3898
SIDNEYW. BENRON AND GILBERT HAUGEN
The Elimination of HI? from “Hot” Fluorinated Ethanes.
An Estimation of
the Activation Energies and Rate Parameters’
by Sidney W. Benson and Gilbert Haugen Department of Thermochemistry and Chemical Kinetics, Stanford Research Institute, Menlo Park, California (Received June 4, 1966)
The classical Rice-Ramsperger-Kassel theory of unimolecular reactions is shown to give a quantitative description of the decomposition of a “hot” molecule of CH2FCH2F*. The analysis also makes possible an estimate of the activation energy for the elimination of H F from this molecule within narrow limits: CHZFCH~F + CH2 = CFH HF; Eaot= 62 3 kcal./mole; AE02ss0~.= 8 kcal./mole. From the theory one predicts the observed reductions in the rate of the elimination reactions for the series of “hot” molecules C2He-zFz as R: is increased. A similar analysis gives a theoretical explanation of the observed pressure dependence of the rates of stabilization of the “hot” molecules (CH2CI.CHzC1)*,(CH2C1. CHC12)*, and (CHC12 CHCI2)*. A quantum modification of the classical Rice-RamspergerKassel theory was found necessary when the magnitude of the unfixed internal energy approaches the size of a quantum of vibrational energy. This approximation of the classical theory predicted the correct rate of elimination of a C1 atom from the hot radical (CHCICHC12)*which at the transition state had only 2 kcal./mole of unfixed energy. In these calculations the carbon-carbon bond energy in ethane was assumed to be invariant upon the replacement of hydrogen by halogen atoms.
+
*
Introduction Termination reactions such as radical recombination or disproportionations are strongIy exothermic and give rise initially to very highly excited or “hot” molecules. Although it had been recognized for a long time that such hot molecules might subsequently dem m p x e by unimolecular processes, very few quantitative data have been available for such systems.2 I n contrast to this, an extensive amount of work has been done by Rabinovitch and co-worker~~-~ on the decomposition of “hot” radicals generated mainly by H-atom addition to olefins. A recent papere on the photolysis of CHzFCOCHzF makes available for the first time a sufXcient amount of quantitative data on the decomposition of a “hot” molecule, CH2F-CH2F*, thereby making possible the kinetic analysis of its behavior. In a subsequent note,? it was observed that, whereas CHzF-CHzF* was found to yield CHF=CH2 HF, CHFZCHFz* was completely stable under the same conditions. This appeared to the authors as an anomalous behavior of the latter species.
+
The Journal of Physical Chemistry
It is the purpose of the present paper to make a quantitative examination of the behavior of CH2FCHzF* from the point of view of the classical RiceRamsperger-Kassel theory (RRK) of unimolecular reactions and to show that the behavior of CHF2CHF2* agrees well with the expectations of the RRK theory. In addition, the data will be shown to yield the first reasonably precise value for the activation energy of the normal pyrolysis reaction, CH2F-CH2F-+ (1) This work was supported in part by a Grant No. AP-00353-01 from the Air Pollution Division of the U. S. Public Health Service. and partly by Stanford Research Institute sponsored research project NO. 184531-123. (2) One recent exception is the pyrolysis of ethylene oxide which has been shown to follow a “hot” molecule rearrangement: S. W. Benson, J . C h a . Phys., 40, 105 (1964). (3) B. 5. Rabinovitch and M. C. Flowers, Quart. Rev. (London), 18, 122 (1964).
(4) G. H. Kohlmaier and B. S. Rabinovitch, J. Chem. Phys., 38, 1692 (1963). (5) G. H. Kohlmaier and B. 5. Rabinovitch, ibid., 38, 1709 (1963). (6) G. 0. Pritchard, M. Venugopalan, and T. F. Graham, J . Phys. Chem., 68, 1786 (1964). (7) G. 0. Pritchard and J. T. Bryant, ibid., 69, 1085 (1965).
