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A spectroscopic determination of the methyl radical recombination rate constant in shock waves
CHEMICAL PHYSICS LETTERS
:‘. V$um;e 39,,iumber 2. .
.1
15 April 1976
_-
A SPECTROSCOPIC DETERMINATION METHYL RAMCAE ~ECOMBINA~ON
d)F THE RATE CONSTANT IN SHOCK WAVES
Received 9 January 1976
kD 4-l The reactions Cfi3 f CH3(+ Ar) - Czfl~(+ Ar) and CD3 + CQ(+ Ar) - C&6(+ At) have been studied in shock waves at 1200-1500 K and densities of 2 X lo”-2 X IO4 mol cm” using UV absorption near 216 nm. The rate constants at the highest densities: kH = (1.7 * 0.6) X LO-’ ’ cm3 s.-’ and kD = (2.2 f 0.9) X iO-” cm3 s-’ xe close to the second order Limit. At the lowest den&es the rates ac lower by a factor of 5. The ex_~erimental resuits agree weli with theoretical predictions based on the statistical adiabatic channel model but differ from those of conventional RRKM calculations. A direct observation of the equ~ibrium C2H6 + 2CH3 fsvours the “high value for A& (87.76 kcaI/mof).
1. Introduction The recombination of two methyl radicals to form ethane can be considered to be the simplest elementary reaction leading to the formation of the alkyl C-C single bond. Its rate has been widely studied near room temperature. [l--S] , whereas only few high temperature determ~~latioRs are available. Clark et al. 191 have studied the recombination in shock waves near 1350 I( using mass spectrometric detection after fast thermal decomposition of azomcthane. At the total gas densities of these studies, near 2 X 1W6 moi cme3, the reaction was still in the fall-off range. Also, due to the relatively high concentrations and long reaction times, some complications of the mechanism arose. At high temperatures, the reverse dissociation of e&me has been investigated more frequently, near 900 IS in static systems flO,l 11 zind in shock waves near 1300 K [12,13] _ There is considerable theoretical interest in obtaining accurate data for the re~omb~a~on rate constants over large temperature and pressure ranges. From the temperature depender.ce of the high pressure limiting values one can infer the energy dependence of the total compound cross section, s&i& co&a& informa-
.
-.
.
tion on the dynamics of highIy excited ethane molec&es [14,15] . ~thoua~ the temperature coefficient of recombination rate constants is usua!ly believed to be quite small, there may be sizeable effects if the temperature range studied is sufficiently large. Recent theoretical RRKM studies of this system predict an irzcrease of the recombination rate coefficient with temperature by a factor of about lo-30 between 300 and 400 K [ 12,14,16] _ The statistical adiabatic channel model [14] predicts a small decrease in this same range. Finally, if one extrapolates the recombination rate constant via dissociation rate constants from room temperature to 1400 K u&g an Arrhenius activation energy for the dissociation rate constant E._ = Alifj, which might appear to be reasonable, one predicts a decmzse by a factor of about 10. An expe~ental value for the temperature coefficient of the recombination rate can, in principIe, be derived from the determinations ofethane dissociation rate constants near 900 K [lo,1 11. In this spirit Waage and Rabinovitch in their review of the methyl-ethane system discovered a considerabIe discrepancy between the kinetics,.thermochemistry and a detailed RRKM caIculation [I 63. It was later shown that the discrepancy can be removed using the adiabatic channel model [ 143 instead of the KRKM calcuIation and a value 4 = 87.76 kcallniol [171 instead of 86.3 kcal/mol
Volume 39, number 2
CHEhflCAL PHYSICS LETTERS
[18] fdr the bond dissociatkm energy. The significance of this comparison of dissociation and recombination data is, however, uncertain as long as m is not established beyond doubt. On the other hand, the theoretical predictions of recombination rate coetxcients are quite insensitive to A@. It was therefore the aim of the present investigation to provide sufficiently accurate data for the recombination rate coefficient at high temperatures, near the high pressure limit, to allow for a quantitative comparison with the various theories. We used the fast thermal decomposition of azomethane in shock waves between 1300 K and 1400 K as methy radical source. We monitored methyl concentrations very sensitively through the absorption in the ‘A\ + ‘A: system near 2 1G run, as has been done in most of the room temperature work using kinetic spectroscopy. We have aiso measured the combination rate of perdeutero methyl radicals as a check. In agreement with room temperature measurements [7,8] , dissociation measurements near 900 K [l I] and theoretical expectation [ 141, the isotope effect near the high pressure limit is too small to be determined accurately within the present experimental uncertainties. A determination of the bond dissociation ener,T 4 was possible as well through a measurement of equilibrium constants. Although we cannot give a definite conclusion, due to experimental uncertainties, our results support the “high” value of AE$j in agreement with Chupka’s measurements [ 171.
