High temperature UV absorption and recombination of methyl radicals in shock waves

H I G H T E M P E R A T U R E UV ABSORPTION A N D R E C O M B I N A T I O N OF M E T H Y L RADICALS IN SHOCK WAVES K. GLANZER, M. QUACK, AND J. TROE

Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, Lausanne, Switzerland AND

Institut fiir Physikalische Chemie der Universitiit D-34 GiSttingen Germany * The UV absorption of CH 3 and CD 3'in the 2A~ *-- 2A~ electronic transition has been studied in shock wave experiments using the fast thermal decomposition of azomethane at T > 1300 K as the radical source. With a spectral resolution A,k (FWHM) = 1.6 nm, the maximum effective decadic absorption coefficients at T = 1400 K are, near 216 nm .... (CH3) = (1.8 _+ 0.6) 9 106cm 2 mo1-1 ~max(CD3) = (2.0 ~ 0.7) " 1 0 6 c m g m o l

and 1.

Calculations on the temperature and b a n d w i d t h dependence of the spectra show that these results agree well with room temperature data. The recombination rate coefficients for the reactions C H 3 + C H 3 (+Ar)---~ C 2 H ~ ( + A r )

and

CD 3 + CD 3 (+Ar)---~ C 2 D 6 (+Ar) have been measured at JAr] = 2 . 1 0 6 _ 2" 10 -4 mol cm 3 in the falloff range near the high pressure limit. Extrapolation gives kH~ = (2.9 -----1.5) 9 10 - t t cm 3 s -1, kD, ~ = ( 3 . 2 _ + 1.7)- 10 - l l c m 3 s -1

and

atl400K.

The temperature dependence of the rate coefficients obtained by combination with room temperature data agrees well with predictions of the statistical adiabatic channel model but is in conflict with conventional RRKM calculations. A direct observation of the equilibrium C 2 H 6 ~ 2CH 3 gives agreement with the " h i g h " value for A H ~ (87.76 kcal mol-1). The thermal decomposition of azomethane between 850 and 1200 K, the kinetics of methyl radicals at T < 2700 K, and kinetic isotope effects are discussed briefly.

radicals near 216 nm by Herzberg and Shoos m i t h 2 led to a c o n s i d e r a b l e n u m b e r of acc u r a t e d e t e r m i n a t i o n s b y m e a n s of k i n e t i c s p e c t r o s c o p y . 3-9 T h e s e also led to a r e l i a b l e k n o w l e d g e of t h e o s c i l l a t o r s t r e n g t h s a n d a b s o r p t i o n c o e f f i c i e n t s i n t h e (ZA'l * - - 2 A ~ ) 0 ~ b a n d at r o o m t e m p e r a t u r e . 3,4,9,s At h i g h t e m p e r a t u r e s , t h e r e a p p e a r s to b e o n l y q u a l i t a t i v e m e a s u r e m e n t s of f l a m e s p e c t r a J ~ T h e r e c o m b i n a t i o n r e a c t i o n n e a r 1300 K h a s

1. Introduction T h e r e c o m b i n a t i o n of m e t h y l r a d i c a l s to form ethane has long been a model reaction i n gas k i n e t i c s . A f t e r t h e e a r l y d e t e r m i n a t i o n of its rate c o n s t a n t b y G o m e r a n d Kistiakowsky 1 using the rotating sector method, the d i s c o v e r y of t h e U V a b s o r p t i o n of m e t h y l * Present address 949

950

KINETICS OF ELEMENTARY REACTIONS

been studied b y Clark et al. 11 in shock waves, using mass spectrometric detection. However, due to relatively h i g h concentrations and long reaction times, mechanistic complications could n o t b e excluded completely. Also, at total gas densities of 2 - 10-6 mol em -3, the reaction was still in the falloff range. At high temperatures, the reverse dissociation of ethane has been investigated more often, near 900 K in static systems ~2,13 a n d in shock waves near 1300 K. 14,1~In these studies a composite mechanism always had to be taken into account. Direct observation of the isolated u n i m o l e e u l a r primary step in dissociation has not been reported to date. The aim of the p r e s e n t study was twofold: First, we wanted to determine the absorption coefficient of methyl radicals at high temperatures. The k n o w l e d g e of the absorption coefficient and its temperature d e p e n d e n c e is useful for a detailed study of the kinetics of methyl radical reactions in h i g h temperature systems. Second, we w a n t e d to obtain a reliable value for the high pressure limiting rate constant for the methyl radical recombination. Together with the room temperature data, this extends our knowledge on this important reaction over more than 1000 K, a u n i q u e example for the recombination of two polyatomie radicals. This information is of some relevance for theories of unirnolecular reactions. Although all theories in general predict only a small temperature d e p e n d e n c e of the high pressure rate coefficient for simple recombination reactions, there are sizeable effects and discrepancies in predictions of more than a factor of ten if one considers such a large temperature variation. 16,17 Methyl radical recombination and ethane d e c o m p o s i t i o n are particularly suitable for a more detailed study, because they have been test cases for theories for a long time. 16-18 It has been pointed o u t 19 that the direct m e a s u r e m e n t of the r e c o m b i n a t i o n reaction is more suitable for comparison w i t h theory than a c o m b i n a t i o n of dissociation a n d recombination data, since the calculations for the recombination d e p e n d only slightly on the still somewhat uncertain b o n d dissociation energy.

