J. CHEM. SOC. FARADAY TRANS., 1994, 90(9), 1197-1204 Investigation into the Kinetics and Mechanism of the Reaction of NO, with CH, and CH,O at 298 K between 0.6 and 8.5 Torr: Is there a Chain Decomposition Mechanism in Operation? Peter Biggs, Carlos E. Canosa-Mas, Jean-Marc Fracheboud, Dudley E. Shallcross and Richard P. Wayne* Physical Chemistry Laboratory, South Parks Road, Oxford, UK OX1 302 The reactions CH, + NO, +products (l), and CH,O + NO, -+ products (2),have been studied using a flow system at T = 298 K and at pressures between 0.6 and 8.5 Torr. The laser-induced fluorescence (LIF) technique was used to detect CH,O and multi-pass optical absorption to detect NO,. The chemical systems were studied as a pair of consecutive reactions; however, a simple analytical treatment was not sufficient to describe them because CH302 was formed as one of the products in the major channel of reaction (2).This species also reacts with NO, regenerating CH,O. Use of a numerical model to correct for this regeneration process allowed rate parameters of k, = (3.5+_ 1.0) x lo-'' cm3 molecule-' s-' and k, = (2.3 & 0.7) x lo-', cm3 molecule-' s-' to be determined at 2.4 Torr. There is no pressure dependence observed for reaction (1) between 1 and 2.4 Torr, but the possibility of a slight pressure dependence for reaction (2) exists. These pressure effects are examined using the semi-empirical quantum RRK method. The importance of the nitrate radical (NO,) as a night-time oxidant in the troposphere has become apparent in recent years.' Although the two reactions CH, + NO, -,products (1) CH,O + NO, +products (2) would not be expected to be significant sinks for methyl and methoxyl radicals in the troposphere, where reactions with molecular oxygen CH, + 0, + M +CH,O, + M (3) CH,O + 0, -+ HCHO + HO, (4) are by far the most important reaction pathways, they are nevertheless worthy of study.First, they are examples of radical-radical reactions where the possibility of more than one product channel exists. Secondly, a knowledge of the product channels and rate parameters for these reactions is essential in the interpretation of our laboratory studies of the interactions of the nitrate radical with CH,O,, which may itself be involved in atmospheric chemistry (see following paper)., No kinetic results have been reported previously for either reaction (1) or reaction (2).Experimental The apparatus is shown in Fig. 1. It is similar to that described in detail elsewhere., A conventional discharge-flow apparatus is used with a double sliding-injector arrangement, coupled to a fluorescence cell. An optical multi-pass absorp-tion cell (12 passes, base path 10 cm) and a quadrupole mass spectrometer were incorporated in the flow tube downstream of the LIF cell. Nitrate radicals were prepared by the reaction of fluorine atoms with dry nitric acid F + HNO, +HF + NO, (5) and detected by optical absorption at Iz = 662 nm.4 An effec-tive absorption cross-section was determined experimentally for NO, [o = (1.1 & 0.1) x lo-'' molecule cm-,] via the titration of NO, with NO NO, + NO -+ 2N0, (6) from which absolute concentrations of NO, could be assign- ed.The minimum detectable [NO,] for a signal-to-noise ratio of unity with a 10 s integration time was ca. 10" mol-ecule cm-,. Experiments were performed at T = 298 K and between 0.6 and 8.5 Torr total pressure, with helium as the carrier gas. The NO, was maintained in excess over the other reactants. Initial concentrations of NO, were typically in the range (0.5-3.5) x lo', molecule cm-, and the organic rad- icals were present initially at concentrations of (0.3-5) x lo', molecule ern-,. For the investigation of reactions (1) and (2), methyl radicals were prepared by the reaction of F atoms with CH, . Methyl radicals reacted rapidly with NO, forming CH,O (see later) in the reaction CH, + NO, +CH,O + NO, (14 The methoxyl radicals so produced could further react with NO, to form products CH,O + NO, -+ products (2) and a consecutive reaction sequence was established in a similar fashion to that observed when NO, reacts