J. Chem. Soc., Faraday Trans. I, 1982, 78, 677-693 Chlorine-catalysed Pyrolysis of 1,2-Dichloroethane Part 2.-Unimolecular Decomposition of the 172-Dichloroethyl Radical and its Reverse Reaction PHILIP G. ASHMORE* AND ANTHONY J. OWEN Department of Chemistry, University of Manchester Institute of Science and Technology, P.O. Box 80, Manchester M60 1QD AND PETER J. ROBINSON Department of Chemistry, Manchester Polytechnic, Manchester M 1 5GD Received 30th December, 1980 Fall-off curves for the unimolecular rate constant k , of the reaction C2H3C12 C,H,Cl + C1 have been calculated by the Forst and RRKM methods and compared with the experimental results reported in Part 1 and by Huybrechts et al. The Forst calculations can be fitted to the Part 1 results, but then predict kern) values that lie below the experimental results of Huybrechts et al.which refer to lower temperatures and higher pressures. In contrast RRKM calculations using higher Arrhenius parameters give fall-off curves that are compatible with all available experimental data. The preferred RRKM models without allowance for the centrifugal effect have Edrn) x 19.6 kcal mol-l (82 kJ mol-l) and Aim) x 1014.0 s-l. When a reasonable centrifugal effect is allowed for the early transition state (Z+/Z x 2) the preferred models have E2 x 20.0 kcal mol-I (84 kJ mol-’) and Aim) x s-l. Our experimental evaluations of kLP,, are used in conjunction with earlier experimental results and RRKM-based calculations for the reverse reaction Cl + C,H,Clz C2H3C12 to evaluate Ai?) and EL?). The decomposition of 1,2-dichloroethane (DCE) catalysed by chlorine or by chlorine plus nitric oxide proceeds by the chain-propagating steps (1) and (2) with competition from step (3) (1) C2H3C12 + C2H3Cl+ el (2) (3) The competitive reactions allow evaluation of k , / k , and experimental studies’ have shown that k , is in the unimolecular fall-off region for pressures p between 8 and 150 Torr.? Extensive measurements of yi,)p = k$”)/k3 as a function of p were made at five temperatures between 520 and 572 K.The mean values @-’) were calculated at chosen levels of p using the published2 Arrhenius parameters for k , and are here shown in table 1 with the standard errors of the means. It is clearly of importance to see how these results conform with various theories Cl + C,H,Cl, + C2H3C12 + HCl C,H,Cl, + Cl, -+ C2H,C1, + Cl.t 1 Torr = 101 325/760 N m-*. 677c z TABLE ME MEAN VALUES OF p, kip) (WITH STANDARD ERRORS OF MEANS AND NUMBERS OF RUNS) OF pDCE, M VESSEL I3 AT THE TEMPERATURES INDICATED 572 K p f s.s./Torr ~ p ) + ~ . ~ . / 1 0 5 S-1 k p ) f ~ . ~ . / 1 0 5 s-1 kip) +s.E./~o~ s-1 ~ p + ~ . ~ . / 1 0 5 s-1 k p k ~ . ~ . / 1 0 5 s-1 no. of runs 560 K p f s.E./Torr no. of runs 547 K p f s.E./Torr no. of runs 534 K p f s.e./Torr no. of runs 521 K p f s.E./Torr no. of runs 9.0 f0.08 0.92 f 0.03 19 9.2 f0.13 0.88 f 0.04 5 9.3 f0.33 0.63 f 0.66 4 9.4 f0.12 0.38 f 0.01 6 9.6 f0.46 0.26 f 0.03 5 22.8 f0.33 2.04 f 0.05 18 24.5 k0.66 1.84 f 0.06 8 22.5 f0.38 1.3 1 f 0.06 4 23.0 f0.26 0.85 f 0.03 6 18.6 f0.25 0.37 f 0.01 9 36.5 f0.29 2.82 f 0.03 19 36.8 f0.48 2.22 f 0.10 7 36.8 f0.76 1.75 f 0.08 5 35.6 f0.78 1.14f 0.03 6 27.3 k0.46 0.58 f 0.03 11 63.4 f0.61 4.03 f 0.08 24 64.3 f0.96 3.12 f 0.12 6 65.0 1.26 2.30 0.12 4 65.2 & 1.35 1.65 f 0.03 6 55.0 f0.38 0.83 f 0.02 11 101.2 f0.58 5.30 f 0.09 23 100.4 f 1.51 3.82f0.14 6 97.3 f0.90 2.72 f 0 .11 6 100.2 f 1.35 1.97 f 0.07 6 91.8 f0.77 1.20 f 0.04 11 134.6 f0.90 6.13 f 0.13 11 138.3 f 1.82 4.51 fO.ll 4 131.7 f2.33 2.17 f 0.08 4 134.8 f 1.57 1.35 f 0.02 4 z 0 r 0 x 0 Z 1P. G. ASHMORE, A. J. OWEN A N D P. J. ROBINSON 679 of unimolecular fall-off. Our first theoretical calculations were based on the Forst approach3 which requires a detailed knowledge of molecular parameters only for the reacting species. These did not result in a completely satisfactory explanation of the experimental results.However, full RRKM calculations gave a much more satisfactory explanation of our own and of other investigators' results reported in Part 1. The agreement between theory