(10 -a

-<

XAM ~- 5

--2'

"

10 -6, 2 " 10 -6 --< fAr]

10-4molcm

3, T~> 1300K)

AM was synthesized from sym- dimethylhydrazine by oxidation with mercuric oxide. 21 After drying, fractional distillation and degasing, the product was essentially pure (>99%). The perdeuterated Compound (AMD) was prepared 22 from perdeutero-methylamine (Merck-Sharp and Dohme). AMD was used without further purification. Its gas ehromatogramm showed about 5% of a volatile nonhydrocarbon impurity. The IR-spectrum showed, that deuteration was > 95%. Absorption signals of azomethane (near 200 nm) and of methyl radicals (between 200 a n d 230 nm) were m o n i t o r e d with an E M I 6256 B photomultiplier. The light was from a high pressure Xe are. It was predispersed with a quartz prism to reduce scattered light and analyzed with a 0.25 rn Jarrel-Ash grating monochromator w i t h a spectral b a n d w i d t h of 1.6 nm ( F W H M ) . T h e wavelength reproduc, ibility was better than +0.4 nm. The results reported below are based on more than 200 single experiments in incident and reflected shock waves. 3. Results

3.1. Thermal Decomposition of Azomethane We have studied the thermal d e c o m p o s i t i o n of azomethane b e t w e e n 850 and 1200 K and under experimental conditions (i.e. fAr] a n d Xn~a) similar to the recombination experiments, in order to insure that the generation of C H 3 proceeds in a clean manner. In one set of experiments we obtained the first-order rate constants kAM = - d l n [ A M ] / d t by monitoring the AM absorption profiles near 200 nm. In a second set of experiments at 1050 < T / K < 1200, C H 3 profiles were measured via absorption near 216 nm. Assuming the validity of the two-step mechanism AM ( + M ) --* 2 C H 3 + N 2 ( + M ) C H 3 + C H 3 (+ M ) --~ C 2 H 6 ( + M )

2. E x p e r i m e n t a l The shock tube a n d details of the experimental technique have been described previously. 20 Methyl radicals have been p r o d u c e d in the fast thermal d e c o m p o s i t i o n of azomethane (AM) in high p u r i t y (>99,99%) Ar

for short reaction times (<50 txs), one can then derive values for k AM, using the recombination rate coefficient and absorption coefficient for methyl radicals as determined below. T h e results are shown in Fig. 1. The excellent agreement of the direct determination with the somewhat more uncertain values obtained indirectly strongly suggests that the simple

UV ABSORPTION

T/K 1000

1200

\

i

I

!

~x |

10 5

I/I

10 z,

103 I

I

I

I

E8

E9

1.0 103 K/T

1J

1.2

FIG. 1. Arrhenius plot for the thermal decomposition of azomethane. 9 From measurements of azomethane absorption profiles; X From measurement of methyl absorption profiles, [Ar] = (1.7 -+0.7). 10-4 mol era-3 for points without circles, JAr] = (3 -+ 2)" 10 -5 mol cm -3 for points with circles; 9 Results of Ref. 11 with [Ne] = 10-6 tool cm -3.

mechanism describes the important features of the AM and CH 3 profiles at T ~> 1100 K and t ~< 50 txs. This is in agreement with the mass spectrometric analysis of the reaction products of AM decomposition in Shock waves. 11 Considerable variation of [Ar] has only a very slight (if any) influence on kA~ (see Fig. 1). A fit of our data in terms of an Arrhenius expression gives (T = 850 - 1200 K) kAM = 1011"3exp (--33.5 kcal mol i / R T ) s -~ Clark et al. report even lower Arrhenius parameters. 1~ Our Arrhenius expression differs significantly from the one recommended by Benson and O'Neal on the basis of "low temperature" (~<600 K) pyrolysis experiments (=10 x6"~ s -1 exp ( - 5 2 . 5 kcal m o l - 1 / R T ) ) . 23 However, as discussed in detail by Knoll et al., and P a q u i n an d Forst, at low temperatures the reaction proceeds via a complicated chain mechanism. 24,25Also at the lower temperatures of our experiments the AM disappearance

951

presumably is considerably accelerated by reaction of CH 3 with AM a n d subsequent reactions, the CH 3 yields b e i n g u n m e a s u r a b l y small. This then accounts for the apparent activation energy b e i n g m u c h lower than the threshold energy (=55 kcal mol-i),2s in spite of the fact that the reaction is quite near to the high pressure limit. Taking our kaM at T > 1100 K as the true unimolecular rate constant and assuming E a = 55 kcal tool -I, one obtains a preexponential factor of = 10 as.6 8-1 The investigation shows, in any case, that u n d e r the conditions of the recombination experiments (T ~> 1300 K) the decomposition of AM is sufficiently fast to exclude any radical-parent molecule reactions. The decomposition follows the stoichiometry AM 2CH 3 + N 2 (see also 11) and the removal of C H 3 occurs p r e d o m i n a n t l y by recombination to C2H 6. The latter was further supported b y the following experiments. The methyl profiles b e h i n d both incident ( T ~> 1300 K) a n d reflected shock waves (T ~> 2600 K) were observed in one experiment. In one case CH 3 was produced by AM decomposition b e h i n d the incident shock wave. It recombined to C2H 6, which was then pyrolized b e h i n d the reflected shock. In another case the initial reactant was C2H6, which was practically stable b e h i n d the incident shock and was decomposed to CH 3 only b e h i n d the reflected shock. In both cases we observed the same profiles with respect to CHa-yields a n d its decay behind the reflected shock. This again strongly suggests, that methyl radicals quantitatively react to give ethane at temperatures near 1300 K. 3.2. The UV Absorption of Meth~tl Radicals

at High Temperatures o

We have studied the absorption of CH 3 and CD 3 radicals in the range of the 2A' 1 ~-- 2A"2 electronic transition between 200 and 230 nm. Since the experimental error in the effective decadic absorption coefficient ~ is the most important source of systematic error for the recombination rate constant (and even more so for the e q u i l i b r i u m constant) to be reported below, we have also done some calculations on the dependence of e on temperature and on spectral resolution. This allows for a quantitative comparison of our high temperature results with room temperhture data currently available. It turns out that there is excellent agreement between all data, if the effects of temperature and finite spectral resolution are properly taken into account. As shown above, the decomposition of azo-