with methyl radicals., Thus, by monitoring the concentration- time profile of the methoxyl radical by the LIF technique, the rate coefficients k, and k, could be determined.The details of the LIF detection of the methoxyl radical are described else-where., For calibration purposes, and in some kinetic experiments, we generated CH,O directly in the sliding injector via the reaction of fluorine atoms with methyl nitrite' F + CH,ONO +CH,O + FNO (7) and used this system to study reaction (2).Mass spectro- metric analysis showed that the signal from the species FNO at m/e = 49 remained essentially constant while CH,O decayed, indicating that FNO chemistry does not interfere. Materials Nitric acid (BDH, 99.9%) was dehydrated by sulfuric acid (BDH, 99.5%) in a 1 :2 volume-to-volume mixture and held at ca. 258 K. Helium (BOC) was passed through two traps held at 77 K containing molecular sieve 4A (BDH) to remove water and an OXISORB cartridge (Messer Griesheim) to remove oxygen. Methane (BOC) and fluorine (5% in He) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 He optical absorption system I I 1 I +to flow Pump A1 microwave discharge He excimer pumped dye laser reactant at injector A1 B1 reaction HNO, CH4 CH,ONO F + HNO, +HF + NO, F + CH, +CH, + HF F + CH,ONO --$ CH,O + FNO ~~ Fig.1 Experimental arrangement of the flow tube and detection system. Sources of radicals are indicated in the table. were used without further purification. For the experiments using deuteriated reagents, the chemicals used were : helium (Messer Griesheim), CD, (MSD isotopes, 99% D) and fluorine (5% in He). Methyl nitrite (CH,ONO) was synthesised by the dropwise addition of sulfuric acid (33% in H20, 150 ml) onto a 1 :1 mixture of water and methanol (20 ml each) and sodium nitrite (25 g, Aldrich) at 273 K. The brown methyl nitrite gas produced was pumped through two traps, the first containing CaCO, powder (Aldrich) and the second contain- ing KOH pellets (Aldrich) to remove any residual acid.The gas was then trapped in a cold finger held at 196 K. The resulting yellow liquid was stored in the dark at this tem- perature until required. As will appear later, it is essential to minimise residual methanol in the methyl nitrite. To purify the CH,ONO, it was vacuum distilled from 196 K to 77 K several times (typically three) until the CH,OH impurity, as determined mass spectrometrically, was less than 5%. Results and Their Analysis Reaction of CH,O with NO, using CH,ONO as the Source of CH,O A preliminary investigation of the kinetics of reaction (2) was performed in which CH,O was generated uia the reaction of fluorine atoms with methyl nitrite’ in reaction (7). At first sight, this method seemed to be successful and a good com- bined second-order plot was obtained at 1.6 Torr total pres- sure (see Fig.2), which gives the result k, = 1.6 x lo-’, cm3 molecule-’ s-’. However, we observed anomalous effects when NO, concentrations were lower than 8 x 10l2 mol- ecule ern-,. For these concentrations, rather than a drop in CH,O signal following addition of NO,, an increase occurred. We attributed this effect to the presence of the hydroxymethyl radical (CH20H) and its reaction with NO,. The source of CH,OH was the reaction697 F + CH,OH +CH,OH + HF (8) the methanol being an impurity in the methyl nitrite samples. When methanol alone was used as a source of CH,O, these anomalous effects were more pronounced, confirming our hypothesis. NO, may react with CH,OH to form CH,O directly, or the removal of CH,O in reaction with CH,OH may be suppressed.It is inappropriate to speculate further about this phenomenon, but the value obtained for k, at 1.6 Torr should only be treated as approximate, and an alterna- tive source of CH,O was sought. 0.01 0.02 0.03 0.04 time,/s Fig. 2 Plot of ln([CH,0]o/[CH,0])/~03]o as a function of time. P = 1.6 TOR. