Gas Phase Addition of HI to Ketene and the Kinetics of Decomposition of the Acetyl Radical BY LAJOS SZIROVICZA AND ROBIN WALSH * Department of Chemistry, The University, Whiteknights, Reading RG6 2AD Received 11 th May, 1973 The addition of HI to ketene results in the rapid formation of acetyl iodide at temperatures 498-525 K. The subsequent slower reaction between HI and acetyl iodide, which produces methane and acetaldehyde has been investigated at low conversions (c 10 %), at various initial pressures at 507 K. The results are shown to be consistent with the mechanism Most experiments were done in the presence of the inert additives N2 or cyclo-C4Fs. (M)+CH3CO + CH3+CO+(M) (5) CH3CO + HI + CH3CHO + I (3) CHs+HI + CH4+I. (6) The data at 507 K yield kF/k3 = (2.4k0.3) x mol dm-3 and Z/S = 65+ 8 dm3 mol-', where I and S refer to the intercept and slope of a Lindemann plot for the unimolecular step (5).An in- dependent estimate of k3 is used in conjunction with theoretical calculations on the acetyl decomposition reaction to show that, The limits cover all reasonable uncertainties, both experimental and theoretical. This result disposes of previous reports of a " low " A factor for this reaction. log (@/s-') = (13.3 +0.5)-(91.2+ 7.5 kJ m01-~)/2.303 RT. The first order rate constant for the decomposition of the acetyl radical (CH3CO) is known to be pressure dependent under experimentally accessible conditions.' * This behaviour is characteristic of a unimolecular reaction in its " fall-off " region. In their study of the photolysis of acetone in the presence of HI, O'Neal and Benson (hereafter referred to as OB) obtained, by an extrapolation technique to infinite pressure log (km/s-') = 10.3-62.8 kJ mol-'/2.303 RT.In a separate study, using a different system, Kerr and Calvert (hereafter refmed to as KC) concluded that their results were consistent with this expression. The A factor of 1010.3 s-l is considerably lower than that for propionyl de- composition and Frey and VinaII have carried out theoretical calculations which show that the observed pressure dependence of these rate constants is more consistent with an A factor - 1012e5 s-l. In view of these inconsistencies we decided to attempt a reinvestigation of this system. In a previous publication it was noted that the addition reactions of HI to unsaturates provided a means of generating radicals and studying their unimolecular reactions by a competitive method.This technique is applied here to the case of HI addition to ketene. 'r present address : Institute of General and Physical Chemistry of the University of Szeged Szeged 1, Hungary. 1-2 3334 ADDITION OF HI TO KETENE EXPERIMENTAL APPARATUS This was similar to that described in an earlier paper.6 MATERIALS HI vapour was prepared from a solution (Fisons) by dehydration with P205. The gas was passed through a trap at - 78°C and collected at - 196°C. It was stored at room temperature in a blackened bulb. KETENE was prepared by the pyrolysis of acetic anhydride by the method of Jenkin~.~ The gas was passed through 2 traps at -78°C and collected at - 196°C. It was stored at room temperature (at pressures < 100 Torr*) in a blackened bulb.V.P.C. analysis showed the presence of small quantities of C2H4 (-0.1 %) impurity, but the absence (<0.01 %) of CH4 and CH3CH0 or other impurities. CH4 was obtained from Cambrian Chemicals. CH3CH0 was obtained from Fisons. N2 (white spot) was supplied by British Oxygen Co. PERFLUOROCYCLOBUTANE (c-C4F8) was obtained from Matheson. It was >98 % pure and contained no impurity which interfered with reaction product analysis by V.P.C. PROCEDURE Prior to a kinetic run, HI and ketene (CH,CO) were both degassed at - 196°C. CH2C0 was shared into the reaction vessel at a known pressure. HI was then added and the total pressure monitored by the pressure transducer.Inert gas (N, or c-C4FC) was added 3-4 min after HI. After a suitable time the run was ended by expansion of the contents of the reaction vessel through a tube containing solid glycine