Chlorination of Paraffin Hydrocarbons
decomposition products CH31 and C2HJ and complex addition to propyne. We suggest that the CH3CHICH3 enhancement yield increase is due to the caging of the electronically excited complex. Similar to the iodine-acetylene systern,l5we believe that kinetic energy, positive charge, and preferential electrophilic attack on the propyne r-bond system results in a highly excited complex with unimolecular (low pressure) and caged complex and cage radical (high pressure and liquid) characteristics.
References and Notes (1) This research was supported by the United States Department of Energy Contract No. EY-76-5-02-1617001. This is DOE Document NO. COO-1617-59. (2) R. L. Ayres, 0. C. Gadeken, and E. P. Rack, J . Phys. Chem., 75, 2880 (1971). (3) R. L. Ayres, C. J. Michejda, and E. P. Rack, J . Am. Chem. Soc., 93, 1389 (1971). (4) A. Loventhal, M. Kim, and E. P. Rack, Radiochem. Radioanal. Lett., 26, 239 (1976). (5) R. R. Pettijohn and E. P. Rack, J . Phys. Chem., 76, 3342 (1972). (6) D. Urch and R. Wolfgang, J . Am. Chem. SOC.,81, 2025 (1959). (7) J. K. Lee, B. Musgrave, and F. S. Rowland, J . Am. Chem. SOC., 82, 3545 (1960). (8) E. K. C. Lee and F. S. Rowbnd, J. Am. Chem. SOC.,84, 3085 (1962). (9) A. H. Rosenberg and R. Wolfgang, J. Chem. Phys., 41, 2159 (1964). 94, 1047 (10) R. L. Williams and F. S. Rowland, J . Am. Chem. SOC., (1972). (1 1) R. L. Williams and F. S.Rowland, J . Phys. Chem., 77, 301 (1973). (12) R. Milstein, R. L. Williams, and F. S.Rowland, J . Phys. Chem., 78, 857 (1974). (13) W. S. Smith, S.H. Danile, and Y. N. Tang, J . Phys. Chem., 76, 271 1 (1972). (14) K. C. To, M. E. Berg, and E. P. Rack, J . Phys. Chem., 81, 1239 (1977). (15) K. C. To, M. E. Berg, and E. P. Rack, J . Phys. Chem., 80, 1411 (1976). (16) M. E. Berg, A. Loventhai, D. J. Adeiman, W. M. Grauer, and E. P. Rack, J . Phys. Chem., 80, 837 (1977).
The Journal of Physical Chemistry, Vol. 83,
No. 18, 1979 2321
(17) M. D. Loberg, K. A. Krohn, and M. J. Welch, J . Am. Chem. SOC., 95, 5596 (1973). (18) M. E. Berg, W. M. Grauer, R. W. Helton, and E. P. Rack, J . Phys. Chem., 79, 1327 (1975). (19) The total organic product yield (TOPY) is the fraction of activity bound organically in the system. TOPY = OA/(OA IA) X 100% where OA is the activity retained in the organic fraction of the extraction and IA is the activity in the inorganic fraction. Corrections for isotopic decay were made. Individual organic product yields (IOPY) represent the fraction of activity chemically bound in a specific organic substrate. Integration of the areas of radio chromatographic peaks, corrected for radioactive decay and normalized to the TOPY value, are used in the assignment of values. Combined organic product yields (COPY) are the summation of selected individual organic product yield values for quantitative and qualitative discussion, e,g., summation of individual organic products with a two carbon structure (cC,COPY). (20) W. E. Rice and J. E. Willard, J . Am. Chem. Soc., 75, 6156 (1953). (21) 0. Maass and C. H. Wright, J . Am. Chem. Soc., 43, 1098 (1921). (22) The critical values for propyne are T, = 128 OC; P, = 52.8 atm. (23) At low temperature fractional crystallization may occur. (24) M. Yoong, Y. C. Pao, and E. P. Rack, J . Phys. Chem., 76, 2685 (1972). (25) T. A. Carlson and R. M. White, J . Chem. Phys., 44, 4510 (1966). (26) S.Wexler and H. Davis, J . Phys. Chem., 20, 1688 (1952). (27) E. P. Rack and A. A. Gordus, J . Chem. Phys., 34, 1855 (1961). 82, 2661 (1960). (28) P. J. Estrup and R. Wolfgang, J . Am. Chem. SOC., (29) R. Wolfgang, J . Chem. Phys., 39, 2983 (1963). (30) S. Giasstone, "The Elements of Nuclear Reactor Theory", Van Nostrand, New York, 1952. (31) H. J. Machulla and G. Stocklin, J . Phys. Chem., 78, 658 (1974). 132) . , A. J. Cole. M. D. Mia, G. E. Miller, and P. F. D. Shaw. Radiochim. Acta, 9, 194 (1968). (33) M. Milman, Radjochim. Acta, 1, 15 (1963). 92, 3480 (34) A. E. Richardson and R. Wolfgang, J . Am. Chem. SOC., (1970). (35) J. Franck and E. Rabinowitsch, Trans. Farachy SOC., 30, 120 (1934). (36) D. L. Bunker and B. S. Jacobson, J . Am. Chem. Soc., 94, 1843 (1972). (37) C. T. Ting and F. S. Rowland, J . Phys. Chem., 74, 4080 (1970). (38) J. D. Rynbrandt and B. S. Rabinovich, J . Chem. Phys., 54, 2275 (1971). (39) D. L. Bunker, J . Chem. Phys., 57, 332 (1972). (40) Y.-N. Tang and Y. Y. Su, J . Chem. Phys., 57, 4048 (1972). (41) D. L. Bunker and W. L. Hase, J . Chem. Phys., 59, 4621 (1973).