2. Experimental The shock tube and details of the experimental technique have been described previously [ 191. Absorption signals of azomethane (near 200 nm) and of methyl radicals (between 200 and 220 nm) were monitored with an EMI 62568 photomultiplier. The light was from a high pressure Xe arc. Predispersion with a quartz prism reduced the scattered light to a negligible amount. The main dispersion element was a 0.25 m Jarreli-Ash grating monochromator with a spectral bandwidth of 1.6 nm. The wave length reproducibility was better than kO.4 nm as determined from various calibration experiments_ The slit function was measured to be nearly the theoretical triangle. In spite of the relatively large bandwidth, the Lambert-Beer ab-
15 April 1976
sorption law was fulfdled with good accuracy under our experimental conditions with high transmissions, in agreement with calculations [30] . High purity Ar @99.99%) and ethane were obtained commercially. Azomethane was prepared from symdimethylhydrazine by oxidation with mercuric oxide [21]. The dried product was purified by fractional distillation and degassed. The gas chromatographic analysis indicated a purity of much higher than 99%. The perdeuterated ccrmpound was prepared from perdeutero methylamine (Merck, Sharp and Dohme) following the method reported in ref. [22] _ It was used without further purification. The gas chromatogramm showed about 5% of a volatile non-hydrocarbon impurity. The deuteration was essentially complete @950/o) as estimated from the IR spectrum. The azocompounds were stored at low temperatures. Reaction mixtures of azomethane and Ar were prepared in a 0.05 m3 glass vessel, with mole fractions of azomethane in the range 10m3-5 X 10e6. Analysis by gas.chromatography showed, that no decomposition ofazomethane occurred while storing these mixtures. In another set of experiments, mixtures were prepared and introduced immediately into the shock tube by passing a controlIed stream of Ar over cooled solid azomethane. The influence of a possible oxygen impurity in Ar was checked by experiments with Ar-azomethane mixtures to which twice the amount of total possible impurity was added as pure 02. The CH3 disappearance rates were indistinguishable from the results obtained in the original mixtures. A few experiments were done with Kr as the diluent gas, at densities of 2.6 X 10e5 mol cmT3. The rate constants did not differ significantly from those obtained in Ar. The results of this study are based on a total of more than two hundred single experiments in incident and refl ected shock waves.
3. Results First we investigated the decomposition of azomethane between 850 and 1200 K under pressure and concentration conditions similar to the recombination experiments. The disappearance of azomethane (AM) was followed via its absorption near 200 nm and the appearance of CH3 near 216 mu. At total gas densities of 20e5 -lo4 mol cms3 we obtained an Arrhenius expres305
Voluine39, lminiler 2
sioti for the first order decomposition
rate constant:
.kAhf = --dfn[AM] jdt 25 101r3e+(-33
kcal mol-l/~T)s-l,
which is given as a preliminary value. Clark et-al. [9] reported a lower activation ener,qy at densities of lo6 mdl cmm3. An extrapolation of the low temper&e Arrhenius expression &r k~~f from Benson and O’Neal [23] to temperatures above 1000 K would lead td rate constants larger than ours by
a factor of 35. The extrapolated value of the rate constant, however, ensures in any case that the initial decomposition step of azomethane at T 3 1300 K is sufficiently fast to exclude a bimolecular reaction between CH3 radicals and the parent molecule. There is a suffcient amount of evidence that the decomposition leads to two methyl radicals 191. In the second part of the experiments we have studied the absorption of CH3 and CD, between 200 and 220 nm. Since the decomposition of the parent molecule is very fast, the concentration [CH3 ] u directly after passage of the shock wave (reaction time t = 0) is given by the stoichiometry (CH&N, + 2CH3 + N2. In order to keep corrections due to the recombination of CH, within the time of the Schlieren signal (typically 1-2~s) very small, these measurements were done at small [CHs] 0 fG2 X lWsl mol cme3) and [Ar] (=(4-l 5) X 10e6 mol cm’3). The effective decadic absorption coefficients at T = 1400 K have their maxima near 216.0 -I-0.4 nm for CH,, $g
15 A&
CHEMICAL PHYSICS LETTERS
= (1.8 St0.6) X lo6 cm2 mot’1
the investigated range using the theoretical temperature coefEcient. Details on the high temperature spectra of CH, and CD, will be reported elsewhere [20]. Having determined the effective absorption coefficients of CH3 and CD,, we obtained recombination rate coefficients k by fitting the function ]los&J0,1
-l = (WEI)t + Pos&$“)t=(J
-l3
[Arl I mol cni3 -6 5.0
*
2:m
Iii5 ,
.
16” 1
%?
20 +t+
WE 1.a = ‘g = ~/
05
I
t .*
+
-t+
+
a2
a1[ ,
,
‘~18
I)
J
.
I9
lo20
fAr1 I zti3
Fig. 1. Recembination rate coefficients for CHBf CH3 2 C2N6. The values marked by X are from ref. 19] (where Kr ZII~~ Ne ha-mebeen used instead of Ar). The points without error bars are from sin$e experiments. [Arl
= (2.0 + 0.7) X IO6 cm2 mol-‘.
These values correspond to a bandwidth (fwhm) AX = 1.6 nm of a triangular intensity distribution. The given error limits include both the statistical 95% confidence intervals from a t&l of about 20 experiments in each case and a rather conservative estimate of the systematic errors. When the computed temperature dependence of the extinction coefiicient is taken into account [ZO], our results are consistent with previous measurements at room temperature and higher resolution which led to E&?I = 1.12 X lo7 cm2 molt-l [2,25]. in the results reported below, we haue taken into account the s.mall temperature dependence of E within 306
_-
.
..
:
(I?
which results from the second order rate law -d [CHS ] [dt = 2k [CH3] 2. The experimental data were welI represented by the functional form fi > for reaction times to 50 ,QSand for all initial concentrations studied. The slopes of the closely linear (correlation coefficients often >0999) plot were determined by least squares fits. Figs. 1 and 2 show the resulting second order rate coefficients for methyl disappearance as a function of [Ar] . The points arc average val-
and near 214.5 rt 0.4 mn for CD, +jg
1976.
ml, , ml%
lmol
‘lo*
cni3
1020
tArI lcmm3 Fi.