to remove HI and into a sample pipette. The contents of the sample pipette were then taken for V.P.C. analysis. The sampling system, pipette and sample inlet valve and tubes on the V.P.C. were all heated to - 60°C to avoid condensation or adsorption (other than of HI). Separate tests showed that no losses of either CH4 or CH3CH0 occurred during the sampling operation and that, furthermore, these products were not generated from others amongst the reaction products during sampling or analysis. ANALYSIS AND PRODUCT IDENTIFICATION Routine analysis by V.P.C. of the contents of the sample pipette was performed on a 2.5 mx 3 mm Porapak Q column heated to 100°C with N2 carrier gas at an inlet pressure of 10 p.s.i.This was used to separate CH4 and CH3CH0. The flame detector was calibrated with carefully made up mixtures of these products in the presence of known quantities of the inert gases. This was important since, in the presence of c-C4F8, the detector response for CH3CH0 depended to some extent on the quantity of c-C,F8 (which eluted before it). Product analyses were, therefore, always carried out in the presence of a fixed quantity of c - C ~ F ~ . CO, which was expected amongst the products, was not analysed since it gave no signal on the flame detector. All analyses were performed in duplicate and the results averaged. The major product (>90 %) of addition of HI to CH2C0 at 488 K was shown to be acetyl iodide CH3COI by comparison of the n.m.r.spectrum (z = 7.04), and i.r. spectrum (v for >C=O stretch = 1757 an-') with those of an authentic sample made by reaction of CH3COCI and HI. Attempts at V.P.C. analysis (on a ppG column) of CH3COI were un- successful and the only (unidentified) impurity (7+3 %) in the reaction product n.m.r. spectrum has an absorption at z = 2.7 (singlet). In particular CH31 and iodoacetaldehyde. CH21CH0, were clearly absent (< 0.5 %). * 1 Tom = 133.3 N m-".L. SZIROVICZA AND R . WALSH 35 RESULTS PRELIMINARY EXPERIMENTS When HI and CH2C0 were mixed at 488 K an immediate rapid pressure decrease occurred. It was complete in <2 min (pressures up to 100 Ton of each reactant).The product of this reaction was identified as CH3COI (see experimental section). Although the initial pressures of the reacting mixtures were impossible to record, calculations from apparatus sharing ratios showed the pressure changes to correspond within f 5 % to the completion of the reaction ; HI + CH2C0 -+ CH3COI. No further pressure changes were recorded for up to 30 min. of excess HI, corresponds closely with that of Benson and O’Neal temperature range 495-539 K, investigated the kinetics of the reaction ; This reaction system, therefore, after the initial rapid addition and in the presence who, in the CH,COI+HI + CH,CHO+12. observed the formation of CH,CHO, but found no CH4. We have also obtained CH,CHO, but in addition our detailed analytical evidence shows that at 506.7 K during the first 10 % conversion to CH,CHO, small quantities of CH4 (from 1-5 % of the CH3CHO) are produced.The accepted mechanism ’* of formation of CH,CHO is the following : Benson and O’Neal M+I2 +21+M I + CHSCOI + CH3CO + 12 CH3C0 + HI e CH3CH0 +I. The formation of CH4 suggests in addition ; (M) + CH3C0 -+ CH, + CO + (M) (5) CH3+HI -+ CH4+I CH3+12 -+ CH31+I. Supporting evidence for the occurrefice of these added steps was obtained from the kinetic tests described in the next section. KINETIC TESTS OF THE MECHANISM In a series of experiments at 506.7 K, the ratio R = [CH,]/[CH,CHO] was measured as a function of time at three different initial pressures of HI and in the presence of excess N2 to a constant total pressure of -340 Torr.The results are plotted in fig. 1. They support the proposed mechanism in two ways. First the decrease in the ratio R, with time, at fixed initial conditions, is consistent with the competition between steps (6) and (7). At the start of the reaction in the virtual absence of 12, all CH3 is scavenged by HI in step (6), but as the reaction proceeds and I2 is formed, it competes for CH3 in step (7) thus reducing the CH4 yield. This effect is most marked for the lowest HI concentration, since at a given conversion of CH3COI to CH3CH0 the highest conversion of HI to I2 occurs. The effective competition of I2 with HI for CH3 even during these early stages of reaction (80 min corresponds to II 10 % conversion of CH,COI) is consistent with the known ratio l o of rate constants, k6/k, 2: 0.14.36 ADDITION OF HI TO KETENE I 2 0 4 0 6 0 8 0 time /min FIG.1.