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Kinetics of the gas-phase reaction between ethyl and hydroxyl radicals
CHEMICAL PHVSlCS LETTERS
Volume 208, number 3,4
I I June 1993
Kinetics of the gas-phase reaction between ethyl and hydroxyl radicals Kjell Fagerstrijm, Anders Lund, Gharib Mahmoud Chemical Physics Laboratory, Department ofphysics and Measurement Technology, University ofLinkiiping, S-581 83 Link@&, Sweden
Jerzy T. Jodkowski and Emil Ratajczak Department ofphysical Chemistry, MedicalAcademy, PI. Nankiera 1,50-140 Wroc!aw, Poland Received 15 March 1993
The kinetics of the reactions CsH,+OH( t M) +products ( + M ) ( I ) were studied at room temperature by pulse radiolysis of C2H6/H20/SFb mixtures. The ethyl radical decay was followed by monitoring the UV absorption signals at 205 nm. The experimentally determined value of k, is (7.1 f 1.0) x lOto M-t s-t. No pressure dependence ofk, in the pressure range 250-1000 mbar SFs was observed. The calculated k,, value for the temperature range 200-400 K is (7.7 f 1.0) X 10” M-’ s-’ for the addition reaction. The low-prcssurc limiting rate constant for the addition reaction should not bc lower than 10” M-l s-r at room temperature.
1. Introduction Ethyl and hydroxyl radicals are formed at an early stage in several types of reactions taking place in hydrocarbon combustion processes. In the present study the ethyl radical spectrum was monitored and the reactions between these two radicals (( la)-( Id) below) were investigated C2HS +OH( +M)-C2HSOH(
+M) ,
CZH5+OH(+M)+C2H4+H20(+M),
(Ia) (lb)
CzHs +OH( +M) +CH3 +H+HCHO( CrH, +OH( +M)-CH3
+M) , +CH*OH( +M) ,
(lc) (Id)
where M is the bath gas. The radicals were generated by pulse radiolysis of stable parent gas mixtures. One of the advantages with pulse radiolysis combined with UV absorption spectrometry is that direct spectrakinetic measurements of the transient species are possible. Reaction ( 1) was studied by monitoring the ethyl radical UV absorption signals at 205 nm where ethyl radicals ooO9-2614/93/S
have the strongest absorption band. To establish the branching ratios the possible build-up of methyl and hydroxymethyl radicals was followed by monitoring the transient UV absorption signals at 2 16.4 [ 1 ] and 285.3 nm [2] respectively. In the present study of the reaction ( 1) we did not observe any pressure dependence of the rate constant, k,, in the pressure range 250-1000 mbar SF6. Tsang and Hampson [ 31 suggest a value of k,,=k,,=2.4~ 10” M-r s-’ at temperatures in excess of 800 K and 1 atm N2 with an estimated uncertainty factor of 4. Reaction (1) takes place in competition with the self-reactions of ethyl and hydroxyl radicals respectively. In the experiments the sum of the radical yields, [ C,H,] + [OH], was constant while the relative yields of the radicals could be varied by adjustment of the concentration ratio of the parent compounds, i.e. C2H6 and H,O. Thus, reaction ( 1) could be studied at a wide range of [C,H,]/[OH] ratios. At low ratios reaction ( 1) is the main sink for ethyl radicals, while the ethyl radical self-reaction dominates at high ratios.
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2. Experimental
The experimental technique, described in detail previously [4], is pulse radiolysis combined with transient UV-absorption spectrometry. The electrons are generated by a Febetron 708 which is an electron accelerator of the field-emission type. The maximum electron energy is 800 keV, the half-width of the electron pulse 3 ns and the energy per pulse 10 J. The average absorbed dose is about 0.4 kGy based on ozone dosimetry. The dose can be varied by inserting attenuators with an equal number of holes but with different hole diameters in the electron path. The Febetron is equipped with two field emission tubes in such a way that the sample can be irradiated from opposite sides. This arrangement minimizes the dose distribution along the electron beam. The dose distribution perpendicular to the electron beam was measured with radiochromic dye film and the effect of the dose distribution on second-order rate constants was calculated [ 41. Those calculations show that the effect on the rate constant is negligible. The relative dose is measured by using two thermocouples mounted in front of each electron tube. The gaseous samples are prepared on a stainlesssteel vacuum line connected to a specially designed stainless-steel irradiation cell with a volume of approximately 1 dm3. By use of an Alcatel turbo pump one can obtain a vacuum of about 9 x lo-’ mbar. Gas mixtures are prepared by admitting one component at a time and reading the corresponding partial pressure with a MKS Baratron Model 170 absolute membrane manometer with a resolution of 0.1 mbar. The optical arrangement in the irradiation cell consists of a set of optical mirrors that allow for multiple passages of the analyzing light beam through the sample. The experiments were carried out using 4 or 8 traversals, corresponding to an optical path length of 40 or 80 cm, respectively. The analyzing light source is a Varian 150 W high-pressure xenon lamp with an aluminized parabolic reflector and sapphire windows. Using a pulsing device constructed at Riser National Laboratory, Denmark, it is possible to obtain reproducible flat light pulses with a duration of a few milliseconds depending on the wavelength and 322
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1993
a roughly 50-fold gain in brightness in the ultraviolet region. Suprasil quartz lenses pass the light through the irradiation cell at right angles to the electron beam and further to a McPherson 2061, 1 m scanning monochromator. The monochromator is equipped with a grating with 1200 lines/mm which gives a reciprocal dispersion of 8 A/mm. The light intensity is monitored with an R928 photomultiplier tube. The output signals from the photomultiplier are digitized in a Tektronix 7912 transient recorder. To trigger the lamp pulse, the transient recorder and the Febetron we use a pulse sequencing device developed at Studsvik AB, Nykiiping, Sweden. Conversion of raw data into transient absorption versus time and display of kinetically relevant functions are accomplished with a personal computer [ 41. Computer modelling. For computer modelling of the kinetic data we used the VAX version of “CHEMSIMUL” [ 5 1, a software developed at Risra National Laboratory, Denmark and the PC version of “MAXIM’ [6], developed at Chalk River Nuclear Laboratory, Ontario, Canada. Materials. Research grade gases, Ar, SF, and C,H,, from Alfax with a minimum purity of 99.95% were used without further purification. (C,H,),CO from Merck with a purity of > 99% was thoroughly outgassed before use. H,O was triply distilled and thoroughly degassed before use.