and experiment led to the evaluation of the parameters A and Eiw) of the high-pressure rate constant ki") which is inaccessible by direct experiment. CALCULATIONS OF FALL-OFF CURVES AND FIT TO THE EXPERIMENTAL kp) DATA FORST CALCULATIONS Programs were written by P. J. R. to calculate the collision rate constant kcoll, the density of states N(Ev,) by the Hoare and Ruijgrok4 method of steepest descent, the partition function Q, for the radical, and hence k(E) = A ia)N(E- Ei"))/N(E) (with E > Ei")) for suitable pairs of A 8") and Ei").Finally k i p ) was calculated from eqn with M, the collision partner, at p = 5, 10, 25, 50, 75, 100, 125, 150 and 200 Torr. The first calculations ignored the centrifugal effe~t,~ partly for simplicity, partly because the low level of Aim), ELw) values led to the view that the transition state was formed early in the dissociation (2) of the radical, with some tightening due to rapid formation of the n-bond before the C-C1 bond is much extended. This kind of transition state would give rise to comparatively low values for I z / I and hence a small centrifugal effect. This point is taken up later in this paper. Molecular parameters for the dichloroethyl radical have been proposed by previous As exemplified later, the two sets of parameters gave very similar results, and once this was settled, the Beadle, Knox, Placid0 and Waugh (BKPW)6 parameters were used in the Forst calculations. In later calculations, convenient groupings of frequencies, based on the BKPW values, were used to simplify the computations.The BKPW and other required parameters for the radical C2H3C12 are given in table 2. Calculations of k i p ) with a wide range of Aim) and ELa) values identified a comparatively small network of values that gave kip) close to the experimental kip) means at 572 K. From this network pairs of A ia), EL") values could be selected that gave kpoo) for p = 100 Torr equal to the value obtained from short interpolation to p = 100 Torr between the experimental means. These pairs lie on the line lipoo) shown in fig. 1 (a), and show a compensation effect (high A , goes with high E,, and low A , with low E,) similar to that in pairs of A$"), EL") required to produce a given /tia).However, the higher pairs produce a fall-off curve that lies below the experimental E L P ) value at p < 100 Torr and above them at p > 100 Torr, i.e. is too straight. In contrast, the lower pairs lead to kip) above the experimental values for p < 100 Torr and below those at p > 100 Torr, i.e. is too bent. The result is, of course, that each pair gives a different value of the high-pressure rate constant kiw). These changes of shape of the calculated curves passing through k&loo) can be applied to identify A iw) and and hence ki") within closer limits. A simple way is to repeat the procedure used for the kgoo) curve for a much lower pressure. Thus the line kp5) in fig.1 (a) represents values of A and ESm) that give ki25) equal to the experimental * Equations with lower numbers are in Part 1.'680 UNIMOLECULAR DECOMPOSITION e2H3C12 -P C2H3Cl+e1 TABLE 2.-PARAMETERS FOR FORST AND RRKM CALCULATIONS (a) Data for radical internal rotation I = 33 x vibration frequencies/cm-l [ref. (6)] grouped frequencies/cm-l collision diameter 0.55 nm collision bath C,H4C12 g cm2, degeneracy 1, symmetry number 1 3005 (2), 2957, 1450, 1304, 1264, 1230, 3000 (3), 1280 (4), 1020 (2), 754 (3), 301, 220 1052, 986, 768, 754, 709, 301, 220 (b) Data for Forst models model A B C D 16.00 E'&.)