Chlorine Kinetic Isotope Effects Thermal Decomposition of 1 -Chloroethane and Evaluation of Possible Models of Activated Complex BY ALLAN MACCOLL* AND MARGARET N. MRUZEK Christopher Ingold Laboratories, University College London, 20 Gordon Street, London WC1H OAJ Received 23rd November, 1977 Chlorine kinetic isotope effects have been investigated for the pyrolysis of 1-chloroethane in a static system in the temperature range 395482°C. The temperature dependence of the kinetic isotope effects has been determined. The mass spectrometric isotope ratio analysis was made on the hydrogen chloride produced. A model for the chlorine involvement in the four-centre activated complex is advanced and various alternative geometries are evaluated in terms of heavy-atom approximation and first-order high temperature kinetic isotope effects.Best agreement with the experimentally determined values of kJ5/k3’ is given by a model of the activated complex which involves chlorine participation in the reaction coordinate with three degrees of freedom. The effect of the individual geometric parameters that includes the C-CI stretching, the C-C-CI bending and the C-CH3 stretching and their combinatioc, is evaluated. The kinetics of the thermal deconiposition of chloroalkanes in the gas phase has been the subject of many systematic studies and reviews.lm8 Despite different opinions on the nature of the activated complex all authors are agreed that in a seasoned vessel dehydrohalogenation follows first-order kinetics and proceeds by a unimolecular mechanism. Two recent reviews have dealt with this topic in great detail.** A range of possible models of the activated complex for the pyrolysis of chloroalkanes has been considered.They vary from those with a large carbonium ion character, where the C-Cl bond breaking is well advanced in comparison to other bond changes, to those involving a four-membered ring with simultaneous C-C1 and C-H bond rupture and H-Cl and C=C bond formation with a significant degree of charge separation. * Previous studies of heavy atom isotope effects have emphasised that they can provide unique mechanistic information about the nature of the activated complex. l-l and is now well established. The magnitudes of the kinetic isotope effects are known to be related to vibrational changes in bonds involving the isotopic atom in proceeding from the reactant to the activated complex and consequently connected with structural changes.With modern computer techniques it is possible to evaluate the magnitude of the isotope effects that can be expected from various models of the activated complex and correlate them with the experimental results. The aim of this study was to determine the participation of chlorine atom in the activated complex in gas phase elimination reactions by measuring the relative k3 5/k37 ratios and their temperature dependence. The chlorine kinetic isotope effects were particularly suited for the purpose of the activated complex study, since unimolecular dehydrohalogenation reactions involve reduction in force constants associated with the C-Cl bond and therefore an appreciable isotope effect might be expected for The theory was pioneered by Bigeleisen 2714A .MACCOLL AND M. N . MRUZEK 2715 the isotopic substitution on either carbon or halogen. Blades and his co-workers l6 have determined the HID intramolecular isotope effects in the pyrolysis of ethyl chloride but their method might include also the secondary isotope effects, which, being temperature independent, could have a significant influence on the magnitude at the reaction temperat~re.~. l2 The H/D isotope effects determined for the decomposition of chemically activated ethyl chloride in the gas phase were interpreted in terms of four-centre activated complex with a considerable C-H bond extension.” EXPERIMENTAL KINETICS Ethyl chloride was pyrolysed in the temperature range 395482°C using the static method.