Mutual Reaction of Isopropyl Radicals BY P. ARROWSMITH Department of Physical Chemistry, University of Cambridge, Lensfield Road, Cambridge L. J. KIRSCH" AND Shell Research Ltd, Thornton Research Centre, P.O. Box 1, Chester CHI 3SH Received 17th February, 1978 The second order mutual reaction between isopropyl radicals has been studied over the temperature range 301-424 K. Kinetic measurements of the overall termination rate, using a molecular modula- tion spectrometer, have been combined with product analysis studies to determine Arrhenius para- meters for the recombination (kr) and disproportionat ion reactions. The values obtained : )] cm3 molecule-1 s-1 - 1340 J mol-l ( RT kr = 1 . 4 ~ lo-" give good agreement with product analysis studies over a wide range of temperatures. These rate coefficients are correct to +20 % over the stated temperature range, and the error in the activation energies is f2600 J mol-I (95 % confidence limits).The parameters for kf extrapolate to a value that is about twice the value measured by the very low pressure pyrolysis method at 750 K. Until recently the rates of alkyl radical recombination were the subject of some controversy in the 1iterature.l This situation has been remedied by the develop- ment of techniques capable of more direct, absolute measurements of the rates of these processes. Thus data produced by the very low pressure pyrolysis (VLPP) method of Golden and co-workers and by the molecular modulation (MMS) method of Parkes and Quinn have generally been in acceptable agreement by comparison with the order of magnitude discrepancies that have existed hitherto.For the recombination of isopropyl radicals : kr 2C3H7. + C6HI4. Golden et aL2 report log (k,/cm3 molecule-l s-l) = - 1 1.3 & 0.2 over the temperature range 683-808 K ; the MMS technique yields log (kr/cm3 molecule-l s-l) = - 11.1 +0.1 at 298 K. In the present note we report measurements of isopropyl radical recombination over the intermediate temperature range 301-424 K based on kinetic studies using the MMS method. The MMS technique has been described in detail by Parkes et aL3 and was used in the present experiments without essential modification. Briefly, isopropyl radicals were generated by square wave modulated photolysis of azo-isopropyl (AIP) and were detected by absorption spectroscopy using the transition at 235 nm.The modulated absorption signal lags behind the photolysis lamp modulation by an amount depending upon the radical removal rate and the modulation frequency. 3016TABLE ~ . - E X P E ~ N T A L RESULTS FOR THE MUTUAL COMBINATION OF ISOPROPYL RADICALS ref. temperature/K kt/cm3 molecule-1 s-1 o/cm2 molecule-1 kci/kr kr/cmJ molecule-1 s-1 ka/cm3 molecule-1 s-1 present work 301 (9.1k6.6)~ (3.6IfI:l.O)~ 0.60f0.01 (0.62) (8.63.2.0)x 10-12 b 5 . 2 ~ 10-12 Parkes and Quinn 298 1 . 4 ~ 10-l' 3.9 x 10-1 0.65k0.05 (0.62)) present work 323 0.57 f 0.02 (0.60) present work 382 (1.3k0.3)~ 10-l1 (4.25k0.6)~ 0.545+0.01 (0.57)[373 K] (8.2k1.9)~ 4 . 6 ~ present work 424 (1.5+0.3)x 10-l' (5.0k0.6)~ 0.52 C (0.545) (9.91 1 . 9 ) ~ 10-l2 5.1 x Golden et aL2 683 1.0 (0.48) 4.1 x 10-l2 4.1 x 10-l2 Golden et aL2 723 0.75 (0.48) 5.1 x 3.8 x 6 .4 ~ Golden et aL2 768 1.4 (0.47) 4 . 6 ~ 10-l2 Golden et aL2 808 1.5 (0.47) 5.9x 8 . 9 ~ ment of kd/k,. C By extrapolation. a Values in parentheses computed from the expression given by Klein et d4 b Derived from the value of kt from ref. (1) and the present measure-301 8 MUTUAL REACTION OF ISOPROPYL RADICALS This signal was digitized and fed into two up-down counters. The first of these (in phase) counts up when the lamps are on and down when they are off. The second count (in quadrature) lags behind the in-phase count by 90". Such data are obtained over a range of modulation frequencies and substrate pressures. The relationship between the in-phase and in-quadrature counts and their magnitudes permit both the ouerd termination rate coefficient, k,, and the radical adsorption coefficient, 0, to be determined, provided that the photolysis rate is known.The latter was calculated by measuring the decline in the absorption signal (due to removal of the substrate) over an extended photolysis period. The temperature of the reaction vessel was controlled by circulating hot air through a coaxial annular vessel : a temperature of -470 K could be achieved in this manner, although in the present experiment there was a practical limit of -423 K because of the onset of thermal reactions. reduced photolysis period, 7 2/B/cm-2 molecule3 s+ FIG. 1 .