+
Chlorination of Paraffin Hydrocarbons. 2. Ethanes and Propanes T. N. Bell, Department of Chemistry, Simon Fraser University, Burnaby, British Columbia, Canada
K. A. Perkins, and P. G. Perkins" Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow GI IXL,Scotland (Received November 2, 1978; Revised Manuscript Received March 13, 1979)
Using the molecular-orbital-bond-index (MOBI) method for activation energies and an improved group contribution method for A factors, we have calculated Arrhenius parameters for the abstraction of hydrogen by chlorine atoms from ethane and both carbon atoms in C2H5C1,C2HC16,and CC13CH3. Hydrogen abstraction from every possible position in propane and the two monochloropropanes has also been studied. In each case, Arrhenius parameters for the reverse reaction have been calculated and the equilibrium constant has been derived. The calculated equilibrium constants show better agreement with thermodynamic data than do those derived from published experimental Arrhenius parameters.
Introduction In the first part of this work' the activation energies and A factors for methane and chlorinated methanes were calculated by using the molecular-orbital-bond-index (MOBI) and group contribution method.2" Using a similar, though improved, method, we have now studied the abstraction of hydrogen by C1 atoms from ethane, three chlorinated ethanes, propane, and the two possible monochlorinated propanes. Our objective in carrying out this work is to predict the relative ease of chlorination in the gas phase a t different 0022-3654/79/2083-2321$01 .OO/O
positions in a long-chain hydrocarbon or a chlorinated derivative. We have studied the C3H8 system as the simplest example of such a system, and from these studies we expect to derive general principles. In propane, it is possible to abstract a hydrogen atom lying in either the primary or secondary position C3H8 + C1. CH3CHZCHZ. HC1 (CH3)ZCH. + HCl C3H8 + C1. We are able to predict the relative rate of each reaction. The monochlorinated propane, CH3CH2CH2C1,may un-
--
(E 1979 American Chemical Society
+
2322
The Journal of Physical Chemistry, Vol. 83, No. 18, 7979
T. N. Bell, K. A. Perkins, and P. G. Perkins
TABLE I : Bond Energy Parameters (kJ mol-') CX-CI
C*-H* length, nm 0.109 0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15 0.155 0.16 0.17 0.18 0.19 0.2 0.25 0.3 0.35 0.4 0.45 0.5
C*-H
primary c-c*
secondary
in -c / ____ H \
420.66 417.98 415.39 413.59 412.79 412.12 411.87 411.29 410.79 410.32 409.91 409.40 408.94 408.48 407.98 407.02 406.60 406.68 407.02 407.94 410.79
334.76 339.53 343.09 346.02 348.53 350.54 352.21 353.59 354.68 355.60 356.39 357.86 359.03 360.20 361.37 364.09 365.05 365.18 364.89 364.05 361.46
334.76 338.15 340.66 342.75 344.51 345.93 347.10 348.11 348.86 349.49 350.07 351.12 351.96 352.79 353.63 355.56 356.23 356.31 356.10 355.51 353.67
336.70 328.07 322.80 318.40 314.85 312.34 310.45 308.99 307.78 305.98 304.68 302.00 299.95 297.98 295.89 291.00 289.28 288.99 288.82 288.74 288.65
c-c*
dergo a second hydrogen abstraction from the a, p, or y position, and (CHJzCHCl from the a or /3 position. All these reactions have been studied theoretically and the relative rates of hydrogen abstraction computed. Calculation of Activation Energies In each case the method used for obtaining the activation energy was essentially the same as that for methane,' i.e., the heat of atomization for the system R- - -H- - -C1 was computed in the standard state and at 298 K at positions in the coordinate space so that the minimum enthalpy path for the reaction could be obtained. Bond energy parameters derived for the methane calculations remained the same and some additional parameters were derived for the larger molecules of the present study. The derivations of the new bond energy parameters are described under the appropriate heads. Ethane. In the chlorination of ethane C Z H G t CI
- \/
/ \
-C-C-----H----CI
-
in
+
HCI
