J. Chem. SOC., Faraday Trans. I , 1984,80, 3391-3398 Reactions of Methyl Radicals with 3-Methyloxetane, 3,3-Dimethyloxetane and 2,2-Dime thyloxe tane BY MARTIN G. DUKE AND KENNETH A. HOLBROOK* Department of Chemistry, University of Hull, Hull HU6 7RX Received 19th March, 1984 The reactions of methyl radicals with 3-methyloxetane, 3,3-dimethyloxetane and 2,2- dimethyloxetane have been studied. The overall rates of hydrogen-atom abstraction from these three compounds have been obtained over the temperature range 100-200 "C by assuming the value of Quinn and coworkers (J. Chem. SOC., Faraday Trans. 1, 1976, 72, 1935) for the rate of recombination of methyl radicals. The following rate expressions were found : loglo(k4/cm3 mol-l s-1)(30x) = 11.69 (kO.20)-38.23 (k0.84) kJ mol-l/2.303RT loglo(k4/cm3 mol-1 s-1)(3,30x) = 1 1.72 ( f 0.20) - 39.47 (& 1.0) kJ mol-l/2.303RT loglo(k4/cm3 mol-l s-1)(2,20x) = 1 1.99 ( k 0.23) -41.24 ( f 1.13) kJ mol-l/2.303RT.From these rate expressions and those obtained previously for three other oxetane molecules, the rate parameters for hydrogen-atom abstraction from five distinct sites in the substituted oxetane molecules have been obtained. Very little information is available concerning the abstraction reactions of methyl radicals with cyclic molecules.' In an attempt to remedy the deficiency, and in connection particularly with studies of the thermolysis of various oxetane molecules, we reported previously the results of work on hydrogen abstraction by methyl radicals from oxetane, 2-methyloxetane and 2,4-dimeth~loxetane.~ Two different types of ring hydrogen atom were distinguished, namely secondary and tertiary hydrogen atoms, and Arrhenius parameters for their removal were obtained by assuming those for removal of primary hydrogen atoms in the methyl groups to be similar to the parameters for removal of primary hydrogen in ~ r o p a n e .~ In the present paper this work is extended to three other oxetane molecules. Five types of hydrogen-atom sites can now be distinguished, and by analysing the present and previous results it was hoped to obtain individual Arrhenius parameters for abstraction from all five types of site assuming only a value for the rate of recombination of methyl radicals. EXPERIMENTAL APPARATUS AND PROCEDURE All reactions were carried out in the gas phase by photolysing reaction mixtures in a Pyrex cell (volume 180cm3) with a plane glass window.The apparatus and procedure have been described previously. MATERIALS Acetone (A.R.) was supplied by Koch-Light Ltd, and, after thorough degassing and on-line distillation, was found to be > 99.5% pure. The oxetane samples were prepared in these laboratories by Mrs B. Worthington. The 2,2-dimethyloxetane was prepared from 3- 339 13392 REACTIONS OF METHYL RADICALS WITH OXETANES Poxetanelpacetone Fig. 1. Plots for calculation of k,lkf: (-A-) 3-methyloxetane at 2,2-dimethyloxetane at 197.0 "C and (-n-) 3,3-dimethyloxetane at 192.0 "C. 197.2 "C, (---O---) bromoethylpropionate by reacting it with methylmagnesium iodide to form 2-methyl-4- bromopropan-2-01.This was then ring-closed using tributyltin ethoxide to give the product. A sample of 3,3-dimethyloxetane was prepared by ring-closing 2,2-dimethylpropan- 1,3-diol using concentrated sulphuric acid and sodium hydroxide. The 3-methyloxetane was prepared from diethylmonomethyl malonate which was reduced to 2-methylpropan- 1,3-diol using lithium aluminium hydride. The diol was then converted by acetyl chloride to the chloroester, which was ring-closed using a concentrated solution of sodium and potassium hydroxides. After purification by preparative g.1.c. and on-line distillation, all samples of oxetanes were found to be > 99.5% pure. RESULTS REACTIONS BETWEEN METHYL RADICALS AND OXETANES The results for the photolysis of acetone between temperatures of 100 and 192 "C have been reported previously2 and were shown to be in good agreement with