‘Wk.
2. Recombination rate coefficients for CD3 + CD3 2
V0lurr.e 39,
number 2
CHEMICAL
ues of R at an average density in the interval indicated by the horizontal lines. The vertical lines give 9 5% confidence limits based on a t-distribution for eech‘individual set of experiments. No temperature dependence of k could be observed between 1200 and 1400 K. The data points of figs. 1 and 2 mostly belong to temperatures near 1350 K. The dependence of the rate constants upon the total gas concentration corresponds well to the behaviour of a recombination reaction in the fall-off range near the high pressure limit 1241. We obtained further evidence that the removal of CH3 by reactions other than recombination is unimportant under the conditions of the reported experiments, in agreement with the direct mass spectrometric product analysis of Clark et al. [9]. Between 1500 and 1700 K a fast initial decay of [CH,] towards [CH3] eq was observed in agreement with the recombination data at lower temperature. On a much longer time scale, CH, is then removed slowly by unidentified subsequent reactions. At temperatures between 2200 and 2700 K one can also follow the then quite rapid disappearance of CH, radicals. Assuming as a rough approximation a first order rate law, the data (for [CH, ] u = (3-9) X lOa mol cmm3) could be combined to give kapparent< (T =
101’exp(-50
15 April 1976
PHYSICS LETTERS.
kcal mol”/R@-’
1500-2700 K). It follows that these processes are negligible with respect to CH3 recombination at temperatures at or below 1400 K. In addition, we carried out some experiments where the disappearance of CH3 behind the incident shock (T x 1300 K) as well as its reformation from CzH6 and final decay behind the reflected shock (T a 2600 K) were all observed. The heights and time dependence of the absorption signals behind the :eflected shock were indistinguishable from those obtained with mixtures initially containing an equivalent amount of ethane. Although this “analysis” is not sufficiently precise for quantitative purposes, it is a further indication that CH3 recombination proceeds in a clean manner in our experiments. The above mentioned equilibration of CzH6 + XI& observed for I500 < T/K < 1700 led us to an experimental determination of the equilibrium constant. Since a large amount of data would be necessary to obtain a reasonably accurate experimental temperatuce dependence for the equilibrium constant, we chose to evaluate as the only significant quantity the bond
dissociation energy from the relation do
= -~Tln[(~~RTZcZH,/Z~Hs)~=I,
with the Avogadro constant NA, the molecular partition functions X(RT/V’)Z~-H~ and &~a and the experimental equilibrium constant Kc = [CH,] $&l16]
,-
The partition functions were calculated as usually in the harmonic oscillator-rigid rotor approximation apart from torsion in C,H, [14]. Any error due to incomplete data or anharmonicity is much smaller than the uncertainty in Kc. We obtain then an experimental value for CH3 : MO = 88.0 i 0.9 (k3.4) kcal mol-’, for CD3 : 9 = 88.7 f 1.1 (23.5) kcal mol-l . The
first error limits are the statistical 95% confidence intervals assuming a t-distribution for 8 experiments each. The errcr limits in brackets result from the (systematic) uncertainty in the absorption coefficient. The value for normal ethane is more reliable, because of the impurities present in the deuterated compound for which we could not apply corrections. Although the larger error limits include all values of AE$ presently discussed in the literature [12,16,18] our data favour the “high” value (87.76 kcal mol-1 for CH3) based on Chupka’s results [17].
4.
Discussion
From the present experiments as from earlier investigations in shock waves [9] one can conclude that in the temperature range 1ZOO- 15c)O K and at total densities of 2 X 10-6-2 X lOA mol cmS3 methyl radicals recombine cleanly to ethane. The average rate constants at the highest densities kH =
(1.7 f 0.6) X lo-!’
cm3 s-l
(2.2 * 0.9) X 10’”
cm3 s-l
and k,
=
(including systematic errors) can be expected to be no more than about a factor of 2 below the second order limit 1201. At the lowest densities our results are lower than those obtained by Clark et al. [9] (see fig. 1). This may be due to the lower methyl concentrations 307.
yo~&tiii~9, .“.. ‘__. Ta,&fe‘l
ri”mber 2 . _
:
: .
‘. -
:
.C~B;ICAL,PHYSiCS-L~TTEKS
.. 15 Aprii.~976
:
_-
: :.
fipti&iIentd ana theCketica1 n&S
found in-ref. EL611
-
. _
:
Etperimental, Sector
on methyl radial recombinatioti and ethane de~ornpo~t~o~ (references to dtder work c.an be ,
recombi~~io~ 400
4.0
293
4.4”)
Rash ptiotolysis of AM, kinetic spectroscopy
29s
4.3
Flash photolysis of’ AM, DMhi and keteneiH2, kinetic spectroscopy
295
9.5
Flash
293
5.6
Flash photolysis of CH31, mass spectrometric detection
313
4.0
Photolysis of AM, modulation spectroscopy
2.50-450
4.0
Ffash photolysis of DMhI, kinetic spectroscopy
295
5.5
” Uecom. of AM in shock waves, total density of Ne and Kr < 1.8 x IO= cm-+, mass spectrometric detection
1350
>0.9
Shock waves, total density of Ar Q 1.6 X 10” cmw3, kinetic spectroscopy
t300-1400
21.7
1400
>I .6 (3.3jcs
Ffrtsh photolgis
of AM and DhfM, kinetic spectroscopy
photolysis of A.&f,kinetic spectroscopy (photoelectric)
Experimental, dissociation of Cz Hc Sin& pulse shock tube total. densitij of Ar < 3.4 X lOi cme3 Thermal reactor
900
2.6
Thermal reactor
838
23.4
.
