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The Journal of Physical Chemistry, Vo/. 83, No. 20, 1979
to competitive molecular halogen elimination, as seen in this case.
This work was by the National Research Council of Canada. We also thank Dr. T. Yano for helpful discussions. References a n d Notes (1) T. Ichimura, A. W. Kirk, G. Kramer, and E. Tschuikow-Roux, J . Photochem., 6, 77 (1976). (2) D. Salomon, A. W. Kirk, and E. Tschuikow-Roux, Int. J. Chem. Kinet., 9, 619 (1977). (3) D. Salomon, A. W. Kirk, and E. Tschuikow-Roux, J . Photochem., 7, 345 (1977). (4) K. A. Holbrook and A. R. W. Marsh, Trans. Faraday Soc., 83, 643 (1967). (5) D. W. Setser and J. C. Hassler, J . Phys. Chem., 71, 1364 (1967). (6) S.W. Benson and H. E. O’Neal, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 21 (1970). (7) T. Ichimura, A. W. Kirk, and E. Tschuikow-Roux, Int. J. Chem. Kinet., 9, 697 (1977).
T. Yano and E. Tschuikow-Roux (8) T. Ichimura, A. W. Kirk, and E. Tschuikow-Roux, Inf. J. Chem. Klnet., 9, 743 (1977). (9) P. Cadman, A. W. Kirk, and A. F. TrotmanDickenson, J. Chem. Soc., Faraday Trans. I, 72, 996 (1976). (10) T. Ichimura, A. W. Klrk, and E. Tschuikow-Roux, J . Phys. Chem., 81. 1153 11977). (11) D. Salomon and A. A. Scala, J . Chem. Phys., 62, 1469 (1975). N 14.4 kcal mol-‘; for (12) For CH2FCH2CI HCI -t C,H3F, CH,FCH2CI FCI -t C2H4,AHopQ8= 68.4 kcal mol-‘, based on AHf0298(CHPCH2CI)= -68.0 kcal- mol (computed by group additlvlty) and other heats of formatlon taken from S. W. Benson, “Thermochemical Kinetics”, 2nd ed, Wiley, New York, 1976. (13) The activation energy for CpH3CI HCI -I-CH , , is E, N 61 kcal mol-’; S. W. Benson and G. R. Haugen, J. Phys. Chem., 70, 3336 (1966). For C,H,F -+HF 4- C2H2,E, 71 kcal mol-’: J. M. Simmie, W. J. Quiring, and E. Tschulkow-Roux, /bid., 74, 992 (1970). (14) For CpH, H2 -I-C2H,, E, 80 kcal mol-’: A. W. Klrk and E. Tschuikow-Roux, J . Chem. Phys., 51, 2247 (1969). (15) A. F. Trotman-Dickenson and G. S. Milne, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 9 (1967). (16) J. A. Franklin and G. H. Huybrechts, Int. J. Chem. Kinef., 1, 3 (1969). (17) T. Ichimura, A. W. Klrk, and E. Tschuikow-Roux, J . Phys. Chem., 81, 2040 (1977).
--
-
-+
-
-
Photodecomposition of 1,l-Difluoro-I ,2-dichloroethane at 147 nm T. Yano and E. Tschuikow-Roux” Department of Chemistv, University of Cabav, Ca/gav, Alberta, Canada TZN IN4 (Received May 1, 1979)
The 147-nm photolysis of CFzClCHzCl was studied at 25 “C with and without nitric oxide as additive. In the absence of NO the principal reaction products are CF2CH2,CFzCHC1, (CF2C1CH2)2, CF2ClCHC1CH2CF2C1, and the two isomers of (CF2C1CHC1)2. Addition of NO completely suppresses the formation of the chlorofluorobutanes, while it enhances the olefin quantum yields at high conversion. These observations are interpreted in terms of reactions of chlorine atoms, which are produced either directly (by near simultaneous expulsion of two C1 atoms) or the dissociation of an excited Clz*molecule, produced by molecular elimination in the primary process. Chlorine atoms abstract hydrogen from the parent or add to the product olefins, both processes yielding haloethyl radicals. Thus, addition of NO has a dual effect: it serves to scavenge radicals, and it suppresses radical formation through NO-catalyzed recombination of C1 atoms. The production of CF2CHC1, a relatively minor process, is believed to occur, primarily, via molecular HCl elimination. The limiting quantum yields of CFzCH2and CFzCHCl are found to be 4o = 0.68 f 0.07 and 4,,’ = 0.14 f 0.02, respectively. The ratio of rate constants for the addition/H abstraction reactions by C1 atoms are found to be kB/k,=, 360 for CFzCHz and h9/k5 540 for CF,CHCl. The extinction coefficient for CF2ClCH2Clat 147 nm and 25 “C was determined = 242 f 8 atm-’ cm-l. to be = (l/PL) In (lollt)
