Pressure and temperature dependence of the gas-phase reaction between methyl and hydroxyl radicals

8 July 1994

ELSEVIER

CHEWCAL PHYSICS

Chemical Physics Letters 224 ( 1994) 43-50

Pressure and temperature dependence of the gas-phase reaction between methyl and hydroxyl radicals Kjell Fagerstriim ‘, Anders Lund ‘, Gharib Mahmoud ‘, Jerzy T. Jodkowski b, Emil Ratajczak b a Chemical Physics Laboratory, Department ofPhysics andMeasurement Technology, Lintiping University, S-581 83 Lintiping, Sweden b Department ofPhysical Chemistry, MedicalAcademy, PI. Nankiera 1, RF140 Wroclaw, Poland

Received 3 1 March 1994

The kinetics of the reaction CHs + OH ( +M ) -CH,OH( + M ) was studied in the temperature range 283-373 K and in the pressure range 85-1000 mbar SF, by pulse radiolysis combined with UV absorption spectroscopy. The methyl and hydroxyl radical decays were followed by monitoring the transient UV absorption signals at 216.4 nm and 309.0 nm respectively. The reaction was studied in the fall-off region and by Troe’s analysis the following high- and low-pressure limiting rate constants were obtained: &_= (8.7f0.7)~ 10Lo(T/300)o~LM-r s-r and ko/[SF,] = (9.0f2.4)~ 1014(T/300)-3~8 Me2 s-r. The lowpressure limiting rate constant for the OH radical self-reaction was also derived: k&.r+oH,O /[SF,]=(4.0f0.7)x10”(T/300)-‘~4 Mm2s-’ using the value of kou+oH,m= 1.8~ 10Lo(T/300)-0~37M-’ s-r for the high-pressure limit.

1. Intmdoction For the reaction between CHS and OH radicals, the following reaction channels, besides the collisional stabilization to form CHsOH ( la), can be accessed via the vibrationally excited association complex [ l319 CH,+OH(+M)+CH,OH(+M),

(la)

CH3+OH(+M)+CH,0H+H,

(lb)

CHj+OH(

(lc)

+M)-CH30+H,

CH3+OH( +M)+‘CH2+H20.

(IdI

At near ambient pressures and temperatures, the radical cross-combination reaction channel ( 1a) seems to be the only one of importance [ 2,4,5 1. Furthermore, the shock tube study [ 6 ] performed at 1200

K and 1 bar of Ar has shown that under these conditions the primary reaction mechanism (75%) for the removal of OH by CH3 is their combination to form CHJOH ( la). However, it should be noticed that the importance of the other reaction channels, particularly at high temperatures, has recently been emphasized [3,7]. The kinetics of the reaction between CH3 and OH radicals has been studied both experimentally [ 2,3,8lo] and theoretically [ 3-5111. The first experimental study of this reaction was carried out by Sworski et al. [ 81 who flash photolyzed HZ0 in the presence of CH4 using 1000 mbar N2 as the diluent gas. They monitored the CH3 absorption, and a rate constant of 5.6~10’~ M-l s-i was obtained. A value of (5.7 f0.8) x 10” M-’ s-‘, again at ambient temperature and pressure, was determined by Anastasi et al. [ 91 who used Ar-sensitized pulse radiolysis of SFs in

0009-2614/94/$07.00 0 1994Elsevier Science B.V. All rights reserved ssDIOOO9-2614(94)00513-P