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Reactions of CH, and CH,O with NO, using the Reaction between CH, and NO, as the Source of CH,O We discovered an excellent alternative source for the gener- ation of methoxyl radicals, which was a branch of reaction (1) itself CH, + NO, -+ CH,O + NO, (14 Using this source, reactions (1)and (2) were studied as a pair of consecutive reactions.With NO, in excess, both processes (1) and (2)could be treated as first order. It was assumed that, for both methyl and methoxyl radicals, some first-order losses independent of NO, could occur, e.g. on the walls. With these rate coefficients for losses identified as kcH3and k;,,, ,the total first-order loss can be written k; = k& + k,[NO,] k; = ~H,O+ k,"O,I (11) The concentration-time profile for CH,O can therefore be expressed as k; aCCH310CCH301, = ki -k; [exp( -k; t) -exp(-kit)] (111) where kia(=k,,[NO,]) denotes the specific channel forming methoxyl radicals and [CH,], is the initial methyl radical concentration. Eqn. (111) could then be used to fit the experimentally derived LIF signal from CH,O as a function of time.We use this equation as the basis for analytical methods of obtaining the rate constants, but, as we shall show shortly, a numerical correction procedure had to be adopted because of complications in the reaction system. A non-linear least-squares fitting procedure was applied, with k;,[CH,],, k; and k; being the three parameters optimised. Fig. 3 shows a set of typical profiles for [CH,O] and the results of the three-parameter fit. Note that the absolute scale for [CH,O] emerges only as an outcome of the modelling procedures to be presented later, but has no bearing on the three-parameter fit, which can use arbitrary units for the cal- culations. The expected rise and decay indicative of consecu- tive processes is evident.Values of k; and k; obtained from the fitting procedure were plotted against [NO,l0 to yield the second-order rate constants k, and k, . There is no ambiguity about which rate constant is the larger, since we already have 14 12 mI 5 10 2 0.005 0.01 0 0.015 0.020 0.025 time/s Fig. 3 Concentration-time profiles for [CH,O] showing the results of the three-parameter fitting in the CH, + NO, system. P = 2.4 Torr. (+) [NO,], = 4.6 x lo'* molecule an-,; (V)[NO,], = 1.z x lo1, molecule cm-,; (m) mO,], = 1.7 x 10'' molecule cm- . The results obtained from numerical modelling are almost identical (see text). an approximate value for k, obtained from the experiments with CH,ONO. An alternative method employed to analyse the CH30 concentration-time profiles was to use just the decay part of the curve to determine k;.Provided that k; is much larger than k;, and at a sufficiently long time t, eqn. (111) can be rewritten ln[CH,O], = In( k;.CCH3k; 1o)-k; t and k; can be determined. Then a two-parameter (k;,[CH,], and k;) fit of the data using the calculated k; could be per- formed to determine k;.The two methods yielded essentially the same rate constants for k; and k;. However, for some experiments where there were not enough points in the decay part of the curve, the first method was used exclusively. In those experiments where the shortest contact time had already exceeded the time for the maximum [CH,O] to be reached, the second method was used.At a pressure of 2.4 Torr, the three-parameter fit could always be used. This pres- sure is particularly important to us, because it is the same as that used in the experiments described in the next paper2 and in support of which the present work was a necessary precur- sor. We shall show in the subsequent paragraphs that the rate constants must be corrected. In this discussion, several modifications to the pseudo-first-order rate constants, k', and k;,will be needed. We shall adopt a superscript 'exp' to indi- cate uncorrected experimental rate coefficients ; other super- scripts for rate constants corrected for secondary reactions or diffusion, or extracted by numerical modelling, are defined in the footnote to Table 1.The table presents the uncorrected rate Coefficients for kYxP and k;'xPderived at 2.4 Torr (columns 4 and 7). This type of approach has been employed previously3 to good effect for the reactions of NOz with CH, and CH,O. There were, however, two important differences between