-Molecular modulation data for the second order termination reaction between isopropyl Values of k, and cr are shown in table 1.The results at 301 K were obtained from a brief series of experiments to ensure compatibility with the earlier data of Parkes and Quinn.2 At 378 and 424 K much more extensive studies over a wide range of modulation frequencies and substrate pressures of 0.66 - 1.33 kN m-2 were carried out to determine k, and 0 with more precision. In all experiments nitrogen diluent was added to a total pressure of 0.1 N m-'. The results at 424 K are plotted in fig. 1. Here, reduced absorption counts [counts (@)-l], both in-phase and in- quadrature, are plotted against reduced photolysis period (@). The theoretical relationships connecting these reduced variables for second order recombination kinetics have been derived previously.They contain, as unknown parameters, the values of k, and cr alone and these may, therefore, be obtained by a non-linear least squares minimization procedure. The curves shown in fig. 1 were computed using the values of k, and 0 shown in table 1. For the present results, the error limits shown for k, and o are an overestimate of the 95 % confidence limits. radicals at 424 K. (a) u = 5.5 x 10-l8 ; (b) u = 5 . 0 ~ ; (c) u = 4.5 xP. ARROWSMITH AND L. J . KIRSCH 3019 The removal rate constant, measured by the MMS method, is given by k, = kd + k,, where kd describes the rate of the disproportionation reaction : kd 2C3H7.3 CsHG+C3Hs. The disproportionation/recombination ratio must therefore be known to derive ICr from our present kinetic measurements. Klein et aL4 have measured this ratio over the temperature range 77-380 K in both solid and gaseous phases and describe their results by the expression : Because our present data require some extrapolation from the temperature range of Klein et aZ.’s measurements in the solid phase, and because their gas phase measure- ments showed some deviation from their overall expression, we have measured kd/k, over the temperature range 298-273 K in the gas phase.The system used, to be described in greater detail el~ewhere,~ was a coaxial photolysis system designed for geometric similarity with that used in the MMS kinetic experiments. Samples were withdrawn after known periods of extended photolysis and the principal products propane, propene and 2,3-dimethylbutane, were estimated by g.1.c.analysis using a Pye Unicam GCD gas chromatograph equipped with a Porapak Q column, flame ionization detector and a DP 88 computing integrator. Experiments were carried out at 298, 323 and 373 K. At 298 and 323 K the yields of propane and propene were equal within experimental error ; at 373 K there was a slight excess of propane ( N 3 %) which probably arises because of the abstraction reaction :G CSH, +AIP + C,H,+AIP 0 . The ratio kd/k, was therefore measured from the ratio of the propene to 2,3-dimethyl- butane yields. The results obtained are shown in table 1. They confirm the decrease in the value of kd/k, with increasing temperature that was found by Klein et aL4 and, more recently, at higher temperatures, by McKay et aLG Various measurements of kd/k, in the literature have been reviewed by the latter workers.The present results are in good agreement with previous studies at similar temperatures (298-400 K), particularly with the formula given by Klein et al. Extrapolation of our own results to the temperatures used by MacKay et al. (518-573 K) gives a slightly lower range of values (0.490-0.478) than they report (0.52-0.49). Fig. 2 shows an