44

K. Fagerstriimet al. / ChemicalPhysicsLetters224 (1994) 43-50

the presence of CH4 and HzO. The reaction was monitored using the UV absorption of CH3. The first direct evidence for the pressure dependence of the rate constant for this reaction was obtained by Oser et al. [ 21. They studied the reaction in He as the bath gas at low pressures (0.3-6.2 mbar) using a dischargeflow system with a time-of-flight mass spectrometry detection. Their simplified analysis of the experimental data yielded an approximate value for the lowpressure limiting rate constant, kl,,o= (9.1 f 0.4) x 1OL4M-* s-i. Preliminary rate data have also been reported by Hughes et al. [ 31 for the pressure range 9-920 mbar He at 290 K. The radicals were generated by laser flash photolysis of CH3COCH, and HN03, and detected by the absorption of CH3 and laser-induced fluorescence of OH. The pressure dependence of the rate constant was analyzed using an inverse Laplace transformation and a value of (4.6f0.5)~10’~M-‘s-‘wasobtainedforthehighpressure limit. Jordan et al. [ 111 have performed calculations of the temperature dependence of ki,,, based on variational transition state theory, using the sinusoidally hindered rotor model as well as the Gorin model. Their results show a significant positive temperature coefficient (approximately cc T”.3) with valuesof 1.02~10”and l.l5~lO”M-‘s-‘at300 K. Previously [ 10 ] we have studied the kinetics of reaction ( la) only at room temperature and at four different pressures in the range 85-1000 mbar SF,, and have shown that under these conditions the reaction is still in the fall-off region. The calculated highpressure limiting rate constant was expressed as (8.7&0.9)x 10’“(T/300)o~’ M-i s-i for the temperature range 200-500 K, and an approximate value of the low-pressure limiting rate constant was estimatedas(2.6f2.3)x1015M-2s-1atroomtemperature. In the present study we report experimental results obtained over a large number of pressures in the range 85- 1000 mbar SF, and in the temperature range 283-373 K, using pulse radiolysis combined with absorption spectroscopy to detect CH3 radicals. The conditions were maintained such that the [ CH,] / [OH] ratio was varied in the range 0.3-9.0. At low ratios, reaction (la) is the main sink for CH3 radicals, while the CH3 radical self-reaction dominates at high ratios. Some additional experiments at 298 and 361 K, but only at 1000 mbar SF6, could be under-

taken by monitoring the transient absorption of OH radicals. The experimental decay profiles of the radicals were used to obtain the rate constants by computer modelling. The pressure dependence of the rate constant was analyzed in terms of the theory developedbyTroeeta1. [12-141.

2. Experimental The experimental technique, described in detail elsewhere [ 10,15,16 1, is pulse radiolysis combined with transient UV-absorption spectroscopy. Some modifications have been made in order to cover a larger temperature range. Electric heat ribbons wrapped around the cell are used for heating. The temperature inside the cell, which is measured by a thermocouple, is controlled by an adjustable transformer. The cooling is performed by means of a cooling liquid that is circulated around the cell. With the present experimental setup, kinetic studies in the temperature range 253-373 K are possible. The variation in temperature along the light path inside the cell is less than & 1 K. The uncertainty of the stated temperature is + 1.5 K. 2.1. Computer modelling CHEMSIMUL [ 17 1, software developed at Rise National Laboratory, was used for computer modelling of the kinetic data. 2.2. Materials Research grade gases, SF6 with a minimum purity of 99.97% and CH4 with a minimum purity of 99.995Oh,from Alfax (Air Liquide) were used without further purification. H20 was triply distilled and thoroughly degassed before use.

3. Results and discussion 3. I. Experimental studies In the present study the methyl and hydroxyl radicals were produced by the H atom abstraction reac-

K Fagerstriim et al. /Chemical Physics Letters 224 (1994) 43-50

tion of F atoms with CH4 and Hz0 respectively according to F+CHd+HF+CHa,

(2)

F+H,O-+HF+OH.

(3)

Pulse radiolysis of SF6 was used as the F atom source according to SFs + 800 keV e- + SF$ + e- , Sq-SF,+2F,

WI

SE-+SF,+F.

(4b)

Under the conditions prevalent in this study, reaction (4a) dominates the F atom production with reaction (4b) making a negligible contribution ( d 1%) according to Anastasi et al. [ 18 1. The maximum F atom concentration that can be obtained is as high as 2.4 PM. The radicals were produced by pulse radiolysis of SFs/CH4/H20 mixtures, with SF6 always in great excess, at varied [ CH4] / [ Hz01 ratios and different total pressures. The sum of the initial concentrations of methyl and hydroxyl radicals equals the initial F atom concentration, [ CH3 ] ,,+ [OH ] ,,= [ F ] 0. The relative yields of the radicals were determined by the competition ratio k2[ CH4] ,/k, [ Hz01 ,,. The initial yield of F atoms was calculated from the observed maximum absorbance in the absence of Hz0 using the well established extinction coefficient of the strong B-X Rydberg transition in methyl radicals at 216.4 nm, e(CHS)=24800 M-’ cm-’ 1191; No= A(216.4),/eLL, where L is the optical path length in the reaction cell. The absorbances were calculated as In (lo/Z). The optical band-pass was 0.4 nm which was chosen as the best compromise between spectral resolution and signal-to-noise ratio. The kinetics of the title reaction were primarily studied by following the CH3 decay at 2 16.4 nm at five temperatures in the range 283-373 K and at several total SF6 pressures between 85 and 1000 mbar. The reaction between methyl and hydroxyl radicals (la) proceeds in competition with the methyl and hydroxyl radical self-reactions: CHS+CHs( +M)+CzHb( OH+OH( +M)+H,Oa( OH+OH-+H20+0.