the results of other workers.When acetone is photolysed in the presence of an oxetane, the following reactions occur : hv CH,COCH, + X H , + CO k, CH, + CH,COCH, --+ CH, + CH,COCH, k, CH, + CH,COCH, -+ C,H,COCH, k, 2CH, --+ C2H, k4 CH, + oxetane + CH, + oxetanyl.M. G. DUKE AND K . A. HOLBROOK 3393 Table 1. Analytical results and rate constant ratios for the methyl radical + 3-methyloxetane reaction Pacetone P3-methyloxetane PCH4 PCzHs (k4lkb T/"C /Torr /Torr Torr /lov2 Torr /cm: mol; s-4 104.3 104.8 105.5 117.5 1 1 7.5a 118.2 124.1 124.3 132.8 132.9 134.9 150.2 150.2 150.3 150.7 167.7 168.2 168.2 168.8 182.9 183.1 183.2 183.3 197.2 197.3b 197.4 30.9 31.1 30.8 31.3 31.3 31.3 32.2 32.1 32.7 32.9 32.6 34.2 34.2 34.0 33.9 36.2 36.2 36.2 36.2 36.5 36.9 36.5 36.8 38.3 37.8 38.1 30.1 30.3 30.6 31.3 31.3 31.3 31.8 31.9 32.1 32.2 32.6 24.8 17.9 33.7 33.9 17.6 22.5 36.2 36.3 36.5 15.8 36.5 36.6 26.2 37.8 18.7 2.99 3.02 3.07 4.02 4.14 3.79 4.50 4.50 5.34 5.14 5.58 6.37 5.73 7.44 7.41 7.3 1 7.81 8.99 8.89 9.56 8.32 9.56 10.1 10.2 11.6 9.12 2.48 2.52 2.48 1.97 2.0 1 1.87 1.65 1.59 1.47 1.39 1.48 1.19 1.44 1.02 1 .oo 0.93 0.79 0.54 0.53 0.29 0.63 0.32 0.29 0.32 0.24 0.39 0.538 0.534 0.542 0.784 0.776 0.753 0.955 0.970 1.16 1.16 1.21 1.87 1.86 1.92 1.92 3.00 3.03 3.03 3.03 4.52 4.55 4.55 4.47 5.47 5.33 5.32 a Photolysis time = 1920 s.Photolysis time = 2040 s. It can be shown that this leads to the expression k, k, Poxetane x Pacetone G ki Pacetone =-T+-€x- RCH4 where RCHl and RCzHs are the rates of formation of methane and ethane, respectively.Plots of the left-hand side of this expression against poxetane/pacetone are shown for the three oxetanes studied in fig. 1. This expression predicts linear plots provided that poxetane and pa,,,,,, are not depleted by formation of products during the experiment. This is shown by the data in table 1. In all three cases the oxetane under study was illuminated alone for 1 h at 150 "C and no products were detected. The three oxetanes were also put separately and admixed with acetone into the furnace and left for 1 h without illumination, to check that there was no thermal decomposition; no breakdown products were detected . 3-METHY LOXETANE An initial pressure of 30 Torr* of 3-methyloxetane at 100 "C was used and the pressure adjusted accordingly to keep the initial concentration constant as the3394 REACTIONS OF METHYL RADICALS WITH OXETANES Table 2. Equivalence of propene and carbon monoxide pco from 3-methyloxetane T/"C / 1 0-2 Torr pCIH/ 1 0-2 Torr 105.5 117.5 132.8 150.7 168.2 183.2 0.20 0.43 1.04 2.61 4.20 8.14 0.23 0.45 1 .oo 2.58 5.60 9.95 temperature was raised.Although most reactions were carried out at a 3- methyloxetane: acetone ratio of 1 .O, several were carried out at a ratio < 1 .O to show that k,/kt was independent of this ratio (see fig. 1). From a series of 26 photolyses in the temperature range 104.3-197 "C, and assuming the value of k, from the work of Quinn and c o ~ o r k e r s , ~ the rate constant (k4)3-0x for the overall abstraction of hydrogen from 3-methyloxetane is given by loglo(k4/cm3 mol-l s - ~ ) ( , . ~ ~ ) = 1 1.69 (k 0.20) - 38.23 ( f 0.84) kJ mol-l/2.303RT the error limits being the 95% confidence limits.The values of k,/k: * used for the Arrhenius plot (fig. 2) are shown in table 1. As well as methane and ethane, propene, carbon monoxide and hydrogen were found in the reaction products. Propene and carbon monoxide were determined quantitatively, but hydrogen was only detected at temperatures above 170 "C and no accurate quantitative work could be carried out. Determination of carbon monoxide formed due to the presence of 3-methyloxetane was made by subtracting the pressure of CO measured by the photolysis of acetone alone.Owing to the small pressures of CO involved and the method of measurement, errors are likely to be quite large. However, at all temperatures, the propene pressure was equal, within experimental