-The time dependence of [CH,]/[CH,CHO] (=R) : 0, HI = 4 Torr ; A, HI = 10 Torr ; 0 HI = 15 Torr. N2 added to total pressure - 340 Torr. Temperature = 507 K. [H1lo /Torr FIG. 2.-The effect of HI on [CH,CHO],/[CH410 (=&I). [CH,CO], - 4 Tom. N2 added to total pressure - 340 Torr. Temperature = 507 K.L . SZIROVICZA AND R . WALSH 37 Secondly the ratio R, is largest at low HI concentrations, where the CH3C0 decomposition step (5) competes most favourably with the CH3C0 scavenging step (3). At the outset of the reaction, steps (4) and (7) are unimportant and a stationary state treatment of steps (3), (5) and (6) yields d[CH3 CHO] /d[CH4] = k3 [HI]/k5. Since d[CH,CHO]/d[CH,] = l/Ro, a plot of l / R o against [HI] should be linear. Fig.2 shows such a plot where Ro values are taken as the intercepts of the lines (assumed linear) shown in fig. 1. Similar plots to those shown in fig. 1 and 2 were obtained in the presence of c-C4F8 (at fixed total pressure). This latter inert gas tended to give higher yields of CH4 (larger values of R,) in support of the fact that k , is in its pressure dependent region, and cyclo-C4F8 is a more efficient energy transfer agent. Because Ro is directly proportional to k,, the effect of variation of pressure of inert gas on Ro offers a direct test of the pressure dependence of k,. This test is described in the next section. PRESSURE DEPENDENCE OF THE ACETYL DECOMPOSITION In a series of experiments at 506.7 K, with [CH3CO1], = 4.3 Torr, HI = 10.0 torr, the ratio R was measured after 25 min for a number of different pressures of added c-C4F8.The conditions of these experiments were chosen to keep the total con- version to CH,+CH,CHO small (in practice between 3 and 5 %), but also to allow sufficient time for reaction that the delay in addition of cyclo-C,F8 leads to only a small overall timing uncertainty. The R values obtained were increased by a factor of 1.125 to convert them to R,. This correction corresponds with the time dependence of R observed previously (fig. 1). The results shown in table 1 indicate a variation of a factor of 10 in the ratio Ro for an 18 fold variation in total pressure. The rate constant k5 is clearly pressure dependent.TABLE THE PRESSURE DEPENDENCE OF Ro AT 507 K Ro - [CH410 pressure/Torr effective a pressure/Torr [CH 3CHOlo 720 713.5 0.0450 634 627.5 0.041 6 504 497.5 0.0371 464.5 458 0.0356 395.5 3 89 0.0286 358.5 352 0.0275 198 191.5 0.01 80 168 161.5 0.01 66 89.5 83 0.00885 65 58.5 0.0073 41 34.5 0.0044 a See text ; b Ro = k5/k3[HIl0 : [HIIo = constant = 10 Torr. To compare this data with previous work and also with theoretical calculations described later, a plot was made of l/R,[HI] against [concentration]-l. Since the composition of mixtures in our experiments was variable, the concentrations have been obtained not from the total pressures, but rather from adjusted pressures expressed in terms of c-C,F,. These have been worked out by allowance for the38 ADDITION OF HI TO KETENE different collisional efficiency, I i , diameter, oI, and reduced mass, pi, of each gas in the mixture according to ; The values for I * , of and pi used were obtained either directly or by analogy from the compilation of Rabinovitch et Q Z .~ ~ and are shown in table 2. The effect of this adjustment is fairly small except for the lowest pressure where HI and CH3COI make up 30 % of the mixture. TABLE 2.-PARAMETERS FOR GAS COLLISIONS WITH CHjCO gas 1 OlA O’lA p/a.rn.u. CH3COI 1 .o 5.1 4.8 34.3 HI 0.6 3.5 4.0 32.2 C~CIO-C,F* 1 .o 5.7 5.1 35.4 a u’ = $(u+ UCH~CO) where UCH~CO = 4.5 A. 80 - 4 7 0 - 6 0 - Q > 5 0 - P qo 40- X 3 0 - .