* The reaction vessel was seasoned with a carbonaceous coating in order to prevent surface reactions. The extent of reaction was determined from the total pressure increase as registered by all-glass pressure gauge and recorded on chart paper. ISOTOPE RATIO DETERMINATION The isotopic analyses were based on hydrogen chloride produced, which was the isotopically substituted product of decomposition. The chloride ion was precipitated with solution of silver nitrate and the dried silver chloride was converted into methyl chloride with MeI, using a modified sealed tube method of Hill and Fry.lS The standard sample of methyl chloride was prepared from hydrogen chloride collected after the total decomposition of ethyl chloride.It was necessary to adopt this method since hydrogen chloride produced is not suitable for direct measurement on the mass spectrometer. The ratios of C137/C135 in methyl chloride samples were measured with an isotope ratio twin collector, double inlet mass spectrometer MS 20 (G.E.C.-A.E.I.). The stability and the reproducibility was checked by determining the zero enrichment on a commerical standard sample of methyl chloride. The reproducibility obtained on four series (10 measurements of 10 samples) was 0.0039 %. The results of the individual zero enrichments were -0.0051+0.0044, - 0.0029+ 0.0040, - 0.00452 0.0029 and - 0.0020+ 0.0041 %. Therefore the mass spectro- metric system was operating satisfactorily. The measured pair of isotopic ion beams was m/e = 52 (CH3C137) and m/e = 50 (CH3C13’).CALCULATIONS All calculations were performed on an IBM System 360/6 and written in FORTRAN LV programming language. The program used for the rigid rotor approximation calculations was divided into five major subroutines. Initially the basic geometric input data and the internal coordinate values were entered and the principal moments of inertia and the MMI factors were calculated. Then the vibrational frequencies and temperatures were entered and the individual terms (VP, EXC, ZPE) evaluated. Finally all the calculations associated with the isotope effects and their temperature dependences were performed. RESULTS EXPERIMENTAL ISOTOPE EFFECTS The ratio of isotopic rate constants was calculated according to the relation derived previously k3’ In [I - f S’] k37 - In [l - r f S ’ ] - where r = R,/R,, R being the ratio of heavy isotope to the lighter isotope in the product at the fraction of reaction f, or at the complete decomposition, a.The factor S’ = [(l +I?,)/( 1 + R,)] is a correction term and can be estimated with sufficient2716 CHLORINE KINETIC ISOTOPE EFFECTS accuracy either from the literature or by the measurement of ratios of the relevant isotopic intensities. For a reaction involving heavy atoms, where the difference in the isotopic ratios is relatively small, the correction term S' is very close to unity. Chlorine kinetic isotope effects in the pyrolysis of I-chloroethane were determined at three temperatures. The fraction of reaction f was determined manometrically.The value Y which is the quotient of the isotopic ratios for the sample R, and the standard R, was averaged from 10 measurements. The values of the isotopic ratios r, fraction of reaction& and calculated k35/1;37 are listed in table 1. TABLE 1 .-CHLORINE KINETIC ISOTOPE EFFECTS IN THE THERMAL DECOMPOSITION OF 1 -CHLORO- ETHANE f 481.6 r temperaturejOC 440.9 r k35/k37 f 394.9 r 0.10 0.99859 1.00149 0.10 0.99852 1.00157 0.10 0.99851 1.00158 0.25 0.99871 1 .OO14g 0.25 0.99869 1.00152 0.10 0.99848 1.00161 0.25 0.99869 1.00152 0.25 0.998'74 1 .OOMg 0.25 0.99866 1.00154 0.50 0.99894 1 .OO153 0.50 0.99891 1.00157 0.40 0.99893 1 .OO157 0.75 0.99908 1.001 56 0.40 0.99866 1.00164 mean k35/k37 = 1.00151 mean k35/k37 = 1.00155 mean k35/k37 = 1.00159 & 0.00002 k ~ .o o ~ o ~ * 0.0000~ The magnitudes of chlorine kinetic isotope effects are small and the dependence on temperature is slight, although significant. The isotope effects studied on the chlorine leaving group appear to be primary, with normal dependence on temperature : their