Arrhenius plot of the values of k, obtained in the present work (by combination of the experimental determination of k, and k,/k,, the latter extrapolated at 424 K) and the results reported by Golden et aL2 The expanded ordinate in this plot accentuates the errors of both experiments. However, there is no evidence from the present measurements of a negative activation energy for k, that would directly reconcile the MMS and VLPP work.Rather, the trend is in the opposite sense, an error-weighted statistical analysis of all the MMS/product analysis results yielding a small positive activation energy of 1340 J mol-1 with the 95 % confidence limits at - +2640 J mol-’. The corresponding extrapolation of k, implies a discrepancy of about two at the temperature of Golden et aZ.’s measurements. We believe the reason for this difference may be that the VLPP method determines k, significantly below the high pressure limit, as was indeed suggested by Golden et aL2 in the discussion of their results. There are two pieces of evidence supporting this view. First, the values O f kd/kr obtained directly from the VLPP experiments (table 1) are substantially higher than the value of -0.45 at 750 K predicted by extrapolation of the various3020 MUTUAL REACTION OF ISOPROPYL RADICALS lower temperature product analysis studies.Secondly, the established temperature dependence of kd/k,, taken in conjunction with a negative activation energy for kr, would imply an even more negative activation energy for kd, which is unacceptable for a reaction of this type. The body of evidence, both kinetic and from product analysis, is better reconciled by attributing the temperature dependence of kd/k, primarily to the small positive activation energy for the recombination reaction that our present experiments suggest. We then conclude that the rate of the dispro- portionation reaction is almost independent of temperature. Significantly, the values of kd that may be derived from the present work at 301-424 K and from the VLPP method at 683-808 K are in acceptable numerical agreement (table 1).[The VLPP method yields k, and an approximate value of kd/k, directly. The apparent trend with temperature of kd (table 1) is insignificant in view of the error (kO.5) in kd/kr.] 12 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 - - - - - 0 - 0 0 - - I 1 I I a 1.0 1.5 ' 2.0 25 3.0 - FIG. 2.-Arrhenius plot of data for the recombination rate constant (kr) for isopropyl radicals. In conclusion, we may derive from our results the following Arrhenius parameters to describe the combination of isopropyl radicals over the temperature range 0, Parkes and Quinn ;I 0, present work; 0, Golden et aL2 301-424 K : k, = 1 .4 ~ [ exp ( - 340 mol- l)] cm3 molecule-1 s-1 RT 210 J mol-' kd = 5.0 x 10-12 [exp ( RT )] cm3 molecule-1 s - 1 . These parameters yield rate constants correct to +20 % over the stated temperature range and the approximate error in the activation energies is +2600 J mol-f (95 % confidence limits). They give good agreement with various product analysis measurements of kd/kr over the temperature range 77-573 K. They are also in good agreement with VLPP measurements at -750 K, subject to the recognition that the VLPP determinations of k, measure this rate constant a factor of approximately two below its high pressure limiting value.P. ARROWSMITH AND L. J . KIRSCH 3021 The authors are grateful for useful discussions with Dr. D. A. Parkes (Shell Research B.V., Amsterdam) and to Mr. K. P. Donnelly (D.P.M.M.S., University of Cambridge) for his assistance with the statistical analysis of the results. D. A. Parkes and C. P. Quinn, J.C.S. Faraday I, 1976,72, 1952. D. M. Golden, L. W. Piskiewicz, M. J. Perona and P. C. Beadle, J. Arner. Chem. SOC., 1974, 96, 1645. D. A. Parkes, D. M. Paul and C. P. Quinn, J.C.S. Faraday I, 1976,72, 1935. R. Klein, M. D. Scheer and R. Kelley, J. Phys. Cltem., 1964,68,598. L. J. Kirsch and D. A. Parkes, to be published. G. McKay, J. M. C. Turner and F. Zark, J.C.S. Faraday I, 1977,73, 803. (PAPER 8/281)