ELIMINATION OF H F FROM “HOT” FLUORINATED ETHANES
+
CHFCFH HF. No quantitative kinetic data are available on the pyrolysis of alkyl fluorides.
Mechanism The recombination of two CH2Fradicals leads to formation of an excited ethane which can be collisionally deactivated or else decomposed to form vinyl fluoride 2CH2F
3899
2.4 -
TEMP. *K
SLOPE mm-’
-
0049 0 043 0037 0 025 0021
A
295 325 375 426 476 523 551
0
581
-
CURVE NO. I
-
2 3 4
2.0 -
7
-
5 6 8
-0 -0 -e -- -+0
--
X
0015
0 0076 0.0047
i
3
(CHZF-CHZF) *
k- t
7CH2=CHF + H F M + (CHzF-CHtF)* 2 M + CH2F-CH2F (CH2F-CH2F)*
Applying stationary-state kinetics to this scheme we find for the rates of formation of products R(CH2CHF) = k1(CH2FCH2F)*m R(CH2FCH2F) = kd(CH2FCH2F)*ss(M)
(1) (2)
For the ratio of quantum yields this gives @(GH&‘2) - R(CzH4Fz) - h ( M ) a(C2HaF) R(CJW” kr
(3)
where (M)is the weighted sum of the concentration of quenching agents. I n the present instance it will be simply the pressure of reacting ketone (CH2F)&O. Figure 1shows the data of PVG6 plotted acording to eq. 3 and, as can be seen, the data are in good accord a t each temperature with the proposed mechanism. From the slopes of the different lines we can obtain the ratio of rate constants kd/kr as a function oi temperature. I n Figure 2 we note that this is, as expected, a slowly decreasing function of temperature.
Kinetic Parameters The RRKs theory of unimolecular decomposition relates the rate constant k, to the internal energy content of the molecule. This is given by IC, = A r ( l
-
gy-’
=
mmHg
Figure 1. Pressure dependence of the z ~represents ~a. the initial quantum yield ratio i P C a ~ z ~ / O ~ P pressure (mm.) of ketone. Runs with a total pressure of 7 mm. and temperature greater than 476°K. were omitted.
0.05 0.04
(4)
where E* represents the critical energy necessary for decomposition, E represents the internal energy of the molecule, and n is the number of effective oscillators. A , is the frequency factor for the unimolecular elimination. Rabinovitch and c o - ~ o r k e r s ~ -have ~ described the rate of collisional deactivation as a vibration cascade of the excess energy. This introduces too many parameters and is unnecessary for the present systems where the data can be satisfactorily reproduced by assuming deactivation to occur in a “single” collision. The rate of deactivation can be written as kd
P-
(5)
-
‘.g 0.03 E
E
I
0.02
212 0.0I
c
2 T-OK
Figure 2. Temperature dependence of
kd/kr.
(8) 8. W. Beneon, “The Foundations of Chemical Kinetics,” MCGraw-Hill Book Co., Inc., New York, N. Y., 1960,pp. 218-220.
Volume 69,Number 11
November 1966
3900
SIDNEY W. BENSON AND GILBERT HAUGEN
where Z is the number of collisions per second per millimeter and X represents the probability of “complete” deactivation on collision. From a cascade point of view 1/X measures the number of collisions required for deactivation. Combining eq. 3,4, and 5 we can write
0.06 0.04
0.02
The temperature dependence of the ratio k d / k r is now contained in the separate terms A, 2, and E. There is a lack of data on the temperature coefficient of X a t high temperature and a disagreement between theory and experiment, at low temperature. 3-5 Accordingly, it is prudent to neglect the temperature dependence of the collision terms, XZ. These are, in any case, expected to be very much smaller than the temperature dependence of E. We have evaluated E , the total internal energy content of the (CHZF-CHzF)* as follows. We estimate values for Cvvib,the vibrational specific heat of the CHzFradicals, over the temperature range of interest. This allows us to estimate E v i b , the total vibrational energy content of the two radicals, at each temperature. To this we add 3/2RT for translational energy of one radical and another 3/2RT of rotational energy of one radical which are converted into internal energy of the hot molecule. If we define ACvVibas the difference in vibrational specific heat of the two radicals and the “hot”molecule, then we can write
E
=
Eo
+ AC,’ib(T
- 298)
(7)
where Eois the energy change in the recombinati~n.~ Table I gives values of E at different temperatures.