a bond energy parameter for the C-C bond is required in addition to the parameters for the C1 systems. In the C2Hj moiety, the configuration around one C remains constant, while at the "reacting end" of the molecule, the geometry changes from tetrahedral (C2H6)to planar (C2H5.). Using AH; for ethane as -84.68 kJ mol-' and the C-H parameter of 420.66 kJ mol-' as for CH4for both directly bonded and nonbonded C-H bonds, we found that the C-C parameter for ethane is 334.76 kJ mol-'. For the ethyl radical, AH,' is 108.4 f 5.4 kJ mol-'.4 If we use the parameter of 420.66 kJ mol-' for tetrahedral and nonbonded C-H and 410.79 kJ mol-' for the two C-H bonds in a planar geometry (as in planar CH,.), then we obtain a C-C parameter for the ethyl radical of 361.46 kJ mol-'. Hence in the reaction CzHs + C1- CZHj----H*----Cl- CZH5* + HC1 we assume that the C-C parameter varies from 334.76 kJ mol-l when C-H* is 0.109 nm (the equilibrium distance
"distant "
336.70 330.20 326.31 323.42 321.58 319.87 318.32 316.90 315.68 314.85 314.26 312.63 310.95 309.57 308.11 304.68 303.46 303.30 303.17 303.09 303.05
312.29 284.93 264.55 247.78 233.38 221.88 212.30 204.39 198.11 192.84 188.32 179.91 173.18 166.48 159.74 144.18 138.66 137.95 139.62 144.43 159.28
c*-Cl
CI
CI
in C2H6) to 361.46 kJ mol-l when C-H* is 0.5 nm (effectively total separation of C2H5.). Concomitantly, the C-H parameter varies from 420.66 to 410.79 kJ mol-l, and the geometry changes from tetrahedral to planar. Values for the C*-H parameter are shown in Table I. A few of these have been amended slightly (up to 0.1 70)from those used previously to give a smoother curve. We allow the C-C parameter to vary with the configuration of the carbon atom in the same way as previously for C-H and C-C1, the parameters for C-C in C2H6, CzH5. (planar), and CzH5.(pyramidal) contributing in the ratios previously described. We therefore need to compute a parameter for +C-C*< where C* is in a pyramidal environment. To achieve this the reorganization energy for the conversion H
H H-C-C* \ H
/
/ \
H
- \ c
H
H-C-C
H
C* planar C2H5'
c*-c1 / -C----H \
/
H
\
H
C* pyramidal
was computed from an ab initio calculation and was found to be -31.25 kJ mol-'. This yields AH: (ethyl pyramidal) to be 139.6 kJ mol-l. Using the pyramidal methyl C-H parameter of 398.3 kJ mol-l, we found a C-C parameter for pyramidal ethyl of 373.0 kJ mol-'. Hence, we are able to tabulate values for the C-C parameter as the C*-H* bond length varies from 0.109 to 0.5 nm (Table I). We refer to this as a C-C* primary bond. Using these data, we calculated the reaction path with minimum energy and, hence, activation energies for the forward reaction C2H6 C1 and the reverse reaction CzH5 HC1. The temperatures were chosen to coincide with the mean temperatures of published experimental values. Table I1 lists the predicted activation energies together with values from the literature. Chlorinated Ethanes. We have previously used the quantity 336.70 kJ mol-' for directly bonded C-C1 in a tetrahedral environment, In chlorinated ethanes, however, we have also chlorine atoms on an adjacent carbon atom. The radial functions for chlorine 3d orbitals are more complex and, therefore, are more sensitive to distance and environment than is that of the 1s orbital of hydrogen.
+
+
The Journal of Physical Chemistry, Vol. 83, No. 18, 1979 2323
Chlorination of Paraffin Hydrocarbons
TABLE 11: Arrhenius Parameters for Ethane and Propane Reactions mean A E , kJ mol-’ reaction reaction temp, K calcd exptl C,H, t CIS+ C,H,.
Forward Reactions
+ HCl
C,Cl,H t C1*+ C,Cl,- t HCl C,H,Cl t C1*+ CH,ClCH,* + HC1 C,H,Cl + C1*+ CH,CHCl. + HCl CCl,CH, + C1. + CCl,CH,~+ HCl C,H,
t
C1. + n-C,H,.
t
i475 378 378 378
14.60 20.08 ,12.13 18.99
i373
13.01
1353 353 363 363 363 363 363
16.77 10.66 18.03 13.01 14.81 15.89 17.94
HCl
C,H, t C1. + l’-C,H,. + HCl CH,CH,CH,Cl t C1. + CH,CH,CHCla t HCl CH,(CH,Cl)CH, + C1. CH,(CH,Cl)CH* + HCl CH,ClCH,CH, t C1- -+ CH,ClCH,CH,* t HCl (CH,),CHCl t C1. + (CH,),CCl. t HCl CH,CHClCH, t C1. + CH,CHClCH,. t HC1 --f
log A calcd
4.35 * 0.33 4.18 15.06 6.28 6.28 15.06 14.6 4.10 3.22’ 2.76 3.22 * 0.84’ 1.25 1.67‘ 3.22’
exptl
14.4d 13.78 12.76 13.25 13.01
13.96 14.08 12.65 13.05 13.55 12.4 13.5 14.03 13.93‘ 13.87 13.4‘ 13.3‘ 13.4‘
13.20 13.78 13.25 13.01 13.51 13.33 13.06 13.89
*
ref ___ 15 16 16 16 16 15 15 15 15 15 15
Reverse Reactions C,H,, t HCl+ C,H, t C1. C,Cl,. t HCl+ C,Cl,H t C1. CH,ClCH,. + HC1 + CH,ClCH, t C1.