the NO, and the NO, systems. First, the maximum concentration which could be attained for NO, was an order of magnitude less than for NO, ([NO,],,, = 3.5 x lOI3 mol-ecule ern-,); thus, in the NO, case, methyl radical loss via its self reaction could not be neglected. Secondly, at long contact times in the NO, system, the LIF signal for CH,O decayed to zero, whereas in the NO, experiments there was a distinct CH,O signal still present even at contact times as long as 120 ms.In fact, this signal was virtually constant after 80 ms. This second phenomenon is demonstrated in Fig. 4, which shows a typical experimental concentration-time profile for CH ,O together with a fit from a numerical model (see later). It is evident that some process is in operation that regenerates CH,O. A probable explanation for this regeneration is that the products of reaction (2) are predominantly CH,O, and NO2 CH,O + NO, -+ CH302+ NO, (24 and that CH,O, itself reacts with NO, reforming CH,O CH,O, + NO, -+ CH,O + NO, + 0, (9) The regeneration process appears to be efficient, as demon- strated by the very small decay of CH,O seen at long contact times, which itself points strongly to reactions (2a) and (9) being the major channels in the reaction of CH,O and CH302 with NO,.Model calculations show that the fraction of CH,O radicals passing through the reactions that regener- ate these radicals is between 0.6 and 0.7 for t > 60 ms. To test the hypothesis that CH,O was regenerated, a set of experi- ments was performed to look specifically for CH302 as a product, as we shall discuss later. Regeneration of CH,O makes simple application of the three-parameter fitting J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Values of k; and k2 at P = 2.4 Torr P/Torr [N0,],/10'3 molecule cm-, A[NO,]/~O,], k':xP/s-' k?/s-l k';um/s-l k;'"P/s-' k;d"'/s -' 2.37 0.81 0.18 595 368 324 69 72 2.40 0.46 0.20 364 212 189 60 62 2.40 0.58 0.14 370 252 220 61 63 0.14 442 303 307 74 772.40 0.83 2.40 0.80 0.14 366 250 240 78 81 2.40 1.24 0.12 593 440 397 74 77 2.40 1.64 0.09 856 675 656 69 71 2.40 2.27 0.02 863 88 92 2.31 1.20 0.14 496 341 336 74 77 2.31 1.92 0.12 1047 766 730 103 108 2.31 1.42 0.10 622 482 383 82 86 2.38 0.94 0.11 520 394 329 68 71 2.38 1.23 0.12 486 356 332 82 86 2.38 1.53 0.10 717 547 459 71 73 2.47 2.28 0.06 95 100 2.39 1.21 0.12 570 412 424 71 74 2.39 0.63 0.16 293 192 189 54 56 2.43 1.67 0.13 719 508 451 83 87 2.40 1.97 0.14 89 93 2.40 1.28 0.16 592 39 1 384 64 66 2.38 1.35 0.13 567 400 378 69 72 2.38 0.68 0.15 364 246 204 54 55 Column 3 displays the values of A[NO,]/[NO,], averaged over all contact times.Column 4 shows the values of k; derived from applying the three-parameter fitting method to the experimental data.In column 5 are the corrected values of k', (see text). In column 6 are the values of k', derived from application of the numerical model to the experimental data. Column 7 shows the values of k; derived from application of the numerical model to the experimental data. Column 7 shows the values of k; derived from either a ln(CH,O) us. time plot (see text) or the three-parameter fitting method. Column 8 shows the values of k2 corrected for axial diffusion and radial concentration gradients. method as used previously for the NO2 system subject to error., We therefore adopted a correction procedure in which a numerical model was used to refine the results of the three- parameter fit in an iterative way.We prefer this procedure to straight fitting to a numerical model. Preliminary trials indi- cated that there was no advantage in using such a model to fit the data from our experiments at relatively short contact times (t < 25 ms). It is not possible either to distinguish between the reaction of CH,O with NO, to form CH302 and other losses of CH,O, or to define a value for the rate coefficient for reaction between CH302 and NO,. The numerical integrations for the model were performed using a program written in BASIC that employed a second-order single-step backward-differentiation method. 