magnitudes increase as the temperature falls. The calculated values of k35/k37 appear to be insensitive to the fraction of decomposition f. Plots of In (k35/k37) against 1/T2 give straight lines. THEORETICAL ANALYSIS The theoretical calculations are based on Bigeleisen's heavy atom approximations for the reduced ratios of partition functions.20 The abbreviated forms of individual contributing factors were introduced by Wolfsberg and Stern.21 The RRA (the rigid rotor approximation)13 is the isotopic rate coiistant ratio on the harmonic oscillator model multiplied by the ratios of symmetry numbers and transmission coefficients The MMI factor is the contribution from rotational and translational partition functions, the EXC factor includes the product of vibrational excitations and the ZPE involves the differences in the vibrational zero-point energies in reactants and the activated complexes.With the use of the Teller-Redlich product rule 22 which relates the vibrational frequencies, principal moments of inertia and masses of nuclei in isotopically substituted molecules, an alternative expression for the isotope effects of the form is obtained where the VP factor is the product of ratios of isotopically different vibrational frequencies and vz/vg is the ratio of imaginary frequencies along the path of decomposition.At infinite temperature this ratio is the limiting value for the kinetic isotope effect and can be determined by the extrapolation of the plot of In (k35/k37) against 1/T2 to zero. In order to evaluate the individual factors contributing to the expression for the rigid rotor approximation, it is necessary to know the geometries and the vibrational RRA = MMI x ZPE x EXC. RRA = (v$/v%) VP x ZPE x EXCA . MACCOLL A N D M. N . MRUZEK 2717 frequencies of the reactants and the activated complexes for both isotopic species. Lack of sufficient information in the spectroscopic literature about isotopic shifts in individual vibrational frequencies necessitated the use of some related approxima- tions.The individual isotopic bands are not usually reported, either because of low resolution or large band broadening. In the case of primary alkyl chlorides where the chlorine isotopic splittings have been determined, only those concerning the C-Cl stretching modes have been MODEL OF THE ACTIVATED COMPLEX On the assumption that the thermal activation of alkyl chlorides resulting in HCl elimination is a unimolecular reaction proceeding through a single molecular step, the activated complex involves a four-centre cyclic structure. As the reaction progresses, the C-Cl and the C-H bonds are gradually increasing in length whilst the C-C bond is shortening and the H-C1 bond is forming. The true geometry of the activated complex might be visualised as some intermediate combination of all four processes.The reaction can be written schematically as \ / \ / \ / C- + C===C +HCl. -c-c- .-* -c=== A planar ring structure of the activated complex with relatively weak interactions between the H and C1 atoms has been used in our calculations. The advantage of such a cyclic structure is that the vibrational modes of the activated complex are similar to those of the reactant molecules and therefore the assignment of the individual frequencies is less difficult. Considering two isotopically different mole- cules, a further simplification can be used, namely that only the vibrational modes with appreciable isotopic shifts have to be included, since in the relative ratios the contributions of the other modes cancel themselves out. The hydrogen vibrations are assumed not to be affected by chlorine isotopic substitution according to the high-frequency separation approximation.In order to develop a model of the activated complex that would reproduce the experimental data to some degree of accuracy a special emphasis was placed on the influence of the relative changes in geometry on the MMI terms. The motions of heavy atoms are represented in the ground state of