3. Experimental studies 3.1. Radical source reactions and spectrum of ethyl radicals To obtain a clean source of ethyl radicals, we have compared the spectra of the transient species produced in the argon-sensitized radiolysis of diethyl ketone ( (2) below), and via the abstraction reaction ( (4) below). These reactions were initiated by pulse radiolysis of the parent hydrocarbon/third body gas mixtures specified in table 1. Pulse radiolysis of diethy1 ketone/argon mixtures initiates the following reactions:
Table 1 Composition of gas mixtures for comparison of different CzHs source reactions Gas mixture
Partial pressure (mbar)
[C1H6],,
&He/SF6 (C21WICOIAr C2H6/SF6/Ar
IO:990 51995 10:,50:940
2.0 (reduced dose) 0.5 0.7
Ar*tC2H5-CO-C2H5+Ar+2CzH5
tC0.
-YE -y1000 I .
(FM)
800keVe-tAr+Ar*+e- , (2)
A wide range of free radicals can be produced by the H atom abstraction reaction of F atoms with suitable hydrocarbon containing species, F+RH-+HFtR. The second studied ethyl radical source is H atom abstraction of ethane ( (4) below) by F atoms produced by pulse radiolysis of C2H,/Ar/SF6 mixtures or CzHs/SFs mixtures, 800 keV e-+M+M*te-
11June 1993
CHEMICAL PHYSICS LETTERS
Volume 208, number 3,4
,
M*+SF6-+SF4+2F+M,
(3a)
M*tSF6-SFStFtM,
(3b)
FtC2H6+HFtCzH5.
(4)
The bath gas, M, was in these two cases Ar or SF6 itself. Under the conditions prevalent in this study, reaction (3a) dominates the F atom production with reaction (3b) making a negligible contribution ( 6 1%) according to Anastasi et al. [ 71. The absorption signals were measured with a 4 8, band-pass, which was chosen as the best compromise between spectral resolution and signal-to-noise ratio. The stray light was measured by UV cutoff filters. The stray light level was less than 1%. The absorption spectra obtained with the three different gas mixtures were practically identical in shape. The yield of ethyl radicals differed between the three gas mixtures according to table 1. As shown in fig. 1 the ethyl radical spectrum is composed of two broad bands centered at 205 with an extinction coefficient, c = (2000 2 245 ) M- ’ cm-’ ,andat245nmwithe=(810f80)M-‘cm-‘. The calculations of the extinction coefficients were
w
/
0' 200
220 240 260 wavelength / nm
Fig. 1, Ethyl radical spectrum monitored by single-pulse irradiation of 990 mbar SF6 and 10 mbar C2H6 with an optical bandpass of 4 A and a step length of 5 A over the peaks.
made by assuming that [C,H,],= [Flo, and t(C,H,)=A(C,H,)/( [F]J), where the absorbance was calculated as A =log(&,/l). The initial F atom concentration, [F]c, was calculated from methyl radical experiments using the well established extinction coefficient of the strong B-X Rydberg transition in CHS radicals at 216.4 nm, r(CHs)=10800 M-’ cm- ’ [Flo= ill; A( 2 16.4),/ (EL) = 2.0 uM at 990 mbar SFs. Methyl radicals were produced by pulse radiolysis of 10 mbar CH4 and 990 mbar SF,, and detected by the transient UV absorption signals at 216.4 nm. The absorption spectrum for ethyl radicals produced via reaction (2) shows an absorption peak at 2 16 nm which coincides with the B-X Rydberg transition of the methyl radical. This peak was not observed in the spectra for ethyl radicals produced via reactions (3) and (4). In the argon-sensitized reaction (2) it seems likely that methyl as well as ethyl radicals may be formed because argon carries an excitation energy sufficient to break any of the molecular bonds in the diethylketone molecule. The 216 nm peak was also observed in other studies of the ethyl radical spectrum [ 8,9] and explained as minor methyl radical impurities. The ethyl radical spectrum was also monitored by Pagsberg and co-workers [ 8 ] in four different chemical gas mixtures: Ar/N, ( CzH5)*, Ar/CO ( C2H5)z, Ar/H20/C2Hs, and H1/C2H4. They found that the 205 nm band exhibits a partly resolved fine structure. This was not observed by us, or by Wendt and Hunziker [ 91. The optical band-pass was the same in our experiments as in the ones reported by Pagsberg et al. However, the overall shape of the 323
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spectra is the same in the three studies and the reported extinction coefficients are in good agreement. According to our experiments the most clean ethyl radical source that gives the highest ethyl radical yield is the C2H6/SF, mixture without Ar. Therefore this parent gas mixture was used in our further ethyl radical experiments. 3.2. Measured rate constants The kinetics of the reaction between ethyl and hydroxyl radicals ( ( la)- ( Id) ), which proceeds in competition with the ethyl and hydroxyl radical selfreactions (6a) and (6b) and (7a) and (7b) below, was studied by pulse radiolysis of C2Hs/H20/SF, mixtures, with SF, always in great excess, initiating the following reactions in addition to reactions ( la)(Id), (3a) and (3b) and (4):
C2HS+C2HS(+M)-'C4H,O(tM),
(ha)
C2HS+C2HS+CZH4tC2H6,
(6b)
tM) ,
OH+OH( tM)-+H202( t 0,
Ua) (7b)
0H+C2H6+H20+C2H5,
(8)
CH,tCHJ(+M)-rC,H,(tM),
(9)
CHI+C,H,( HtC,H,( HtOH( HtH(
+M)+products( tM)+C*H,(
tM)-+H*O( tM)+H2(
+M) ,
+M) ,
SM) ,
tM) .