error, to the CO pressure, as shown for 6 temperatures in table 2. This is in accordance with the breakdown of the 3-methyloxetanyl radical as shown below: C3H6 + HkO HkO - CO+H 3,3-DIMETHYLOXETANE AND 2,2-DIMETHYLOXETANE Similar procedures were used for the other two oxetanes studied. From a series of 30 photolyses in the temperature range 100.4-192.3 "C, the rate constant (~k~),.,~~ for overall hydrogen abstraction by methyl radicals from 3,3-dimethyloxetane is given by loglo(k4/cm3 mol-1 s-1)(3.30x) = 1 1.72 (k0.20) - 39.47 (& 1 .O) kJ mol-l/2.303RT the error limits being the 95 % confidence limits.Isobutene and carbon monoxide were analysed quantitatively and it was found that reasonable agreement was obtained between the amounts of these products. For 2,2-dimethyloxetane, 2 1 photolyses were carried out in the temperature rangeM. G. DUKE AND K. A. HOLBROOK 3395 103 KIT Fig. 2. Arrhenius plots: (a) 3-methyloxetane and (b) 3,3-dimethyloxetane. The plot for 2,2-dimethyloxetane is very similar to that for 3,3-dimethyloxetane and has been omitted for clarity. 100.1-197.8 "C and the rate constant (k4)2.20x for overall hydrogen abstraction by methyl radicals is given by loglo(k4/cm3 mol-l s-1)(2,20x) = I 1.99 (f 0.23) -41.24 (If: 1.13) kJ mol-l/2.303RT the error limits being the 95% confidence limits. Isobutene and carbon monoxide and hydrogen were also detected in the reaction products, but ethene was absent, unlike the reaction of methyl radicals with 2-methyloxetane.DISCUSSION The Arrhenius parameters for the abstraction of a hydrogen atom by methyl radicals from three oxetane molecules have been obtained, and these supplement the previous results that we have reported.2 A summary of all the results and the overall rate constants at 164 "C are given in table 3. Although it is evident that both 2-methyloxetane and 2,4-dimethyloxetane have a higher rate constant at 164 "C than the other four oxetanes studied, it must be realised that this overall rate constant is the sum of H-atom abstraction from all sites in the molecules. We have shown previously that the tertiary H atoms in the 2-position are removed much faster than the secondary methylene H atoms.From the results obtained in this present work, the rate constants for H-atom abstraction by methyl radicals at all positions in the oxetane ring can be calculated. If it is assumed that the overall rate constant can be calculated by addition of the3396 REACTIONS OF METHYL RADICALS WITH OXETANES Table 3. Comparison of rate parameters for hydrogen abstraction log,o(k log,o(A /cm3 mol-l s-l) substrate /cm3 mol-I s-l) E/kJ mo1-I at 164 "C ref. 11.29 35.22 7.08 11.42 34.04 7.35 11.51 33.52 7.51 11.69 38.23 7.12 11.72 39.47 7.00 11.99 41.24 7.06 9 t! DO 2 2 2 this work this work this work rate constants for attack at all sites in the molecules, five H-atom sites may be distinguished in the six oxetanes studied.These may be labelled a, b, c, d and e as shown below, and rate constants for their abstraction by k,, k,, kc, kd and k,: C c b a b b CH Z-CH 2 CH2-CH CH,-CH CHZ-0 I I CH,-o I Is /CH-0 a a CH3 I Is C Assuming that the rate constants are additive, it can be shown that the individual rate constants are given by k~ = ( k 3 , 3 0 X -k 'OX- k Z , Z O X ) / 6M. G. DUKE AND K. A. HOLBROOK 3397 Table 4. Rate parameters for H-atom abstraction from oxetane molecules a 10.2 33.0 b 11.0 38.5 C 12.5 56.9 d 11.6 41.3 e 10.7 30.4 6.26 6.40 5.70 6.67 7.07 Table 5. Arrhenius parameters for the H-atom-abstraction reactions of methyl radicals (per H atom) species log,,A/cm3 mol-1 s-l E/kJ mol-l ref. CH3CH20H A A Ha (adj. to 0) H, (remote from 0) He (adj.to 0) H, (remote from 0) primary C-H 11.25 10.20 10.8 10.20 12.5 11.52 11.12 1 1.30 10.89 10.49 10.22 11.01 10.39 9.80 11.43 10.2 11.0 tertiary C-H 11.38 10.98 10.7 11.6 secondary C-H 50.2 41.8 49.4 39.7 56.9 42.4 41.8 40.5 43.5 38.9 43.1 55.2 40.2 37.7 49.5 33.0 38.5 33.6 33.0 30.4 41.3 7 8 5 8 