5 4E4 n \ _/------_ I 0.02 0.04 0.06 0.08 0.10 time/s Fig. 4 Experimental (CH,O) and modelled (CH,O, CH,O,) concentration-time profiles for long contact times in the CH,+ NO, system.P = 0.6 Torr; pTO,l0 = 2.5 x lo', molecule ~rn-~. (D)Expenmental [CH,O]; (-) modelled [CH,O]; (---) model-led [CH,02]. Correction Procedures Data for the numerical model are given in Table 2. Fitting was achieved largely by eye, assisted by examination of mean-square deviations. The approximate values of k,, k2 and k, so derived are then used as the starting point for a correction procedure based on the numerical model. This procedure consisted of first generating simulated concentration-time profiles of [CH,O] for a variety of start- ing conditions, including input values of k; and k;, called here k';'" and k';'". We then ran the three-parameter fit on these generated data to recover the values of ,;,Utand kpt.In all experimental runs, we observed a drop in [NO,] on addi- tion of methyl radicals to the system (Table 1).This drop, identified as ACNO,], was usually about 10-15% of the [NO,] in the absence of CH, ([NO,l0). A simple empirical relationship was found relating R = k'li"/k'out to AINO,]/[NO,]o. This relation is R = (0.97 f0.02) -(1.86 & 0.12) x A[NO,]/[NO,]o (V) R was used to modify the values of k;exp, obtained from the three-parameter fit to the experimental data. The modified values for k; (termed k'y)at 2.4 Torr are shown in Table 1, column 5. Fig. 5 shows k'? (= R x l~':"~)plotted as a func- tion of [NOJ0. Although there are generally few points on the rise portions of the concentration-time profiles, the time dependence of the maximum of the [CH,O] provides a good definition of k;,as indicated by the relatively small scatter in Fig.5. Indeed, the statistical error on the slope of this figure is k0.24 x lo-" cm3 molecule-' s-l (95% confidence limits), but an additional error arises from uncertainty in the zero of time that is itself due to mixing effects and axial diffu- sion. We therefore quote k, as (3.5 f1.0) x lo-" cm3 molecule-' s-'. The intercept in Fig. 5 is zero, the reason for which is that the correction procedure corrects for any first- order losses that are independent of [NO,]. Correction of the rate constant for reaction (2) proceeds in a similar manner, but here there appears to be no simple factor to be applied to the pseudo-first-order rate coefficient J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 2 Rate parameters used in the numerical model reaction k/cm 'molecule -' s -' number ref. CH, + NO, CH,O + NO, 3.3 x lo-" (14 a4 CH, + CH, -+ CH,CH, 4 x lo-" (10) 8 CH,O + CH,O -,products 1.0 x lo-" (1 1) 9 CH, + CH,O +products 4 x lo-" (12) b CH,O -,products 25-50 s-' (13) see text CH,O + NO, -,CH,O, + NO, CH302+ NO, +CH,O + NO, + 0, 2-3 x lo-', (24 see text 1 x lo-', (9) see text CH, + NO, -+ CH,O + NO 2.3 x lo-" (14) 3, 10 CH,O + NO, products 2.0 x lo-', (15) 3, 11, 12 CH,O + NO -,products 5.0 x lo-', (16) 13 NO,+NO,+M-+N,O,+M 4.0 10-14 (1 7) 14 NO, + NO -,2N0, 3.0 x lo-" (6) 15 a The numerical model yields a value k, = (3.3 f0.9) x lo-" cm3 molecule-' s-'; the corresponding first-order rate constants are listed in Table 1.For reaction (12) the rate constant was estimated to be twice the geometric mean of k,, and kl,. k;. Instead, we plot the values of Py' (generated by applica- the evaluation of the rate constant k; by the analytical tion of the three-parameter fit to the simulated data) against method. The only way of extracting kinetic parameters from [NO,] to obtain a predicted value of the second-order rate these data was to use the numerical model. It was possible to constant, ko;l*,and compare k? with this value to provide the distinguish clearly between the numerical fits to the experi- correction. The relation is k? = 1.1 x ko;lf. Values of k;'"p mental data at these long contact times (up to 120 ms), for were obtained from the three-parameter method or from values of k, in the range (1.5-2.5) x lo-'' cm3 molecule-' direct logarithmic analysis at relatively long contact times.s-'. Similar calculations were carried out for the experiments These values