952

KINETICS OF ELEMENTARY REACTIONS

methane near 1400 K is sufficiently fast for the initial concentration [CH3] o after the passage of the shock wave (reaction time t = 0) to be given by the stoichiometry (CH3)zN2 ~ 2 C H 3 + N~. The fraction of methyl radicals w h i c h recombined d u r i n g the finite duration (1 - 2p.s) of the Schlieren signal was very small with [CH3] 0 <~ 2 9 10 -9 mol cin -9 and [Ar] = 4 - 15 9 10 -8 mol cm -3. The results for ecn ~ are shown in Fig 2. The points are mostly from single experiments near 1400 K with a spectral resolution of AK(FWHM) = 1.6 n m (in a few experiments we also chose AK = 0.8 nm). We verified experimentally that the intensity distribution of the analysis light corresponded closely to the theoretical triangle, the entrance and exit slits of the monochromator having equal widths. The c o n t r i b u t i o n to the oscillator strength between 202 a n d 225 nm, obtained by integration, for C H 3 is

ft.z =- 4.317 9 10 -12"

e(v) d v / ul

cm 2tool l ( c m 1)_~1.6.10 -2 and for CD 3 b e t w e e n 201 and 218 nm it is fl,2 = 1.8" 10 -2. No error limits are given for these quantities, since especially the results for low e are uncertain, due to the necessity of larger [CH3] o which introduces some uncertainities because of nonnegligible recombination d u r i n g the

2~ l "7

I

200

I

I

210

X

220 ). I n m

-~P

FIc. 2. Absorption spectrum of CH 3 at 1400 K in the ZA[ *- aA~ electronic transition, using a spectral resolution hMFWHM) = 1.6 nm. X = measured points; solid line = calculated, starting from room temperature data (see text).

schlieren signal. Outside the indicated range of wavelengths, the absorption was too small to be detected with certainty. The effective decadic absorption coefficient at the m a x i m u m at 216.0 -+ 0.4 n m for C H 3 has been determined to be (at 1400 K)

.C.H. .3. .

(1.8 + 0.6)" 106 cm 2 mo1-1

and for CD 3 at 214.5 -+ 0.4 n m e~

= (2.0 _+ 0.7)" 106 cm 2 mo1-1.

In both cases AK(FWHM) = 1.6 nm. The error limits include both the statistical 95% confidence intervals for 20 experiments in each case and a rather conservative estimate of systematic errors. Table I summarizes results obtained for e m a x and f in room temperature work and at high temperaures in the present work, together with calculated values. I n the calculations we first fitted the high resolution spectra 26 for C H 3 and CD 3 at 300 K, u s i n g the formulae for the line positions and strengths of a parallel b a n d of a rigid symmetric top. 27 K n o w i n g the molecular constants of C H 3 (and CD3), 2 (v o = 46 205. (46 628.5) cm-1); A" = 4.789 (2.3965) cm-1; A' = 4.4133 (2.2083) cm 1; B = 2A) there remains only the line width F free to be adjusted. Since both CH 3 and C D3 are quite strongly predissociated in the upper state, the line shapes can be well approximated b y Lorentzians. The best fit to the shape of the spectra at room temperature was obtained with a constant F = 60 cm -1 for C H 3 and F = 8 cm -1 for CD 3. Although the line widths will depend on the rotational state, in principle, it appears from the good fit that this dependence is not too strong. I n c l u s i o n of centrifugal distortion leads to a somewhat better fit for CD3, but it has b e e n neglected for the present purposes. Once the shapes of the spectra are known, one can obtain the absolute strength of absorption either by fitting to the m a x i m u m experimental absorption coefficient or to the integrated oscillator strength. The values quoted in the line "calc." for CHa have been chosen to be a compromise b e t w e e n the various experimental data. Although the quantity f e ( v ) d v / IEm a x is smaller for the calculation than for most experiments, a value of F > 60 cm -1, leading to larger f e ( v ) d v / e . . . . no longer leads to such a good fit of the features of the spectrum. I n any case, the differences are not important at the present level of precision. For CD3, there are m u c h less spectral data, so we assumed, as a first guess, that f(0 ~ , C H 3) = f (0~ , CD a )"

UV ABSORPTION

953

TABLE I Summary of results on the 2A~ ~ 2A~ electronic transition of CH 3 and CD 3. The effective decadic absorption coefficients era, ~ are given for the actual experimental spectral resolution AX indicated in brackets. The values marked by "'*'" are corrected for the effect of finite resolution using the calculated e ~ / e .... (AX), see text. a) Room temperature results (300 K) Emax// 107 cm 2 m o l i

Ref. [3], [3], [9], [4],

CH a CH a CH 3 CH 3

[8,28], CH a calc., CH 3 [9], CD a [8,28] CD a

1.02 1.12 0.96 1.02 t0.84 1.09

-+ 0.11 --- 0.06 _+ 0.04 (0.5nm) *

1.2 1.68 --+ 0.17 (0.17nm) |2.07 * 0.78 (1.2nm) ~ 2.7 * 2.84

calc., C D 3

f(Og)/lO_Z

~max-1 f e ( v ) d v / cm-1

1.20 _+ 0.2 1.32 +- 0.2 1.37 1.05 ---

270 270. 330. 240. ---

1.2 0.99 _+ 0.1 ---

230 140. 114. ---

1.2

100.