-
-
Introduction Our studies on the vacuum ultraviolet (147 nm) photolyses of chloro- and chlorofluoroethanes have ~ h o w n l - ~ that the predominant photodissociation process is molecular HC1 elimination in the case of poly-halogen substitution on the same carbon atom, while substitution of chlorine or fluorine in the p positions leads to a decrease in the quantum yield of HC1 and an increase in dehalogenation processes.6i6 With the exception of CH3CH2C1, the conspicuous absence or only low yield of products of free radical origin has led us to postulate that dehalogenation occurs via molecular processes (elimination of C12 or FC1). While such processes are forbidden from ground electronic states, they are not precluded from an electronically excited state and have been attributed to “Rydberg” type transitions.’ However, more recent work a t 147 nm has shown a reversing trend: with increasing degree of (cr,p) halogen substitution the overall quantum yield of molecular elimination processes decreases and there is a shift to primary processes involving bond fission. Thus in the 147-nm photolysis of CF3CH2C1the limiting low pressure quantum yields for CFzCHF and CF2CH2, 0022-365417912083-2572$0 1.OO/O
corresponding to HCl and FC1 elimination, were found to be -0.22 and 0.13, respectively, while a t 123.6-nm FC1 elimination was still predominant.* In our continuing effort to better understand the effect of halogen substitution and wavelength dependence of these primary photochemical processes, we report in this paper on the 147-nm photolysis of CF2C1CH2C1. With improved analytical procedures particular attention was focused on the identification of products of bond fission reactions and the characterization of subsequent processes. Experimental Section Photolyses were carried out a t room temperature in a conventional “static” apparatus similar to that described p r e v i ~ u s l y . ~Total , ~ conversions were held at less than 1% . The light sources were either liquid oxygen cooled or titanium filament gettered xenon resonance lamps equipped with LiF windows (1mm thickness) and operated by an improved microwave generator (KIVA Instruments, Inc., Model MPG4M). The spectral purity of the lamps was checked routinely with a McPherson (Model 218-0.3 m) vacuum ultraviolet grating monochromator and
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0 1979 American Chemical Society
The Journal of Physical Chemistry, Vol. 83,No. 20, 1979 2573
Photodecomposition of l,l-Difluoro-l,2-dichloroethane
TABLE I: Product Quantum Yields in the 147-nm Photdysis of CF,CICH,Cla PCF,C~CH,C~, PNO, torr torr
60.3 60.0 21.9 10.7 10.7 10.8 3.6 3.5 2.3 3.4 2.1 2.5 2.1 3.6 20.1 10.8 8.7 3.4 3.4 3.6 3.2 11.9 2.5 3.4 2.4 a
0.090 0.12 0.15 0.055 0.10 0.64 0.36 0.26 0.18 0.06 0.07
quantum yield @ CF,CH,
CF,CHCl
0.69 0.65 0.62 0.62 0.68 0.56 0.63 0.54 0.52 0.40 0.48 0.41 0.36 0.17 0.63 0.61 0.58 0.60 0.54 0.53 0.54 0.56 0.50 0.47 0.44
0.14 0.14 0.15 0.12 0.14 0.094 0.079 0.087 0.056 0.038 0.039 0.048 0.023 0.011 0.12 0.091 0.11 0.061 0.076 0.080 0.079 0.077 0.078 0.061 0.056
C1,-B
0.018 0.010 0.042 0.030 0.027 0.033 0.050 0.12
10-131 C1, -B
Cl,-B
0.057 0.12 0.053 0.087 0.091 0.19 0.049 0.078 0.14 0.22 0.20 0.13 0.21 0.33
0.14 0.30 0.17 0.20 0.14 0.40 0.088 0.14 0.44 0.23 0.24 0.25 0.25 0.30
(photons s-' ) 103(Zt/N) 3.2 7.3 3.4 3.5 3.6 7.8 3.2 4.2 7.7 11.0 7.1 7.3 16.0 41.0 3.2 3.8 6.0 3.5 4.5 6.4 5.9 28.0 8.2 14.0 11.0
0.074 0.17 0.22 0.46 0.47 1.0 1.2 1.7 3.1 3.6 4.1 4.1 7.0 17.0 0.22 0.49 0.96 1.4 2.2 2.5 2.6 2.6 4.6 5.7 6.4
The cell volume was 200 cm3.