chloroethane by C-C1 and C-CH3 stretchings and by a C-C-Cl bending and therefore these three geometric parameters were considered to change on going to the activated complex. The effect of individual variations is shown in fig. 1. The relative percentage increase in the C-C1 bond length and the reduction in the C-C-C1 angle were taken from the ground state equilibrium values.The minimum C-CH3 interatomic distance that was considered considered as an extreme was that of the C=C double bond of ethylene. Since the initial assumption was that the model should resemble the reactant more than the products, the relative changes of geometric parameters were considered to be of the order of only a few percent. A set of models was generated as shown in table 2, where either one, two or all three of these internal coordinates were varied. The computer program was set up to evaluate the individual moments of inertia, their products and isotopic ratios of each model and to calculate the MMI factors. The set of Cartesian coordinates was determined for each atom in the ground state equilibrium configuration, using the structural parameters reported by Schwendemann2718 CHLORINE KINETIC ISOTOPE EFFECTS and The molecule was orientated in such a way that the x and y principal axes were in the plane of symmetry and the z axis was perpendicular to them.The same set of Cartesian coordinates was used for the evaluation of the principal moments of inertia for the C13' substituted molecule, since the substitution of heavier isotope changes the C-Cl bond length by <0.01 nm. Sets of Cartesian coordinates for E E I 1.0040 1.0030 1.0020 1.0010 1 / 1.0010 1.0000 0.9990 0.9980 I I f l l I 1 0 20 40 60 80 100 % change in reaction coordinate FIG. 1 .-Dependence of the MMI terms on reaction coordinate : (a) C-C-Cl bend ; (b) C-CH3 stretch ; (c) C-Cl stretch.-_ TABLE 2.-RELATIVE VARIATIONS IN THE INTERNAL COORDINATES FROM THE GROUND STATE FOR MODELS OF THE ACTIVATED COMPLEX AND THE MMI TERMS model Cl-Cl! % C-C-Cl/ % C-CHSI % MMI 1 2 3 4 5 6 7 8 9 10 11 12 13 0.5 3.0 5.0 0.5 2.0 2.0 3 .O 3 .O 3 .O 4.0 4.0 4.0 4.0 0.0 0.0 0.0 2.7 2.7 5 .O 0.7 2.7 5.0 5.0 2.7 5 .O 0.0 0.0 0.0 0.0 0.0 3.0 5 .O 1 .o 4.0 7.0 1 .o 3 .O 5 .O 5 .O 0.999 96 0.999 75 0.999 59 0.999 91 0.999 86 0.999 87 0.999 76 0.999 86 0.999 84 0.999 68 0.999 70 0.999 70 0.999 80 selected models of the activated complex were determined in a similar way by varying the individual internal coordinates according to table 2. The values of the MMI terms (table 2) consist only of the ratios of the products of moments of inertia in the ground state to those of the activated complexes, since the ratio of masses in both states is equal to unity.The MMI factors are not dependent on temperature. VIBRATIONAL MOTIONS OF THE ACTIVATED COMPLEX Three vibrational motions of the ground state ethyl chloride that exhibit a significant dependence on chlorine isotopic mass are the C-C1 and the C-CH3 stretchings and the C-C-Cl bending mode. The largest isotopic splitting has beenA . MACCOLL AND M. N. MRUZEK 2719 observed 23 for the C-C1 stretching where the frequency assigned to chlorine 37 is 4.6cm-l lower than that for chlorine 35. The other isotopic splittings for the C-C-Cl bending and the C-CH3 stretching frequencies are 1.5 and 0.5 cm-', respectively. These motions were considered to undergo significant changes in the activated complex.Since other frequencies were assumed not to be isotopically dependent on the mass of chlorine atom, the model calculations type A were using only those three frequencies and their changes in the activated complex. For model calculations type B we have extended the number of isotopically dependent frequencies according to a recent p u b l i c a t i ~ n . ~ ~ The other vibrational frequencies that appear to have a small isotopic dependence on chlorine are the CH2 wag (0.3 cm-l), the CH, twist (0.4 cm-') and the CH, rock (0.3 cm-l). The frequencies in the activated complex have been estimated by use of the