1400 400 400
30.04 37.17 33.93
33.9 45.2 ‘38.07
400 20.17/ CH,CHCl. + HCl CH,CH,Cl + C1. CCl,CH,* -t HC1+ CCl,CH, t C1. 400 33.22 46.86 400 30.25 n-C,H,* + HCl+ C,H, t C1. 400 41.25 i-C,H,- t HCl+ C,H, + C1. 400 40.00 CH,CH,CHCl. + HC1 + CH,CH,CH,Cl t C1, CH,(CH,Cl)CH. t HCl+ CH,(CH,Cl)CH, t C1* 400 42.05 CH,ClCH,CH,. t HCl+ CH,ClCH,CH, t C1* 400 35.98 (CH,),CCl* + HCl + (CH,),CHCl t C1. 400 52.47 400 26.65 CH,CHClCH,. t HCl+ CH,CHClCH, t C1. Frequency Factors for Reactions CH,Cl(,.,) CH, t C1. 389 CH,Cl t C1. 423
12.3 10.61 10,7(e~t)~ 10.99 10.8 11.17 \12.0
17 15 17
10.75 11.00 11.21
17
17
--f
CH,Cl, CHCl,
+ C1. + C1.
a Values for corresponding butanes. Value based on ref 7.
11.39 11.17 11.53
+ C1. 13.24 13.18
423
13.14
423
12.90
* Extrapolated by comparison with HI reactions.
Hence, we might expect there to be a difference in the way chlorine atoms directly and nondirectly bonded to carbon are to be treated. This proves to be the case. The electronic structures of the series of chlorinated ethanes CzClnH(6-n), where n = 1-5, were computed and the “distant” (i.e., not “directly bonded”) C-C1 parameter necessary to yield the experimental heat of atomization was calculated for each molecule. The C-C parameter was taken as 334.76 kJ mol-’ (as for ethane) and the directly bonded C-C1 parameter was 336.70 kJ mol-l. This treatment yields an average value for the “distant” C-C1 parameter of 312.29 kJ mol-I. The root mean square difference in the heat of atomization between calculated and experimental values over the whole range of chlorinated ethanes is then 11.7 kJ mol-l. By analogy, a study of the heats of atomization7 of the chlorinated ethyl radicals C2C16and C2Cl3H2,and the monochloropropane radicals CH3*CHCH2C1 and CH2ClCH2*CHzaffords an average value for the “distant” C*-C1 bond energy parameter of 159.28 kJ mol-l. This applies when C* is in the planar environment. Thus, the “distant” C*-C1 parameter varies from 312.29 kJ mol-l when C*-H* in C b C - C * t ---H*---C1 is 0.109 nm to 159.28 kJ mol-l when C*-H* is 0.5 nm. The variation is assumed to follow that of “bonded” C*-C1, described in the previous paper,l and its values are listed in Table 1.
11.5
13.42‘ 13.5 i: 0.7‘ 13.76‘ 13.5‘ 13.43c 13.4‘ 12.84‘ 13.2’
Value taken from ref 15.
Bond energy parameters for directly bonded C*-C1 are also listed for /H
and
-C----H
\
/“I -C----H
\
CI
CI
These are essentially those used previously for CHzCl and CHClzbut have been improved slightly to give a smoother curve. CzCI,H. Using the bond energy parameters described above and the “bonded” C*-C1 parameter variation for -C----H CI
/
we plotted the reaction path for the reaction C 2 C I 5 H + Cl
-
* CI3C-CCI----H-CI
\c
-
CZCI5. + HCI
I
and the forward and reverse activation energies were determined at appropriate temperatures. The results are shown in Table 11. C2H&1. Hydrogen abstraction from ethyl chloride may give rise to either of two radicals: CH3CHC1. if hydrogen
2324
The Journal of Physical Chemistry, Vol. 83, No. 18, 7979
TABLE 111: Heats of Atomization AHatom, kJ mol‘’
exptla
calcd
3994.13 3577.7 i 1 . 5 3596.1 i 6 . 3
3991.79 3571.24 3594.35
-_
a
--
C3H8 n-C,H,. i-CpH,‘ Reference 4 ,
is abstracted from the CHzCl group, or CH2C1CH2.if hydrogen is abstracted from the CH, group. The activation energies for both reactions have been calculated and are given, along with results for the reverse reactions, in Table 11. C2C13H3. The activation energies for the reaction C13CCH3 + CI.
-
-
/H C13C--C*----H*----CI
\H
+
HCI
and its reverse were calculated and are given in Table 11. Propane. In the propane molecule there are two possible sites for attack by a chlorine atom. Reaction may occur by abstraction of a primary hydrogen, yielding the nspropyl radical C3Hs + C1. CH3CH2CH2- - -H- - -C1+ CH3CHpCH2. HCl
and P. G.Perkins
the carbon atom C, is in a planar environment and is directly bonded to two carbon atoms. Use of the C-C bond energy parameter appropriate to the ethyl and n-propyl radicals was found to predict incorrect values for the heat of atomization for both the isopropyl radical and the sec-butyl radical, which has a similar structure around C,. Hence, a new C-C bonding parameter for “secondary” C-C radicals was derived, using the calculated electronic structures of the isopropyl and sec-butyl radicals. The new parameter is 353.67 kJ mol-‘. Experimental and calculated values for the heat of atomization are given in Table 111. In studying the reaction C 3 H 8 t CI.