(10) (11) (12) (13)
The experiments were performed at room temperature and at three different total pressures, 250, 500 and 1000 mbar SF,. The decay rate of ethyl radicals was followed at several [ C,H,] / [ H,O] ratios by monitoring the transient absorption signals at 205 nm. The measurements were made with a 4 A bandpass. In the absence of water the ethyl radical decay was second order in accordance with the self-reaction (6a) and (6b). A typical CzHS decay curve in the absence of OH is shown in fig. 2a. The solid curve going through the experimental points is predicted by modelling using the values of kba= 1.1 x 1O’OM- ’ 324
0
50
100
time I ps
(5)
FtH20+HFtOH,
OH+OH+H20
o-
Fig. 2. C&radical decaymonitored at 205 nm after singlspulse irradiation of SF6/C2Hs/H20mixtures. The solid lines are those predicted by computer modelling. (a) p(SF,)=494 mbar, p(C&)=6 mbar and p(H,O)=O mbar; self-reaction with 7=33.1~sfor[C~H&_=1.16~;kg=1.1~1O”’h4-’s-’and ,&=l.4x10g M-l s-l. (b) p(SF,)=987.8 mbar,p(C,H,)=2.2 mbar and p(H,O)= 10 mbar; r=27.0 ps for [C,H,],=0.86 ~M;k,=7.1~10’~M-‘s-‘.
s-i [lo] and&,= 1.4x 10gM-is-’ [lo]. Pulse radiolysis of ethane in the absence of SF6 showed no transient signal indicating that there were no other ethyl radical sources than reaction (4). The conditions to monitor the k value for the reaction between ethyl and hydroxyl radicals are listed in table 2. The effect of reaction ( 1) on the overall decay kinetics of ethyl radicals was studied by varying the concentration ratios of ethane and water in the gaseous mixtures according to table 2. By varying this ratio the relative yields of ethyl and hydroxyl radicals were controlled. The variation in the ethyl radical yield as a function of the water to ethane ratio is shown in fig. 3. Methyl radicals may be formed via the reaction channels (lc) and (Id). By monitoring the transient absorption signals at 2 16.4 nm and comparing these signals with methyl and ethyl radical absorption curves obtained by simulation it was possible to establish the rate constant for the overall formation
Table 2 Conditions to monitor the CIHS decay in the reaction system SF6/C2H6/Hj0 P(SF6) (mbar)
WC&) (mbar)
MP(H0) ( mbar)
WzOl/ [C&l
[C& lmu (PM)
1000 500 250
1.0-20.0 0.5-10.0 1.1-4.5
5.0-16.0 2.5-17.0 2.0-8.0
0.25-16.0 0.25-31.0 0.5-7.3
0.7-1.9 0.3-1.2 0.3-0.6
s-l and k,,= (6.0f3.0)x109M-’ ” k,.+ ,b= (6.5k l.O)~10’~M-’ of which were using reduced doses.
0
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CHEMICAL PHYSICS LEI-TERS
Volume 208, number 3,4
10
20
30
[H,Ol&Hd as a function of the [ Hz01 / [ C2Hs] ratio for Fig. 3. W-M, three different total pressures. The solid lines are those predicted by modelling. (4) 1000 mbar, ( x ) 500 mbar; ( + ) 250 mbar.
of methyl radicals. In those simulations the sum (k,*+lb+klC+ld) was kept constant with a value obtained by modelling of the transient absorption signals monitored at 205 nm. The transient signals monitored at 216.4 nm are a combination of both the methyl and the ethyl absorption, signals. However, the extinction coefficient for methyl radicals is approximately 10 times higher than that of ethyl radicals at this wavelength (see section 3.1). Thus the monitored signal is sensitive to the formation of methyl. The measurements at 216.4 nm were made for a wide range of water to ethane ratios.
(k205
nm, 4 A band pass, T=298 K) ‘)
11.8-21.7 16.4-34.4 63.5-69.0
No. of expts.
Wlo
L
(W)
(cm)
45 38 22
1.4, 1.9 1.2 0.6
40 80 80
s-l. Two sets of experiments were performed at 1000 mbar, both
Hydroxymethyl has several absorption bands in the UV range [2]. The one at 285.3 nm is in this case suitable for the detection of hydroxymethyl as neither methyl nor ethyl has any absorbance at this wavelength. Several measurements were made at 285.4 nm for a wide range of water to ethane ratios. However, no hydroxymethyl was detected indicating that the reaction channel (lc) is the only route for the formation of methyl radicals at room temperature and in the studied pressure range. The values of the rate constants for reaction (la), (lb) and (lc) at the three different total SF, pressures were obtained by detailed computer simulation of the experimental data taking reactions (4)) (5L (ha), (6b), (7a), 01, (81, (9), (IO), (II), ( 12) and ( 13) into account in addition to reaction ( 1a)- ( Ic ) . The following k values were used in the simulations (units M-l s-l): k,=l.OxlO” [ll], k5=1.2x10”’ [12], k6,=l.lx10Lo [lo], kab= 1.4~10~ [lo], k,,=9.0x109 [II], k,,=1.0x109 [ll], ks=1.5x10s [lo], kq=3.5x10Lo [1,13], k,o=4.0x10’o [14], k,,=l.OxlO” [14], k12= 6.3~10’~ [3] andk19=1.4x109 [3]. Fig. 2bshows an example of the best fit of the model curve to the experimental curve at 500 mbar SF,. The reaction of the oxygen atoms produced in the hydroxyl radical self-reaction with the ethyl and hydmxyl radicals respectively is not important in this pressure range, and has therefore not been included in the reaction scheme. At the highest studied water to ethane ratios the initial hydroxyl radical concentration is two to three times higher than the initial ethyl radical concentration. Under these conditions the model is sensitive to the values of k,,_,, and the effect of the selfreaction on the overall ethyl radical decay rate is small. The effect of reaction ( 1) can clearly be seen in 325
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reaction between methyl and hydroxyl radicals, (8.7f0.9) x 1O’OM-’ s-l [ 151, under the same conditions.
4. Analysis of the limiting rate constants of the reaction (la) Analysis of the limiting high-pressure rate constant, k,,,,, for the addition reaction ( 1a), has been carried out using one of the versions of the statistical adiabatic channel models - the maximum free energy method of Quack and Troe [ 161. According to this version kl,,, is given by .m nt
Fig. 4. Reciprocal half-life(T) of CZHS radicaldecayas a function of [&HI] - (and [ Hz01 / [ C2H6] ratio) for three different total pressures.The solid lines are those predictedby modelling. (+ ) 1000 mbar; ( 0 ) 500mbar; ( x ) 250mbar.