contributions from the 129.5-nm resonance line were found to be insignificant. Chemical actinometry was based on the production of C2H2in the photolysis of ethyleneg (&d2 = 1.0 a t 147 nm). Two series of experiments were carried out in which the effects of pressure, photointensity, cell volume, and the addition of nitric oxide as a radical scavenger were examined. In these series, two reaction cells were used: one a cylindrical Pyrex cell of 200 cm3and a second gold-coated spherical cell of 620 cm3 volume. The latter was used to test for possible surface effects, though none were found. Product analysis was by gas chromatography (Hewlett-Packard Model 5830 A, with twin ionization detectors) with six product peaks being isolated and identified. Lower molecular weight products (CF2CH2and CF2CHC1) were separated with a 3.6-m Porapak N column (3 mm diameter) a t 130 OC with a He flow rate of 30 cm3/min, while higher molecular weight products were separated by use of temperature programming with a 1.8-m n-octane/Porasil C (Durapak) column with a He flow rate of 30 cm3/min. CF2CH2and CFzCHCl were identified, and their sensitivities subsequently determined by comparison of their retention times with those of authentic samples. The other four reaction products (chlorofluorobutanes) were identified by means of coupled gas chromatography-mass spectrometry (Hewlett-Packard, Model 5992A GC/MS System). Since authentic samples of these chlorofluorobutanes were not available, relative sensitivities for these compounds were estimated from 1,3-dichlorobutane and 2,3-dichlorobutane by assuming the group additivity principle and neglecting the presence of fluorine substitution. The reactant, CF2ClCHzCl,was obtained from Peninsular ChemResearch and purified to better than 99.99% by fractional distillation with a spinning band column (B/R Glass, Inc.). Nitric oxide (Matheson) was subjected to trap-to-trap distillation at 77 K and used without further purification. Precise low pressure measurements were facilitated by using an electronic, fused quartz Bourdon gage (Texas Instruments, Model 145). The extinction coefficient of CF2ClCH2Cla t 147 nm was determined as
6 = (l/PL) In &/It) = 242 f 8 atm-l cm-l at 296 K, using the double-cell method described by Gorden et al.1°
Results The observed reaction products are CF,CH,, - -. CF,CHCl, and significant quantities of four chlorofluorobitanes; CF,ClCH,CH,CF,Cl (C19-B). CF,ClCHClCH,CF,Cl (Cli-B), aGd t h i diastereomers of CF~ClCHClCHelCF~Cl (C14-B). In one very long photolysis run we observed a trace amount of CF2C1CHC12. Quantum yields of the principal products are summarized in Tables I and 11, for the two reaction cells, respectively. Also listed are the pressures of the reactant CF2C1CH2C1,the additive NO, and th'e light intensity determined by chemical actinometry immediately prior to each CFzClCH2Clphotolysis. Early experiments had shown no significant correlation of the quantum yield of the principal product CF2CH2 with pressure, however, as may be seen from Tables I and 11, there appears to be a dependence of @cF2cH1with respect to the total absorbed light intensity, I. Yet, despite considerable scatter in the data, empirical plots of &F CH2 vs. I showed two distinct curves for the two sets of Lata in the different reaction vessels. On the other hand, simple diffusion calculations indicate that surface effects cannot be important in this system. A unified correlation was deduced by plotting $CF2CH2 vs. I t / N (Figure 1)where t is the photolysis time, and N = PVNo/RT is the total number of reactant molecules in the reaction cell of volume, V, at a pressure, P. The product (It)is a measure of the total radiant energy input. Since in the present experiment all light is absorbed even at the lowest reactant pressures, it follows that It also provides a measure of the total number of reactant molecules dissociated, assuming a total quantum yield of unity. The ratio I t / N is therefore a measure of conversion. A further rationale for the use of this function is provided in terms of the proposed mechanism and its mathematical analysis (see Discussion). Table I shows that in the absence of NO the quantum yields of CF2CH2and CF2CHCl decrease with increasing I t / N . The corresponding data for the chlorofluorobutanes show considerably more scatter reflecting analytical dif-
2574
T. Yano and E. Tschuikow-Roux
The Journal of Physical Chemistry, Vol. 83, No. 20, 1979
TABLE 11: Product Quantum Yields in the 147-nm Photolysis of CF,CICH,Cla*b quantum yield I$ PCF.C~CH.C~, torr 153.2 154.7 121.1 59.9 49.3 60.7 11.7 4.6 3.0 2.5 1.4 4.0 89.6 36.3 23.9 7.5
PNO,torr
CF,CH,
CF,CHCl 0.15 0.13
0.93 0.40 0.27 0.08
0.75 0.67 0.65 0.66 0.68 0.64 0.64 0.60 0.53 0.57 0.52 0.34 0.68 0.69 0.62 0.63
a The cell volume was 6 2 0 cm3. mined.