Table I: Value of E a t Different Temperatures
X , OK.
298 325 375 426 476 523 551
581
Thermal energy,’ ACvVib(T- 298), kcal./mole
0 0.5 1.4 2.6 3.9 5.4 6.9 8.1
E, koal./mole
85.4b 85.9 86.8 88.0 89.3
90.8 92.3 93.5
‘The change in the internal energy with temperature was calculated from the relation, ACvvib(T - 298) = 3R( T 298) 2[Cvvib(T)] T - 2[Cvvib(298)J298. Vibrational contribution to heat capacity of CHzF estimated from the measured heat capacity of CHsF. * See ref. 9.
-
The Journal of Physical Chemistry
+
N B ”
0.01 0.008
0.006
0.002
t
0.00I 250
CURVE 2 IO - - - ) CURVE 3 ( 0
-
330
---I
E * = 6 2 kcol/molc,
log lo^
E*= 59 k c d / m o l t , logio
* -6.91 *
-6.44
EXPERIMENTAL POINTS
410
490
570
T-”K Figure 3a. Comparison of the theoretical and observed temperature dependence for n equal to 11.
In Figure 3 the theoretical curves computed from eq. 6 and 7 are compared with the experimental curve represented in Figure 2. The use of a logarithmic plot simplifies the curve fitting. The term, log U / A , shifts the curve vertically by a constant amount and the parameter n changes the slope of the curves. An inspection of Figure 3b demonstrates that the theoretical curve approaches the experimental curves at low temperature when E* is equal to 59 kcal./mole and at high temperature when E* is equal to 65 kcal./ mole. Curve 2 (E* = 62 kcal./mole) in Figure 3 indicates that theoretical fit of the experimental data improves with low temperature and smaller value for n or high temperature and larger value for n. The fact that this analysis does not completely match the experimental data is anticipated since the influence of temperature on the number of effective oscillators and the efficiency of collisional deactivation has been ignored. The variation of number of effective oscillators, n, with temperature is suggested by Figure 3. A collection of harmonic oscillators would be expected to behave in this manner. It would not be fair to include (9) EO = D H o (CHa-CHa) - AnRT = 85.4 kcal./mole. Benson, J . Chem. Educ., in press.
See S. W.
ELIMINATION OF H F FROM “HOT”FLUORINATED ETHANES
390 1
0.08
0.06
0.06
0.04
0.04
0.02
0.02
A n
LL
m I N
5“, N Sv
W
0.01
0.01
0.008
0.008
0.006
0.006
--la
7 0.004 Y
-
cr,
CURVE I
0
( t ---I
CURVE 2 ( 0---I
E*= 65 kcol/mole, loqlo
y*
EL*62 h c ~ l / m o l e , l o q l o ~
.
0.004
t
-8.04 -7.43
0.002
-
0 EXPERIMENTAL POINTS
0 001 250
330
410
490
570
T --OK Figure 3b. Comparison of the theoretical and observed temperature dependence for n equal to 12.