+M) +M) ,

,

(5) tea) (6b)

45

By varying the relation between the methane and water concentrations the relative yields of methyl and hydroxyl radicals were controlled. Typical values for the [ CH3] / [OH] ratio were between 0.3 and 9.0. An example of a CHS radical decay curve in the absence of OH is shown as the upper curve in Fig. la. The decay is second-order in accordance with the self-reaction ( 5 ) . The solid curve is predicted by modelling using a consensus value of k5=3.5x 1O’OM-l s-r [ 19,201. Measurements of the hydroxyl radical decay kinetics in the presence of methyl radicals were also made at 298 and 36 1 K, and 1000 mbar SF6. The hydroxyl radical absorption spectrum consists of discrete lines with sharp peaks with the strongest at 309.0 nm. The 0.801

I a

5C

0.15

iii y

0.10

3 8 3

0.05

9

0.00’ 0

_ _ 50

100 TlME

150

I

(~4

Fig. 1. CH3radicaldecay profdes (a) as well as OH radical decay profiles (b) monitored at 216.4 and 309.0 nm, respectively, under different experimental conditions at 36 1 K. The solid lines are those predicted by computer modelling. (a) Upper transient: p(SFs) ~690.0 mbar, p(CH,) = 10.0 mbar, self-reaction with ~18.7 u.s for [CH,]-= 0.76 uM; ks=3.5~10’~ M-’ s-‘. Lower transient: p(SF,)=690.6 mbar, p(CHd)=2.0 mbar, p(H,O)=7.4 mbar, r=l8.2 us for [CH,],=O.48 uM, &=8.0x10r” M-r s-r. (b) Upper transient: p(SFs)=989.1 mbar, p(H,O)=l0.9 mbar; self-reaction with r=35.7 us for 04; koH+ori= 4.4~10’ M-r s-r. Lower tran[OHI ,=2.3 sient:p(SF6)=985.6mbar,p(HzO)=l2.34mbar,p(CH,)=2.l mbar, r= 14.4 us for [OH],=O.87 pM, k-=8.1 x 10” M-’ S-I.

46

K. Fagerstrd’m et al. /Chemical Physics Letters 224 (1994) 43-50

dispersion limited band-pass of the monochromator is 0.08 nm which is much wider than the width of the OH line. This means that the Beer-Lambert law is not obeyed. An approximation for relating the absorbance, A = In ( lo/Z), to the concentration, c, in such a case is A = (CL)“, where L is the optical path length. In that equation n is an empirical constant that has to be determined experimentally by examining the effect of L or c on A. The exponent n is unique for each experimental apparatus. This method is described in detail in Ref. [ 211. The n factor determined in this study is 0.78 f 0.08. This value was frequently checked during the experimental period. The values of the rate constant for the cross-combination reaction ( la), monitored under the differ-

ent experimental conditions listed in Table 1, were obtained by computer simulation of the methyl and hydroxyl transients taking reactions ( 2)) ( 3 ), ( 5 ) and (7)-( 12) (below) into account in addition to reactions (la), (6a) and (6b), OH+CH4+CHS

+H,O

,

(7)

0H+O-+H+02,

(8)

CHa+O+HCHO+H,

(9)

CHS +H-CH4,

(10)

CHS +H20-CH_,

+OH ,

(11)

0H+H202+H02+Hz0.