0.12 0.13
0.12 0.12 0.19
0.10 0.067 0.091
0.11 0.048 0.099 0.13 0.084 0.078
10-* 31 (photons s-l)
103 ( z t / ~ ) 0.042 0.043 0.056 0.061 0.099
6.9 7.4 1.6 5.8 5.4 7.4 14.0 14.0 7.9 14.0 12.0 30.0 7.8 6.9 7.3 9.0
0.11 0.65 1.4 2.4 2.5 3.8 5.0 0.078 0.17 0.27 0.65
In these experiments the quantum yields of the chlorofluorobutanes were not deter.
small contributions from radical sources could possibly be masked by other overriding effects. Production of CFzCH2and CF2CHCl. The above observations suggest the following primary processes in the 147-nm photolysis of CFzCICHzCl: CFZClCHzCl+ hv +
0
N
LI 0
8
001 00
1
I 001
I 0.02
(It/N 1
Flgure 1. Quantum yield of CF,CH, as a function of conversion: (circles) runs without NO; (squares) runs with NO.
ficulties (peak broadening and possibly adsorption on wall surfaces). Nevertheless, at least qualitatively, the quantum yields of ClZ-Band C13-B increase with increasing It/N. There is less of an apparent trend in the case of C14-B. The addition of NO completely suppresses the formation of the chlorofluorobutanes and there is a distinct and significant diminution in the relative decrease of $ c F ~ c H ~ and $CF2CHCI with increasing conversion, ItlN. The data in Table I1 shows analogous behavior, though in this case no analyses were carried out for the chlorofluorobutanes.
Discussion The complete disappearance of the chlorofluorobutanes in the presence of NO confirms that these products result from radical precursors. Moreover, their structural identity points toward chlorine atom reactions in the system. Also, diagnostically most significant is the effect of NO addition on the production of CFzCH2and CF2CHC1. As may be seen from Figure 1the quantum yield of CF2CH2increases in the presence of NO at the higher values of the conversion, It/N. Conversely, in the absence of NO the more rapid decrease of $CF2CH2 at high conversions appears to be linked with the production of CFzC1CHzCH2CF2C1and CFzClCH2CHC1CF2Cl. Further, the lack of inhibition in the presence of NO strongly suggests that CFzCH2and CFzCHCl are produced predominantly molecularly, though
CFZClCH<
(Rl)
CFzCHz + 2C1
-
CF2ClCHZCl'
N
I
-
CFzCHCl
032)
+ HC1
(R3)
where the dagger denotes electronic excitation. In reaction R2 the rapid sequential expulsion of two chlorine atoms is implied. Since our data show no evidence of radical contribution to the yield of CF2CHz,single carbon-chlorine scission leading to stabilized CFzCHzCl or CFzCICHz radicals in the primary process is omitted. However, as discussed below, an alternate source of CFzClCH2radicals does exist. The production of chlorine atoms may also proceed via the concerted molecular a,@elimination of an excited chlorine molecule followed by its dissociation:
-
CF2C1CH2Clt
Clz*
CFzCHz + ClZ*
-
(R4)
2c1
(R4a)
The absence of CFCH among reaction products indicates that the energy content of CFzCHzproduced in reaction R2 or R4 does not exceed the activation energy of -86 kcal mol-' for HF elimination, the principal reaction channelll in the thermal decomposition of CFzCH2. This allows an estimate of the energy content of C12*. Thus, the enthalpy change12-15for ground state reaction R4 is AH 40-44 kcal mol-l, and, since the photon energy is 194 kcal mol-', a lower limit of the energy content of C12*is -64-68 kcal mol-l which exceeds the bond dissociation energy of C12, Similar considerations can D(C1-C1) = 58.2 kcal be applied to reaction R3 for which AH 25 kcal mol-l and hence the available excess energy is ca. 169 kcal mol-'. Again the absence of either CFCCl or CFCF as products indicates that neither HF nor HC1 elimination occurs. The latter process would require the formation of a carbene intermediate followed by subsequent transfer of a fluorine atom. Although the activation energies for these reactions are not known, they may be expected to be similar to that for H F elimination from CF2CH2. Using this value as an upper limit estimate of the energy content of CFZCHC1, we obtain -83 kcal mor1 as the lower limit for the energy content of HC1 in reaction R3, assuming zero relative