-
CH3\*
CH3
CC13CH2.
CH
____ H* ____ CI
/
-
(CH3)zCH.
+
HCI
in keeping with previous methods, the C-C* parameter was varied from 334.76 kJ mol-I when C*-H* was 0.109 nm to 353.67 kJ mol-l when C*-H* was 0.5 nm. The variation followed the “primary” C-C variation (Table I). This set of “secondary” C-C parameters will be appropriate for any reaction involving the moiety
+
+
or by abstraction of a secondary hydrogen atom, yielding the isopropyl radical C3Hs C1. (CHJZCH---H---Cl (CH3)2CH*+ HC1 Primary Hydrogen Abstraction. The experimental heat of formation (AH:) for propane is given as -103.847 kJ mol-I and for the n-propyl radical as +94.5 f 7.5 kJ m01-I.~ These values give rise to the heats of atomization for C3H8 and n-C3H7shown in Table 111. We have computed the electronic structures of both systems and have calculated the heats of atomization. For propane the bond energy parameters for C-C and C-H were taken to be the same is shown in Table as for ethane and the calculated AHatom 111. In the n-propyl radical
+
T. N. Bell, K. A. Perkins,
-
+
Ua
H3C-
b
CH2-
a
C
/“ H ‘a
the C,-C,, parameter was taken as that for the ethyl radical, those for C,-Ha interactions were as for the CH3 radical and the remaining C-C and C-H parameters were those for ethane. The heat of atomization thus calculated is given in Table 111. It can be seen that for both C3H8and n-C3H7our calculated heat of atomization is very close to the experimental one and hence the data for ethane are appropriate for the study of this reaction. Values for the heat of atomization along the path of the reaction CH3CHzCHZ- - -H- - -C1 were, therefore, calculated in the usual way and the activation energies for the forward and reverse reactions are given in Table 11. Secondary Hydrogen Abstraction. In the isopropyl radical b
H3C\
\
C‘-Hu
The activation energy calculated for the abstraction of a secondary hydrogen atom from propane is shown in Table 11, together with experimental values. The activation energy for the reverse reaction is also predicted. Chlorination of Monochloropropanes. The abstraction of a hydrogen atom from each of the three positions in CH3CH2CH2C1and from the two positions in (CH3)&HC1 has been studied. Thus, activation energies for reactions i-v are predicted. In reactions i, iii, and v a range of
+
CH3CHzCH2C1+ C1- CH3CH2CHC1. HC1
-+ + -
CH,(CH2C1)CHz + C1. CHzC1CH2CH3+ C1.
CH3(CH2C1)CH.+ HCl
CH2C1CH2CHz.+ HC1
(CH3)zCHC1 C1. CH3CHClCH3
C1.
(CH3)2CC1.+ HC1
(i) (ii) (iii) (iv)
CH3CHClCHZ. + HC1 (v)
parameters for “primary” C-C* was required and in reactions ii and iv, those for “secondary” C-C* (Table I). The C*-C1 parameters for >(-Cl)- - -H were used for reaction i and reaction iv. Since no experimental activation energies are available for these reactions, all the calculated values are quoted at a temperature of 363 K, which corresponds to the mean temperature of the experimental work on chlorobutanes by Fredricks and Tedder.5 The calculated activation energies are given in Table 11. Calculation of A Factors The preexponential Arrhenius parameter, A, has been calculated for each of the reactions studied, using the expression
where Tmis the mean temperature for the reaction, u is a symmetry factor denoting the number of equivalent hydrogen atoms and ASo,‘ is the difference in entropy between the transition state and the reactants in concentration units. Also
The Journal of Physical Chemistry, Vol. 83, No. 18, 1979 2325
Chlorination of Paraffin Hydrocarbons
ASoc* = AS”,*
-
(1 - r ) R In R’Tm
where ASo,* is the entropy change in pressure units, R is the gas constant in J K-’ mol-l, R’ is the gas constant in atm K-l mol-l, and y = 2. The treatment is the same as that used previously except that the method for obtaining AS0,*has been improved somewhat in the present work. In addition the symmetry factor, u, has been included for these reactions. In the group contribution scheme some implicit allowance was previously made for the factor3 but this does not distinguish between primary and secondary hydrogen abstraction. Hence, using the present method, explicit inclusion of u is necessary. Consider the reaction R-H + C1. + R- - --H- - - -C] the activation entropy is given by ASo,* = So,(R bound) + So,(H bound) + So,(C1 bound) - So,(R-H)
-
So,(C1*)
We assume that So,(R bound) = So,(R-H) - Sop(Hbound) Thus, the effective activation entropy is given by ASo,* = So,(C1 bound) - So,(C1-)
Tables giving Sop(C1.) for varying temperatures are available,6 so we need merely to compute Sop(C1bound). We assume that the entropy of the “bound” C1 in the transition state is identical with the entropy of a “bound” C1 in the C12 molecule apart from the vibrational contribution. Thus Sop(Clbound in C1--H--R) = l/[So,(Cl,) - (vibrational contribution in Cl,)] + (vibrational contribution in C1--H--R) For a diatomic species, the vibrational contribution to entropy may be calculated from the enthalpy and free energy functions thus s o .