-( “E X Y 1 H I o, 20- I 100 200 300 400 500 600 700 6 0 0 9 0 0 1000 [MI-’ /dm3 mol-’ FIG. 3.-Lindemann-type plot for product formation at 507 K : 0, upper line, this work ; lower line OB.Fig. 3 shows a least-mean-squares linear plot of our data and also includes the line obtained by OB’ for the same product function at 508.7 K. Although the inter- cepts are similar, there is clearly a substantial disagreement on slopes. The data are fitted reasonably well by straight lines, as predicted by the original Lindemann treatment of unimolecular reactions. Although modern RRKM theory l2 in prin- ciple predicts a curve for such a plot, this curve can, as is shown later, approximate closely to a straight line. In these circumstances such a plot can be usefully employed as a criterion of “ f a l l - ~ f f ” . ~ For this plot the intercept and slope correspond closely to k3/kg and k3/k; where and k; are high pressure (first order) and low pressure (second order) limiting rate constants respectively. The ratio intercept/ slope ( = I / S ) approximates to kz/ky and is independent of k3.Thus I/S is a para- meter of the acetyl decomposition alone (regardless of the inadequacies of theL. SZIROVICZA AND R . WALSH 39 Lindemann treatment). Our data at 506.7 K gave I / S = 65.4f7.9 dm3 mol-'. In addition? Z = (4.77k0.57) x lo4 dm3 mol-l. The theoretical calculations show this to be a 15 % overestimate of k 3 / k y and hence k y / k , = (2.41 f0.34) x lo-, mol dm-3. DISCUSSION Our values for k y / k , are in satisfactory agreement with those of OB1 but our quoted Z/S values for the Lindemann plot differ considerably from theirs (252.4 dm3 mol-' at 508.7 K).We do not understand the reason for this difference but note that the discrepancy is greatest at low pressures, with OB finding a greater extent of acetyl decomposition. A possible explanation is that the acetyl radical carries over some internal energy when formed photochemically in OB's system. This could not occur with our purely thermal method of generation. Further support for the validity of our results is obtained from the A factor derived from theoretical consideration of the pressure dependence of k,. Following the approach adopted by Vinall and Frey we have employed the Forst procedure l 3 to calculate k5 as a function of pressure for various values of A? and Ey and followed this by subjecting a plot of k; against (concentration)-l to a least squares analysis in our experimental (adjusted) pressure range, in order to obtain Z/S values for com- parison with experiment. The Forst procedure calculates the specific rate constant for decomposition as a function of energy, k(E), where N(E) represents the density of states at energy E, for the reactant, and A" and E" are the high pressure Arrhenius parameters.k(E) = 0 for E < E*. The important feature of eqn (A) is that it enables unimolecular fall-off curves to be calculated without consideration of the structure of the transition state. Only the reactant species requires a vibrational assignment. It should be noted, however, that while k(E) calculated by this method gives the correct average, (k(E)), for thermal systems, it is not the k(E) as normally defined in RRKM theory.13 Using the same assignment for acetyl as Vinall and Frey we obtained the Z/S values shown in table 3.k(E) = A"N(E-E")/N(E) (E 3 E") (A) TABLE 3.-THEORETICAL VALUES OF I / s AT 506.7 K FOR ACETYL DECOMPOSITION 17 19 21 25 23 11.5 537.2 912.8 1487 2346 3609 5445 12.1 149.7 260.7 433.6 692.7 1069 1606 12.7 40.07 71.42 121.8 199.4 315.0 481.6 13.3 10.36 18.76 32.60 54.54 88.15 138.0 13.9 2.626 4.791 8.411 14.26 23.44 37.39 14.5 0.6614 1.209 2.131 3.633 6.016 9.670 Collision parameters in table 2. Acetyl vibrational assignment, vlcm-': 3024, 2996, 2967, 1743, 1441(2), 1352, 1122,919, 867, 509,128. I/S in dm3 mol-' : ( I / S ) obs = (65.4f 7.9) dm3 mol-I. Bath gas is cyclo-C4F8. The plots from which these I / S values were obtained? in all cases