were corrected for radial and axial diffusion at 1.01 and 1.40 Torr. For the higher pressures, 2.4-8.5 Torr, using the standard methods of Walker,16 Brown1' and the numerical model produced very good fits to the experi- Keyser" to yield the rate constant k;diff. Fig. 6 is a plot of mental data using the values of k, shown in Table 3 (column k;diff against [NO,], for three pressures, and is the source of 4).In making this fit, k, is used as an adjustable parameter the uncorrected value of k, . Table 3 collects the uncorrected and a value for this rate constant can therefore also be and final corrected values for k, at each pressure. At the derived. The value obtained for k, is (l.O?A:!) x lo-'' m3 lowest pressure (0.6 Torr), the available linear flow velocity molecule-s-'. The error limits indicate the highest and was not sufficient to give a range of contact times suitable for lowest possible rate coefficients that could be used to fit the 200800 U 150600 c cI I9 5100400 0-?m* 50 V I 0.5 1.o 1.5 2.0 1 2 3 4 molecule ~m-~[N0,],/1 013molecule ~m-~ [N03]0/1013 Fig. 5 Corrected pseudo-first-order rate coefficient (see text) for the Fig.6 Pseudo-first-order rate coefficient (derived from the three- reaction CH, + NO,, plotted as a function of [NO,], . (V)1.0; (A) parameter method) for the reaction CH,O + NO,, plotted as a func- 2.4 Torr. tion of WO,], .(V)1.0; (0)1.4and (0) 2.4 and (a)5.4 Torr. Table 3 Summary of the values obtained for k, at various pressures ~ ~___ pressure/Torr no. of experiments k,/10-I2 cm3 molecule-'s-' k,/10-I2 cm3rnolecule-'s-' k,/10-cm3 molecule-'^-^ 0.60 6 2.2 f0.5 1.01 9 1.6 f0.3 1.7 f0.3 2.1 0.6 1.40 6 1.8 0.6 2.0 f0.6 2.1 0.6 2.40 22 2.1 f0.7 2.3 f0.7 5.44 10 3.0 f1.2 3.3 f1.2 8.50 6 3.3 f1.5 3.6 f1.5 Column 3 shows the values of k, derived from the three-parameter fit corrected for axial diffusion and radial concentration gradients. Column 4 shows the values of k, from column 3 corrected by the numerical method.Column 5 shows the values derived for k, by fitting to the numerical model. 0.01 0.02 0.03 0.0 4 time/s Fig. 7 Mass-spectrometric determination of the relative concentra- tion of CD,O, in the reaction of CD, with NO,. (m) Experimental points; (-----) a fit using the numerical model (see text). experimental data. However, the fits using these limiting values are not as good as those employing the centre value, requiring values of k,/k, which are incompatible with the experiments presented in the next paper., Identification of CH,O, We cannot detect CH,O, directly in our system. In experi- ments where CH,O, is produced directly (see subsequent paper),2 titration with NO CH,O, + NO +CH,O + NO, (18) can be used as an indirect method of monitoring the peroxy radical.However, in the present studies the NO would react mainly with NO, and CH,O so that the method is not satis- factory. An alternative series of experiments was used to demonstrate the occurrence of reaction (2a).A discharge-flow system at the University of Kiel (Germany) equipped with a quadrupole mass spectrometer that had a high sensitivity towards the peroxy radical CH,O, (1 x lo1' molecule cm-,) was used for this purpose. In these experiments, CD, was substituted for CH,. Unambiguous assignment of CD,O, at its parent ion (m/e= 50) was possible, whereas the CH,O, peak (m/e= 47) suffered from strong interferences from sec- ondary peaks of other species in the system.The deuteriated peroxy radical was indeed identified; it arises from the reac- tion sequence F + CD, +CD, + DF (19) CD, + NO, +CD,O + NO, (20) CD,O + NO, +CD302+ NO, (21) A typical experimental run showing the build up of CD,O,, together with the calculated [CD,O,] from the numerical model, is shown in Fig. 7. We are confident, therefore, that the inclusion of reaction (2a) in the numerical model is justi- fied. Discussion Reaction between CH, and NO, It is clear that the reaction between CH, and NO, is fast; the major channel appears to be process (la). It is also evident that the reaction does not show a significant pressure depen- dence, at least over the range 1.0-2.4 