vib
=
(A - no)-
( G O
-ROO) Tvib
Tvib
where
(A - no) =---1.9872~ Tvib
-(Go
-
(ex
-
1)
Ao)/Tvib = -1.9872 In (1 - e-’)
and x = DhcjkT where D is the fundamental vibration frequency in wavenumbers and T(K) is, in our case, the mean reaction temperature. If the transition state (RH-Cl) is treated as a diatomic species RH-C1, we can obtain D by comparison with the vibrational frequency for H-Cl. Thus, the fundamental vibration frequency for a diatomic molecule depends upon the force constant (h)and the reduced mass (1)of the molecule, i.e.
is proportional to the square root of the force constant. Thus we obtain D R H C ~ D H C= I
(BIRH-c~/BIH-c~)(~~HcI/~~RH-cI)~
Hence, using the fundamental vibrational frequency for H-Cl, the calculated bond indices for the H-C1 bonds in the transition state R- -H- -C1 and in the H-C1 molecule and the reduced masses of the two species, we can calculate the fundamental vibrational frequency for any reaction intermediate. We may thus obtain x at the appropriate reaction temperature and, hence, the vibrational contribution to the entropy. The vibrational contribution to the entropy of C1, is calculated in a similar way, using D for Cl,. By this method, A factors were calculated for all the hydrogen abstraction reactions studied. Temperatures were again selected so as to make the calculated values comparable with published results. Calculated and experimental values are listed in Table 11. We also recalculated, by the above method, the A factors published in our earlier paper1 dealing with the chlorination of methane. The results are also presented in Table 11. The agreement with experiment is significantly improved. Values of log A were also calculated for the reverse reactions R H C 1 4 R---H---Cl* RH C1.
+
+
+
The entropy change at 298 K between the transition state and the reactants was first calculated from ASo = So(RH) So(Cl bound) - So(R.) - So(HC1)
+
Here So(C1bound) was obtained as described above and, where not available d i r e ~ t l y ,entropies ~,~ for Re and RH were calculated with Benson’s group contribution table^.^ Since entropy values were only available at 298 K, the entropy change at 400 K was obtained by using ASo400 = ASo298 + 2.3O3ACop(T,, log (400/298) where ACp(T,) is the average value of ACO, over the temperature interval 400-298 K. The A factors are then calculated in the usual way.
Calculation of Equilibrium Constants The availability of Arrhenius parameters for the forward and reverse reactions allows the rate constants for the forward and reverse reactions, kf and k,, respectively, to be Calculated. From these we can calculate an equilibrium constant for each of the reactions studied, i.e. kf Af K,, = - = k, A ,
-(A&
-
RT
rn,)
]
Table IV shows calculated values for the enthalpy of and the equilibrium constant, reaction AHT = (AEfK,,(calcd). Values of AH, and K,,(Th) derived from thermodynamic data are quoted for the chlorination of ethane, propane, and methane; for the chlorinated hydrocarbon reactions values of AH,, AST, and, hence, K,,(Th) have been obtained by using Benson’s group contribution methoda7 In calculating K,,(calcd), the calculated AE and A values for the forward and reverse reactions have been adjusted to the quoted temperature. Hence, if we consider the transition state as a diatomic For the reaction CH, + C1+ CH3 + HC1 the Arrhenius molecule RH-C1, we obtain parameters are taken from our previous paper except for Af, has been recalculated here (Table 11). Where ~ R H C ~ / D H C=I ( ~ R H c I / ~ H c I ) ~ ’ ~ ( ~ H c I / ~ ~ R H c ~ ) ~ ’ which ~ possible, values of AHT and K,,(expt) have also been However, if the anharmonicity constant remains the same derived from published experimental Arrhenius paramfor all the species, the bond index (BI) between the atoms eters.
2326
T. N. Bell, K. A. Perkins, and P. G. Perkins
The Journal of Physical Chemistry, Vol. 83, No. 18, 1979
TABLE IV: Equilibrium Constants for the Reactions RH t C1. + R.
+ HCl calcd Arrhenius parameters
thermodynamic data
exptl Arrhenius parameters
__I_
AH,,
AS,,
CH4
CH 3
J T, K mol-’ -___ 400 t8.4 31.7
C2H6
C,H*
450
-19.9
49.8
C3H8 C,H* C,CI,H C,H,CI CCI,CH,
n-C,H, i-C,H, C,CL CH,CICH, CCI,CH,
400 400 400 400 400
-21.1 -35.4 -11.9 -23.1 -20.7
CH,(CH,CI)CH, CH,(CH,Cl)CH, CH,(CHCI)CH,
CH,(CH,Cl)CH CH,(CH,Cl)CH, CH,(CHCl)CH,
400 400 400
-35.3 -22.4 -22.4
RH
kJ mol-’
R
-
’ With log A,
= 12.3.
With log A , = 10.7.