fig. 4, which shows the reciprocal half-lives of ethyl radicals as a function of the maximum ethyl radical concentration. Tbe points at [ CzHSlmBx=O correspond to the half-life of reaction ( 1) proceeding under pseudo-first-order conditions where [OH], = [F], and r1/2 = In 2/k, [F] ,,. The other points on the curves were obtained experimentally. The solid line through the origin represents the theoretical variation of the half-life of the pure ethyl radical se!f-reaction (6) proceeding under second-order conditions where [C2Hslm,= [F], and .r1,2=l/2k6[F]0, In fig. 4 it can be seen that reaction ( 1) becomes increasingly important at low [ C2HSlmax,i.e. at high [OH In-m. No pressure dependence of the rate constants for the reactions ( 1a)- ( lc) was observed in the studied pressure range, 250-1000 mbar SF6. The obtained k,,+,,va1ueis(6.5f1.0)~10’~M-‘s-’andthek,, value is (6.0&3.0)x lo9 M-l SK’. The overall k, value is slightly lower than the calculated high-pressure limiting rate constant for the cross-combination 326
where Q is the complete rovibrational partition function of CIHSOH, Qt is the partition function of the “activated complex” and K, denotes the equilibrium constant Kc=k,a/k_la (for details see ref. [ 161). A value of the Morse parameter, p= 1.54 A-’ (according to the threshold energy &= 385 kJ/mol and the force constant for the C-O stretch as in methanol [ 17 ] ) has been used in the k,,,, calculation with the exponential extrapolated parameter, y=0.75a, where (Yis the “looseness parameter”. Computational details, as well as the thermodynamic functions for the C2H, + OH=C,H,OH reaction (calculated on the basis of molecular parameters taken from refs. [ 1820] ), are given in table 3. The obtained high-pressure limiting rate constant for the “standard” value of CY=1.0 ii-‘, k,_= 7.7~10’~ M-’ s-l at room temperature, is in line with experimental data. The temperature dependence of k,,,, is weak, so that in the temperature range of 200-400 K the limiting rate constant, kla_ can be considered as temperature independentwithavalueof(7.7~l.0)x10’0M-*s-1 (the error limits as for the experimental ones). Because of the lack of experimental evidence for a pressure dependence of k,,, we could only estimate the strong collision limiting low-pressure rate constant, ks& (for the collision efficiency, a= 1) using the factorized expression derived by Troe [ 211. The calculation leads to the values of the limiting strong collision ones of the order of lOL9Mm2 s-l, for all bath gases (see table 3). Therefore the limiting lowpressure rate constants, klqo should not be lower than
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CHEMICALPHYSJCSLETTERS
Volume 208, number 3,4
Table 3 Ideal gas thermodynamic functions and the calculated limiting rate constants for reaction (la) T
(K)
AC:,r (J mol-’ K-l)
0
200 298 300 400 500 1000
0.000
-21.428 - 14.436 - 14.334 - 9.531 - 6.074 0.522
A.%-
m
k Iam
(klmo-‘)
(lO’“M-‘s&)
k%l[Hel ( 10’9M-‘s-‘)
k%I[SFJ
(Jmol-’ K-‘)
1.45 1.65 7.66 7.80
21.5 4.21 4.10 1.16
22.7 4.13 4.02 1.09
0.000
- 144.311 -151.461 -151.550 - 154.983 -156.716 - 158.257
-385.142 - 390.568 - 392.287 -392.313 - 393.496 -394.266 - 395.192
10” M-2 s-l (for /$x0.01) at room temperature. It implies a narrow fall-off range, with the pressure dependence of the rate constant expected at pressures below 0.1 mbar.
Acknowledgement This work was carried out within the CEC program “Chemical Kinetics for Combustion”. We are indebted to NUTEK for financial support. One of the authors (ER) acknowledges financial support from the Swedish Institute. P. Pagsberg, Rispl National Laboratory, Denmark, is acknowledged for his valuable suggestions during these experiments.
References [I] M.T. MacPhenon, M.J. Pilling and J.C. Smith, J. Phys. Chem. 89 (1985) 2268. [ 21 P. Pagsberg, J. Munk, A. Sillesen and C. Anastasi, Chem. Phys. Letters 146 (1988) 375. [ 31W. Tsang and R.F. Hampson, J. Phys. Chem. Ref. Data I5 (1986) 1087. [4] K. Fagerstrijm, A. Lund, P. Pagsberg and A. Sillesen, Acta Cbem. Stand., submitted for publication. [5] O.L. Rasmusen and E. Bjergbakke,R&R-395 (1984).
(10’9M-2~-‘)
[6] MB Carver, D.V. Hanley and K.R. Chaplin, AECL6413 (1979). [ 71 C. Anastasi, D.J. Muir, V.J. Simpson and P. Pagsberg, J. Phys.Chem.95 (1991) 5791. [ 8 ] J. Munk, P. Pagsberg,E. Ratajczakand A. SiIIesen,J. Phys. Chem. 90 (1986) 2752. [9]H.R. Wendt and H.E. Hunziker, J. Chem. Phys. 81(2) (1984) 717. [lo] D.L. Baulch,C.J. Cobos, R.A. Cox, C. Euer, P. Frank, Th. Just, J.A. Kerr, M.J. Piling, J. Troe, R.W. Walker and J. Warnatz, J. Phys. Chem. Ref. Data 21 (1992) 411. [ 1 l] W.B. DeMore, S.P. Sander, D.M. Golden, M.J. Molina, R.F. Hampson,M.J. Kurylo,C.J. Howardand R.J. Ravishankara, NASA chemical kinetics and photochemical data, Evaluation No. 9 (JPL Publication, Pasadena, 1990). [ 121 C. Anastasi, S. Ekverton, T. Ellermann and P. Pagsberg, J. Chem. Sot. Faraday Trans. 87 (1991) 2325. [ 131 H. Hippler, K. Luther, A.R. Ravishankara and J. Troe, Z. Phys.Chem. 142 (1988) 1. [ 141 A. Sillesen, E. Ratajczak and P. Pagsberg, Chem. Phys. Letters 201 (1993) 171. [ 151 K. Fagerstriim, A. Lund, G. Mahmoud, J.T. Jodkowski and E. Ratajnak, Chem. Phys. Letters 204 (1993) 226. [ 161 M. Quack and J. Tme, Ber. Bunsenges. Phys. Chem. 81 (1977) 329. [ 171 G. Zerbi, I. Overend and B. Crawford Jr., J. Chem. Phys. 38 (1963) 122. [ 181 J.H.S. Green, Trans. Faraday Sot. 57 (1961) 2132. [ 191 J. Pacansky and M. Dupois, J. Am. Chem. Sot. 104 (1982) 415. [20] A.F. Wagner, IX. Slagle, D. Sarzynski and D. Gutman, J. Phys. Chem. 94 (1990) 1853. [21] J. Troe, J. Chem. Phys. 66 (1977) 4758.