rules of Pauling and Badger.26 These proved to be a valuable guide to the extensions of the internal coordinates, since according to them small changes in the ground state bond length cause considerable changes in the vibrational frequencies.The preliminary calculations showed (fig. 1) that the changes in internal coordinates cannot be larger than a few percent. The values of the isotopic splittings in the activated complex were estimated in the first approximation according to the values reported for 2-chloro-2-methylpropane and I -chlorobutane.2 DISCUSSION Chlorine kinetic isotope effects in the thermal decomposition of 1-chloroethane are relatively small and they exhibit normal dependence on temperature.* In order to limit the great number of possible models the calculated values of the rigid rotor approximation (RRA) were compared with the experimental results. The number of models was further reduced by comparison with the temperature dependence values, which proved to be a very valuable indicator.Some values of the RRA were in a very good agreement with the experimental data at one temperature but they could not be included as possible models of the activated complex, since the discrepancies at other temperatures were too large. Although the four-centre activated complex appears to be rather a complicated model, the theoretical calcula- tions on some models using the assumptions mentioned above could provide reason- able agreement with the experimental results. Since the ratios of masses in the assumed models are identical with reactants, the only contribution to the MMI terms comes from relative products of moments of inertia. The effect of systematic changes in individual geometric parameters on the MMI is shown in fig.1. The increase in the C-Cl bond length has the greatest effect on moments on inertia. Beyond a value corresponding to an extension of 100 % of the ground state internal coordinate, the curve approaches the asymptotic limit. The influence of the C-C-Cl bending coordinate on MMI is in the opposite direction to those of the C-Cl and C-CH3 stretching and appears to be a more effective geometrical parameter than the C-CH3 stretching mode in adjusting the model of the activated complex. The plots of calculated values of the RRA terms in their dependence on relative changes in the individual internal coordinates (fig. 2) show similar relationships to those for the MMI factors. The values of the RRA for the C-Cl stretching and also the temperature dependence are much higher (24.2 x than those determined experimentally (8.0 x The high ratio of the decomposition frequency would require extremely large isotopic splitting in the reaction coordinate and therefore * They are the smallest in the series of five chloroalkanes that were measured.272720 CHLORINE KINETIC ISOTOPE EFFECTS the simple extension of the C-Cl bond is not likely to account for the chlorine kinetic isotope effects.The C-CH3 distance appears to be a considerably less sensitive parameter as regards values of the RRA and also the temperature dependence is much smaller ( 3 . 0 ~ in comparison with the experimental data. The C-C-Cl bending motion increases the values of the RRA considerably over a very small change in the angle but the temperature dependence remains low (4.2 x 1.0080 C (b} 1.0070 1.0060 1 1 .m o y 1.0030 id 1.0020 1.0010 k) 1.0000 0 20 40 60 80 100 % change in reaction coordinate FIG. 2.-Dependence of the RRA values on reaction coordinate : (a) C-C-Cl bend ; (b) C-CI stretch ; (c) C-CH3 stretch ; (d) expeiimental k35/k37. TABLE 3.