this temperature effect without considering the temperature dependence of XZ/A,. However, the accuracy of this analysis does not seem to warrant the additional complications. The most reasonable value for the number of effective oscillators, n,for analysis of this type is about twothirds of the total number of oscillators; that is, n is equal to 12.1° Once n has been chosen, it is possible to determine a probable value of E* and XZ/A, by obtaining the best fit of eq. 7 to the experimental data. Figure 3b demonstrates an adequate fit with E* equal to 62 f 3 kcal./mole and log XZ/A equal to -7.43 f 0.56. A reasonable value for the frequency factor, A,, of the unimolecular elimination would be 1013.5. Combining this value with that for the collision frequency, 2 = lO6Se6 mm.-‘, allows the magnitude of the collision efficiency X to be estimated. This is shown in Table 11. I n this system the amount of energy that must be removed by collisional deactivation to stabilize the “hot” molecule is much larger than the corresponding quantity in the systems studied by Rabinovitch and K ~ h l m a i e r . ~ -We ~ would expect a much smaller collision efficiency than those suggested by Rabinovitch’s investigations. Accordingly, a value of X between 0.10 and 0.20 seems justifiable. Our original choice of
t
0.00 I 250
CURVE 1
It---)
CURVE 2 ( 0 - - - ) CURVE 3 ( 0
E*:65
E‘:
--- 1 E*:
kcol/mole, IOq,Of
62 kcol/rnole.
10q,O
59 k c o l / m o l t , loq,o
:
- 8 56 Io-
2* 2
:
7.95
- 7.38
-
0 EXPERIMENTAL POINTS
410 T--OK
330
570
490
Figure 3c. Comparison of the theoretical and observed temperature dependence for n equal to 13.
Table 11: Variation of X with Different Choices of n and E*
----
---tI
E*
11
12
13
65 62 59
0.12 0.43 1.3
0.032 0.13 0.41
0.0096 0.039 0.14
E* = 62 kcal./mole and n restriction on value of A.
= 12 is
consistent with this
Calculation of E* An activation energy of 54 f 3 kcal./mole has been calculated” for the addition reaction, H F CZH~ C2H5F. These theoretical calculations yield a similar value for the activation energy of the reaction CHF= . reactions HCl CHCl= CH2 H F C Z F ~ H ~The = - 15.2 kcal./mole) CH2-t CH2C1-CH2C1(AHozNOK. and HC1 C Z H ~ CzCIHs ( A H o 2 9 a=~ ~ .15.5 kcal./
+
+
+
-+
+
-+
-+
(lo! n is a parameter which represents the number of “effective” oscdlators. This ambiguity in the concept of n springs from the use of the classical viewpoint. It has been shown (G. M. Wieder and R. A. Marcus, J . Chem. Phys., 37, 1835 (1962)) that all vibrational modes participate in energy exchange in the active molecule when the quantum treatment is employed. (11) S.W. Benson and G. R. Haugen, to be published. Volume 69,Number 11
November 1966
SIDNEY W. BENSONAND GILBERT HAUGEN
3902
-REPRESENTS STATES AT 298.K --- REPRESENTS STATES THERMALLY ACTIVATED ABOVE 298.K
100
I---
REPRESENTS PROCESS ASSOCIATED WITH THE TRANSITION STATE
COLLISIONAL DEACT IVAT I O N
I
> 60-
0
C Y
W
E 40-I
U
z
Ez
M
20-
0-
(GROUND STATE AT 298' K)
Figure 4. Relationship between E*, activation energies, and internal energies.
mole) liberate nearly the same heat. Thus, it is expected that the heat liberated by the reactions HF C2FHa --t C2F2H4 and HF 4- CZH4 C2FH5, ( h E O 2 9 8 ' K . = -8 kcal./moles) are the same.12 This then gives for the activation energy of C2F2H4 -t C2FH3 HF; the value of E = 62 f 3 kcal./mole. This is in excellent agreement with the value suggested for E* in this paper. The relationship between the two methods for estimating E* is illustrated in Figure 4; consequently, the theoretical activation" energy for HF is confirmed. This the process C2H5F-+ c2H4 value is a reasonable extension of the observed halogen series, Table 111.
+
-+
+
+
Table I11 : Activation Energies for the Elimination of HX from CZH~X'
CsHsX
CZHJ CSHbBr
CsH&I CzHd a
E,,$ (kcal./mole) at 298'K.