/kcal mol-1 17.15 17.40 17.80 log,o(A 6.p,,/s-') 12.60 12.80 13.00 12.00 (c) Data for RRKM complexes grouped log10 A $72 / AS&,/ EO/ EL%)/ frequencies complex S-' cal mol-1 K-' kcal mol-1 kcal mol-l /cm-l F 13.70 0.864 16.30 19.12 3008 (3), 958 (3), 777 (21, 447 (3)Y 777 (2), 431 (3), 737 (2), 379 (3), 199 (2), 131 (1) G 14.00 2.241 16.60 19.57 3025 (3), 957 (3), 175 (2), 93 (1) H 14.30 3.613 16.81 20.03 3028 (3), 957 (3), 157 (2), 89 (1) (d) Data for RRKM complexes which allow for the centrifugal effect with Iz/I= 2.0 Eo/kcal mo1-l 16.5 17.0 17.5 Eim)/kcal mol-l 19.5 20.0 20.5 A p/ 1014 S-1 Xl x, x3 y, y 2 y 3 Zl z2 z3 0.7 0.8 0.9 1.7 1.8 2.0 4.0 4.4 5.0 value obtained by short interpolations of the experimental means t o p = 25 Torr.The intersection of the two lines k$25) and k$lo0) gives the values of A am) (close to 1012.7 s-l) and Elm) (close to 17.5 kcal mol-l) that give a fall-off curve passing through the experimental means 6 $ p ) close to p = 25 and 100 Torr.Two more sophisticated procedures confirmed the results of the simple procedure. Method (l), based on Szirovica and Walsh,8 involved comparison of the locus of A am), Earn) values fitting the slope of the Lindemann reciprocal plot (1 / k i p ) against l/p) at a given temperature with the locus of the values fitting k i p ) at a specific pressure. Lindemann plots of two Forst calculations for 572 K are shown in fig. 2; they are nearly linear over the pressure range of interest. A network of values of theoretical slopes can be constructed for suitable ranges of A 6") and Earn), and pairsP. G. ASHMORE, A. J. OWEN AND P. J .ROBINSON 68 1 1L.O n I - 2 13.5- 5.. - s 2 13.0- 0 - 12.5 12.0 - - I I I I 1.0 4.0 7.0 10.0 100 TO=/PDCE FIG. 2.-Lindemann plots of l/k$p) for Forst calculations with model B (0) and with model D (A) (see table 2) at 572 K. of ASw), ESm) values can be found, by interpolation, that give slopes equal to that of the line fitted (by least-mean-square procedures) to the Lindemann plot of l/kiP) against 1 / p . These pairs are plotted as line L in fig. 1 (a). The three lines intersect within a small range of Aim), Edm) values which are therefore consistent with the shape of the fall-off curve at 572 K. Table 3 shows the 572 K values using method (1) and BKPW parameters. Method (2) involved the direct fitting ofempirical equations for the theoretical fall-off 23 FAR I682 UNIMOLECULAR DECOMPOSITION C,H3Cl, -+ C,H,Cl+Cl TABLE 3.-A am), Earn) VALUES HTTING EXPERIMENTAL DATA AND FORST CALCULATIONS.UNLESS NOTED OTHERWISE, METHOD (1) AND BKPW PARAMETERS WERE USED. 52 1 534 547 560 572 572" 572b 12.85 12.90 12.60 12.60 12.80 12.70 12.80 74.2 73.8 71.9 71.9 73.0 72.3 73.4 17.7 17.6 17.2 17.2 17.4 17.3 17.5 a Method (2) and BKPWs parameters; method (2) and SR7 parameters. curves to the experimental k i p ) , p points. No simple function will describe these curves over a wide range of pressures. However, quartic polynomials in p , developed over the range 1-250 Torr, could be fitted accurately to k$p)(calc) over the more limited range 5-1 50 Torr for each pair of A am), Eim) values. The sum of the squares of the residuals (s.s.r.) of the experimental points from the quartic curve could then be computed, and a small network of A Ei") pairs was identified with the lowest s.s.r.An additional discrimination was obtained by examining the distribution of the signs of the residuals over the pressure range. The results for 572 K, shown in table 3 for both BKPW and SR parameters, are very close to those found by method (1) or the simple method. Method (1) was applied, using the BKPW parameters, at four other temperatures with results also shown in table 3. Giving equal weightings to these values at the five temperatures, the mean values found for the Arrhenius parameters are Eim) = 72.9 f 1.1 kJ mol-1 = 17.42 f 0.26 kcal mol-l and i.e. log,,(A $")/s-') = 12.75 & 0.25 17420 4.576 T/K' 10glo(k$")/s-l) = 12.75 - In fig.3 the values of 6 $ p ) are plotted for each temperature with the theoretical Forst curve (full line) appropriate to the overall mean A $"), Ei") values. The overall pattern from fig. 3 indicates that the mean Arrhenius parameters Aim) and Earn) give a reasonable fit to the fall-off at all five temperatures. However, they are much lower than the values found by Huybrechts et aL9 for fairly high pressures [E, = 20.7 kcal mol-1 and log,,(A,/s-l) = 14.331. Moreover, eqn (XI) predicts values of kam) that lie below those found experimentally by Huybrechts et al. until very low temperatures are reached, as illustrated in fig. 4 by the positions of the lines (XI) and (XII)g 20 700 4.576 T / K ' 10glo(k$"~/S-') = 14.33 - This conflict might arise from errors in our fitting procedures, which is unlikely because of the cross-checks from different procedures, or from systematic errors in the experimental results (those of Huybrechts et aL9 and our own1) or from the acknowledged3 decrease in accuracy of the, Forst method at lower pressures.Incorpor-P. G. ASHMORE, A. J. OWEN A N D P. J. ROBINSON 683 FIG. 3.