this work 9 5 10 5 11 11 5 12 13 6 this work this work 9 5 this work this work * 1 Torr = 133.33 Pa. Values of these rate constants per H atom have been calculated at temperatures between 100 and 200 "C, and the corresponding Arrhenius parameters are given in table 4 with the rate constants per H atom at 164 "C. The rate of H-atom abstraction follows the expected order of tertiary > secondary > primary since He, H, > Ha, H, > H,. A comparison of the rate constants for H-atom abstraction from the sites in oxetane molecules with those from other molecules is given in table 5.Comparison of the Arrhenius parameters in table 5 reveals some interesting facts. Secondary H atoms in small-ring compounds have slightly lower A factors and3398 REACTIONS OF METHYL RADICALS WITH OXETANES activation energies for abstraction by methyl radicals compared with secondary H atoms in comparable open-chain compounds. The presence of an adjacent oxygen atom lowers the activation energy to approximately the same extent in both 3-membered and 4-membered rings; thus E(*, [ref. ( ~ ) ] - E , A , , [ref. (6)] = 55.2-49.5 = 5.7f3.0 kJ mol-1 E,o, [ref. ( 5 ) ] - E , (this work) = 43.5-33.0 = 10.5f2.7 kJ mol-l. The parameters from ref. ( 5 ) have been used in this comparison as they are considered more reliable than those from earlier work cited in table 5 .A similar lowering of the activation energy for removal of a tertiary hydrogen atom adjacent to oxygen is noted when comparing values for the hydrogen atoms He and H,. Baldwin et have recently shown that an Evans-Polanyi type equation which fits the variation of activation energy with bond dissociation energy for methyl attack on alkanes, viz. : E = 30.0 + 0.504[D(R-H) - 38 1.51 kJ mol-1 can be extended to include data for cycloalkanes, oxirane and oxetane. Applying this equation to the activation energies derived here for hydrogen abstraction at the various sites we obtain the following values of dissociation energies in kJ mol-l: D, = 387.5, D, = 398.4, D, = 434.9, Dd = 403.9, D, = 382.3.From these data it can be shown that the relative ease of removal of secondary and tertiary H atoms in an oxetane ring is comparable to the difference between such atoms in open-chain analogues, i.e. D, (sec)- D, (tert) = 5.2 kJ mol-1 cp4 The least reliable of our data are the Arrhenius parameters for the removal of primary H atoms in the methyl side-groups where the A factor and activation energy appear too high by comparison with previously measured values on hydrocarbon^.^ We hope to obtain more reliable values for these parameters from a study of H-atom abstraction from the fully methylated compound hexamethyloxetane in the near future. P. Gray, A. A. Herod and A. Jones, Chem. Rev., 1971, 71, 247. M. G. Duke and K. A. Holbrook, J. Chem. Soc., Faraday Trans. I , 1980, 76, 1232. J. R. McNesby and A. S. Gordon, J. Am. Chem. Soc., 1950,72, 101. D. A. Parkes, D. M. Paul and C. P. Quinn, J . Chem. Soc., Faraday Trans. I , 1976,72, 1935. J. A. Kerr and M. J. Parsonage, Evaluated Kinetic Data on Gas-phase Hydrogen Transfer Reactions of Methyl Radicals (Butterworths, London, 1976). R. R. Baldwin, Annette Keen and R. W. Walker, J. Chem. SOC., Faraday Trans. I , 1984, 80, 435. ' J. A. Kerr and D. Timlin, J . Chem. SOC. A , 1959, 1241. * A. F. Trotman-Dickenson, J. R. Birchard and E. W. Steacie, J . Chem. Phys., 1951, 19, 163. * W. M. Jackson, J. R. McNesby and B. de B. Darwent, J . Chem. Phys., 1962,37, 1610 and references therein. lo P. Gray and A. A. Herod, Trans. Faraday SOC., 1968, 64, 1568. l1 A. F. Trotman-Dickenson and E. W. R. Steacie, J . Chem. Phys., 1951, 19, 329. '* M. K. Phibbs and B. de B. Darwent, Can. J . Res., Sect. B, 1950, 28, 395. l 3 R. Gomer and W. A. Noyes, J. Am. Chem. Soc., 1950, 72, 101. l4 J. A. Kerr and A. F. Trotman-Dickenson, in Handbook of Chemistry and Physics, ed. C. R. Weast (C.R.C. Press, Boca Raton, 62nd edn, 1982), p. F192. (PAPER 4/445)