(12)

Table 1 Conditions to monitor the CH, decay profiles in the reaction system SFs/CH4/H20

T

Pc3F6)

lF10

44CI-M

4W20)

(K)

(mbu)

(PM)

(mbar)

(mhr)

283

85 170 500 1000

0.16 0.32 0.80 1.30

2.0 1.0-3.0 1.0-3.5 0.6-3.3

2.0-10.3 3.0-10.3 3.3-7.0 3.3-6.7

1.0-5.2 1.0-5.0 0.9-6.4 1.0-10.2

0.08-0.13 0.16-0.26 0.32-0.60 0.37-0.90

298

85 120 170 240 340 380 500 700 1000

0.20 0.13 0.41 0.32 0.58 0.68 1.20 1.02 0.40

0.5-2.0 2.0-3.0 1.0-5.0 2.0-3.0 2.0-3.0 2.0-3.0 1.6-4.0 2.0-3.2 1B-5.0

1.0-5.0 3.0-7.3 3.8-l 1.0 3.0-15.0 3.0-l 1.2 3.0-14.8 2.7-14.0 3.2-13.4 3.0-15.0

0.5-10.0 1.0-3.7 0.8-l 1.0 1.0-6.0 1.0-5.6 1.0-7.4 0.7-8.8 1.0-6.7 0.7-15.0

331

85 170 340 500 700 1000

0.11 0.19 0.43 0.66 0.90 1.20

2.0-3.0 2.0-3.0 2.0-3.5 2.0-3.0 2.0-3.0 2.0-3.0

3.0-7.3 3.0-20.0 3.3-6.4 3.0-17.4 3.0-14.0 3.0-20.4

361

85 170 340 414 500 700 1000

0.11 0.18 0.42 0.44 0.61 0.85 1.10

2.0-3.4 2.0-4.4 2.0-6.0 2.0-4.0 2.0 2.0-3.0 1.1-3.1

373

340 500 700 1000

0.33 0.35 0.70 1.10

2.0-3.0 2.0-3.0 2.0-3.0 2.0-3.0

Td

IV9

(w)

(M-’ s-‘)

lo-‘Ok, (M-’ s-‘)

83.8-90.7 40.4-46.2 16.5-19.8 9.7-13.0

1.3 2.2 4.7 6.9

7.5 7.8 7.8 8.0

0.07-0.18 0.08-o. 11 0.13-0.34 0.15-0.26 0.26-0.45 0.26-0.52 0.39-0.90 0.39-0.74 0.10-0.33

65.0-73.9 110.0-l 13.0 30.5-37.2 42.4-46.7 23.0-26.5 19.1-22.8 10.9-14.1 13.2-16.0 28.6-37.8

1.1 1.5 2.0 2.6 3.4 3.6 4.2 5.2 6.3

6.7 1.2 7.2 7.3 7.9 1.9 8.0 8.1 8.1

1d-3.7 1.0-10.0 0.9-3.2 1.0-8.7 1.0-7.0 1.0-10.2

0.07-0.09 0.07-o. 16 0.27-0.34 0.25-0.52 0.37-0.68 0.37-0.87

137-139 74.6-78.3 33.5-35.3 19.7-23.6 15.1-17.9 10.9-13.9

0.88 1.6 2.7 3.5 4.3 5.3

7.0 7.5 7.8 8.0 8.1 a.2

3.4-7.3 4.0-10.2 3.0-14.2 4.0-20.4 6.4-10.0 3.0-16.3 3.1-15.1

1B-3.6 1.0-5.1 1d-6.2 1.O-9.7 3.2-5.0 1.0-8.2 1.0-13.7

0.07-0.09 0.10-0.15 0.21-0.35 0.17-0.36 0.33-0.38 0.35-0.66 0.31-0.82

144-163 87.2-95.3 36.4-36.8 33.3-35.3 23.5-24.2 16.1-18.9 11.4-15.1

0.72 1.3 2.2 2.6 2.9 3.6 4.4

5.0 5.5 6.6 7.0 7.9 8.0 8.1

3.0-10.2 3.0-16.0 3.0-16.0 3.0-20.0

1.0-4.4 1.0-8.0 1.0-8.0 1.0-9.5

0.20-0.28 0.16-0.29 0.30-0.56 0.40-0.82

46.3 42.0-43.6 19.8-22.6 12.6-15.1

2.1 2.7 3.4 4.2

7.0 7.3 7.9 8.0

lH201/1~1

[CH3Im.x (PM)