49.2 53.9 57.1 62
Difference between consecutive activation energies
4.7 3.2 4.9
S. W. Benson and A. N. Bose, J. Chem. Phys., 39,3463 (1963).
Kinetic Parameters for the Series (CF,Hs+*CF,H3-J * The mechanism for the kinetic behavior of the chemically activated species in the series (CF,Hs+. CF,H&,)*can be separated into two cases.13 The Journal of Physical Chemistry
kd ---f
M -I- GFz+jH~-t-j
The analysis presented in this article can be applied to the comparison of the rates of both elimination, k,, and fragmentation, k + to the rate of collisional deactivation, k d . These comparisons are represented in the equations
I I cfi4F2 (GROUND STATE AT 298" K )
+ (CtFt+j&-t-j)
nR298
(9)
In the case of the fragmentation, the activation energy is zero and the frequency factor is generally about lo1' sec.-'.14 The ratios of the rates k d / k - t and k d / k r aredependent only on the number of effective oscillators, n, and the activation energies for the eliminations, E*. We have calculated values of E* for both cases I and I I . I 1 E* is expected to be nearly the same for the similar molecules of case 11; E* for cases I and I1 are 73.4 and 61.8, respectively. The replacement of a hydrogen atom by a heavier fluorine atom increases the number of effective oscillators by 1 or 2. The probable value of n for the fluorinated ethane series increases as the number of fluorine atoms increases (see Table IV). The trends in the ratio of rates k d / k - t and k d / k r for the series of fluorinated ethanes are depicted in Table V. The influence of the number of effective oscillators on the rates k-t and kr is apparent. The fragmentation rate is enormously reduced as the ineffective C-H oscillators are replaced by more effective C-F oscillators (ie., lower frequency). A similar reduction is observed for the rate of elimination of HF (12) This is also the result anticipated from the law of additivity of group properties (S.W. Benson and J. H . Buss, J . Chem. Phys.. 29, 546 (1958)). (13) The case CFrCFs is not considered here because the elimination of Fz from CzFs is prohibited by the enormous activation energy for this process (239 kcal./mole). See ref. 9 and 11. (14) S. W. Benson, "Advances in Photochemistry," Vol. 2, Interscience Publishers, Inc., New York, N. Y., 1964, Chapter 1.
ELIMINATION OF H F
FROM
“HOT”FLUORINATED ETHANES
and C Z H ~ indicates F~ that, the rate of elimination of H F from C2H3F3 is approximately 0.14 of the rate of elimination from C2H4F2. This is seemingly not in accord with the findings of Alcock and Whittle.’C Their studies indicated a ratio of R(CF3CH3)/R (CFz=CH2) equal to 1.0 for the “hot” molecule, CF3CH8*, over the temperature range 353-488°K. This ratio is smaller than the comparable ratio for the “hot” molecule, CFH2CFH2*. The analysis of Alcock and Whittle’s system is complicat,ed by the presence of two quenching agents, and because of this a weighted sum of the quenching agents must be used in eq. 3
Table IV: Mean Number of Effective Oscillators in Fluorinated Ethanes Molecule
n
9.0 10.5
12.0 13.5 15.0 16.5
18.0
Table V : Ratios of kd/k- and Eq. 8 and 9 at 298°K. Molecule
C2H6 CsHsF CdV” CZH~FB CdU” Ci”s
CzFa
k d / k - t , mm.-’
(1.00)” 1 . 5 x IO’ 1 . 8 x 102 1.8 x 103 1 . 4 x 104 8.9 x 104 5 . 6 x 106
kd/k,
Calculated from
ka/&, mm.-1
1.9 5.9 4.1 2.9 1.8
13
3903
x x x x
10-1 10-3 10-2 10-1
&/k-
5.3 2.5
x
t
103
4.4 x 103 6 . 2 x 103 7 . 8 x 103 6.8 X I O 3
Equation 9 does not represent a satisfactory method for estimating the relative rates, kdlk-t. This inadequacy is a consequence of the discrete distributions of the unfixed energy among the quantum states. This manifests itself when the unfixed energy approaches the size of a quanta. An exact count of the number of configurations of the distribution of the quanta among the active states requires the complete description of the quantum states. T o indicate the influence of the number of active oscillators on the ratio k d / k t , without doing a detailed count, we have computed the ratio kd/k- t relative to the molecule C2Hs.