-RRA OUTPUT FOR MODELS OF THE ACTIVATED COMPLEX OF ETHYL CHLORIDE AT 481.6"C model A vfs/v& VP EXC ZPE VPXEXCXZPE RRAa d i f f ~ 1 0 5 b 1 2 3 4 5 6 7 8 9 10 11 12 13 1.006 93 1.006 71 1.006 55 1.000 81 1.001 10 1.001 47 0.999 91 1.001 12 1.002 06 1.001 18 1.000 96 1.001 29 1.001 43 0.993 08 0.993 08 0.993 08 0.999 09 0.998 76 0.998 41 0.999 85 0.998 74 0.997 79 0.998 49 0.998 74 0.998 41 0.998 37 1.003 46 1.004 39 1.003 46 1.004 39 1.003 46 1.004 39 0.999 89 1.001 35 1.000 03 1.001 60 1.000 37 1.001 59 0.998 97 1.001 64 1.000 05 1.001 59 1.000 93 1.001 64 1.OOO 30 1.001 59 1.000 05 1.001 59 1.Ooo 37 1.001 59 1.000 67 1.001 69 1.OOO 89 1.007 83 24.2 1.000 89 1.007 62 24.2 1.000 89 1.007 46 24.3 1.000 34 1.001 16 9.3 1.000 39 1.001 50 10.4 1.00037 1.001 83 10.0 1.000 46 1.000 37 12.3 1.000 39 1.001 51 10.6 1.000 35 1.002 41 9.7 1.00039 1.001 58 11.1 1.00039 1.001 35 10.5 1.OOO 37 1.001 66 10.0 1.00067 1.002 16 11.7 a Experimental value of k3'/k3' = 1.00151 +0.00002. b (RRA at 394.9"C-RRA at 481.6"C), experimental difference = 8 x As none of the variations in the internal coordinates can bring the calculated RRA in agreement with the experimental results, it is necessary to study the effect of combination of these modes (table 2).Since the MMI and the VP terms are independent of temperature, the contributions to the values of the RRA as a function of temperature come from the vibrationalA. MACCOLL AND M. N. MRUZBK 2721 modes, namely from the EXC and ZPE terms. Their magnitudes change with temperature but in opposite directions, with the ZPE term increasing about twice as fast as EXC as the temperature is lowered. The change in the EXC factor is relatively minor but it reduces the effect of the ZPE factor, so the total temperature dependence on their product, which is the real contribution to the ratio of reduced partition functions, is small. The values of the products of VP x ZPE x EXC for all selected models vary between 1.000 35 and 1.000 89 (table 3).From the selected set of models of the activated complex that were examined in the theoretical analysis, two models that agree best with the experimentally observed chlorine kinetic isotope effects and their temperature dependence, appear to be numbers 5 and 8. The values of k35/k37 and the RRA values for both models are TABLE 4.-cALCULATED VALUES OF THE RRA OF MODELS 5 AND 8 COMPARED WITH THE EXPERIMENTAL VALUES temperature/% model 5A model 8A model 8B experimental 4 8 1 . 6 1.001 50 1.001 51 1.001 51 1.001 51 440.9 1.001 55 1.001 55 1.001 55 1.001 5 5 3 9 4 . 9 1.001 60 1.001 6 1 1.001 60 1.001 59 compared in table 4. The geometrical parameters are close for both models (table 5 ) and the values of the MMI. terms are identical (0.999 86).Model 5 requires the C-Cl internal coordinate to be extended by 2 %, the C-CW3 bond to be shortened by 3 % and the C-C-C1 angle to be decreased by 2.7 % from the ground state equilibrium values. For model 8 the C-Cl bond is increased by 3 % and the C-CH3 bond is decreased by 4 %. The C-C-C1 angle decrease is the same in both cases. The association of the decomposition frequency with the C-C1 stretching in the model calculation of mixed modes necessitates higher isotopic splittings for the C-C-Cl bending than the C-CH3 stretching frequencies (table 6). This phenomena remained unchanged when other isotopically dependent frequencies were included. TABLE 5.-INTERNAL COORDINATES FOR CHLORINE PARTICIPATION IN THE ACTIVATED COMPLEX ground state model 5 model 8 0.1788 0 .1 8 2 4 0 . 1 8 4 2 m - C H h m 0 . 1 5 2 0 0 . 1 4 7 4 0 . 1 4 5 9 L c--c-Cl/deg 1 1 1 . 3 108.3 108.3 Y c c l /nm The temperature dependence for model B with more vibrational motions appears to make the range smaller and to improve the agreement with the experimental data, but the effect is not very significant. The values of the temperature dependent terms (ZPE and EXC) are also very similar for both types as listed in table 7. The effective frequency for model A with fewer frequencies is M 80 % of the ground state value. The derecase to 74 % for model B might be the reason for the smaller temperature range since the ZPE is the factor which is basically affected by the sum of the real iso- topic shift changes in the models of the activated complexes.It can be observed from fig. 3 that the isotopic splittings have a significant influence on the calculated values of the RRA. The increase in from 3.5 to 4.3 