kli+oIi

K. Fagerstdm et al. / Chemical Physics Letters 224 (1994) 43-50

The following recommended values of the rate constants were used in the simulations: k2 = 1.8 1 x lO”exp( -4OOK/T) M-l s-’ [22], ks=8.43x lo9 M-’ s-’ [22], k5=3.5x10’0 M-’ s-’ [19,20], bb=2.53x109exp( -240KlT) M-’ s-’ [22], k, =5.28x lO*( T/298)1.83 exp( - 1400KlT) M-’ S-’ [I], k8=1.21X1010eXp(l12~/T) M-’ S-’ [l], k9=8.43x10ro M-’ s-’ [l], klo=2.18x 1013(T/298)-1.8 M-’ s-’ [ 11, k,, =7.23x 106(T/298)2.9 exp( -7480K/T) M-’ s-’ [4], k12=1.75x lo9 exp( - 160K/T) M-l s-’ [22]. The hydroxyl radical recombination reaction (6a) plays an important role in the kinetic scheme under investigation. The time profiles of the CH3 and OH concentrations obtained by computer simulation are sensitive to the value of the rate constant for the OH radical recombination reaction, bH+oH. Therefore, knowledge of this value for the experimental conditions is of significant importance to the precision of the estimated rate constant for reaction (la). The most recently recommended values for the high-pressure limiting rate constant for the recombination reaction between hydroxyl radicals (6a) vary by a factor of two [22,23 1. Because of this uncertainty, the rate constant for this reaction, which is pressure and temperature dependent, was obtained in a separate study which is described at the end of this section. The bFCOH+oH values employed in the simulations are included in Table 1. The results of the computer simulations of a large number of CH3 transients, recorded under different experimental conditions, are listed in Table 1. The lower curve in Fig. la shows an example of the best fit of the model curve to the experimental curve at 361 K and at a total pressure of 700 mbar SF6. The maximum uncertainty of the values for the rate constant for the recombination reaction between methyl and hydroxyl radicals, k,, given in Table 1 is f 20%. This value is based on the sensitivity analysis of a large number of experiments. A better accuracy was obtained at higher pressures and lower temperatures. A pressure and temperature dependence of the rate constant for reaction (la) is clearly observed. At the lowest studied [ CH3] / [OH] ratios the model is sensitive to the value of k, and the effect of the selfreaction on the overall methyl radical decay is small. An example of the effect of reaction ( la) at 36 1 K is illustrated in Fig. 2 for different experimental condi-

47

c;

(I)

b

E -7 P

Fig. 2. Reciprocal half-life (5) of CH, radical decay as a function of [ CH,], (and the [ H,O] / [ CH,] ratio) for seven different total pressures at 361 K. The solid lines are those predicted by computer modelling. ( 0 ) 1000 mbar; ( V ) 700 mbar; (n ) 500 mbar; (A) 414 mbar; (+) 340 mbar; (A) 170 mbar, (0) 85 mbar.

tions which are summarized in Table 1. The points at [CH,],= 0 correspond to the half-life of reaction (la) proceeding under pseudo-first-order conditions where [OH],_= [Flo and rl12=ln2/ (k,[ F],). The other points were obtained experimentally. The solid line through the origin represents the theoretical variation of the pure methyl radical self-reaction proceeding under second-order conditions. The variation in half-life between the different total pressures is basically an effect of the different initial F atom concentrations which decrease with decreasing SF6 pressure. From this figure it can be seen that in this model, reaction ( la) becomes increasingly important at low [CH,],, i.e. at high

[OHLax. Additional measurements of the OH decay kinetics in the presence of CH3 were made at 298 and 36 1 K, and at 1000 mbar SF6. Measurements at lower pressures are less accurate due to the low OH absorption. Two examples of OH transients are shown in Fig. lb, where the upper one shows OH decay in the

& Fagerstrlim et al. /Chemical Physics Letters 224 (1994) 43-50

48

absence of CH3 and the lower one shows the decay in the presence of CHS. The solid lines are those predicted by computer modelling. The shape of an experimentally monitored OH transient is sensitive to the value of the n factor. Thus, the kinetic results obtained from OH measurements are less accurate than those obtained from detailed CH3 studies. However, simulation of the experimental data obtained by monitoring the transient UV absorption signals at 309.0 nm gives a good tit when using the same k, values as those that were used for the simulations of the CH3 decay profiles. The kinetics of the self-reaction between hydroxyl radicals (6a) were studied at two temperatures, 298 and 361 K, and at four different total SF6 pressures: 350,500,750 and 1000 mbar. The OH radicals were produced by pulse radiolysis of SF6 in the presence of HZ0 via the reactions (4a) and (3) as described in the previous section. The rate constants, which are included in Table 1 and shown in Fig. 3, were obtained by computer modelling of the OH transients