from the fluorinated ethanes with an increase in the number of effective oscillators. The rate of elimination of H2 from chemically activated ethane is much smaller than that expected from just a consideration of the number of active oscillators. This is attributed to the larger E* for the elimination of HB. This elimination is also deterred by the fast fragmentation of the “hot” ethane molecules. The reported kinetic behavio9J of the series CHZFCH~F,CF&H3, CHFZCHFZ, and CF3CHFzis simply explainable in terms of the change in the number of effective oscillators along this series. Table V demonstrates that the relative rate of elimination and fragmentation for this series is independent of the number of effective oscillators. In view of this, the appearance of elimination products depends on the relative rates of elimination and deactivation, k&,. This quantity is extremely sensitive to the number of fluorine atoms in the “hot” molecule. A comparison of the ratios kd/kr a t 298°K. for C2H4F2
We would have expected a temperature dependence of the ratios kd’/k, and kd“/k, (see Figure 2); this was not observed. This lack of a temperature variation suggests that the ratio R(CH3CF3)/R(CH~CF2) is not simply related to the intrinsic ratio, kd/kr. It would be appropriate at this point to emphasize caution in extrapolating the ratios kd/kr in Table V to other temperatures. I n accordance with eq. 6 and 7 the ratio kd/k, will change with a variation in temperature. The extent of this change will depend on the quantities nand ACvvib. On the basis of these considerations we can state that the “hot” molecules, CHF2CHFz* and CF3CF2H*, wilI be completely stable under the conditions that cause the H F elimination from the “hot” molecule, CHsFCH2F*. This has been experimentally verified for the molecule CHF2CHFr.’ The current investigation (see ref. 7) of the reactions of the “hot” molecule, CF3CF2H*, have failed to detect C2F4. These experiments were not primarily designed to study the elimination reaction, and subsequently experimental justification of the stability of this ‘(hot” molecule is lacking. h comparison of the predicted values of the ratios k d / k r at 298°K. for the “hot” molecules, C2H5F* and CHzF CH&’*, indicates that the rate of elimination of HF from CzH4F2*is approximately 0.14 of the rate of elimination from CzHbF*. The kinptic parameters for the series of chlorinated ethanes are listed in Tables I11 and VI. Introducing these values into ey. 4 allows the comparison of the rates of the chlorinated and fluorinated ethane series (1 I ~ , ( c ~ H ~F )1013.5 k,(C2H5C1)
(
E)(0*15-1)
57 )(1’3-5-1) 85.4
=
1.0
(15) W. G . Alcock and E. Whittle, Tra?as. Faraday SOC., 61, 244 (1965).
Vo1um.e 69,Number 11 November 1986
SIDNEYW. BENSONAND GILBERTHAUGEN
3904
and
Table VI: The Estimated Values or Kinetic Parameters in Eq. 10
kr(CH2FCHZF) 1013e5 -= 1.7 kr(CH2C1CH2C1) (1 - S4)(12-l) Thus, the rate of elimination of HC1 from CHzCl CH2Cl*is approximately 0.082 of the rate of elimination from CH&H2Cl*. This is in agreement with the estimates recently reported16 for this ratio, Icr(CH2C1CH2C1*)/kF(CzH5C1*) 0.095.