‘.Theoreticxtl studies PRKhl, A& = 86.3 kc&moI
350 900 1400 300 900 f40d
RI&M, &
= 87.76 kcal/mol
Statistical adiabatic cihannel model 4
= 87.76 ktaflmol
2.2 (0.7j&) 10.6 21.1 0.07 0.79 1.48
300 900 1300
1.3 16.6 41.5
300 900 1350
5.0
5-i .4.8
” Siiihtly corrected value from ref. [25]. b, These authors have us 9 definitionkz = d[CH3 1.-’ /df, difsering from ihe present paper and’from most other work- This has&en tzken into account, ’ ExtrapoIated to infinite pressure. ) The first’v&& is from table I. of reE [ 161, the value h breckets froni the Arrhenius expression in table 111of ref. f 16;1_See&o text; 308 ..
-_
:
-._
..
Volume 39, number 2
.:
CHEMICAL
PHYSICS LETTERS
timi resolution achieved in the present work‘. One should further compare with room temperature. work on the rgcombination reactiori and with _experimesits on e&an& dissociation. Table 1 shows presently available experimental and theoretical data on this system (further references to aider work may be found in ref. [ 161). All data are expressed in terms of high pressure recombination rate constants k,, assuming fl = 87.76 kcal mol-l for the conversion of the dissocialion rate constants. If one takes into account that most of the high temperature resuhs are below the second order limit (indicated by > and 2 for data near the second order Emit), most of the experimental results obtained by~quite different techniques in a large range of temperature and pressure conditions lead consistently to.approximately constant values or possibly to a small decrease of the high pressure recombination rate coefficient with temperature. However, all RRKM calculations quoted predict a considerable increase of the recombination rate constant between 300 and 1400 K. The statistical adiabatic channel model predicts a small decrease, in agreement with experiment. One should emphasize that all the theoretical predictions for the recombination rate constants depend only insignificaritly on the value of A,@ chosen. an@ higher
Acknowiedgement The present work has profited greatly from discuswith Dr. Hubert van den Bergh and Professor W.C. Gardiner. Professor A.B. CaIlear and Professor G. Herzberg provided copies of room temperature spectra of CH3 and CD3. The assistance of Dr. M. Stockburger, Ho Dac Thang, S. Lukacs, and A. Heusler and the financial support by the Fonds National Suisse de la Recherche are also gratefully acknowledged. sions
’
_-
,
15 April 1976
References R. Gomer and G.6. Kistiakowfky, J. Chem. Phys. 19 11951) 85, H.E. van den Bergh. A-B. Caile& and R.J. Norstrom, Chem. Phys. Letters 4 (1969) 101, N. Basco. D.G.L: James and R.D. Suart, Intern. J. Chem. Kinetics 2 (1970) 215. A.hL Bass and A.H. Laufer, Intern. J. Chem. Kiqetics 5 (1973) 1053. F.C. James and J-f. Simons. Intern. J. &em. Kinetics 6
(1974) 887. F.K. Truby and J.K. Rice, Intern. J. Chem. Kinetics S (1973) 721. D.A. Pa&es, D.hf. Paul and C.P. Quinn, preprint (1975). A.B. Callear and M.P. hletcalfe, preprint (1975). T-C. Clark, T-P- Izod, ‘M-A.Di Valentin and LE. Dove, J. Chem. Phys. 53 (1970) 2982; T-C. Clark, T.P. Izod and G.B. Kistiakowsky, J. Chem.
Phys. 54 (1971) 1295. C-P. Quinn, Proc. Roy. Sot. A275 (1963) 190; hf.C. Lin and M.H. Back, Can. J. Chem. 44 (1966) 505, 2357,2369; 45 (1967) 2115. LA. Clark and C-P- Quinn, preprint (1975). A. Burcat, G.B. Skinner, R-W. Crossley and K. Scheller, Intern. J. Chem. Kinetics 5 (1973) 345. 1-N. BradIey and MA. Frend, J. Phys. Chem. 75 (1971) 1492. M. Quack and J. Tree, Bcr. Bunsenges. Physik. Chem. 78 (1974) 240. hi. Quack and 5. Troe, Ber. Bunsenges. Physik. Chem. 79 (1975) 170. E.V. Waage and B.S. Rabinovitch, Intern. J. Chem. Kinetics 3 (1971) 105. W-A. Chupka, J. Chem. Phys. 48 (1968) 2337. D.M. Golden and S.W. Benson, Chem. Rev. 69 (1969)
125. K. Clanzer and J. Troe, J. Chem. Phys. 63 (1975) 4352. K. Ghnzer, M. Quack and I. Troe, in preparation. R. Renaud and L.C. Leitch, Can. J. Chem. 32 (1954)
545. Organic Synthesis 52 (1972) 11. S.W. Benson and H.E. O’Neal, Kinetic Data on Gas Phase Unimolecular Reactions, NSRDS-NBS 21 (1970). I. Troe, in: Physical chemistry, an advanced treatise, Vol. 6, ed. W. Jost (Academic Press, New York, 197.5) p. 835. H.E. van den Bergh, Dissertation, Cambridge, UK (1971).