cm-1 produces the linear drop of the RRA from 1.002 57 to 1.000 38. The slope is about twice the value ( - 2.74 x for any of the other vibrational motions (- 1.33 x for the C-CH3 stretch). So it appears possible to adjust the value of the RRA by varying the isotopic splitting for the bending coordinate in the activated complex.2722 CHLORINE KINETIC ISOTOPE EFFECTS The theoretical analysis of models of the activated complex shows that the use of the reduced partition function ratios, together with the heavy atom approximation, provide satisfactory agreement with the experimental results. The chlorine motion in the activated complex generates changes in the other vibrational modes, with the significant contribution coming from the C-C-C1 bending and C-CH3 stretching.All changes in geometrical parameters are only a few percent from the ground state TABLE 6.-FREQUENCIES AND ISOTOPIC SPLITTINGS FOR MODEL 8 OF ETHYL CHLORIDE/Cm-* ground state model 8A model 8B EtCW Av EtC135 Avf EtC135 Av* - - 664.9 4.6 - - vc-CI VC-CHL, 974.0 0.5 1053.9 1.2 1053.9 0.74 vc-c-CI 336.0 1.5 389.8 3.7 389.8 3.85 VCH2 wag 1287.0 0.3 1426.0 1.2 VCH2twist 1245.0 0.4 1224.4 0.24 VCHzrock 785.0 0.3 1070.8 0.1 TABLE 7.-cOMPUTER OUTPUT FOR MODELS 8A AND 8B AT 481.6"C MMI v & M VP EXC ZPE ZPE X EXC model 8A 0.999 86 1.001 12 0.998 74 1.OOO 05 1.001 59 1.001 64 model 8B 0.999 86 1.001 21 0.998 65 1.00005 1.001 61 1.001 65 values, Model calculations reveal that it is possible to achieve satisfactory agreement with the experimentally observed values of kinetic isotope effects by varying the isotopic splittings in those reaction coordinates that have low vibrational frequencies. The temperature dependence seems to be influenced by the changes in reaction coordinates with higher vibrational frequencies.This effect is so strong that the 1.0022 1.0020 1 .OO I8 d '. 0°16 Fr: 1 0014 1.0012 1. 0010 1.00081 . 1 1 t I I I I 1 - 0 1.0 2.0 3 .O 4.0 cm-' stretch ; (c) CH2 twist ; (d) CH2 rock ; (e) C-C-Cl bend ; (f) experimental k3'/k3'. FIG. 3.-Dependence of the RRA terms on isotopic splittings at 394.9"C : (a) CH3 wag ; (b) C-C increase in the shift of the CH, wag by more than five times its ground state value results eventually in the inverse dependence of the RRA on temperature.The chlorine kinetic isotope effects measured on pyrolysis of 1-chloropropane, 1 -chloro- butane, 2-chloropropane and 2-chloro-2-methylpropane, where the temperature dependence is much more significant than in the case of 1-chloroethane, are in betterA . MACCOLL AND M . N. MRUZER 2723 agreement with the theoretical calculations for model 8 than mode1 5.27 Since the individual factors do not reflect the value of kinetic isotope effects consideration of the complete equation is essential in the evaluation of theoretical models of the activated complexes. We thank the S.R.C. for a grant for the purchase of the M520 (A.E.I.) isotope ratio mass spectrometer.D. H. R. Barton and K. E. Howlett, J. Chem. Soc., 1949, 165. K. E. Howlett, J. Chem. Sac., 1952, 3695. W. Tsang, J. Chem. Phys., 1964,41,2487. H. Hartmann, H. G. Bosche and H. Heydtmann, 2, phys. Chem. (Frankfurt), 1964, 42, 329. D. H. R. Barton, A. J. Head and R. S. Williams, J. Chem. Soc., 1951,2039. H. Heydtmann and G. Knck, 2. phys. Chem. (Frunkfurt), 1961,28,85. W. H. Saunders Jr and A. F. Cockerill, Mechanisms of Elimination RLactions (Wiley-Inter- science, New York, 1973). ' K. A. Holbrook and A. R. Marsh, Trans. Faraday Soc., 1967,63, 643. ' A. Maccoll, Chern. Rev., 1969, 69, 33. lo K. C. 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Cross, Molecular Vibrations (McGraw Hill, New York, 23 R. C. Williams and J. W. Taylor, J. Amer. Chem. Suc., 1973, 95, 1710. 24 R. H. Schwendeman and B. D. Jacobs, J. Chem. Phys., 1961,36,1245. 2 5 R. L. Julian and J. W. Taylor, J. Amer. Chem. SOC., 1976,98,5238. 26 H. S. Johnston, Gas Phase Reaction Rate Theory (Ronald Press, 1966), p. 81. 27 M. N. Mruzek, Ph.D. Thesis (University of London, 1976). (PAPER 7/2055)