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Kinetics of the gas-phase reaction between ethyl and hydroxyl radicals Kjell Fagerstrijm, Anders Lund, Gharib Mahmoud Chemical Physics Laboratory, Department ofphysics and Measurement Technology, University ofLinkiiping, S-581 83 Link@&, Sweden
Jerzy T. Jodkowski and Emil Ratajczak Department ofphysical Chemistry, MedicalAcademy, PI. Nankiera 1,50-140 Wroc!aw, Poland Received 15 March 1993
The kinetics of the reactions CsH,+OH( t M) +products ( + M ) ( I ) were studied at room temperature by pulse radiolysis of C2H6/H20/SFb mixtures. The ethyl radical decay was followed by monitoring the UV absorption signals at 205 nm. The experimentally determined value of k, is (7.1 f 1.0) x lOto M-t s-t. No pressure dependence ofk, in the pressure range 250-1000 mbar SFs was observed. The calculated k,, value for the temperature range 200-400 K is (7.7 f 1.0) X 10” M-’ s-’ for the addition reaction. The low-prcssurc limiting rate constant for the addition reaction should not bc lower than 10” M-l s-r at room temperature.
1. Introduction Ethyl and hydroxyl radicals are formed at an early stage in several types of reactions taking place in hydrocarbon combustion processes. In the present study the ethyl radical spectrum was monitored and the reactions between these two radicals (( la)-( Id) below) were investigated C2HS +OH( +M)-C2HSOH(
+M) ,
CZH5+OH(+M)+C2H4+H20(+M),
(Ia) (lb)
CzHs +OH( +M) +CH3 +H+HCHO( CrH, +OH( +M)-CH3
+M) , +CH*OH( +M) ,
(lc) (Id)
where M is the bath gas. The radicals were generated by pulse radiolysis of stable parent gas mixtures. One of the advantages with pulse radiolysis combined with UV absorption spectrometry is that direct spectrakinetic measurements of the transient species are possible. Reaction ( 1) was studied by monitoring the ethyl radical UV absorption signals at 205 nm where ethyl radicals ooO9-2614/93/S
have the strongest absorption band. To establish the branching ratios the possible build-up of methyl and hydroxymethyl radicals was followed by monitoring the transient UV absorption signals at 2 16.4 [ 1 ] and 285.3 nm [2] respectively. In the present study of the reaction ( 1) we did not observe any pressure dependence of the rate constant, k,, in the pressure range 250-1000 mbar SF6. Tsang and Hampson [ 31 suggest a value of k,,=k,,=2.4~ 10” M-r s-’ at temperatures in excess of 800 K and 1 atm N2 with an estimated uncertainty factor of 4. Reaction (1) takes place in competition with the self-reactions of ethyl and hydroxyl radicals respectively. In the experiments the sum of the radical yields, [ C,H,] + [OH], was constant while the relative yields of the radicals could be varied by adjustment of the concentration ratio of the parent compounds, i.e. C2H6 and H,O. Thus, reaction ( 1) could be studied at a wide range of [C,H,]/[OH] ratios. At low ratios reaction ( 1) is the main sink for ethyl radicals, while the ethyl radical self-reaction dominates at high ratios.
06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved
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2. Experimental
The experimental technique, described in detail previously [4], is pulse radiolysis combined with transient UV-absorption spectrometry. The electrons are generated by a Febetron 708 which is an electron accelerator of the field-emission type. The maximum electron energy is 800 keV, the half-width of the electron pulse 3 ns and the energy per pulse 10 J. The average absorbed dose is about 0.4 kGy based on ozone dosimetry. The dose can be varied by inserting attenuators with an equal number of holes but with different hole diameters in the electron path. The Febetron is equipped with two field emission tubes in such a way that the sample can be irradiated from opposite sides. This arrangement minimizes the dose distribution along the electron beam. The dose distribution perpendicular to the electron beam was measured with radiochromic dye film and the effect of the dose distribution on second-order rate constants was calculated [ 41. Those calculations show that the effect on the rate constant is negligible. The relative dose is measured by using two thermocouples mounted in front of each electron tube. The gaseous samples are prepared on a stainlesssteel vacuum line connected to a specially designed stainless-steel irradiation cell with a volume of approximately 1 dm3. By use of an Alcatel turbo pump one can obtain a vacuum of about 9 x lo-’ mbar. Gas mixtures are prepared by admitting one component at a time and reading the corresponding partial pressure with a MKS Baratron Model 170 absolute membrane manometer with a resolution of 0.1 mbar. The optical arrangement in the irradiation cell consists of a set of optical mirrors that allow for multiple passages of the analyzing light beam through the sample. The experiments were carried out using 4 or 8 traversals, corresponding to an optical path length of 40 or 80 cm, respectively. The analyzing light source is a Varian 150 W high-pressure xenon lamp with an aluminized parabolic reflector and sapphire windows. Using a pulsing device constructed at Riser National Laboratory, Denmark, it is possible to obtain reproducible flat light pulses with a duration of a few milliseconds depending on the wavelength and 322
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a roughly 50-fold gain in brightness in the ultraviolet region. Suprasil quartz lenses pass the light through the irradiation cell at right angles to the electron beam and further to a McPherson 2061, 1 m scanning monochromator. The monochromator is equipped with a grating with 1200 lines/mm which gives a reciprocal dispersion of 8 A/mm. The light intensity is monitored with an R928 photomultiplier tube. The output signals from the photomultiplier are digitized in a Tektronix 7912 transient recorder. To trigger the lamp pulse, the transient recorder and the Febetron we use a pulse sequencing device developed at Studsvik AB, Nykiiping, Sweden. Conversion of raw data into transient absorption versus time and display of kinetically relevant functions are accomplished with a personal computer [ 41. Computer modelling. For computer modelling of the kinetic data we used the VAX version of “CHEMSIMUL” [ 5 1, a software developed at Risra National Laboratory, Denmark and the PC version of “MAXIM’ [6], developed at Chalk River Nuclear Laboratory, Ontario, Canada. Materials. Research grade gases, Ar, SF, and C,H,, from Alfax with a minimum purity of 99.95% were used without further purification. (C,H,),CO from Merck with a purity of > 99% was thoroughly outgassed before use. H,O was triply distilled and thoroughly degassed before use.
