Pople and D. L. Beverage, "Approximate Molecular Orbital Theory," McGraw-Hill, New York. N.Y., 1970.
The Journal of Physical Chemistry Vol 78 N o 23 1974