+ C3H8+ C1-
+7.8
5.3
6.5 X 1.9 X 2.6 X 10.4 X 4.1 X l o 4
-12.7 -29.8 -16.7 -21.4 -19.8
3.1 X lo4 0.9 X l o 6 9.5 X l o 3 7.9 X l o 4 11.5 X l o 4
28.4 30.2 32.5
12.2 X lo5 3.1 X l o 4 4.1 X l o 4
-28.4 -20.5 -8.1
With A E F = 15.06, log A , = 12.4.
(b)
He obtains relative rate constants as follows:
(11.7Fk0.13) RT ) 1.86 f 0.13
kn-CsHs
At 389 K, the calculated AE for the CHI reaction is 26.40
kJ mol-’
Keq(exptl)
_ _ _ I
39.7 32.2 35.3 38.4 36.7
i-C3H7+ HC1
-ki-CaH~ - - 0.55 exp(
7.4 X
K,,(calcd)
10.7 X l o 4
(a)
kCHd
3.6
AHT,
-16.7
C3H8 C1- n-C3H7+ HC1
-k C-z H ~ - 3.65 exp
K,,(Th)
kJ mol-’
lo4 lo4 lo6 lo3 lo4
Discussion It can be seen from Table I1 that the calculated values of log A for both forward and reverse reactions are in excellent agreement with experiment. However, the calculated activation energies for the forward reactions are generally somewhat higher than the experimental values. The success of our calculations in predicting equilibrium constants (Table IV) indicates that the Arrhenius parameters calculated here are more reliable than experiment. Where thermodynamic data are available directly, the calculated and thermodynamic equilibrium constants agree to within a factor of 2.2. The agreement of the calculated AHT and K,,(calcd) with the thermodynamic values derived from Benson’s group contribution method is also gratifying. However, the values of AHT and K,, for the methane and ethane reactions which have been obtained from experimental Arrhenius parameters show much poorer agreement with the thermodynamic values. In particular, the kinetic enthalpies, AHT, differ markedly from the thermodynamic values, indicating an error in the experimental measurement of either A& or UT. Forward Reactions. The discrepancy between calculated and measured activation energies suggests that, under experimental conditions, some factor may operate which is not accounted for in the computations. For the present, therefore, it is more pertinent to consider the relative rates of pairs of forward reactions. KnoxE has used a competitive reaction technique to determine the relative rate constants for the two sets of reactions: + C1- CzHS + HC1 (a) CH4 + C1- CH3 + HC1 (b) and
AHT,
7.7 X 7.7 X 2.9 X
los lo4 lo3
13.2 +0.9 -29.6
18.7 37.3 14.0 X 550.0 X
-30.1 -31.8 -31.8 -32.3
6.0 X 10’ 15.7 X l o 4 11.1X lo4‘ 163 X
lo4’
With A E F = 14.6, log A f = 13.5.
TABLE V: Relative Rates per Available H Atom for the Reactions C1. t RH -+ R. t HCl at 298 K relative rates RH calcd ref I O refii CH, C2H6
C,H, (primary) C,H, (secondary) C,HSCl (CHA C,H,CI (CH,Cl)
0.28 100 33 343 126 7.1
2.0 i 0.2 100 1 1 o i 10 480 i 20 7.4 44.0
0.4 100 120 444 12 61
kJ mol-I and the A factor (Table 11) is 1.73 X The corresponding values for ethane at the same temperature are 13.17 kJ mol-I and 3.84 X 1013. Hence, the calculated rate ratio is = 131.93 at 389 K
which agrees well with Knox’s result of 135.66 at this temperature. Calculations on the two propane reactions have been carried out at 353 K and the calculated ratio is
which compares with a value of 1.04 from Knox’s equation. The calculated difference in activation energy of 6.11 kJ mol-I is somewhat larger than that obtained by Knox but agrees well with the value of 6.07 kJ mol-I measured at high temperatures (300-600 “C) by Hass, McBee, and Weber.g Kelly et al.1° have studied the relative rates for the abstraction of hydrogen from CH4, CzH6, the CH3 and CHzCl moieties of C2H6C1,and from the primary and secondary carbon atoms in propane at 25 “C. We have calculated relative rates at this temperature and the theoretical results are compared with those of Kelly et al. in Table V. As the experimental values are quoted per available H atom, the symmetry factor, (r, has been omitted when calculating A. Ratios measured by Knox and Nelsonll are also included in Table V. The rate of the C2H6reaction was taken as a standard in each case and all others are quoted relative to this. The chlorination of n-butane,” n-butyl chloride,I3 and 2-chlorobutane14 has been studied by Anson, Fredricks, and Tedder over a range of temperature. These authors define the quantity “relative selection” which is equal to
The Journal of Physical Chemistry, Vol. 83, No. 18, 1979 2327
Chlorination of Paraffin Hydrocarbons
TABLE VI: Relative Selection (RS) at 308 K for RH f C1. + R. t HC1 calcd exptl RS for RS for RH propanes butanesa -CH3
1
1
\ /CH2
9.7
3.9
-CH2CI
0.3
0.7
CHzCI,
6.7
2.2
1.5
1
-CHCI-CH3
0.8
0.2
\ / CHC I
1.6
3.2
CH2CI
a
'.''