This work, CH 3

b) High temperature Results (1400 K) f(201-225 rim) /10 2 t0.18 -+ 0.06 (1.6nm) 1.6 0.24 *

calc., CH 3

10.19 (1.6nm) ~0.25 *

This work, CD 3

t0.2 _+ 0,07 (1.6nm) {0.38 *

cale., CD a

t0.21 (1.6nm) {0.41 *

emax/10 7 cm 2 tool -1

T h i s a s s u m p t i o n w o u l d b e correct w i t h i n the F r a n c k - C o n d o n a p p r o x i m a t i o n , if the 0o~ b a n d carried the total oscillator s t r e n g t h of the elect r o n i c transition. A l t h o u g h the 0 ~ b a n d is a c t u a l l y d o m i n a n t , o t h e r b a n d s are k n o w n to c o n t r i b u t e a p p r e c i a b l y 9. N e v e r t h e l e s s , there is g o o d a g r e e m e n t b e t w e e n the a b s o r p t i o n coeff i c i e n t c a l c u l a t e d in this w a y for C D 3 a n d the v a l u e r e p o r t e d b y Parkes et al. 8,28. M o r e recently, C a l l e a r a n d M e t c a l f e r e p o r t e d a somew h a t l o w e r v a l u e for b o t h ~max a n d f(O~ 9 I n o r d e r to c o m p u t e the t e m p e r a t u r e dep e n d e n c e of the s p e c t r u m , o n e m u s t also inelude a number of sequence bands (1] 2~, 3~ 4 ~ , 80 b a n d s for C H 3 , 5 0 0 for C D 3 ) . U n f o r t u n a t e l y , the excited state f r e q u e n c i e s are not w e l l k n o w n , so w e h a v e b e e n f o r c e d in part to e s t i m a t e t h e m

(v'~.= 3044 (2150) c m - 1 , tt

v z = 580 (450) c m - 1 , tt v a = 3162 (2380) c m -1,

1.8

v 4 = 1396 (1026) c m - 1 , v 'l = 2650 (2000) c m - 1 , v~ = 1370 (1080) c m - I , v 3 2650 (2000) e m - 1 , v~ = 1300 (970) c m - 1 , for C H 3 ( C D 3 ) ) . T h e t r a n s i t i o n m o m e n t s h a v e all b e e n a s s u m e d to be e q u a l . W e h a v e further e s t i m a t e d f r o m the f r e q u e n c y a n d structural changes that f ( l o ~) --= f ( 2 ~ ) - 0.3 f(0o~ C h a n g e s in t h e s e estimates, w i t h i n r e a s o n a b l e limits, do not greatly c h a n g e the c a l c u l a t e d a b s o r p t i o n s p e c t r u m in t h e r e g i o n of m a x i m u m a b s o r p t i o n , w h i c h is i m p o r t a n t for t h e p r e s e n t c o m p a r i s o n . I n T a b l e 1, the c o m p u t e d emax(1400 K) c o m p a r e s v e r y w e l l w i t h our e x p e r i m e n t a l value. T h i s m e a n s also that there is q u a n t i t a t i v e a g r e e m e n t b e t w e e n t h e r o o m t e m p e r a t u r e a n d the h i g h t e m p e r a t u r e measurements. O n e s h o u l d note that in t h e e x p e r i m e n t s at

954

KINETICS OF ELEMENTARY REACTIONS

high temperatures and in some of the room temperature experiments the spectral resolution was not sufficient to obtain the exact shape of the spectrum and the true m a x i m u m absorption coefficient. In such cases we have also computed the true e m a x (indicated by * in T a b l e I), from the theoretical ratio emax / 9..... (AK) with 9 .... (Ah) being the m a x i m u m value of

1.6 ran, and for a high resolution of Av 10 cm -1 < < C H a. These values have been obtained from the experimental absorption coefficient at 1400 K using the theoretical d e p e n d e n c e on temperature and Ah. T h e y are also consistent w i t h i n a few percent with the room temperature measurements and should, therefore, give an accurate basis for work at high temperatures.

i lim eeff(UN,AV) = lirn - -

3.3.

c'/~0

c" 1 ~ 0

{ lgl~

Recombination of Methyl and Perdeutero Methyl Radicals

C "1

f L(v)" T(vN ,Av) dv } f L ( v ) . T(v N,Av).10 -'(~)c~ du

Usually, the spectral intensity function of the light source, L(v), can be taken to be a constant. T(UN,AV) depends on the dispersion e l e m e n t used. In our experiments, it was a triangular function with Av ( F W H M ) = 340 cm-1 corres p o n d i n g t o Ah = 1.6nm. Although eef~(VN, Av) depends on concentration, calculation and experiment both s h o w e d that Lambert-Beer's law was fullfilled at our experimental conditions. The curve in Fig. 2 shows the c o m p u t e d low resolution absorption coefficient. There is good agreement with experiment in the region near the maximum. At short wavelengths, the calculated absorption is s o m e w h a t weaker than the experimental one. This is probably due to f ( l o1) being larger than assumed in our calculations. 29 The very good consistency of low and high temperature absorption coefficients leads us to believe that the probably error in 9 .... is really somewhat smaller than the one indicated above, w h i c h is based only on an analysis of experimental error in our experiments. In Table II we give a proposed set of 9 .... (CH a) for temperatures between 1000 and 1800 K for a spectral resolution of Ak(FWHM) =

As an example Fig. 3 shows an oscillogramm monitoring the time history of absorption near 216 nm due to methyl radicals. The experimental data could be well represented by the function:

2kt [ l g l o ( I o / I ) t ] -~ =

e-1

+ [lg~o(Io/I),= o] -~

which corresponds to the second-order rate law -d [CHa] /

dt = 2 k

[ C H a ] 2.

The oscillograms were evaluated up to reaction times of 50 ixs and more, leading to closely linear fits (correlation coefficients often >0.999). The rate coefficient was i n d e p e n d e n t of reactant concentration in the range investigated

TABLE II Proposed set of effective decadic maximum absorption coefficients near 216 nm for CH 3 between 1000 and 1800 K. Av is the pertinent spectral resolution.