3. Experimental studies 3.1. Radical source reactions and spectrum of ethyl radicals To obtain a clean source of ethyl radicals, we have compared the spectra of the transient species produced in the argon-sensitized radiolysis of diethyl ketone ( (2) below), and via the abstraction reaction ( (4) below). These reactions were initiated by pulse radiolysis of the parent hydrocarbon/third body gas mixtures specified in table 1. Pulse radiolysis of diethy1 ketone/argon mixtures initiates the following reactions:
Table 1 Composition of gas mixtures for comparison of different CzHs source reactions Gas mixture
Partial pressure (mbar)
[C1H6],,
&He/SF6 (C21WICOIAr C2H6/SF6/Ar
IO:990 51995 10:,50:940
2.0 (reduced dose) 0.5 0.7
Ar*tC2H5-CO-C2H5+Ar+2CzH5
tC0.
-YE -y1000 I .
(FM)
800keVe-tAr+Ar*+e- , (2)
A wide range of free radicals can be produced by the H atom abstraction reaction of F atoms with suitable hydrocarbon containing species, F+RH-+HFtR. The second studied ethyl radical source is H atom abstraction of ethane ( (4) below) by F atoms produced by pulse radiolysis of C2H,/Ar/SF6 mixtures or CzHs/SFs mixtures, 800 keV e-+M+M*te-
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,
M*+SF6-+SF4+2F+M,
(3a)
M*tSF6-SFStFtM,
(3b)
FtC2H6+HFtCzH5.
(4)
The bath gas, M, was in these two cases Ar or SF6 itself. Under the conditions prevalent in this study, reaction (3a) dominates the F atom production with reaction (3b) making a negligible contribution ( 6 1%) according to Anastasi et al. [ 71. The absorption signals were measured with a 4 8, band-pass, which was chosen as the best compromise between spectral resolution and signal-to-noise ratio. The stray light was measured by UV cutoff filters. The stray light level was less than 1%. The absorption spectra obtained with the three different gas mixtures were practically identical in shape. The yield of ethyl radicals differed between the three gas mixtures according to table 1. As shown in fig. 1 the ethyl radical spectrum is composed of two broad bands centered at 205 with an extinction coefficient, c = (2000 2 245 ) M- ’ cm-’ ,andat245nmwithe=(810f80)M-‘cm-‘. The calculations of the extinction coefficients were
w
/
0' 200
220 240 260 wavelength / nm
Fig. 1, Ethyl radical spectrum monitored by single-pulse irradiation of 990 mbar SF6 and 10 mbar C2H6 with an optical bandpass of 4 A and a step length of 5 A over the peaks.
made by assuming that [C,H,],= [Flo, and t(C,H,)=A(C,H,)/( [F]J), where the absorbance was calculated as A =log(&,/l). The initial F atom concentration, [F]c, was calculated from methyl radical experiments using the well established extinction coefficient of the strong B-X Rydberg transition in CHS radicals at 216.4 nm, r(CHs)=10800 M-’ cm- ’ [Flo= ill; A( 2 16.4),/ (EL) = 2.0 uM at 990 mbar SFs. Methyl radicals were produced by pulse radiolysis of 10 mbar CH4 and 990 mbar SF,, and detected by the transient UV absorption signals at 216.4 nm. The absorption spectrum for ethyl radicals produced via reaction (2) shows an absorption peak at 2 16 nm which coincides with the B-X Rydberg transition of the methyl radical. This peak was not observed in the spectra for ethyl radicals produced via reactions (3) and (4). In the argon-sensitized reaction (2) it seems likely that methyl as well as ethyl radicals may be formed because argon carries an excitation energy sufficient to break any of the molecular bonds in the diethylketone molecule. The 216 nm peak was also observed in other studies of the ethyl radical spectrum [ 8,9] and explained as minor methyl radical impurities. The ethyl radical spectrum was also monitored by Pagsberg and co-workers [ 8 ] in four different chemical gas mixtures: Ar/N, ( CzH5)*, Ar/CO ( C2H5)z, Ar/H20/C2Hs, and H1/C2H4. They found that the 205 nm band exhibits a partly resolved fine structure. This was not observed by us, or by Wendt and Hunziker [ 91. The optical band-pass was the same in our experiments as in the ones reported by Pagsberg et al. However, the overall shape of the 323
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spectra is the same in the three studies and the reported extinction coefficients are in good agreement. According to our experiments the most clean ethyl radical source that gives the highest ethyl radical yield is the C2H6/SF, mixture without Ar. Therefore this parent gas mixture was used in our further ethyl radical experiments. 3.2. Measured rate constants The kinetics of the reaction between ethyl and hydroxyl radicals ( ( la)- ( Id) ), which proceeds in competition with the ethyl and hydroxyl radical selfreactions (6a) and (6b) and (7a) and (7b) below, was studied by pulse radiolysis of C2Hs/H20/SF, mixtures, with SF, always in great excess, initiating the following reactions in addition to reactions ( la)(Id), (3a) and (3b) and (4):
C2HS+C2HS(+M)-'C4H,O(tM),
(ha)
C2HS+C2HS+CZH4tC2H6,
(6b)
tM) ,
OH+OH( tM)-+H202( t 0,
Ua) (7b)
0H+C2H6+H20+C2H5,
(8)
CH,tCHJ(+M)-rC,H,(tM),
(9)
CHI+C,H,( HtC,H,( HtOH( HtH(
+M)+products( tM)+C*H,(
tM)-+H*O( tM)+H2(
+M) ,
+M) ,
SM) ,
tM) .