309
:‘. V$um;e 39,,iumber 2. .
.1
15 April 1976
_-
A SPECTROSCOPIC DETERMINATION METHYL RAMCAE ~ECOMBINA~ON
d)F THE RATE CONSTANT IN SHOCK WAVES
Received 9 January 1976
kD 4-l The reactions Cfi3 f CH3(+ Ar) - Czfl~(+ Ar) and CD3 + CQ(+ Ar) - C&6(+ At) have been studied in shock waves at 1200-1500 K and densities of 2 X lo”-2 X IO4 mol cm” using UV absorption near 216 nm. The rate constants at the highest densities: kH = (1.7 * 0.6) X LO-’ ’ cm3 s.-’ and kD = (2.2 f 0.9) X iO-” cm3 s-’ xe close to the second order Limit. At the lowest den&es the rates ac lower by a factor of 5. The ex_~erimental resuits agree weli with theoretical predictions based on the statistical adiabatic channel model but differ from those of conventional RRKM calculations. A direct observation of the equ~ibrium C2H6 + 2CH3 fsvours the “high value for A& (87.76 kcaI/mof).
1. Introduction The recombination of two methyl radicals to form ethane can be considered to be the simplest elementary reaction leading to the formation of the alkyl C-C single bond. Its rate has been widely studied near room temperature. [l--S] , whereas only few high temperature determ~~latioRs are available. Clark et al. 191 have studied the recombination in shock waves near 1350 I( using mass spectrometric detection after fast thermal decomposition of azomcthane. At the total gas densities of these studies, near 2 X 1W6 moi cme3, the reaction was still in the fall-off range. Also, due to the relatively high concentrations and long reaction times, some complications of the mechanism arose. At high temperatures, the reverse dissociation of e&me has been investigated more frequently, near 900 IS in static systems flO,l 11 zind in shock waves near 1300 K [12,13] _ There is considerable theoretical interest in obtaining accurate data for the re~omb~a~on rate constants over large temperature and pressure ranges. From the temperature depender.ce of the high pressure limiting values one can infer the energy dependence of the total compound cross section, s&i& co&a& informa-
.
-.
.
tion on the dynamics of highIy excited ethane molec&es [14,15] . ~thoua~ the temperature coefficient of recombination rate constants is usua!ly believed to be quite small, there may be sizeable effects if the temperature range studied is sufficiently large. Recent theoretical RRKM studies of this system predict an irzcrease of the recombination rate coefficient with temperature by a factor of about lo-30 between 300 and 400 K [ 12,14,16] _ The statistical adiabatic channel model [14] predicts a small decrease in this same range. Finally, if one extrapolates the recombination rate constant via dissociation rate constants from room temperature to 1400 K u&g an Arrhenius activation energy for the dissociation rate constant E._ = Alifj, which might appear to be reasonable, one predicts a decmzse by a factor of about 10. An expe~ental value for the temperature coefficient of the recombination rate can, in principIe, be derived from the determinations ofethane dissociation rate constants near 900 K [lo,1 11. In this spirit Waage and Rabinovitch in their review of the methyl-ethane system discovered a considerabIe discrepancy between the kinetics,.thermochemistry and a detailed RRKM caIculation [I 63. It was later shown that the discrepancy can be removed using the adiabatic channel model [ 143 instead of the KRKM calcuIation and a value 4 = 87.76 kcallniol [171 instead of 86.3 kcal/mol
Volume 39, number 2
CHEhflCAL PHYSICS LETTERS
[18] fdr the bond dissociatkm energy. The significance of this comparison of dissociation and recombination data is, however, uncertain as long as m is not established beyond doubt. On the other hand, the theoretical predictions of recombination rate coetxcients are quite insensitive to A@. It was therefore the aim of the present investigation to provide sufficiently accurate data for the recombination rate coefficient at high temperatures, near the high pressure limit, to allow for a quantitative comparison with the various theories. We used the fast thermal decomposition of azomethane in shock waves between 1300 K and 1400 K as methy radical source. We monitored methyl concentrations very sensitively through the absorption in the ‘A\ + ‘A: system near 2 1G run, as has been done in most of the room temperature work using kinetic spectroscopy. We have aiso measured the combination rate of perdeutero methyl radicals as a check. In agreement with room temperature measurements [7,8] , dissociation measurements near 900 K [l I] and theoretical expectation [ 141, the isotope effect near the high pressure limit is too small to be determined accurately within the present experimental uncertainties. A determination of the bond dissociation ener,T 4 was possible as well through a measurement of equilibrium constants. Although we cannot give a definite conclusion, due to experimental uncertainties, our results support the “high” value of AE$j in agreement with Chupka’s measurements [ 171.