taking the reactions (3), (6a), (6b), (8) and (12) into account. The maximum uncertainty of the ko H+OH values is estimated to be f 30%. Examples of OH decay curves, in the absence of CH,, are shown as the upper curve in Fig. lb and as an insert in Fig. 3. The rate constants for the other experimental conditions, also included in Table 1, were obtained from an analysis of the fall-off behaviour as described in section 3.2. 3.2. Analysisof thefall-offrange Our experimental data for the hydroxyl radical recombination were analyzed by the construction of theoretical fall-off curves. According to the concepts of Troe and co-workers [ 12-141, the rate constant, k, for dissociation/recombination in the fall-off region can be expressed by k/k,=

A 1-A/‘=--

TIME /pS

2.0

FSCFWC

’

(13)

with the limiting high-pressure, k,, and low-pressure, b, rate constants, and the broadening factors, Fsc and Fwc calculated on the basis of the method elaborated by Troe and co-workers [ 12- 14 1. The low-pressure limiting rate constant was derived as ko= Bckv, where kgc is the strong collision low-pressure limiting rate constant evaluated by means of the theory developed by Troe [ 241. The collisional efficiency, j&, is related to the average energy transferred per collision, ( LW) , and the energy dependence of the density of states factor, FE, as

1o.o-

8.5

‘lk-

l+Wk,

2.5

3.0

losplM/mbar Fig. 3. Fall-off curves (together with the experimental points) for the recombination reaction OH+OH( +M)+H202( +M) where M = SF6, at ( 0 ) 298 and ( n ) 36 1 K. The insert is the OH radical transient monitored at 309.0 nm and 361 K under the following experimental conditions: p( SF,) = 737.8 mbar, p(H20) = 12.2 mbar; self-reaction with r=52.7 ps for [OH],= 1.7 PM, k,,“+oH=3.7x 10gM-’ s-l.


(14)

The IUPAC preferred value for the high-pressure limiting rate constant for hydroxyl radical recombi1.8~10’~ M-l s-’ in the temnation, kOH+0~,co= perature range 200-300 K [ 221, is consistent with the early experiments performed below 1 bar [ 25 ] and the experiments conducted close to the highpressure limit (in the pressure range 1.5-l 38 bar) [26] as well as with the theoretical analysis of the photolysis and the thermal dissociation rates of HzOz [ 271. The analysis of the temperature dependence of T-” predicted [ 271 a value of the temko H+OH,_CC perature coefftcient nz0.37 in the range 200-l 500 K, and this value was also adopted in the present cal-

49

K Fagerstriim et al. /Chemical Physics Letters 224 (1994) 43-50

culations. With the molecular parameters from Refs. [25,28], the strong collision low-pressure limiting rate constants, k?&+on,J [ SF61 were calculated. The best tit via Eq. ( 13) to the experimental data was reached using an average energy transferred per collision, - ( A,?) ~4.3 kJ mol”, which corresponds to the following values of the limiting low-pressure rate constant, 10-l’ l(OH+oH,,J[SF6]: 4.0 and 3.1 Mm2s-l at 298 and 36 1 K, respectively. Over the temperature range 283-373 K the following expression was derived: ~H+oH,0/[SF6]=(4.0f0.7)X10”(T/ 300) -I,4 M -’ s-r. The calculated kc,u+oH values are in good agreement with the experimental points obtained in this study as is shown in Fig. 3. The room temperature value of koH+oH,,,/ [ SFs] = (4.0 + 0.7)x10LLM-2s-*canbecomparedwiththatfound for nitrogen as the bath gas, ICOH+or.&[Nz] = (2.5-2.9)x 10” M-2s-1 [25,26]. Thevaluesofthe calculated rate constants, bn+ou, for the experimental conditions used in the kinetic simulations of the CHS decay profiles are given in Table 1. The analysis of the pressure dependence of the rate constant, k,, for the CHS+OH recombination reaction is again based on Eq. ( 13 ) . The high-pressure limiting rate constant, k_,, was derived using one of the versions of the statistical adiabatic channel model - the maximum free energy method of Quack and Troe [ 291. The thermochemical data and molecular parameters needed for the calculation of km,_ and kVO, as well as the computational details were described previously [ 10 1. In that study the preliminary value ofk_,=(8.7+0.9)~ lOi’M-’ s-’ was found at 298 K. The limited number of rate constants obtained experimentally, their discrepancy and the narrow pressure range did not allow us to estimate k,W,O with a satisfactory accuracy, and only an approximate value of k,,,,/ [ SF,] = (0.3-4.9) x 1015