(10) (11) (12) (13)
The experiments were performed at room temperature and at three different total pressures, 250, 500 and 1000 mbar SF,. The decay rate of ethyl radicals was followed at several [ C,H,] / [ H,O] ratios by monitoring the transient absorption signals at 205 nm. The measurements were made with a 4 A bandpass. In the absence of water the ethyl radical decay was second order in accordance with the self-reaction (6a) and (6b). A typical CzHS decay curve in the absence of OH is shown in fig. 2a. The solid curve going through the experimental points is predicted by modelling using the values of kba= 1.1 x 1O’OM- ’ 324
0
50
100
time I ps
(5)
FtH20+HFtOH,
OH+OH+H20
o-
Fig. 2. C&radical decaymonitored at 205 nm after singlspulse irradiation of SF6/C2Hs/H20mixtures. The solid lines are those predicted by computer modelling. (a) p(SF,)=494 mbar, p(C&)=6 mbar and p(H,O)=O mbar; self-reaction with 7=33.1~sfor[C~H&_=1.16~;kg=1.1~1O”’h4-’s-’and ,&=l.4x10g M-l s-l. (b) p(SF,)=987.8 mbar,p(C,H,)=2.2 mbar and p(H,O)= 10 mbar; r=27.0 ps for [C,H,],=0.86 ~M;k,=7.1~10’~M-‘s-‘.
s-i [lo] and&,= 1.4x 10gM-is-’ [lo]. Pulse radiolysis of ethane in the absence of SF6 showed no transient signal indicating that there were no other ethyl radical sources than reaction (4). The conditions to monitor the k value for the reaction between ethyl and hydroxyl radicals are listed in table 2. The effect of reaction ( 1) on the overall decay kinetics of ethyl radicals was studied by varying the concentration ratios of ethane and water in the gaseous mixtures according to table 2. By varying this ratio the relative yields of ethyl and hydroxyl radicals were controlled. The variation in the ethyl radical yield as a function of the water to ethane ratio is shown in fig. 3. Methyl radicals may be formed via the reaction channels (lc) and (Id). By monitoring the transient absorption signals at 2 16.4 nm and comparing these signals with methyl and ethyl radical absorption curves obtained by simulation it was possible to establish the rate constant for the overall formation
Table 2 Conditions to monitor the CIHS decay in the reaction system SF6/C2H6/Hj0 P(SF6) (mbar)
WC&) (mbar)
MP(H0) ( mbar)
WzOl/ [C&l
[C& lmu (PM)
1000 500 250
1.0-20.0 0.5-10.0 1.1-4.5
5.0-16.0 2.5-17.0 2.0-8.0
0.25-16.0 0.25-31.0 0.5-7.3
0.7-1.9 0.3-1.2 0.3-0.6
s-l and k,,= (6.0f3.0)x109M-’ ” k,.+ ,b= (6.5k l.O)~10’~M-’ of which were using reduced doses.
0
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10
20
30
[H,Ol&Hd as a function of the [ Hz01 / [ C2Hs] ratio for Fig. 3. W-M, three different total pressures. The solid lines are those predicted by modelling. (4) 1000 mbar, ( x ) 500 mbar; ( + ) 250 mbar.
of methyl radicals. In those simulations the sum (k,*+lb+klC+ld) was kept constant with a value obtained by modelling of the transient absorption signals monitored at 205 nm. The transient signals monitored at 216.4 nm are a combination of both the methyl and the ethyl absorption, signals. However, the extinction coefficient for methyl radicals is approximately 10 times higher than that of ethyl radicals at this wavelength (see section 3.1). Thus the monitored signal is sensitive to the formation of methyl. The measurements at 216.4 nm were made for a wide range of water to ethane ratios.
(k205
nm, 4 A band pass, T=298 K) ‘)
11.8-21.7 16.4-34.4 63.5-69.0
No. of expts.
Wlo
L
(W)
(cm)
45 38 22
1.4, 1.9 1.2 0.6
40 80 80
s-l. Two sets of experiments were performed at 1000 mbar, both
Hydroxymethyl has several absorption bands in the UV range [2]. The one at 285.3 nm is in this case suitable for the detection of hydroxymethyl as neither methyl nor ethyl has any absorbance at this wavelength. Several measurements were made at 285.4 nm for a wide range of water to ethane ratios. However, no hydroxymethyl was detected indicating that the reaction channel (lc) is the only route for the formation of methyl radicals at room temperature and in the studied pressure range. The values of the rate constants for reaction (la), (lb) and (lc) at the three different total SF, pressures were obtained by detailed computer simulation of the experimental data taking reactions (4)) (5L (ha), (6b), (7a), 01, (81, (9), (IO), (II), ( 12) and ( 13) into account in addition to reaction ( 1a)- ( Ic ) . The following k values were used in the simulations (units M-l s-l): k,=l.OxlO” [ll], k5=1.2x10”’ [12], k6,=l.lx10Lo [lo], kab= 1.4~10~ [lo], k,,=9.0x109 [II], k,,=1.0x109 [ll], ks=1.5x10s [lo], kq=3.5x10Lo [1,13], k,o=4.0x10’o [14], k,,=l.OxlO” [14], k12= 6.3~10’~ [3] andk19=1.4x109 [3]. Fig. 2bshows an example of the best fit of the model curve to the experimental curve at 500 mbar SF,. The reaction of the oxygen atoms produced in the hydroxyl radical self-reaction with the ethyl and hydmxyl radicals respectively is not important in this pressure range, and has therefore not been included in the reaction scheme. At the highest studied water to ethane ratios the initial hydroxyl radical concentration is two to three times higher than the initial ethyl radical concentration. Under these conditions the model is sensitive to the values of k,,_,, and the effect of the selfreaction on the overall ethyl radical decay rate is small. The effect of reaction ( 1) can clearly be seen in 325
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reaction between methyl and hydroxyl radicals, (8.7f0.9) x 1O’OM-’ s-l [ 151, under the same conditions.
4. Analysis of the limiting rate constants of the reaction (la) Analysis of the limiting high-pressure rate constant, k,,,,, for the addition reaction ( 1a), has been carried out using one of the versions of the statistical adiabatic channel models - the maximum free energy method of Quack and Troe [ 161. According to this version kl,,, is given by .m nt
Fig. 4. Reciprocal half-life(T) of CZHS radicaldecayas a function of [&HI] - (and [ Hz01 / [ C2H6] ratio) for three different total pressures.The solid lines are those predictedby modelling. (+ ) 1000 mbar; ( 0 ) 500mbar; ( x ) 250mbar.