had correlation coefficients of better than 0.9994 and the deviations from linearity were very slight over the observed (concentration)-l range, thus fully justifying the linear fit of the experimental data.The intercepts were found to be less than 1-20 % higher than the values of (ky)-'. The calculations were repeated for reasonable alterations in collision diameter, collision efficiency and vibrational assignment, but the resulting40 ADDITION OF HI TO KETENE Z/S values were well within a factor of two of those shown for a given A? and E," From the data of table 3, pairs of A: and EY for which I / S equalled the observed figure (65.4 dm3 mol-l) were extracted (by interpolation). The locus of these values is shown in fig. 4. This graph also shows the locus of AT and E," values required to fit k? = 103e9 s-l.This latter value is obtained from the experimental figure for k?/k3 at 506.7 K and the best available estimate for k3, viz : log (k3/s-l) = 9.20 - 6.3 kJ m01-'/2.303 RT. The intersection of these two lines in fig. 4 then permits a unique estimate of the high pressure Arrhenius parameters for the acetyl decomposition log (kY/s-l) = (13.3*0.5)-(91.217.5 W mol-')/2.303 RT. The error limits quoted here correspond to the shaded area in the figure which was obtained simply by assuming the maximum likely error in either Z/S or k? would be a factor of 2. FIG. 4.-Determination of Am and Em for acetyl decomposition. A, line giving correct ka, at 507 K ; B, line giving correct I / S value at 507 K. This approach to obtaining the high pressure limiting Arrhenius data for uni- molecular reactions in their pressure dependent regions is clearly superior to that of extrapolation of Lindemann plots combined with the traditional Arrhenius plot of the intercepts, which are subject to large error and can usually only be obtained over a restricted temperature range.of acetyl decomposi- tion and obtained log (A?/+) - 12.5 (cf. 10.3 observed) at each of four temperatures at which data was available. These values clearly improve upon the unreasonably low original figures, but our new results remove all remaining inconsistency with transition state theory expectations for bond breaking reactions (viz. A > kT/h = 1013e1 s-l). Furthermore, they show the expected similarity with the propionyl decomposition for which Kerr and Lloyd Vinall and Frey applied the method to the earlier studies obtained log (ka/s-') = 13.32-61.5 kcal m01-~/2.303 RT.L .SZIROVICZA AND R . WALSH 41 Despite the now reasonable A factor, and the agreement in absolute magnitude of k? between this work and that of OB1 there remain discrepancies in the absolute magnitude of k y implied by our Arrhenius Parameters and values obtained by other workers.2* 4* 14* l 5 Table 4 illustrates the differences. TABLE 4.-cOMPARISON OF k r VALUES WITH PREVIOUS DETERMINATIONS reference temp./K k? Is- 1 k?(corr.)/s-1 a kF(caIc.)/s-l b 14 298 2.5 0.4 0.0023 (0.01 3) 15 298 13 2.0 0.0023 (0.013) 2 338 94 20 0.16 (0.74) 2 d 298 - 0.007 0.0023 (0.01 3) 4 325.7 23.4 2.0 0.047 (0.24) a See text ; b calculated from our Arrhenius equation, maximum values in parentheses ; c calculated by OBI ; d data obtained from reverse addition of CH3 + CO.k? calculated via estimated equilibrium constant. Most of the previous work is based on comparative studies where the comparison reaction was either 2 CH3CO -+ (CH,CO), (8) (9) or The rate constants ks and kg have not been directly measured and assumptions about their magnitudes had to be made. Recent studies on alkylradical recombination 6* have shown that recombination rate constants are much smaller than was hitherto thought. The new figures for these are much more consistent with rate constants for the reverse bond-breaking processes for hydrocarbons l8 and the currently accepted thermodynamic data on free radi~a1s.l~ We have therefore taken the rate data 2o for biacetyl decomposition and used it in conjunction with the thermodynamic data (see Appendix) to estimate k8 = 108m4 dm3 mokl s-l.Assuming the