2. Experimental The shock tube and details of the experimental technique have been described previously [ 191. Absorption signals of azomethane (near 200 nm) and of methyl radicals (between 200 and 220 nm) were monitored with an EMI 62568 photomultiplier. The light was from a high pressure Xe arc. Predispersion with a quartz prism reduced the scattered light to a negligible amount. The main dispersion element was a 0.25 m Jarreli-Ash grating monochromator with a spectral bandwidth of 1.6 nm. The wave length reproducibility was better than kO.4 nm as determined from various calibration experiments_ The slit function was measured to be nearly the theoretical triangle. In spite of the relatively large bandwidth, the Lambert-Beer ab-
15 April 1976
sorption law was fulfdled with good accuracy under our experimental conditions with high transmissions, in agreement with calculations [30] . High purity Ar @99.99%) and ethane were obtained commercially. Azomethane was prepared from symdimethylhydrazine by oxidation with mercuric oxide [21]. The dried product was purified by fractional distillation and degassed. The gas chromatographic analysis indicated a purity of much higher than 99%. The perdeuterated ccrmpound was prepared from perdeutero methylamine (Merck, Sharp and Dohme) following the method reported in ref. [22] _ It was used without further purification. The gas chromatogramm showed about 5% of a volatile non-hydrocarbon impurity. The deuteration was essentially complete @950/o) as estimated from the IR spectrum. The azocompounds were stored at low temperatures. Reaction mixtures of azomethane and Ar were prepared in a 0.05 m3 glass vessel, with mole fractions of azomethane in the range 10m3-5 X 10e6. Analysis by gas.chromatography showed, that no decomposition ofazomethane occurred while storing these mixtures. In another set of experiments, mixtures were prepared and introduced immediately into the shock tube by passing a controlIed stream of Ar over cooled solid azomethane. The influence of a possible oxygen impurity in Ar was checked by experiments with Ar-azomethane mixtures to which twice the amount of total possible impurity was added as pure 02. The CH3 disappearance rates were indistinguishable from the results obtained in the original mixtures. A few experiments were done with Kr as the diluent gas, at densities of 2.6 X 10e5 mol cmT3. The rate constants did not differ significantly from those obtained in Ar. The results of this study are based on a total of more than two hundred single experiments in incident and refl ected shock waves.
3. Results First we investigated the decomposition of azomethane between 850 and 1200 K under pressure and concentration conditions similar to the recombination experiments. The disappearance of azomethane (AM) was followed via its absorption near 200 nm and the appearance of CH3 near 216 mu. At total gas densities of 20e5 -lo4 mol cms3 we obtained an Arrhenius expres305
Voluine39, lminiler 2
sioti for the first order decomposition
rate constant:
.kAhf = --dfn[AM] jdt 25 101r3e+(-33
kcal mol-l/~T)s-l,
which is given as a preliminary value. Clark et-al. [9] reported a lower activation ener,qy at densities of lo6 mdl cmm3. An extrapolation of the low temper&e Arrhenius expression &r k~~f from Benson and O’Neal [23] to temperatures above 1000 K would lead td rate constants larger than ours by
a factor of 35. The extrapolated value of the rate constant, however, ensures in any case that the initial decomposition step of azomethane at T 3 1300 K is sufficiently fast to exclude a bimolecular reaction between CH3 radicals and the parent molecule. There is a suffcient amount of evidence that the decomposition leads to two methyl radicals 191. In the second part of the experiments we have studied the absorption of CH3 and CD, between 200 and 220 nm. Since the decomposition of the parent molecule is very fast, the concentration [CH3 ] u directly after passage of the shock wave (reaction time t = 0) is given by the stoichiometry (CH&N, + 2CH3 + N2. In order to keep corrections due to the recombination of CH, within the time of the Schlieren signal (typically 1-2~s) very small, these measurements were done at small [CHs] 0 fG2 X lWsl mol cme3) and [Ar] (=(4-l 5) X 10e6 mol cm’3). The effective decadic absorption coefficients at T = 1400 K have their maxima near 216.0 -I-0.4 nm for CH,, $g
15 A&
CHEMICAL PHYSICS LETTERS
= (1.8 St0.6) X lo6 cm2 mot’1
the investigated range using the theoretical temperature coefEcient. Details on the high temperature spectra of CH, and CD, will be reported elsewhere [20]. Having determined the effective absorption coefficients of CH3 and CD,, we obtained recombination rate coefficients k by fitting the function ]los&J0,1
-l = (WEI)t + Pos&$“)t=(J
-l3
[Arl I mol cni3 -6 5.0
*
2:m
Iii5 ,
.
16” 1
%?
20 +t+
WE 1.a = ‘g = ~/
05
I
t .*
+
-t+
+
a2
a1[ ,
,
‘~18
I)
J
.
I9
lo20
fAr1 I zti3
Fig. 1. Recembination rate coefficients for CHBf CH3 2 C2N6. The values marked by X are from ref. 19] (where Kr ZII~~ Ne ha-mebeen used instead of Ar). The points without error bars are from sin$e experiments. [Arl
= (2.0 + 0.7) X IO6 cm2 mol-‘.
These values correspond to a bandwidth (fwhm) AX = 1.6 nm of a triangular intensity distribution. The given error limits include both the statistical 95% confidence intervals from a t&l of about 20 experiments in each case and a rather conservative estimate of the systematic errors. When the computed temperature dependence of the extinction coefiicient is taken into account [ZO], our results are consistent with previous measurements at room temperature and higher resolution which led to E&?I = 1.12 X lo7 cm2 molt-l [2,25]. in the results reported below, we haue taken into account the s.mall temperature dependence of E within 306
_-
.
..
:
(I?
which results from the second order rate law -d [CHS ] [dt = 2k [CH3] 2. The experimental data were welI represented by the functional form fi > for reaction times to 50 ,QSand for all initial concentrations studied. The slopes of the closely linear (correlation coefficients often >0999) plot were determined by least squares fits. Figs. 1 and 2 show the resulting second order rate coefficients for methyl disappearance as a function of [Ar] . The points arc average val-
and near 214.5 rt 0.4 mn for CD, +jg
1976.
ml, , ml%
lmol
‘lo*
cni3
1020
tArI lcmm3 Fi.