T/K 1000 1200 1400 1600 1800

.... /106 cm 2 tool-1 Av = 10 cm -l Av = 340 cm -1 3.70 2.89 2.36 1.94 1.61

2.57 2.14 1.80 1.54 1.32

FIG. 3. Time history of CH 3 absorption near 216 nm behind reflected shock at T = 1280 K, [Ar] = 5.52" 10-5 mol cm-a

UV ABSORPTION (2 9 10 -9 ~< [ C H 3] o ~< 2 9 10 8 mol c m - 3 ) . There was, however, a marked d e p e n d e n c e on fAr] in the range of 2-10 -6 - 2-10 -4 mol c m

- 3

Figure 4 shows the resulting second-order rate coefficients in the fall-off range of the recombination reaction. T h e points are average values of k at an average density in the range indicated by the horizontal lines. The vertical lines give 95% c o n f i d e n c e limits based on a t-distribution for each individual set of experiments. No temperature d e p e n d e n c e could be observed between 1200 and 1400 K. The data points of Fig. 4 correspond mostly to temperatures near 1350 K. As discussed below, even at the highest fAr] (corresponding to Ptot~l > 20 atm) the reaction has not yet reached its second-order limit completely. We also have studied the possible influence of an oxygen impurity on the reaction by experiments with added oxygen (fAr] = [Ar] / mol cm -3 10-6 '

'

r

10-5 ,

,

10-4

i

i

,

r

,

,Tw 2.0 ~uE 1-0 0.s

.

o 0.2 0.1 I

101"1

1018

J

,

1019

I

955

1.5" 10-5moi cm -a, mole fractions X~H~N2 = 10-4, x~ 2 = 5 9 10-s, this corresponds to about twice the possible total impurity in Ar). The rates of C H a- disappearance were identical to the experiments without oxygen. As a matter of fact, under the conditions of our experiments, the reaction C H a + 0 2 was found to be m u c h slower 30than the recombination CH a + CH3, w h i c h appears to be wholly responsible for the initial CHa-disappearance. 3.4. Measurements of the Equilibrium

Constant for C 2 H e , ~ 2 C H 3 At T ~> 1500 K, a substantial a m o u n t of free methyl radicals is expected to exist in partial e q u i l i b r i u m with ethane. This establishment of a p r e e q u i l i b r i u m at higher temperatures could be observed in our experiments. Figure 5 shows an oscillogram for CD a absorption at 214.5 nm as a function of time at T = 1575 K. Very clearly, after an initial fast disappearance of C D a, the concentration attains a nearly constant value w h i c h decays only on a m u c h longer time scale (probably due to the reactions initiated by C D 3 + C2D6). 11 F r o m the q u a s i e q u i l i b r i u m value [ C H 3 ] e q ([CD3] e, ), one can calculate the e q u i l i b r i u m constant)(At the higher temperatures of these experiments, near 1700 K, one has to apply a small correction for C H 3 disappearance w h i c h is notdue to the recombination reaction; see below). Since a large a m o u n t of data would be necessary to obtain a reasonably accurate ex-

10 20

[ A r ] I cm -3 ['Ar]/tool cm -3 104

10-5

I0-4

2.0 'hE u

_

[

1.0

=k 0.s at

0.2

0.1

1017

1018

1019

1020

t

[Ar] I crn -3

FIG. 4. Log k/log fAr] plot for the recombination rate coefficients of a) CH 3 and b) CD 3. Measured points with error bars (see text): 9 are from single experiments; X are the results of Ref. 11 with Ne and Kr. The curves are calculated fall-off curves fitted to the experimental points (see discussion). The straight lines are the extrapolated high and low pressure limiting rate constants.

FIG. 5. Time history of CD 3 absorption near 214.5 nmat T = 1575K, fAr] = 2 . 2 10 4molcm-a.

956

KINETICS OF ELEMENTARY REACTIONS

perimental temperature d e p e n d e n c e for the equilibrium constant, from our experiments (at 1500 K < T < 1700 K) we chose to evaluate the b o n d dissociation energy as the only significant quantity, AH~=-RTln

NA'RT'Qc2H6 K~]

Q~H~

(N A = Avogadro constant, QC~Hs and Q ~ -molecular partition function 9 RT/V, Ko [CH a ] ~q / [C 2H 6 ] eq --- experimental e q u i l i b rium constant). T h e partition functions were evaluated as usual in the harmonic oscillatorrigid rotor approximation, but using the exact eigenvalues for C 2 H ~ and C2D 6 torsion w i t h Va = 1024 cm -1.16 T h e errors due to i n c o m p l e t e data or a n h a r m o n i c i t y are expected to be m u c h smaller than the experimental uncertainty in Ko. The result of this evaluation is 9

_

_

C H

for C e l l 6 : AH ~ = 88.0 _-_ 0.9 (+-3.4) kcal mol 1 for C2D 6 : AH ~ = 88.7 _+ 1.1 (---3.5) kcal mol - I The first error limits are the statistical 95% confidence intervals based on a t-distribution for eight experiments each. The error limits in brackets result from the systematic uncertainty in the a b s o r p t i o n coefficient. The value for normal ethane is more reliable because of the impurities p r e s e n t in the deuterated c o m p o u n d for w h i c h we could not a p p l y corrections. Also the difference AH ~ (C2D6) -hHo~ = 0.7 kcal mo1-1 is smaller than theoretically expected (2 kcal mol -1), b u t this is well w i t h i n the experimental uncertainties. Although the larger error limits i n c l u d e all values of AH ~ presently discussed in the literature, 14,17'31 our data agree well with the " h i g h " value (87.76 kcal mol -I for C 2 H 6 ) based on C h u p k a ' s results. 32 3.5