Table 2 Calculated

the limiting rate constants,

&,,

and Lo

Mm2s- ’ was estimated at room temperature. In the present study a larger number of experiments conducted in the temperature range 283-373 K allowed us to estimate the limiting rate constants more accurately. The best tit of the experimental data leads to the values of the limiting rate constants given in Table 2. The results of the calculations confirm the previously determined weak temperature dependence of the high-pressure limiting rate constant, k =(8.7+0.7)x1010(T/300)o~1 M-i s-r. Becz; of the strong decrease in the experimentally determined k, values at lower SF6 pressures and at temperatures higher than 350 K, the usual assumption that ( AE) SF6is temperature independent was not kept in k,,o/ [SF61 calculation by using the fitting procedure on the basis of Eq. ( 13 ). The best agreement of the calculated fall-off curves with the experimental data was reached for - (U)sF6 = 0.50 and 0.31 kJ mol-’ for the temperature ranges 283-331 and 361-373 K, respectively. In Fig. 4 the calculated fall-off curves are shown. A strong negative temperature dependence of the low-pressure limiting rate constant was observed, &,o/ [ SF61 = (9.0f2.4) x 10L4(T/3OO)-3.8 Mm2 s-l for the temperature range 283-331 K. The value of k,,,o/[SF,]=(9.2+2.4)x1014 Mb2 s-i at 298 K can be compared with that of &,o/ [He] = (6.2f 1.2) x 1014Mm2s-i for He as the bath gas, which was estimated by a refit [lo] of the experimental data obtained by Oser et al. [ 21 using our value for the high-pressure limiting rate constant. The value of -(AE)Hc=0.41 kJ mol-r was found [lo] which indicates that SF6 is a more efficient collider than He. For the cross reaction CH3+NO( +M)-CH3NO(

+M)

,

forming an association product of comparable com-

for M = SF,

T

kc&a

JG&llMl

(K)

(IO’O M-’ s-‘)

(10’SM-2~-1)

283 298 331 361 373

8.66 8.71 8.82 8.90 8.93

8.85 7.44 5.27 3.95 3.54

(15)

a 0.1292 0.1238 0.1133 0.0708 0.0688

-(A0

L/J/ [Ml

(kJ mol-‘)

( lOI M-* s-‘)

0.50 0.50 0.50 0.31 0.31

11 9.2 6.0 2.8 2.4

50

K. Fagerstrdm et al. /Chemical Physics Letters 224 (1994) 43-50

r 10

?