-Calculated Forst curves for the mean Aim), Egm) optimum values at the five temperatures (see table 3) with mean kip) for 0 572; 0, 560; V, 547; A, 534 and 0, 521 K. 7.0 6.0 n I \ I 4 v 2 M - 5.0 4 .O 1.6 1.8 2.0 2.2 2.4 lo3 KIT FIG. 4.-Arrhenius plots of k, from the experiments of Huybrechts et a1.O (XII), of /cia)) from our Forst from our RRKM calculations (XIII). calculations (XI) and of 23-2684 UNIMOLECULAR DECOMPOSITION C,H,Cl, + C,H,Cl+Cl ation of the centrifugal effect would make only minor changes in the calculations.The Forst estimates of ki") suggest that our experimental pressure range lies just below pi, where the Forst method would still be reliable. On the other hand, extrapolation of the Huybrechts results to our temperatures indicates k, values well above the predicted Forst ki"), which would mean that our experimental pressure range is well below the true pi. It is therefore possible that the discrepancies result from inaccuracies of the Forst method under these conditions. A reaction of the same kind as (2) is the decomposition of the ethyl radical for which the experimental value of k is given by log,,(k/s-l) = 14.4-31 800 K/4.576T [ref.(lo)] log,,(k/s-l) = 13.6- 32400 K/4.576T [ref. (1 l)]. or Benson12 has pointed out that for the ethyl radical there is a positive contribution to AS+- of 3.6 cal mol-1 K-l by loss of symmetry; this loss does not occur in forming the complex from C2H3C12, and for reaction (2) A S z might be 3.0 cal mol-1 K-l lower, i.e. A , might be expected to lie between 1013.6 and lo1,.* s-l. This appears to favour lower A("), E(") values. On the other hand, the higher A,, E, values from Huybrechts' relatively high-pressure experiments appear to fit well with accepted bond energies (such as R-CHC1-H where R = CH,, CH,Cl, CHCl,, CCl,) and the estimated standard (1 atm) entropies of the radicals R.C.HCLg We therefore conclude that our estimation of A$"), Ei") values from the fall-off curves using Forst calculations is not satisfactory, and it is desirable to see whether full RRKM calculations give a better description of our own and the Huybrechts results.RRKM CA LCU L A T I 0 NS Full RRKM calculations were first done for 572 K neglecting the centrifugal effect. A series of activated complexes were constructed to give selected values of Aim) at 572 K. Details of the assignments are not critical since RRKM fall-off calculations are insensitive to the detailed structure of the activated complex, the shape and position of the fall-off curve being determined essentially by the resulting AS+- and by Pa) [ref. (13), pp. 152 and 178].* State sums for the complexes were generated by exact count and densities for the radical by the Whitten-Rabinovitch method.14 and values of ELm) were investigated to locate those that gave fall-off curves close to the experimental mean values kip), using the procedure tested during the Forst calculations.Fig. 1 (b) shows pairs of Aim), values that gave calculated k i p ) in agreement with the experimental values for p = 100, 25 and 10 Torr. As can be seen, the intersection indicated Aim) and Eb") values substantially higher than in the Forst calculations, uiz. close to logl,(A$"3)/s-1) = 14.0 and Eim) = 19.6 kcal mol-1 at 572 K. These parameters define complex G (table 2). The differences between kip) values calculated for this complex and the individual experimental values are expressed in table 4 as the sum CRlp) of the residuals Rip) = [k&P)(exp) - k$p)(model i)] and the sums C Vi(p) of the corresponding variances for the experimental pressure ranges at 572 K.The results of applying a t-test at the 1% level of significance are also shown; model G predictions are