Thermal Decomposition of Ethane

We carried out some experiments on ethane dissociation with C2H6-Ar mixtures (1700 K < T < 2700 K, Xc2H6 = 2" 10 -~- 1-10-4). Methyl radical profiles were monitored as described. At temperatures near 1700 K, one can observe the r a p i d formation of C H 3 and the establishment of the C 2 H 6 ~ 2CH 3 equilibrium. The e q u i l i b r i u m constants are in excellent agreement w i t h the above data. T h e

dissociation rates o b t a i n e d also agree very well with the (extrapolated) recombination data. These observations show that under favorable experimental c o n d i t i o n s (high total gas pressures and l o w reactant concentrations), the kinetics are governed b y ethane d e c o m p o s i t i o n and its reverse, the a p p r o a c h to partial equilibrium b e i n g observable from both sides. At longer reaction times however CH 3 is consumed b y s u b s e q u e n t reactions with the rates increasing rapidly with temperature. At T > 2200 K only d e c a y i n g C H 3 profiles were observed b e h i n d the shock front. The same k i n d of profiles were observed with AM-Ar mixtures (instead of C2H6-Ar) heated to T > 2200 K b e h i n d the incident shock. No attempt was made to describe these C H a - d i s a p p e a r a n c e rates b y a reaction mechanism, because sufficiently accurate information about the n u m e r o u s possible reactions is not available yet. These reactions may even include the u n i m o l e c u l a r dissociation reaction CH3--)CH 2 + H. 33 Since no u n i q u e reaction order was observed, we characterize these concentration-dependent CH 3 disappearance rates b y their half lives: rl/2 ~> 7 9 10-11exp 50 kcal m o l - 1 / R T ) ([CH3]

m a x

=

s

(6 -+ 3)- 10 -9 tool c m - 3 , 1500 K < T < 2700 K)

Most of the experimental r ~/2's were still up to a factor of two larger than given b y this expression. Extrapolation to T < 1500 K shows that this k i n d of process is u n i m p o r t a n t compared to m e t h y l radical recombination, under the conditions of our measurements of recombination rates.

4. Discussion The present investigation indicates that methyl radicals formed in the thermal decomposition of azomethane recombine cleanly to ethane at the pressures and temperatures of our experiments (1200-1500 K, Ptot= 0.2 - 2 5 atm). This is in good qualitative agreement with earlier measurements using a mass spectrometric technique. 11 Where the data overlap (cf. Fig. 4), our results are somewhat lower, however, p o s s i b l y due to the lower methyl concentrations and the higher time resolution achieved in the present work. We have shown that other reactions (unidentified, but p r o b a b l y initiated b y C H 3 + C2H6) are negligible c o m p a r e d with the r e c o m b i n a t i o n

UV ABSORPTION at 1400 K. The results in Fig 4 therefore represent the rate coefficients for methyl radical recombination. I n spite of the high pressures of our experiments, the reaction is still in the fall-off range, though near the high pressure limit. To obtain an extrapolation to the high pressure limit and an estimate of the low pressure rate constant, we used the simple method of doubly reduced Kassel fall-off curves. .4 The curves in Fig. 4 are calculated with S K = 9,0 (10,5), B K = 20 (24) for C a l l 6 (CaD 6) 9 S K was obtained from the relation U v,b SK kT

1 E ~ (T) - E o + -- + + A SK 2 kT

with the vibrational c o n t r i b u t i o n to the internal energy U v~b, the theoretical Arrhenius activation energy Ea= 3~ at 1400 K and an estimated correction ( A S K ~ 1.5) for weak collision effects. 34 This leads to an extrapolated high pressure limit: kH, ~ =

(2.9 -+ 1.5) 10-11 cm ~ s-1

kD. | = (3.2 -- 1.7) 10-1~cm 3 s -1

The error limits contain the statistical 95% confidence intervals, an estimate of the systematic errors and a somewhat less certain estimate of the extrapolation errors. An accurate extrapolation to the low pressure limit is not possible from the present experiments. Nevertheless, the "best fit" to the falloff curves in Fig. 4 corresponds to kH, o = 4 . 1 0 - a 9 cm 6 S-1 kD. o

----- 2 '

10 -as cm 6 s -1

These values are believed to be correct to w i t h i n a factor of about 5. We also computed the "strong collision rate constants" from the equation

ko ~c

ZL1 K - ~ o r i ~~ (2J + 1)

f;.(E, exp(-E/kT) dE o(l)

where Z a t is the Lennard-Jones collision n u m b e r from viscosity data. 36 ( = 5 . 4 " 10- 10 (5.1. 10 -1~) cm 3 s -1 for C z H 6 (CAD6)/ Ar), K c the e q u i l i b r i u m constant, Q~r the rotational-vibrational partition f u n c t i o n of ethane, E o (J) the m a x i m u m of the lowest adiabatic

957

channel for total angular m o m e n t u m jl6 and p(E,J) the rotational-vibrational density of states evaluated b y direct count in the separable a n h a r m o n i c oscillator-rigid rotor approximation, treating torsion exactlyJ 6 O n e obtains at 1400 K: k~.o = 2.9" 10 -as cm 6 s -1 k~.o = 7.1-10 -as cm 6 s -1

From this, one can compute the collision efficiency 34

13~ -

ko -

-

-

0.13

(0.3)

kosc

for C z H 6 (C a D 6)" These figures, although very uncertain experimentally, are of the magnitude to be expected empirically,z7 The kinetic isotope effect is interestingly large in the low pressure limit, both experimentally (if real) and theoretically. However, the isotope effect for the high pressure l i m i t i n g rate constant is negligible, in agreement with theoretical expectation.X6 A large a m o u n t of data is now available on methyl recombination a n d ethane dissociation between 300 and 1400 K. m,38 All these data consistently lead to a slight decrease of the recombination rate constant (by less than a factor of two for the whole temperature range), if one uses AH~ = 87.76 kcal mo1-1 for the conversion of the dissociation data. There are also quite a few recent calculations on this system. I n d e p e n d e n t of details of the assumptions on AH ~ configuration of the activated complex, etc., most of these calculations based on conventional RRKM theory predict an increase of the r e c o m b i n a t i o n rate coefficient e between 300 K a n d 1400 K by a factor of 10-30.14,16,17 This is in severe conflict with our experimental findings. This shortcoming of this type of RRKM-calculations has been discussed theoreticallyJ 6 It is due to a n u m b e r of approximations, which are not justified for simple b o n d fission reactions. Calculations with the statistical adiabatic c h a n n e l model, which contains less approximations, predict a slight decrease of the recombination rate coefficient 1~ with temperature, in good agreem e n t with experiment.