0

TW ? g 10

0

8

0

0

1.5

10

1.5

2.0

[ 5 ] A.M. Dean and P.R. Westmoreland, Intern. J. Chem. Kinetics 19 (1987) 207. [a] J.F. Bott and N. Cohen, J. Chem. Kinetics 23 (1991) 1017. [7] Ch. Dombrowsky, A. Hoffmann, M. Klatt and H.Gg. Wagner, Ber. Bunsenges. Physik. Chem. 95 (1991) 1685. [ 8 ] T.J. Sworski, C.J. Hochanadel and P. Orgen, J. Phys. Chem. 84 (1980) 129. [ 91 C. Anastasi, S. Beverton, T. Ellermann and P. Pagsberg, J. Chem. Sot. Faraday Trans. 87 (1991) 2325. [ IO] K. Fagerstrijm, A. Lund, G. Mahmoud, J.T. Jodkowski and E. Ratajczak, Chem. Phys. Letters 204 (1993) 226. [ 111 M.J.T. Jordan, S.C. Smith and R.G. Gilbert, J. Phys. Chem. 95 (1991) 8685. [ 121 J. Troe, J. Phys. Chem. 83 ( 1979) 114. [ 131 J. Troe, Ber. Bunsenges. Physik. Chem. 87 (1983) 161. [ 141 R.G. Gilbert, L.K. Luther and J. Troe, Ber. Bunsenges. Physik. Chem. 87 (1983) 169. [ 151 K. Fagerstrtim, A. Lund, P. Pagsberg and A. Sillesen, Acta Chem. Stand. 47 (1993) 1057. [ 161 K. Fagersttim, A. Lund, G. Mahmoud, J.T. Jodkowski and E. Ratajcxak, Chem. Phys. Letters 208 ( 1993) 321. [ 171 O.L. Rasmusen and E. Bjergbakke, R&R-395 (1984). [ 18 ] C. Anastasi, D.J. Muir, V.J. Simpson and P. Pagsberg, J. Phys. Chem. 95 (1991) 5791. [ 191 M.T. MacPherson, M.J. Pilling and J.C. Smith, J. Phys. Chem. 89 (1985) 2268. [20] H. Hippler, K. Luther, A.R. Ravishankara and J. Troe, Z. Physik. Chem. 142 ( 1984) 1. [ 2 1 ] M.C. Sauer Jr., in: Advances in radiation chemistry, Vol. 5, eds. M. Burton and J.L. Magge (Wiley, New York, 1976) p. 97. [22] R. Atkinson, D.L. Baulch, R.A. Cox, RF. Hampson Jr., J.A. Kerr and J. Troe, J. Phys. Chem. Ref. Data 21 (1992) 1125. [23 W.B. DeMom, S.P. Sander, D.M. Golden, M.J. Molina, R.F. Hampson, M.J. Kurylo, C.J. Howard and A.R. Ravishankam, Chemical kinetics and photochemical data for use in stratospheric modeling, evaluation No. 9 (JPL Publication 990-l) Pasadena, 1990). [24 J. Troe, J. Chem. Phys. 66 (1977) 4758. 125 R. Zellner, F. Ewig, R. Paschke and G. Wagner, J. Phys. Chem. 92 (1988) 4184. [ 261 R. Forster, Ph.D. Thesis, University of Giittingen ( 1991). [ 27 ] L. Brouwer, C.J. Cobos, J. Troe, H.R. Dtlbal and F.F. Crim, J. Chem. Phys. 86 (1987) 6171. [ 281 R. Patrick and D.M. Golden, Intern. J. Chem. Kinetics 15 (1983) 1189. [29] M. Quack and J. Troe, Ber. Bunsenges. Physik. Chem. 81 (1977) 169. [ 301 J.T. Jodkowski, E. Ratajcxak, P. Pagsberg and A. Sillesen, Chem. Phys. Letters 203 (1993) 491. [ 3 I] W.C. Gardiner, ed., Combustion chemistry (Springer, Berlin, 1984). [32] W. Forst and F. Caralp, J. Chem. Sot. Faraday Trans. 87 (1991) 2307.

*. L! c

2.0

2.5

2.5

3.c

3.0

logp&nbar

Fig. 4. Fall-off curves (together with the experimental points) fortherecombinationre.actionCHs+OH(+M)-CHsOH(+M) where M = SF,, at different temperatures with - ( AE) = 0.50 kJ mol-‘intherange283-331 Kandwith -(AE)=O.31 kJmol-’ (shown as an insert) in the range 361-373 K. (m) 283 K; (0) 298K,(A)331K.Insert:(0)361K,(w)373K.

plexity, the following values of an average energy transferred in collision were calculated [ 301: =0.26kJmol-1and-(AE)s,=0.80kJ -(A&i, mol-‘. Apparently, the low-pressure limiting rate constant for reaction ( 15 ) also exhibits a significant (n= 3.5 ) negative temperature coeficient as do many other addition reactions [ 3 1,32 1.

References [ 1 ] D.L. Baulch, C.J. Cobos, R.A. Cox, C. Esser, P. Frank, Th. Just, J.A. Kerr, M.J. Pilling, J. Tore, R.W. Walker and J. Wamatz, J. Phys. Chem. Ref. Data 21 (1992) 411. [ 21 H. Oser, N.D. Stothard, R. Humpfer and H.H. Grotheer, J. Phys. Chem. 96 (1992) 5359. [ 3 ] K.J. Hughes, A.R. Pereira and M.J. Pilling, Ber. Bunsenges. Physik. Chem. 96 ( 1992) 1352. [ 41 W. Tsang and R.F. Hampson, J. Phys. Chem. Ref. Data 15 (1986) 1087.