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The Journal of Physical Chemistry, Vol. 83,No. 20, 7979 2575
Photodecomposition of l,l-Difluoro-l,2-dichloroethane
energy of translation. Since D(H-Cl) = 103 kcal mol-',16 for HC1 dissociation to occur the HC1 molecule must possess more than -61% of the total available energy. On the basis of this very crude estimate and our previous work in this series,I* we propose here the molecular elimination of HC1. In any case, in terms of relative importance, reaction R3 is a minor process in the present system. Production of Chlorofluorobutanes. The formation of chlorofluorobutanes is directly related to the presence of atomic chlorine in the system. Thus chlorine atoms produced in reactions R2 or R4a will abstract hydrogen from the parent molecule to form CF2ClCHCl radicals C1 CF2ClCH2C1 HC1+ CFzCICHCl (R5)
-
+
The subsequent fate of this secondary radical may include metathetical reactions with the parent, combination, and cross combination with other radicals, and possibly some disproportionation reactions. Of the former three possibilities we note that the most likely process of H-atom abstraction leads to no net change since the parent molecule is regenerated, reaction R6, while C1-atom abCF2ClCHCl CF2ClCH2Cl CFzCICHzCl + CF2ClCHCl (R6)
-
+
straction is apparently not significant since only trace quantities (at long photolysis time) of CFzClCHC12were observed. We therefore conclude that these reactions are not important in this system. The combination of CF2ClCHCl radicals leads to the observed tetrachlorotetrafluorobutane (reaction R7). The corresponding 2CF2C1CHC1 CF2C1CHC1CHClCF2C1 (R7)
-
disproportionation reaction involving chlorine transfer can be neglected from consideration in view of the above statement concerning the product yield of CF2C1CHC12. The production of CF2ClCH2radicals in this system can be inferred from the structure of the other two chlorofluorobutane products and the effect of NO on the quantum yields of CF2CH2and CF2CHC1. Thus, in the absence of NO a second sink for C1 atoms is their addition to the product olefins17 which becomes perceptible at higher conversions
-
C1+ CF2CH2
(+MI
(+M)
C1+ CF2CHCl
(+M)
(+M)
CF2C1CH2
(R8)
CF2CH2Cl
(RW
CF2ClCHCl
(R9)
CF2CHClz (R94 There appear to be no previous investigations of these particular reactions. However, competitive photochlorination studies of chloroethy1enesl8 have shown that chlorine atoms react rapidly with near-zero activation energy to produce vibrationally excited chlorinated ethyl radicals, though, unfortunately, the structure of these radicals was not reported. More recently, Sanhueza and Hei~klenl~-~O have studied the chlorine-atom initiated photooxidation of halogen substituted ethylenes including CH2CC12,19 CHC1CC12,20and CF2CC12.21In all cases both a and p radical adducts were invoked as initiation steps, though at least in the case of CHzCC12the preferential addition of C1 atoms to the non-halogenated carbon atom was clearly indicated. In contrast, based on the cracking patterns of our GC-mass spectrometric analyses of the dichloro- and trichlorobutanes, we must conclude that the site of chlorine atom addition is the fluorinated carbon atom. This unusual finding of a "Markovnikov-type" atom
addition is presently the subject of further investigation, In the foregoing discussion it is both instructive and necessary to consider the relative rates of abstraction and addition reactions of chlorine atoms. With reference to reactions R5 and R8, we obtain - = - 1 h8[CFZCH21f R8 R5 2 k5[CF2ClCH2Cl]
(1)