geometric mean rule then kg = mol-1 s-l . These values, assumed temperature independent, were used to recalculate the figures for kg, which are also shown in table 4. When these corrected figures are compared with our own the discrepancies are somewhat reduced and in the case of KC’s study of CH3 addition to CO there is implied agree- ment within experimental error. Even so the same workers’ direct data on acetyl decomposition remains in disagreement with ours by two orders of magnitude, thus there is inconsistency between KC’s forward and reverse rate constants and currently accepted thermodynamic data (see Appendix and ref.(19)). Whatever the cause of the discrepancies in k y values KC’s study, unlike the others in table 4, is free from possibility that the CH3C0 generated contained any internal photochemically- derived excess energy. The remaining differences, which we cannot account for, are still such that if our results are correct, previous workers should not have seen the purely thermal de- composition of acetyl at lower temperatures. If their results are correct, then acetyl should have predominantly decomposed our system. There is clearly room for further investigation of acetyl decomposition, particularly at room temperature. CH3CO + CH3 -+ CH3COCH3. We thank H. M. Frey and I. C. Vinall for useful discussion and R.A. Smith for help with programming.42 ADDITION OF HI TO KETENE APPENDIX CALCULATION OF THE RECOMBINATION RATE CONSTANT FOR ACETYL RADICALS This was done via k, = k*-/Keq for the reaction f r CH3COCOCH3 + 2 CH3CO where kf = 7.6 x giving k, = 108.41 cm3 mol-1 s-l. s-l at 730 K20 and Keq = 2.95 x moI dm-3 at 730 K (see below) Keq was estimated from the following thermodynamic data. compound AH,O/kJ mol-1* So/J K-1 mol-1* CHSCOCOCHS -329 (I 360 CHSCO -24.3 269 * At 298 K and 1 atm standard state ; a most recent estimate b obtained by bond additivity ;22 Cref. (23); dcalculated from structure and vibrational assignment used in this work for fall-off calculation (see also ref. (4)). Cg corrections were neglected in estimating Keq at 730 K. This calculation updates that of Benson and O’Nea1.24 H.E. O’Neal and S. W. Benson, J. Chem. Phys., 1962,36,2196. J. A. Kerr and J. G. Calvert, J. Phys. Chem., 1965, 69, 1022. J. A. Kerr and A. C. Lloyd, Trans. Faraday SOC., 1967, 63, 2480. H. M. Frey and I. C. Vinall, Int. J. Chem. Kinetics, 1973, 5, 523. P. J. Gorton and R. Walsh, Chem. Comm., 1973. R. Walsh, Trans. Faraday SOC., 1971, 67,2085. H. E. O’Neal and S. W. Benson, J. Chem. Phys., 1962,37,540. D. M. Golden and S . W. Benson, Chem. Rev., 1969,69,125. lo M. C. Flowers and S. W. Benson, J. Chem. Phys., 1963,38,882. S . C . Chan, B. S. Rabinovitch, J. T. Bryant, L. D. Spicer, T. Fujimoto, Y. N. Lin and S. P. Pavlou, J. Phys. Chem., 1970,74, 3160. l2 see, for example, P. J. Robinson and K. A. Holbrook, Unirnolecular Reactions (Wiley-Inter- science, New York, 1972), chap. 4. l 3 W. Forst, J. Phys. Chem., 1972, 76, 342. l4 D. S. Herr and W. A. Noyes, J. Arner. Chem. Soc., 1940,62,2052. l 5 J. J. Howland and W. A. Noyes, J. Amer. Chem. SOC., 1941,63, 3404 ; 1944,66,974. ‘A. D. Jenkins, J. Chem. SOC., 1952,2563. R. Hiatt and S. W. Benson, J. Amer. Chem. Soc., 1972,94,25 ; Int. J. Chem. Kinetics, 1972,4, 151. l7 P. D. Pacey and J. H. Purnell, Int. J. Chem. Kinetics, 1972,4, 657. l 8 W. Tsang, Int. J. Chem. Kinetics, 1970,2, 311 and references cited therein. l9 S . W. Benson, Thermochemical Kinetics (Wiley, New York, 1968), p. 204 ; H. E. O’Neal and 2o K. J. Hole and M. F. R. Mulcahy, J. Phys. Chem., 1969,73, 177. 21 S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O’Neal, A. S. Rodgers, 22 S. W. Benson and J. H. Buss, J. Chem. Phys., 1958,29,546. 23 J. A. Devore and H. E. O”ea1, J. Phys. Chem., 1969,73,2644. 24 S. W. Benson and H. E. O’Neal, Kinetic Data on Gas Phase Unirnolecular Reactions, NSRDS- S. W. Benson, Int. J. Chem. Kinetics, 1969, 1, 221. R. Shaw and R. Walsh, Chem. Rev., 1969,69,279. NBS 21 (U.S. Govt. Printing Office, Washington D.C., 1970), p. 424.