Molecule
Log Ar
X
Log Z
E*, koa]./ mole
CH&l*CHzCl CHZCl.CHC12
12.7 12.7 12.7
0.3 0.3 0.3
7.0 7.0 7.0
59 53 57
CHClz.CHC12
E, kcal./ mole
n
85.4 85.4 85.4
12 13 14
The examination of the rate constants for the elimination of HC1 from a series of chlorinated ethanes allows a reasonably reliable evaluation of the paramKinetic Parameters of “Hot” Chlorinated Ethanes eters A , and E*.l* Wijnen” has studied the rate of formation of chlorinThe restrictions on the range of values of X and n are ated ethanes produced by the recombination of chlorinfully discussed in the preceding example. The reasonated methyl radicals. His investigation demonstrated able values X equal to 0.3 and n equal to 12, 13, and a pressure dependence of the normally expected con14 for the molecules C2H4Cl2,CzH3C13, and C2H2CI4, stant ratio of rates of formation of ethanes: R C H ~ ~ C H C I ~ / respectively, allow the demonstration of the pressure [RCHZC~CH~CI]~’~ [RCHCIZCHC~Z]’/~. The mechanism for dependence of this system. Using reported results for the formation and deactivation of the “hot” molecules total pressure of 20 and 4 mm., the rate ratio k A B / is ( I ~ A A ) ~ ” ( ~ B B ) ~can ” be calculated: p = 20 mm., kI ~ A B / ( ~ A A ) ~ ’ ~ ( ~ B B= ) ~ ’ 1.76; ~ and p = 4 mm., k A B / 2CHzC1-% CHzC1CH2C1*-+ CHC1=CH2 HC1 ( I G A A ) ~ ’ ~ ( ~ B B ) ~ ’ ’ = 1.77. This number is very near the statistical value of 2 expected for the ratio. CH2C1CHzC1* 31 % CHzClCH2CI ill
+ +
+
+ CHClz -% CH,Cl.CHClz* k,:
Decomposition of “Hot” CHCICHC12* Knoxlg has determined the rate of decomposition of CHCl=CHCl+ HC1 chemically activated CHClCHC12* radicals formed in the C1-catalyzed isomerization of cis-to trans-dichloro11 CH2C1CHC12*-% CHzCl.CHCl2 M ethylene, l o g e 4 see.-’. To simplify the analysis, we kr” 2CHCl2 -% CHCl2CHCl2*-+ CC12=CHC1 HC1 have assumed that E* is equal to the internal energy, E, (zero activation energy for the decomposition), M CHClZCHC12* -% AI CHClzCHC12 where the energy, Eo, represents the change in energy for the reaction CHClCHClz + CHCI= The steady-state ratio R c H ~ ~ c H c I ~ / [ R c H ~ C ~ . C H Z Ccontent ~]~~~’ CHCl C1 at 0°K. (Eois about 20 kcal./mole).20 [ R C H C I Z C H C I ~ ] ’ / ~can be represented as a function of The internal thermal energy in this radical under the the total pressure and these primary rate constants experimental conditions reported by Knox was about 2.0 kcal./mole. This is the magnitude of the vibraRCH~C ~CHC i2 1% tional quanta in the radical. Consequently, the classical [RCH~C i . c H C 1 1’” [RCHC12CHCI~ eq. 4 is not the appropriate formula to use for calculating the rate of this decomposition (see footnote in CH2C1
+
+
+
+
+
+
JCAB
(3
+
Substitution of eq. 4 into this expression rfduces the equation to the form (see Table VI)
AB
+ ~)~/‘(1.00 + p)’”
(4.08
kAA1/’kBB”’
The Journal o j Physical Chemistry
(14.8
+p)
(11)
(16) D.W.Setser, R. Littrell, and J. C. Hassler, J. Am. Chem. Soc., 8 7 , 2062 (1965). (17) Presented by M. H. J. Wijnen at Sixth Informal Photochemist Conference held at the Department of Chemistry, University of
California at Davis, Davis, Calif. (18) 9. W. Benson, “The Foundations on Chemical Kinetics.” McGraw-Hill Book Co., Inc., New York, N. Y.,1960,p. 258,ref. 9. (19) J. Knox, Department of Chemistry, University of Edinburgh, Drivate communication. (20) Energy of this reaction was estimated from bond energies in the series CHFCH-H, CHFCH-Cl, CHsCHr-H, CHaCHrCl, and C H z C H y H ; see ref. 9.