Acknowledgment

Helpful correspondence with Prof. A.B. Ca/lear and Dr. D.A. Parkes, who made data available prior

958

KINETICS O F E L E M E N T A R Y REACTIONS

and in addition to published results, is gratefully acknowledged. Prof. N. Basco and Prof. G. Herzberg kindly provided copies of room temperature spectra of CH 3 and CD a. We are also indebted to Dr. H. van den Bergh, Dr. M. Stockburger, Ho Dac Thang, S. Lukacs and A. Heusler for assistance and discussions.

Chem. Kin. 3, 105 (1971) 18. O. K. RICE, Statistical Mechanics Thermodynamics and Kinetics, Freeman, San Francisco 1967. 19. K. GtC4NZER,M. QUACKANDJ. TnOE, Chem. Phys. Letters, 39, 304 (1976) 20. K. Gt~NZERANDJ.TRoE, J. Chem. Phys. 63, 4352

(1975) REFERENCES 1. R. GOMER AND G. B. KISTIAKOWSKY, J. Chem. Phys. 19, 85 (1951). A. Shepp, ibid. 24, 939

(1956) 2. G. HERZBERG AND J. SHOOSMITH, Can. J. Phys. 34, 523 (1956); G. Herzberg, Proc. Roy, Soc. (London), 262A, 291 (1961) 3. H. E. VAN DEN BERGH,A. B. CALLEARAND R. J. NORSTROM,Chem. Phys. Letters 4, 101 (1969); H. E. van den Bergh, Dissertation, Cambridge U. K., 1971 4. N. BASCO, D. G. L. JAMES, AND R. D. SUART, Int. J. Chem. Kin. 2, 215 (1970) 5. A. M. BAss AND A. H. LAUFER, Int. J. Chem. Kin. 5, 1053 (1973) 6. F. C. JAMES AND J. P. SXMONS,Int. J. Chem. Kin. 6, 887 (1974) 7. F. K. TRUBYAND J. K. RmE, Int. J. Chem. Kin. 5, 721 (1973) 7a. M. POHJONEN, L. LEINONEN, H. LEMME~INEN AND J. KOSKIKALLIO,Finn. Chem. Lett. 1974, 207 8. D. A. PARKES, D. M. PAUL, AND C. P. QUINN, preprint 1975 9. A. B. CALLEAR AND M. P. METCALFE, Chemical Physics, 14, 275 (1976) 10. R. HARVEY AND P. F. JESSEN, Nature Physical Science 241, 102 (1973) 11. T. C. CLANK,T. P. Izoo, M. A. DI VALENTtN, ANDJ. E. DOVE,J. Chem. Phys. 53, 2982 (1970); T. C. Clark, T. P. Izod and G. B. Kistiakowsky, J. Chem Phys. 54, 1295 (1971) These authors have used a definition k z = d[CHa]-l/dt, differing from the present paper and from most other work. This has been taken into account. 12. C. P. QUINN,Proc. Roy. Soc. A275, 190 (1963); M. C. LIN anD) M. H. BACK,Can. J. Chem. 44, 505 (1966); ibid 44, 2357 (1966); ibid 44, 2369 (1966);ibid 45, 2114 (1967) 13. J. A. CL*aK AND C. P. QUINN, J. Chem. Soc., Faraday Trans. I, 72, 706 (1976) 14. A. BURCAT,G. B. S~INr~ER,R. W. CROSSLEY,AND) K. SCHELLER,Int. J. Chem. Kin. 5, 345 (1973) 15. J. N. BRADLEYAND M. A. FREND, J, Phys. Chem. 75, 1492 (1971) 16. M. QuAcr AND J. TROE, Ber Bunsenges. Phys. Chem. 78, 240 (1974) 17. E. V. W**GE AND B. S. RABINOVITCH,Int. J.

21. R. RENAUDAND L. C. LEITCH, Can. J. Chem. 32, 545 (1954) 22. Organic Synthesis 52, 11 (1972) 23. S. W. BENSONAND J. E. O'NEAL "Kinetic Data on Gas Phase Unimoleeular Reactions" NSRDS-NBS 21, Washington 1970 24. H. KNOLL,K. SCHERZERANDG. GEISLER,Z. Phys. Chem. (Leipzig) 249, 359 (1972) 25. Y. PAQUINAND W. FOtlST, Int. J. Chem. Kinetics 5, 691 (1974) 26. Copies of high resolution spectra have been kindly provided by N. Basco, A. B. Callear and G. Herzberg 27. G. HERZBERG"Molecular structure and Molecular Spectra I I I " Van Nostrand, Toronto 1966 28. D. PAaKES,private communication 29. In the work of Callear and Metcalfe (Ref.9), a band in this region found with oscillator strengths of 2' 10-2 This and some other results of this work have not been taken into account here since most of the calculations had been performed before these results came to our knowledge. They have only a minor influence on the computations for maximum absorption. 30. C. T. BOWMANXV Symposium (International) on Combustion Tokyo 1974, The Combustion Institute, Pittsburgh 1975 p. 869; T. Tsuboi and H. G. Wagner ibid p. 883; T. A. Brabbs and R. S. Brokaw ibid p. 893 31. D. M. GOLDEN AND S. W. BENSONChem. Rev. 69, 125 (1969) 32. W. A. Crtvpr~, J. Chem. Phys. 48, 2337 (1968) 33. Trl. JusT, private communication, finds for this process k > 3' 108 cm 3 mol -I s -1 at 2300 K, which is not too far from our measured rates. 34. J. T~OE, Ber. Bunsenges. Phys. Chemie 78, 478 (1974), and to be published 35. In the calculations for Ref. 16 Ea~ was found to be temperature dependent and it mirrored AU(T) for the reaction. Near 1400 K, (E,~ E o ) / k T = - 0 . 2 5 (-0.61) for C 2 H 6 (C~D6) dissociation. 36. J. O. HIRSCHFELDER,C. F. CURTISS,AND R. B. Bird9, Molecular Theory of Gases and Liquids, Wiley, New York 1954 37. J. TaOE, Ber. Bunsenges. Phys. Chem. 77, 667 (1973) 38. M. QuAcK, Ant) J. TROE, in "Reaction Kinetics,' ed. P. G. Ashmore (Specialist Periodical Reports), The Chemical Society, London, 1977, Vol. 2, p. 175