not significantly Suitable complexes ( A AS$ In (Akm)/s-') = In [(ekT/L)/s-']+----. R * Note Ekm' = E,,+RT+(E#)-(E) andP. G. ASHMORE, 1. J . wi +I 4 ]WEN A N U l'. J. K U B I N S U N M m m m m m m E 000000 2 ooooo+ 68 5686 UNIMOLECULAR DECOMPOSITION e2H3cl2 -+ C2H3C1+c1 different from the experimental results in each range, but are on the borderline for the lowest pressure range. Table 4 shows that model H, with higher Aim) and ESm) than G, has residuals that are more positive than those of G at the lower pressures, whereas model F, with lower Aim) and Eim), has residuals that are more negative.The t-tests also show that models F and H give less satisfactory fits to the experimental results at 572 K than does G. FIG. 5.-RRKM calculations of kip) for model G with mean kip) for 0 , 5 7 2 ; 0 , 5 6 0 ; V, 547; 534 and 0, 521 K. To investigate how G and other models behave at other temperatures, E, for each model was kept constant and Elm), Aim) were calculated using the equations in the footnote, page 684. The calculations for model G are compared in fig. 5 with the experimental means (shown with the number of contributory runs). At 572 K, the model gives an excellent fit at all except the lowest point. At 560 and 534 K it gives good fits, although a model with slightly lower parameters (but not as low as those of F) gives better fits.At 547 K model F is better than G, and a model with even lower E,, A would fit still better; at 521 K a model with slightly higher E,, Aim) is better than G. In view of the minor scale of these differences, the choice of a single representative model would fall on G, admitting that a small range of values around EJG) (say 16.6kO.3 kcal mol-l) and a correlated (compensating) range of its l~g,,[A(~)(G)/s-~] (say 14.0 If: 0.2) would give very similar fits. Having decided the preferred model without allowance for the centrifugal effect, it remains to match with its predictions a model allowing for centrifugal effects. This is more important than with the Forst calculations, as the larger A-factor suggests that the activated complex is ‘looser’ than had appeared from the Forst value of the A-factor.Simple models for the radical and activated complex suggested that I # / I would probably be ca. 2. A range of I z / I values from 1 to 4 was examined using the approach of Waage and Rabin~vitch.~ The factor bR was calculated for the radical from [for symbols, see ref. (1 3), p. 911 (s- l ) ( I + / I - l)kT)-’ E, + aE,P. G. ASHMORE, A. J. OWEN A N D P. J. ROBINSON Z 7.0- 6.0- 5.0- 4.0- 3.0- 2.0- 1 .o- 0 - 1 60 687 WI vr 2 1 3 to give the values: I + / I 1 1.5 2.0 3 .O 4.0 %R 1 .oo 0.72 0.56 0.39 0.29. The computed fall-off curve for a given Aim), ELm) with no centrifugal effects was then treated as follows: (a) k i p ) was multiplied by P / I , (b) the pressurep was divided by GR and (c) Aim) correspondingly became Aim) x I # / I , with Eim) unchanged.For some of the calculations, the starting data were generated by interpolation between models F, G and H rather than by explicit RRKM computations. After trial comparisons with the experimental results for 572 K, attention was focused on the models X I . . .Z, listed in table 2 with I # / I = 2.0. Note that the final line gives the final A i"), i.e. the initial A im) x I # / I . The predicted curves at 572 K for the nine models are shown with the experimental means in fig. 6. In each triplet the centre curves pass very close to the experimental 0 20 40 60 80 100 120 140 PDCE/TO~ - 1 FIG. 6.