‘Wk.
2. Recombination rate coefficients for CD3 + CD3 2
V0lurr.e 39,
number 2
CHEMICAL
ues of R at an average density in the interval indicated by the horizontal lines. The vertical lines give 9 5% confidence limits based on a t-distribution for eech‘individual set of experiments. No temperature dependence of k could be observed between 1200 and 1400 K. The data points of figs. 1 and 2 mostly belong to temperatures near 1350 K. The dependence of the rate constants upon the total gas concentration corresponds well to the behaviour of a recombination reaction in the fall-off range near the high pressure limit 1241. We obtained further evidence that the removal of CH3 by reactions other than recombination is unimportant under the conditions of the reported experiments, in agreement with the direct mass spectrometric product analysis of Clark et al. [9]. Between 1500 and 1700 K a fast initial decay of [CH,] towards [CH3] eq was observed in agreement with the recombination data at lower temperature. On a much longer time scale, CH, is then removed slowly by unidentified subsequent reactions. At temperatures between 2200 and 2700 K one can also follow the then quite rapid disappearance of CH, radicals. Assuming as a rough approximation a first order rate law, the data (for [CH, ] u = (3-9) X lOa mol cmm3) could be combined to give kapparent< (T =
101’exp(-50
15 April 1976
PHYSICS LETTERS.
kcal mol”/R@-’
1500-2700 K). It follows that these processes are negligible with respect to CH3 recombination at temperatures at or below 1400 K. In addition, we carried out some experiments where the disappearance of CH3 behind the incident shock (T x 1300 K) as well as its reformation from CzH6 and final decay behind the reflected shock (T a 2600 K) were all observed. The heights and time dependence of the absorption signals behind the :eflected shock were indistinguishable from those obtained with mixtures initially containing an equivalent amount of ethane. Although this “analysis” is not sufficiently precise for quantitative purposes, it is a further indication that CH3 recombination proceeds in a clean manner in our experiments. The above mentioned equilibration of CzH6 + XI& observed for I500 < T/K < 1700 led us to an experimental determination of the equilibrium constant. Since a large amount of data would be necessary to obtain a reasonably accurate experimental temperatuce dependence for the equilibrium constant, we chose to evaluate as the only significant quantity the bond
dissociation energy from the relation do
= -~Tln[(~~RTZcZH,/Z~Hs)~=I,
with the Avogadro constant NA, the molecular partition functions X(RT/V’)Z~-H~ and &~a and the experimental equilibrium constant Kc = [CH,] $&l16]
,-
The partition functions were calculated as usually in the harmonic oscillator-rigid rotor approximation apart from torsion in C,H, [14]. Any error due to incomplete data or anharmonicity is much smaller than the uncertainty in Kc. We obtain then an experimental value for CH3 : MO = 88.0 i 0.9 (k3.4) kcal mol-’, for CD3 : 9 = 88.7 f 1.1 (23.5) kcal mol-l . The
first error limits are the statistical 95% confidence intervals assuming a t-distribution for 8 experiments each. The errcr limits in brackets result from the (systematic) uncertainty in the absorption coefficient. The value for normal ethane is more reliable, because of the impurities present in the deuterated compound for which we could not apply corrections. Although the larger error limits include all values of AE$ presently discussed in the literature [12,16,18] our data favour the “high” value (87.76 kcal mol-1 for CH3) based on Chupka’s results [17].
4.
Discussion
From the present experiments as from earlier investigations in shock waves [9] one can conclude that in the temperature range 1ZOO- 15c)O K and at total densities of 2 X 10-6-2 X lOA mol cmS3 methyl radicals recombine cleanly to ethane. The average rate constants at the highest densities kH =
(1.7 f 0.6) X lo-!’
cm3 s-l
(2.2 * 0.9) X 10’”
cm3 s-l
and k,
=
(including systematic errors) can be expected to be no more than about a factor of 2 below the second order limit 1201. At the lowest densities our results are lower than those obtained by Clark et al. [9] (see fig. 1). This may be due to the lower methyl concentrations 307.
yo~&tiii~9, .“.. ‘__. Ta,&fe‘l
ri”mber 2 . _
:
: .
‘. -
:
.C~B;ICAL,PHYSiCS-L~TTEKS
.. 15 Aprii.~976
:
_-
: :.
fipti&iIentd ana theCketica1 n&S
found in-ref. EL611
-
. _
:
Etperimental, Sector
on methyl radial recombinatioti and ethane de~ornpo~t~o~ (references to dtder work c.an be ,
recombi~~io~ 400
4.0
293
4.4”)
Rash ptiotolysis of AM, kinetic spectroscopy
29s
4.3
Flash photolysis of’ AM, DMhi and keteneiH2, kinetic spectroscopy
295
9.5
Flash
293
5.6
Flash photolysis of CH31, mass spectrometric detection
313
4.0
Photolysis of AM, modulation spectroscopy
2.50-450
4.0
Ffash photolysis of DMhI, kinetic spectroscopy
295
5.5
” Uecom. of AM in shock waves, total density of Ne and Kr < 1.8 x IO= cm-+, mass spectrometric detection
1350
>0.9
Shock waves, total density of Ar Q 1.6 X 10” cmw3, kinetic spectroscopy
t300-1400
21.7
1400
>I .6 (3.3jcs
Ffrtsh photolgis
of AM and DhfM, kinetic spectroscopy
photolysis of A.&f,kinetic spectroscopy (photoelectric)
Experimental, dissociation of Cz Hc Sin& pulse shock tube total. densitij of Ar < 3.4 X lOi cme3 Thermal reactor
900
2.6
Thermal reactor
838
23.4
.