Torr (see Fig.5). In a previous study,, we investigated the pressure dependence of the reaction of NO, with CH, and CH,O and used the semi- J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 empirical quantum RRK (QRRK) methodlg to rationalise our observations. If the same approach is adopted here, we must first look at the possible products which arise from the formation of the [CH,-ONO,]* energised complex. There are four possible channels, illustrated by the energy diagram for this reaction system in Fig. 8; simple bond fission of the complex can either regenerate the reactants or yield CH,O + NO, depending on whether the C-ON or CO-N bond breaks. Similarly, the energised complex can undergo exten- sive bond rearrangement and fission to form HCHO and HONO; and finally, the complex can be stabilised to form an adduct, which in this system is likely to be CH,ONO,.The QRRK method allows the calculation of the microcanonical rate constants for each particular channel for a given total internal energy of the energised complex. The data required for this calculation are the high-pressure Arrhenius pre- exponential factor (A;) and the activation energy (E') for each process i; the parameters employed are summarised in Table 4. No information exists for the dissociation of CH,ONO, to CH, and NO,. The activation energy was therefore taken to be the difference between the heat of for- mation of CH,0N02 and the combined heat of formation of CH, and NO, ;the A factor was estimated from A factors for similar simple bond fission reactiom2' Table 5 shows the partitioning of the four channels at four pressures.It is clear that channel (la) should dominate at pressures up to 10 atm and that the stabilised adduct (CH,ONO,) would only become a significant channel beyond this pressure. This result is consistent with our experimental conclusion that channel (la) is the only branch of reaction (1) in our system and indi- cates that a pressure dependence is not expected. Reaction between CH,O and NO, As in the case of reaction (l),several possible channels CH,O + NO, +CH302+ NO, (24 CH,O + NO, + HCHO + HNO, (24 CH,O + NO, + M +CH302N02+ M (2c) exist for reaction (2). As pointed out earlier, the extent to which CH,O is regenerated in the pair of reactions (2) and (9) I CH3+N03-200.-I100 -r I-z2 0-5 -100 -CH,ONO, \L-200t-HCHO+HONO Fig.8 Energy diagram for the reaction between CH, and NO,. The energies on which this diagram is based, and the justifications for their adoption, are presented in Table 4. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 4 Parameters used in the QRRK calculation for reaction (1) reaction A1s-l E/kJ mol-' (v)$cm-m ref. aCH,ONO, + CH, + NO, 1.0 x 1oI6 337.0 972.4 29CH,ONO, -+ CH,O + NO, 3.2 x 1015 166.5 972.4 15 22 CH,ONO, + HCHO + HONO 3.3 1013 151.0 972.4 13 23 The A factor was estimated" and E was ~alculated'~ from ArH(CH,) + ArH(NO,) -A,H(CH,ONO,). (v), is the geometric mean frequency for CH,ONO,, estimated from the vibrational data of Bock et al." m is the critical number of quanta required for reaction, i.e.E/hv + 1 2 rn 2 E/hv; here the lower bound is stated. The number of oscillators, for CH,ONO, is 18. Table 5 Fractional contributions of different channels obtained in the QRRK calculations on the CH, + NO, system Platm process 0 1 10 100 CH, + NO, CH,O + NO, HCHO + HONO ca. 0 0.96 0.04 ca. 0 0.95 0.04 ca. 0 0.90 0.04 ca. 0 0.58 0.03 CH,ONO, (stabilised) ca. 0 0.01 0.06 0.39 indicates an overall efficiency of 0.6 to 0.7, and thus the lower limit for the fractional contribution of reaction (2a)is also in this range. An interesting feature of reaction (2) is the possible weak pressure dependence observed up to 8.5 Torr (Table 3).By analogy with the corresponding reactions of NO, CH,O + NO, --+ HCHO + HONO (19a) CH30 + NO, + M -,CH,ONO, + M (19b) where the pressure-dependent channel (19b) dominates3,' '9' above a pressure of 1 Torr, we might expect reaction (2) to show the same characteristics. In addition, the peroxynitrate (CH,O,NO,) formed in reaction (24 has three more vibra- tional modes than the