-Fall-off curves at 572 K for models X, Y and Z which allow for centrifugal effect with I f / l = 2.0. Parameters of the models are given in table 2.688 UNIMOLECULAR DECOMPOSITION C,H,Cl, + C,H,Cl+t]l means at p = 101 Torr (kip) = 5.30 x lo5 s-l).However, closer inspection shows that curve Y, is a close fit to all the experimental means; curve Z, passes very close to the experimental mean at p = 101 Torr but lies well below the experimental means at p < 100 Torr and above them at p > 100 Torr; curve X, lies above the experimental means at p < 80 Torr, and below them at p > 80 Torr. This is shown more quanti- tatively in table 5, which lists the residuals [6$P)(exp)-kip)(model i)] for each mean pressure. The residuals for Y, are in all cases very much smaller than the standard errors of the experimental means; for Z,, the residuals are very much larger than the standard errors of the mean; for X,, they are comparable or larger and there is a systematic change in sign along the curve.Application of the t-test to the lower pressure ranges gives the significance results at the 1 % level shown in table 5, and these confirm that model Y, is to be preferred to models X, and 2, for representing the experimental results. TABLE 5.-EXPERIMENTAL MEANS p AND Eip) WITH THE RESIDUALS OF THE MEANS ([6ip'(eXp) - kLp'(mode1 i)]/103 s-l> FOR RRKM MODELS X,, Y, AND Z, WHICH ALLOW FOR CENTRIFUGAL EFFECTS. THE RESIDUAL ARE INDICATED AS SIGNIFICANT (s) OR NOT SIGNIFICANT (ns) USING THE GTESTS AT THE 1 % LEVEL OF SIGNIFICANCE. 572 K, VESSEL B. residuals of means/103 s-' 19 9.0 f 0.08 0.92 f 0.03 - 12.0 s 0.0 ns + 14.0 s 18 22.8 & 0.33 2.04 f 0.05 - 1.4 ns + 1.4 ns +18.3 s 19 36.5 f 0.29 2.82 & 0.03 -9.8 s 0.0 ns +10.5 s 63.4 f 0.61 4.03 & 0.08 -4.2 ns 0.0 ns + 11.2 ns 24 5.30 f 0.09 +2.8 ns 0.0 ns + 1.4 ns 23 101.2 & 0.58 1 1 134.6 f 0.90 6.13 f 0.13 +4.9 ns -4.9 ns -14.8 ns We conclude that the preferred model after allowing for centrifugal effects is Y, with Eim) = 20.0 kcal mol-l and A $") = 1.8 x 1014 s-l; other models with parameters close to these, but with A$") and Eim) compensating, would give similar fits.Rather surprisingly, a similar study of models with I it / I = 4.0 pointed to parameters close to those of Y,, with EL") = 20.0 kcal mol-l and Aim) = 1.7 x 1014 s-l. The Arrhenius parameters for Y, lead to the prediction 20 000 4.576 T / K 10glo(k~")/S-l) = 14.26 - (XIII) and this is plotted as line (XIII) in fig.4. The Arrhenius plot for model G would lie slightly below line (XIII). DISCUSSION OF THE RRKM RESULTS Line (XIII) in fig. 4, and that for model G, lie well above line (XII) for the results of Huybrechts et aZ.9 Their results were obtained in the pressure range ofp,,, between 150 to 450 Torr. The general position of their points and of line (XII) are very satisfactory in relation to the RRKM plot (XIII) - much more so than with line (XI) from the Forst calculations. They did not report any fall-off, but the predicted fall-off is, of course, much smaller at the lower temperatures of their work, e.g. at 454 K k&p)(calc) falls by ca. 25% when p changes from 450 to 150 Torr; at 572 K, kip)(calc)P. G. ASHMORE, A.J. OWEN A N D P. J. ROBINSON 689 changes by a factor of nearly two. There is slight evidence for a fall from the spread of their results at 490 K, and rather stronger evidence from their (few) results at 510 K. It is also possible that photolytically generated C1 atoms, comprising states, thermal kip). It therefore appears that the RRKM calculations not only fit our own experimental observations' at five temperatures, but can also resolve the apparent major conflict between our early results and those of Huybrechts et aL9 What appeared to be systematic errors in one or both of the experimental determinations of k,/k, from the thermal- or the photo-sensitised decompositions are now seen to be a natural consequence of the unimolecular behaviour of k, at different pressures.Our evaluation of A $a) and Eia), and the statistical treatment of our experimental data, have of necessity ignored possible systematic errors, for example in the experimental evaluation, of k, or in the parameters quoted in table 2. The direct experimental investigation of kip) at high pressures, in the absence of competitive chlorination, is very difficult as evidenced by earlier work referenced in Part 1. The thermal decomposition of l,2-C,H4C1, in the absence of chlorine shows complicated rate relationships (as referenced in Part 1) and cannot provide a check on k i p ) at high pressures. A further check on our evaluation of Aim) and Eim) may be provided by applying the methods advocated by Troe15 and