ELIMINATION OF HF FROM “HOT” FLUORINATED ETHANES
Table V). A precise counting of the number of ways of distributing the energy among the quantum states will modify eq. 4 in the following manner8s21
where q is the number of vibrational states that can be excited by the energy E - Eo and likewise s is the number excited by energy E; hv, is the energy of the i vibrational state, E is the total internal energy, and Eo is the internal energy at 0°K. The quantity ( ( E - Eo)/hv,) depicts the maximum number of quanta in the vibrational state i that can be excited by energy E - Eo. The fundamental frequencies of vibrations of the molecule CH2C1CHC122*were assumed to represent those of the radical, CHC1CHC12, with the exception that one C-H stretching and two G H bending frequencies should be omitted in view of the differences in numbers of H atoms (see Table VII). Table VII : Estimated Fundamental Frequencies of Vibrations of CHClCHClz Cm.-1
Cm.-1
Cn-1
3014 2998 1437 1306 1260
1161 1050 936.5 792.5 742
676.5 422 390 332 255
Counting the number of these quantum states that can be excited by energies E (22 kcal./mole) and E Eo (2 kcal./mole) establishes the number of effective oscillators as 15 and 6, respectively. Combining eq. 12 with these kinetic parameters (E = 22 kcal./ mole, E - Eo = 2 kcal./mole, q = 6, s = 15, and A = 1013e5)gives a mean predicted rate of decomposition for this radical of logs2sec.-l. Using eq. 9 with an effective number of oscillators, n, of 10 predicts a rate of lo7.*sec.-1, an obvious example of the error that can
3905
appear when the unfixed energy approaches the magnitude of the vibrational quanta. Equation 12 predicts a rate of 1.6 X lo9 sec.-l, in excellent agreement with Knox’s experimental value 2.5 X lo8sec.-l. Giles and Whittle23have studied the photolysis of mixtures of acetone and hexafluoroacetone. Their investigation established that the behavior of the “hot” molecule CH3CF3* is similar to that of the molecule CH2FCH2F*. The ratio k d / k r at 423°K. was reported for the following quenchers : acetone, hexafluoroacetone, nitrogen, and perfluorocyclohexane. The observed temperature coefficient for this system allows the adjustment of these ratios to 298°K. These adjusted values are : perfluorocyclohexane, 2.1 X lo-’ (rnm.-l) ; hexafluoroacetone, 1.4 X lo-’ (mrn.-’) ; acetone, 6.5 X (mm.-l); nitrogen, 1.1 X (mm.-’). This demonstrates the variation of the quenching efficiency with molecular structure. In particular, the relative values of X for this series of quenchersZ3 are : perfluorocyclohexane: 1.0; hexafluoroacetone, 0.75; acetone, 0.39; nitrogen, 0.075. The value of k d / k , observed for “hot” CH3CFs*, where the quencher is CF3COCF3, is a factor of 0.5 smaller than the predicted value (see Table V). The calculation of the ratio kd/kr is sensitive to the value of n ; if this parameter for the molecule CH3CF3 is reduced to 13.0, then the calculated value of the ratio k d / k , decreases to 1.5 X lo-’ mm.-’. Consequently. upon consideration of the allowable margin of variation in the kinetics parameters n and X, the concord between the theoretical model and the actual system is quite reasonable. Acknowledgment. We are indebted to Dr. G. 0. Pritchard for his constructive comments on the correlation of the material presented in this paper with the experimental observations. (21) R. A. Marcus and 0. K. Rice, J. Phys. Colloid Chem.. 55, 894 (1951). (22) R. H. Harrison and K. A. Kobe, J. Chem. Phys., 2 6 , 1411 (1957). 61,1425 (1965) (28) R. D.Giles and E. Whittle, Trans. Faraday SOC.,
Volume 60,Number 11
Nozember 1965