corresponding alkyl nitrate (CH,ONO,) formed in reaction (19b), so that, for a given fractional excess internal energy and pressure of the bath gas, the stabilisation of a peroxynitrate energised complex relative to redissociation would be expected to be greater than that for the alkylnitrate.Once again, the QRRK method was used to investigate this hypothesis. The data relevant to the calcu- lation are summarised in Table 6. There were no data in the literature for the high-pressure dissociation of methyl per- oxynitrate to form either CH,O + NO, or HCHO + HONO, ; the A factor was therefore estimated from the kinetics of similar reactions.20 The activation energy for the first of these channels was estimated from heats of forma- tion," and for the second an estimate was made based on the dissociation of CH,ONO, to HCHO + HONO.,, The QRRK calculations show that complex bond fission of the energised complex leading to HCHO + HONO, is negligi- ble, even when the largest possible A factor is used (Table 7). The calculations show that the relative importance of stabili- sation of the energised complex is also small.The redissociation channel reforming reactants is negligible even when the assumed A factor is some ten times greater than that for channel (24. A measurable pressure dependence of rate of reaction is only expected if changes in bath-gas con- centration alter the relative rates of reaction into the various channels as a consequence of the redistribution of the inter- nal energy. As Table 7 shows, no channel other than (24 appears to contribute in the pressure range of our experi- ments. No dependence of k, on pressure is thus expected. We note that if we use the smallest possible activation energy for redissociation (i.e.the minimum possible energy difference as dictated by the error limits quoted for the heats of formation), we find that at zero pressure a fraction of 0.1 of the energised complexes formed do redissociate to reactants and 0.9 form CH,O, + NO,.There is then the possibility of a small pressure effect. Although there is some tendency for k, to increase with pressure (Table 3), we believe that the experimental uncertainties in the individual rate constants do not allow us to be more dogmatic at present. The real problem is that the QRRK method cannot be applied in cases where the energy difference between different possible product channels is small enough to make the predicted dif- ferences in rate coefficients comparable with the inherent errors in the calculation of those coefficients introduced by the approximations.This problem is compounded where there are uncertainties in the thermochemical data. We would like to express our gratitude to the NERC (grant GR3/7359) for support for this project, and to the CEC and the Institute Franqais du Petrole, under whose auspices various parts of this and related work were carried out. We are indebted to Professor R. N. Schindler for the use of the discharge-flow mass spectrometer apparatus in Kiel and to Tim Jungkamp for his assistance with the experiments on CD, carried out with this equipment. We thank Richenda Table 7 Fractional contributions of different channels obtained in the QRRK calculations on the CH,O + NO, system Pporr process 0 1 10 760 CH,O,NO, -+ CH30,N0, -+ CH,O + NO, CH30, + NO, ca.0 0.98 ca. 0 0.98 ca. 0 0.95 ca. 0 0.80 CH,O,NO, -+ HCHO + HONO, 0.02 0.02 0.02 0.01 CH,O,NO, (stabilised) ca. 0 ca. 0 0.03 0.19 Table 6 reaction A/s- E/kJ mol- CH30,N0, + CH,O + NO, CH,O,NO, + CH,O, + NO, CH,O,NO, -+ HCHO + HONO, 1 x 1017 1.1 x 10l6 1 x 1015 130.0 87.8 100.0 a The A factor was estimated,' and E was ~alculated'~ from Af H(CH,O) + Af H(N0,) and the energy barrier was estimated by comparison with the reaction" CH,ONO, quency for CH,O,NO, ,calculated from the vibrational data of Zabel et aLZ4 Parameters used in the QRRK calculation for reaction (2) (v>,/cm - m ref. 724 15 a 724 12 b 724 11 24 -Af H(CH,O,NO,). The A factor was estimated2' + HCHO + HONO.(v), is the geometric mean fre- 1204 J. CHEM. SOC. 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