this will be set in motion. In the meantime the satisfactory explanation based on RRKM theory of experimental results from different laboratories over a wide range of temperatures would seem to justify our evaluation of Eia) within a few kJ mol-l, with corresponding limits on Aim), and the resulting eqn (XIII).Some further support comes from consideration of the rate constant kL$) for the reverse reaction (- 2). ARRHENIUS PARAMETERS FOR THE REACTION (-2) Our experimental investigations' of k-, through the inhibitory effects of VC on the decomposition of DCE clearly showed that k-, is pressure-dependent and increases with increase in temperature. These results did not allow accurate determinations of A L$) and ELg), but by combining them with data from studies of reaction (- 2) at lower temperatures, reasonably accurate values of the Arrhenius parameters of reaction (- 2) and their variation with pressure can be obtained.Reaction (- 2) has been studied experimentally in the course of extensive investi- gations of the chlorination of ethylene and the chloroethylenes. Knox and WaughlG found difficulties with heterogeneous reactions in studying v c + a -+ R and produce excited k in reaction (l), which results in a k, value rather f arger than the but evaluated k-, indirectly as 3.5 x 1O1O dm3 mol-' s-' at all temperatures. Ayscough et al." quoted an earlier value18 (1010.2 dm3 mol-1 s-l) but preferred their own assessments over the range 20-50 OC, with low pressures of VC around 5-30 Torr, of loglo(k~,/dm3 mol-' s-l) = 10.3 - 1500 K/4.576 T. In a theoretical study of several related reactions, BKPW5 calculated rate constants for the following detailed mechanism (using our nomenclature) : Cl+VC 5 R* kbi R*+M R+M R* 2 vc+c1 which combine to give d[kl - kbi [vcl dt ka + kbi[MlTABLE 6.-CALCULATED AND EXPERIMENTAL VALUES OF k-, AT VARIOUS CONCENTRATIONS AND TEMPERATURES equivalent calculated experimental pressure loglo(k~;b~e)/dm3 mol-l s-l) l ~ g ~ ~ ( k l _ a j ~ ~ ~ ) / d r n ~ mol-1 s-l) ~ ( a .0 ) A ( a , b , c ) M/10-3 mol at 560 K h:al fik3 label dmF3 /Ton 308 K 352 K 406 K 520 K 544 K 570 K 595 K mol-l mol-l s-l - - - - - - BKPW +co +co 9.51 9.64 9.69 2.87 100 9.43 9.53 9.54 9.74 9.83 9.85 9.88 1.37 1010.38 109.98 (4 (b) (c) 1.60 55 9.38 9.48 9.48 9.61 9.64 9.66 9.69 0.80 0.73 25 9.32 9.4 1 9.39 9.50 9.51 9.49 9.56 0.46 109.70 c) "3: 4P.G. ASHMORE, A. J . OWEN A N D P. J. ROBINSON 69 1 and hence From this expression it is clear that kL$) = A , and BKPW gave the values of A at 308, 352 and 406K shown here in the top line of table 6 . They also gave kbi = 1.23 x dm3 mo1-l s-l at 352 K, from their fig. 5 it is possible to estimate k , at the three temperatures and at chosen pressures or concentrations, so that kL%) can be calculated for their temperatures from eqn (XIV). The results of these calculations are listed in table 6. It seemed more appropriate to consider constant concentration rather than constant pressure, in view of the wide temperature difference between those calculated and our experimental results. Accordingly, kLadbJ) was calculated for three concentrations which are equivalent to pressures of (a) 100, (b) 55 and (c) 25 Torr at 560 K, the mid-temperature of A.J. O.'s experimental values which are given in the right half of table 6. Before comparing the calculated and experimental results, a fundamental difficulty must be mentioned. It arises from the complex relations between the reversible reactions (2, - 2) and the function of DCE and VC as collision partners (M). In studies of the photochlorination of VC, VC itself is usually the effective collision parameter (chlorine is less effective); in studies of the thermal decomposition of DCE, DCE is the effective collision partner. Our experiments summarised in fig. 9 of Part 1 show that VC and DCE are of very similar but not identical efficiency as M. Unfortunately we can see no rigorous way of allowing for this difference in the data at present available for reaction (2) and for reaction (- 2), so that our comparisons that follow are limited by that consideration.When the results in table 6 are plotted as an Arrhenius diagram (fig. 7) the points for each concentration are reasonable fits to straight lines. The activation energy E-, 9 . 