where [CF2CHZ],is the final concentration and the factor 1/2 corrects for the average concentration of the olefin assuming a linear dependence with irradiation time. The Arrhenius parameters for H abstraction from CF2C1CH2C1 can be estimated from the chlorination studies on fluoroethanes22and c h l o r o e t h a n e ~ .The ~ ~ experimental data for these series show that the activation energies increase and the A factors decrease with (a) increasing halogen substitution on the a-carbon atom, and (b) with H-abstraction occurring from the carbon atom P to the halogen substituted one. From a consideration of the variation of these parameters we estimate E5 5 kcal 1012.4cm3 mol-I s-l. For the C1-atom mol-1 and A5 addition reaction the data on the photochlorination of chloroethylenes18 may be used as a rough guideline, Making allowance for fluorine substitution in the olefin we estimate E8 2 kcal mol-l and As N 1013cm3 mol-I s-l. Using these values, we obtain R8/R5 0.3 a t 25 "C = 1X Despite conand [CF2CH2]f/[CF2C1CH2C1] siderable uncertainty in the Arrhenius parameters this calculation shows that in the present system the addition reaction is by no means negligible even a t these low conversions. Reaction R9 provides another, but minor, source of CF2C1CHC1radicals. The combination of CF2ClCHzand CF2C1CHC1radicals produced in reactions R8, R9, and R5, respectively, gives rise to the other observed chlorofluorobutanes 2CF2C1CH2 CF2ClCHzCH2CFzCl (R10) CF2ClCH2 CF2ClCHCl CF2ClCH2CHClCF2Cl (R11) Other conceivable reactions of these radicals, including disproportionation and metathetical reactions, do not appear to be important, and can be neglected on the basis of our product analysis (no evidence for CF2C1CH3, CF2HCH2C1,or CF2HCHClZ,and only trace amounts of CF2ClCHC12as stated earlier). We therefore refrain from further speculation except to note that generally disproportionation/combination ratios are small, while Habstraction reactions by halogenated ethyl radicals may have a significant activation energy in analogy to the perfluoroethyl radical.24 Unfortunately, there is a lack of information on partially substituted chlorofluoroethyl radicals. E f f e c t of Nitric Oxide. The apparent relative increase in the quantum yields of CFzCH2and CF2CHC1 in the presence of NO is the result of the suppression of the secondary inhibition reactions R8 and R9. An analogous effect has been observed, for example, in the gas-phase photodecomposition of methyl iodide (CH31 CH, I) for which the quantum yield is quite small (-0.05), but is increased about tenfold in the presence of excess nitric oxide.25 The explanation is that NO suppresses the inhibiting step CH, + I2 CHJ + I (or CH, + I + M CH31 + M) by scavenging methyl radical^.^^$^^ In the present system nitric oxide plays a dual role. It serves as the usual radical scavenger (of any primary or residual radicals) and it suppresses radical formation by removing chlorine atoms. Hippler and T r ~ recently e ~ ~
-
-
+
-
- -
-
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+
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T. Yano and E. Tschuikow-Roux
The Journal of Physical Chemistty, Vol. 83, No. 20, 1979
2576
1
3.0
0
0 40
I
I
1.0
20
I 30
0
I 40
1 1
(It/N) X I O 3
Flgure 2. Plot of reciprocal of the quantum yield of CFpCH, vs. I f l N for small values of conversion and in the absence of NO (eq 16).
reported the NO-catalyzed recombination of chlorine in helium over a wide range. The increase in the rate of recombination in the presence of NO was attributed to the reactions c i + NO
k5[CF2ClCH2Cl] - kg[CF2CH2] k5[CFzC1CHzC1]+ k8[CFzCHz] (7) Since in the present system total conversions are very low, the concentration of CF2ClCH2Cl is virtually constant. Hence, making the substitutions X = [CF2CH2],a = k5[CF2C1CH2C1],and p = kg, we obtain d[CF,CHzI dt
Some further underlying assumptions in the derivation of eq 8 are given in the Appendix. Integration of eq 8 subject to the boundary condition X = 0 a t t = 0 leads to X = (a/p)[1 - (e-~d~t/2")(e-BX/Pa)] (9) where we can identify the exponents as _ OX -- k8[CF2CHZI = - -Ra 2a 2k5[CF&lCH2Cl] 2 R5 and
(10)
+ M -%C ~ N O+ M
C1+ ClNO -.%Clz + NO
(R13)
Subject to the condition kli[M][NO]