fig. 4, which shows the reciprocal half-lives of ethyl radicals as a function of the maximum ethyl radical concentration. Tbe points at [ CzHSlmBx=O correspond to the half-life of reaction ( 1) proceeding under pseudo-first-order conditions where [OH], = [F], and r1/2 = In 2/k, [F] ,,. The other points on the curves were obtained experimentally. The solid line through the origin represents the theoretical variation of the half-life of the pure ethyl radical se!f-reaction (6) proceeding under second-order conditions where [C2Hslm,= [F], and .r1,2=l/2k6[F]0, In fig. 4 it can be seen that reaction ( 1) becomes increasingly important at low [ C2HSlmax,i.e. at high [OH In-m. No pressure dependence of the rate constants for the reactions ( 1a)- ( lc) was observed in the studied pressure range, 250-1000 mbar SF6. The obtained k,,+,,va1ueis(6.5f1.0)~10’~M-‘s-’andthek,, value is (6.0&3.0)x lo9 M-l SK’. The overall k, value is slightly lower than the calculated high-pressure limiting rate constant for the cross-combination 326
where Q is the complete rovibrational partition function of CIHSOH, Qt is the partition function of the “activated complex” and K, denotes the equilibrium constant Kc=k,a/k_la (for details see ref. [ 161). A value of the Morse parameter, p= 1.54 A-’ (according to the threshold energy &= 385 kJ/mol and the force constant for the C-O stretch as in methanol [ 17 ] ) has been used in the k,,,, calculation with the exponential extrapolated parameter, y=0.75a, where (Yis the “looseness parameter”. Computational details, as well as the thermodynamic functions for the C2H, + OH=C,H,OH reaction (calculated on the basis of molecular parameters taken from refs. [ 1820] ), are given in table 3. The obtained high-pressure limiting rate constant for the “standard” value of CY=1.0 ii-‘, k,_= 7.7~10’~ M-’ s-l at room temperature, is in line with experimental data. The temperature dependence of k,,,, is weak, so that in the temperature range of 200-400 K the limiting rate constant, kla_ can be considered as temperature independentwithavalueof(7.7~l.0)x10’0M-*s-1 (the error limits as for the experimental ones). Because of the lack of experimental evidence for a pressure dependence of k,,, we could only estimate the strong collision limiting low-pressure rate constant, ks& (for the collision efficiency, a= 1) using the factorized expression derived by Troe [ 211. The calculation leads to the values of the limiting strong collision ones of the order of lOL9Mm2 s-l, for all bath gases (see table 3). Therefore the limiting lowpressure rate constants, klqo should not be lower than
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Table 3 Ideal gas thermodynamic functions and the calculated limiting rate constants for reaction (la) T
(K)
AC:,r (J mol-’ K-l)
0
200 298 300 400 500 1000
0.000
-21.428 - 14.436 - 14.334 - 9.531 - 6.074 0.522
A.%-
m
k Iam
(klmo-‘)
(lO’“M-‘s&)
k%l[Hel ( 10’9M-‘s-‘)
k%I[SFJ
(Jmol-’ K-‘)
1.45 1.65 7.66 7.80
21.5 4.21 4.10 1.16
22.7 4.13 4.02 1.09
0.000
- 144.311 -151.461 -151.550 - 154.983 -156.716 - 158.257
-385.142 - 390.568 - 392.287 -392.313 - 393.496 -394.266 - 395.192
10” M-2 s-l (for /$x0.01) at room temperature. It implies a narrow fall-off range, with the pressure dependence of the rate constant expected at pressures below 0.1 mbar.
Acknowledgement This work was carried out within the CEC program “Chemical Kinetics for Combustion”. We are indebted to NUTEK for financial support. One of the authors (ER) acknowledges financial support from the Swedish Institute. P. Pagsberg, Rispl National Laboratory, Denmark, is acknowledged for his valuable suggestions during these experiments.
References [I] M.T. MacPhenon, M.J. Pilling and J.C. Smith, J. Phys. Chem. 89 (1985) 2268. [ 21 P. Pagsberg, J. Munk, A. Sillesen and C. Anastasi, Chem. Phys. Letters 146 (1988) 375. [ 31W. Tsang and R.F. Hampson, J. Phys. Chem. Ref. Data I5 (1986) 1087. [4] K. Fagerstrijm, A. Lund, P. Pagsberg and A. Sillesen, Acta Cbem. Stand., submitted for publication. [5] O.L. Rasmusen and E. Bjergbakke,R&R-395 (1984).
(10’9M-2~-‘)
[6] MB Carver, D.V. Hanley and K.R. Chaplin, AECL6413 (1979). [ 71 C. Anastasi, D.J. Muir, V.J. Simpson and P. Pagsberg, J. Phys.Chem.95 (1991) 5791. [ 8 ] J. Munk, P. Pagsberg,E. Ratajczakand A. SiIIesen,J. Phys. Chem. 90 (1986) 2752. [9]H.R. Wendt and H.E. Hunziker, J. Chem. Phys. 81(2) (1984) 717. [lo] D.L. Baulch,C.J. Cobos, R.A. Cox, C. Euer, P. Frank, Th. Just, J.A. Kerr, M.J. Piling, J. Troe, R.W. Walker and J. Warnatz, J. Phys. Chem. Ref. Data 21 (1992) 411. [ 1 l] W.B. DeMore, S.P. Sander, D.M. Golden, M.J. Molina, R.F. Hampson,M.J. Kurylo,C.J. Howardand R.J. Ravishankara, NASA chemical kinetics and photochemical data, Evaluation No. 9 (JPL Publication, Pasadena, 1990). [ 121 C. Anastasi, S. Ekverton, T. Ellermann and P. Pagsberg, J. Chem. Sot. Faraday Trans. 87 (1991) 2325. [ 131 H. Hippler, K. Luther, A.R. Ravishankara and J. Troe, Z. Phys.Chem. 142 (1988) 1. [ 141 A. Sillesen, E. Ratajczak and P. Pagsberg, Chem. Phys. Letters 201 (1993) 171. [ 151 K. Fagerstriim, A. Lund, G. Mahmoud, J.T. Jodkowski and E. Ratajnak, Chem. Phys. Letters 204 (1993) 226. [ 161 M. Quack and J. Tme, Ber. Bunsenges. Phys. Chem. 81 (1977) 329. [ 171 G. Zerbi, I. Overend and B. Crawford Jr., J. Chem. Phys. 38 (1963) 122. [ 181 J.H.S. Green, Trans. Faraday Sot. 57 (1961) 2132. [ 191 J. Pacansky and M. Dupois, J. Am. Chem. Sot. 104 (1982) 415. [20] A.F. Wagner, IX. Slagle, D. Sarzynski and D. Gutman, J. Phys. Chem. 94 (1990) 1853. [21] J. Troe, J. Chem. Phys. 66 (1977) 4758.
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