CH3
Values taken from ref 12, 13, and 14.
the ratio of the rate constants for abstraction of the different types of hydrogen atoms in a molecule. Although the present calculations have been carried out on propanes, we would expect them to be comparable with the experimental results for butanes. Again, the symmetry factor is omitted from the calculation of rate constants, since the experimental values are quoted per H atom. The experimental and calculated values for the relative selection at 308 K, based on standards of CH3CHZCHzCH3 C1- CH3CHzCH2CH2 + HC1
+
and CH3CHZCH3
+ C1-
CH3CH2CH2 + HCI
respectively, are shown in Table VI. Although not identical, the relative selection values calculated for propanes follow, in every case, the trend measured for butanes by Fredricks and Tedder. The calculated data for the abstraction of hydrogen from CpH5C1follow precisely the same trends. Considering the molecules CH3CH2C1,CH3CH2CH2C1,and CH3CHzCH2CHzCl, abstraction of hydrogen from the CHzCl end of the molecule is, in every case, more difficult than abstraction from the parent hydrocarbon, whereas abstraction from the CH3 end is from 1 to 1.5 times faster. The experimental results for CzH5C1'oJ1in Table IV are clearly at variance with these trends. The trends observed in Table VI which relate to our calculated values for propanes and experimental values for butanes may be summarized in the following general set of rules: (1)Hydrogen abstracti~nis more rapid from a secondary carbon (whether or not C1 substituted) than from a primary carbon. (2) The effect of a chlorine atom in the cy position is to retard hydrogen abstraction from both the CY and the p positions; in general, the effect of chlorine substitution diminishes the further away the substitution is from the site of hydrogen abstraction.
TABLE VII: Rate Constants at 400 K rate constant, cm3 mol-' s - ' reaction exDtla calcd C,H,* t HC1 CH,ClCH,* t HCl CCl,CH,* t HC1 CCl,CCl,. t HCI
1.1x lo' 2.3 X 10' 7.6 X l o 4
5.6 X 10' 2.5 X lo6 1.4 X l o 6
Values taken from ref 17.
(3) Chlorine substitution at a secondary carbon atom decreases the rate of both secondary and primary hydrogen abstraction. However, the rate of secondary H abstraction never falls below that for a primary H group. Since the predictions based on the propane calculations are qualitatively valid for butanes, it seems reasonable that these rules should also obtain for longer-chain hydrocarbons. We will consider these cases in a future publication. Reverse Reactions. The experimental values for AI3 and log A given in Table 11for the reactions CzH5+ HC1, C2C15 + HCl, C2C13H2+ HC1, and C2C1H4+ HC1 are taken from the review by Chiltz et al.17 For the first reaction, a value for log A has also been obtained by extrapolation of the published valued5 for the reaction of CzH5*,CH3., and H. with HI and HCl. No experimental data are available for the reaction of propyl radicals with HC1. It is of interest to compare the predicted reaction rates for the four ethane reactions with the measured rates from Chiltz et al.17 Accordingly, the data from Table I1 have been used to compute the calculated and experimental rate constants for these four reactions at 400 K. These are listed in Table VII. The order of reactivity is essentially the same for both sets of results, reaction of the polychlorinated ethyl radicals being slower than reaction of the unsubstituted or monosubstituted radicals.
References and Notes T. N. Bell, K. A. Perkins, and P. G. Perkins, J. Phys. Chem., 81, 2610 (1977). T. N. Bell and P. G. Perkins, Nature (London), 256, 300 (1975). T. N. Bell and P. G. Perkins, J. Phys. Chem., 81, 2102 (1977). "Handbook of Chemistry and physics," 56th ed, CRC Press, Cleveland, Ohio, 1975. P. S. Fredricks and J. M. Tedder, Chem. Ind. (London),490 (1959). "JANAF Thermochemical Tables", Dow Chemical Co., Midland, Mich., 1965. S. W. Benson and H. E. O'Neal, Nat/. Bur. Stand. U.S.,Circ., NO. 21 (1970). J. H. Knox, Chem. Ind. (London), 1631 (1955). E. Hass, J. W. McBee, and H. Weber, Ind. €ng. Chem., 28, 333 (1936). C. C. Kelly, W. H. S. Yu, and M. H. J. Wijnen, Can. J. Chem., 48, 603 (1970). J. H. Knox and R. L. Nelson, Trans. Faraday Soc., 55, 937 (1959). P. C. Anson, P. S. Fredricks, and J. M. Tedder, J . Chem. Soc., 187, 918 (1959). P. S. Fredricks and J. M. Tedder, J. Chem. Soc., 28, 144 (1960). P. S. Fredricks and J. M. Tedder, J . Chem. Soc., 682, 3520 (1961). A. F. Trotman-Dickenson and G. S. Milne, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 9 (1967) E. Ratajczak and A. F. Trotman-Dicksnson, "Supplementary Tables of Bimolecular Gas Reactions", UWIST, Cardiff, 1969. G. Chiitz, P. Goldfinger, G. Huybrechts, G. Martens, and 0 . Verbeke, Chem. Rev., 83, 355 (1963).