0 t , , , , 2.0 2.5 3.0 3.5 1.5 1 O3 KIT FIG. 7.-Arrhenius plots of kL$) for concentrations that are equivalent to (a) 100 Torr at 560 K with A (this work) and from BKPW;5 (c) 25 Torr at 560 K with (this work) and dfrom BKPW;5 ( d ) very high pressures, estimated from this work, with + from BKPW5 table 3. etc. from BKPW;5 (6) 55 Torr at 560 K with 0 (this work) and692 UNIMOLECULAR DECOMPOSITION C2H3C12 + C2H3Cl+C1 falls as the concentration falls, and so does the pre-exponential factor A-,.These changes would be expected from the corresponding falls in E, and A , as the pressure is lowered, by the requirements of microscopic reversibility. As a result eqn (XV) and (XVI) bear the same relation to each other as do eqn (VIA) and (VIIA) [derived from the eqn (VI) and (VII) of Part 1 using the Arrhenius expression2 for k,] 1370 (100 Torr) 4.576 T/K loglo(k-,/dm3 mol-1 s-l) = 10.38 - 460 (25 Torr) 4.576 T/K loglo(k~,/dm3 mol-1 s-l) = 9.70- 10g~~(k,/~-~) = 12.40 - 4.576 420 T/K (1 00 Torr) (VIA) 16470 (25 Torr). (VII A) 4.576 T/K loglo(k2/~-l) = 1 1.61 - These equations for kL%) and k i p ) have been derived from quite separate experiments and separate calculations. They correspond within very close limits to an equilibrium constant for reactions (2, -2) given by eqn (VXII), where Keq = k,/k-, for R+VC+Cl 16 000 4.576 T/K logl,(Keq/mol dmb3) = 2.00 - (XVII) If the concept of microscopic reversibility can be extended to kim) and kLT) then by combining eqn (XVII) with the Arrhenius equation for ki") there emerges eqn (XVIII) 4000 4.576 T / K log (k'lf',/dm3 mol-1 s-l) = 12.26 - (XVIII) This equation gives the line ( d ) in fig. 7.It passes close to Knox's calculated kLT) at the lower temperatures (+). The large changes in A+, E-, with increasing pressure are of course, reflections of the correspondingly large changes in A,, E, over the same pressure range. It may be recalled that the values of E&lo0) and were derived from RRKM calculations that fit the experimental results at these pressures; however, they are substantially independent of whether one chooses model G, or the model Y, with centrifugal effects. On the other hand, ELm) does depend on which model one uses, but the difference Eim)(Y,) - Eim)(model G) is only 400 cal mol-l, and if the Arrhenius equation for kim) for model G were used in place of eqn (XVIII) the plot would be only very slightly displaced from the line ( d ) in fig. 7. P. G. Ashmore, J. W. Gardner, A. J. Owen, B. S. Smith and P. Sutton, J . Chem. SOC., Faraday Trans. I , 1982, 78, 657. F. S. Dainton, D. A. Lomax and M. Weston, Trans. Faraday SOC., 1962, 58, 308. W. Forst, J . Phys. Chem., 1972, 76, 342. M. R. Hoare and T. W. Ruijgrok, J. Chem. Phys., 1970, 52, 113. E. V. Waage and B. S. Rabinovitch, Chem. Rev., 1970, 70, 377. P. C. Beadle, J. H. Knox, F. Placid0 and K. C. Waugh, Trans. Faraday SOC., 1969, 65, 1571. ' G. B. Skinner and B. S. Rabinovitch, Bull. SOC. Chim. Belg., 1973, 82, 305. L. Szirovica and R. Walsh, J, Chem. SOC., Faraday Trans. I , 1974, 70, 35. G. Huybrechts, J. Katihabwa, G. Martens, M. Nejszaten and J. Olbregts, Bull. SOC. Chim. Belg., 1972, 81, 65. lo L. F. Loucks and K. J. Laidler, Can. J. Chem., 1967, 45, 2795.P. G . ASHMORE, A. J. OWEN AND P. J. ROBINSON 693 l1 M. C. Lin and M. H. Back, Can. J . Chem., 1966,44, 505, 2357. l3 P. J. Robinson and K. A. Holbrook, Unimolecular Reactions (Wiley Interscience, New York, 1972). l4 G. Z. Whitten and B. S. Rabinovitch, J. Chem. Phys., 1963, 38, 2466. l5 J. Troe, Ber. Bunsenges. Phys. Chem., 1974, 78, 478. l6 J. H. Knox and K. C. Waugh, Trans. Faraday Soc., 1969, 65, 1585. l7 P. B. Ayscough, F. S. Dainton and B. E. Fleischfresser, Trans. Faraday Soc., 1966, 62, 1838. S. W. Benson, Thermochemical Kinetics (Wiley, New York, 1968), pp. 67 and 68. G. Chiltz, P. Goldfinger, G. Huybrechts, G. Martens and G. Verbeke, Chem. Rev., 1963, 63, 355. (PAPER 0/1987)