‘.Theoreticxtl studies PRKhl, A& = 86.3 kc&moI
350 900 1400 300 900 f40d
RI&M, &
= 87.76 kcal/mol
Statistical adiabatic cihannel model 4
= 87.76 ktaflmol
2.2 (0.7j&) 10.6 21.1 0.07 0.79 1.48
300 900 1300
1.3 16.6 41.5
300 900 1350
5.0
5-i .4.8
” Siiihtly corrected value from ref. [25]. b, These authors have us 9 definitionkz = d[CH3 1.-’ /df, difsering from ihe present paper and’from most other work- This has&en tzken into account, ’ ExtrapoIated to infinite pressure. ) The first’v&& is from table I. of reE [ 161, the value h breckets froni the Arrhenius expression in table 111of ref. f 16;1_See&o text; 308 ..
-_
:
-._
..
Volume 39, number 2
.:
CHEMICAL
PHYSICS LETTERS
timi resolution achieved in the present work‘. One should further compare with room temperature. work on the rgcombination reactiori and with _experimesits on e&an& dissociation. Table 1 shows presently available experimental and theoretical data on this system (further references to aider work may be found in ref. [ 161). All data are expressed in terms of high pressure recombination rate constants k,, assuming fl = 87.76 kcal mol-l for the conversion of the dissocialion rate constants. If one takes into account that most of the high temperature resuhs are below the second order limit (indicated by > and 2 for data near the second order Emit), most of the experimental results obtained by~quite different techniques in a large range of temperature and pressure conditions lead consistently to.approximately constant values or possibly to a small decrease of the high pressure recombination rate coefficient with temperature. However, all RRKM calculations quoted predict a considerable increase of the recombination rate constant between 300 and 1400 K. The statistical adiabatic channel model predicts a small decrease, in agreement with experiment. One should emphasize that all the theoretical predictions for the recombination rate constants depend only insignificaritly on the value of A,@ chosen. an@ higher
Acknowiedgement The present work has profited greatly from discuswith Dr. Hubert van den Bergh and Professor W.C. Gardiner. Professor A.B. CaIlear and Professor G. Herzberg provided copies of room temperature spectra of CH3 and CD3. The assistance of Dr. M. Stockburger, Ho Dac Thang, S. Lukacs, and A. Heusler and the financial support by the Fonds National Suisse de la Recherche are also gratefully acknowledged. sions
’
_-
,
15 April 1976
References R. Gomer and G.6. Kistiakowfky, J. Chem. Phys. 19 11951) 85, H.E. van den Bergh. A-B. Caile& and R.J. Norstrom, Chem. Phys. Letters 4 (1969) 101, N. Basco. D.G.L: James and R.D. Suart, Intern. J. Chem. Kinetics 2 (1970) 215. A.hL Bass and A.H. Laufer, Intern. J. Chem. Kiqetics 5 (1973) 1053. F.C. James and J-f. Simons. Intern. J. &em. Kinetics 6
(1974) 887. F.K. Truby and J.K. Rice, Intern. J. Chem. Kinetics S (1973) 721. D.A. Pa&es, D.hf. Paul and C.P. Quinn, preprint (1975). A.B. Callear and M.P. hletcalfe, preprint (1975). T-C. Clark, T-P- Izod, ‘M-A.Di Valentin and LE. Dove, J. Chem. Phys. 53 (1970) 2982; T-C. Clark, T.P. Izod and G.B. Kistiakowsky, J. Chem.
Phys. 54 (1971) 1295. C-P. Quinn, Proc. Roy. Sot. A275 (1963) 190; hf.C. Lin and M.H. Back, Can. J. Chem. 44 (1966) 505, 2357,2369; 45 (1967) 2115. LA. Clark and C-P- Quinn, preprint (1975). A. Burcat, G.B. Skinner, R-W. Crossley and K. Scheller, Intern. J. Chem. Kinetics 5 (1973) 345. 1-N. BradIey and MA. Frend, J. Phys. Chem. 75 (1971) 1492. M. Quack and J. Tree, Bcr. Bunsenges. Physik. Chem. 78 (1974) 240. hi. Quack and 5. Troe, Ber. Bunsenges. Physik. Chem. 79 (1975) 170. E.V. Waage and B.S. Rabinovitch, Intern. J. Chem. Kinetics 3 (1971) 105. W-A. Chupka, J. Chem. Phys. 48 (1968) 2337. D.M. Golden and S.W. Benson, Chem. Rev. 69 (1969)
125. K. Clanzer and J. Troe, J. Chem. Phys. 63 (1975) 4352. K. Ghnzer, M. Quack and I. Troe, in preparation. R. Renaud and L.C. Leitch, Can. J. Chem. 32 (1954)
545. Organic Synthesis 52 (1972) 11. S.W. Benson and H.E. O’Neal, Kinetic Data on Gas Phase Unimolecular Reactions, NSRDS-NBS 21 (1970). I. Troe, in: Physical chemistry, an advanced treatise, Vol. 6, ed. W. Jost (Academic Press, New York, 197.5) p. 835. H.E. van den Bergh, Dissertation, Cambridge, UK (1971).
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