UV ABSORPTION

959

COMMENTS John N. Bradle~t, Universitg of Essex, England9 You mentioned that you find a rate constant for the C H 3 + CzH6--~ C H 4 + C 2 H 5 reaction lower than that obtained by Clark, Izod and Kistiakowsky. Measurements of this rate constant have recently been reported by Pacey and Purnell (Ref. 1) and by Bradley and West (Ref. 2) which also fall below this value but are still well above any extrapolation from the low-temperature work. It would be helpful to know whether your result is consistent with the later findings.

REFERENCES 1. PAcEY P. D., *No PURNELL, J. M.,: J. Chem. Soc. Far. I, 68, 1462 (1972). 2. BnADLEY J. M., AND WEST, K. O.,: ibid 72, 558 (1976).

Sidney W. Benson, Universitg of Southern California, USA. Can the authors please say a bit more about how they avoided the problem of metathesis of C H a + C 2 H 6 ----~C H 4 + C z H s ?

Authors" Reply1. The largest value presently discussed for the rate coefficient of the metathesis reaction C H 3 + C2H6----~ C z H 5 + C H 4 appears to be k M = 5.9 9 10 -13 cm 3 s -1 at 1350 K (see ref. 11). Since during the initial reaction stages relevant for the evaluation of our experiments [C a H6] ~< [CH3] , this reaction cannot compete with the recombination reaction, which is faster by a factor of 100 in the high pressure limit and by more than a factor of 10 at the lowest densities of our experiments. Furthermore, our experiments on methyl radical disappearance above 1500 K, which is not due to recombination (see section 3.5), indicate by extrapolation to 1350 K, that k M is really a factor of 4 --- 2 (and possibly more) lower than found by Clark et al. This is in line with the other recent findings (Pacey and Purnell, Bradley and West). Although this should be taken to be a rough, qualitative estimate, it underlines that any influence of the metathesis reaction on methyl dissappearance is negligible under the conditions of our recombination experiments.

D. M. Golden, SRI, USA. We find that an RRKM calculation based on a freely rotating Gorin model placed at an average centrifugal maximum (4.3A) shows the correct temperature dependence in the

high pressure limit and comes within a factor of ~ 2 of fitting the data absolutely. Hindering the rotation to take into account the van der Waals interactions of the H-atoms yields a fit within experimental error of the ethane decomposition fall-off, the high pressure recombination, and (kE) from chemically activated ethane.

Authors" Reply. In the limit of a loose activated complex ("Freely rotating Gorin model") conventional RRKM theory in the high pressure limit placing the transition state at the centrifugal maxima, phase space theory, and the statistical adiabatic channel model (which comprises the other two theories as particular cases) become equivalent; for a discussion of this point see ref. 1 below, and ref. 16. In this limit, the rate coefficient for methyl radical recombination takes the particularly simple form: k~ =

kT 9 Q~T ( C H 3 )

" 0.5

9 Q~.t

h 9 K~-1. Q ~ ( C 2 H 6 )

(1)

where Q~r is a rovibrational partition function (including symmetry corrections) and Q~e,t is: Q .... ~' = ~ (2l + 1) exp ( - Vm~ ( l ) / k T ) /=o

(2)

which is evaluated from the centrifugal maxima of the relative rotation of the two methyl fragments. Evaluating these expressions properly (for the molecular parameters see appendix of ref. 16) one finds poor agreement with experiment, the calculated rate coefficient at 1400 K being larger by~a factor of 6.5 than our experimental result. This is far outside the experimental error. Although it is always possible to fit the experimental results b y a Gorin type model by adjusting Q~ent (this can be done either by computing the reduced moment of inertia at some fixed appropriate C - - C b o n d extension, or by choosing a "suitable" electronic potential function), we do not think that this is a physically reasonable procedure. Rather, we believe that the methyl radical recombination does not correspond to a completely loose activated complex. The adiabatic channel model describes the situation in terms of coupled hindered internal rotations, with the maxima of all channels being taken at their individual locations 9 We give, for convenience, a short summary of experimental and theoretical results on methyl radical recombination, including the loose activated complex model:

960

KINETICS O F E L E M E N T A R Y REACTIONS 3. M. Quack had J. TROE, Ber. Bunsenges. physik. Chem, 80, (1976) to be published.

k ~ / l O - n c m 3 s -1 300 K

800-900 K

1300 K1400 K

Experiment

4.8

3.6

2.9

RRKM (ref. 17) Adiabatic channel model (ref. 16) Minimum density of States 2 Maximum free energy a Loose activated complex (Gorin model)

2.2

10.6

21.1

5.1

5.0

4.8

3.6

6.5

8,1

4.6

6.2

6.2

12.7

17.1

19.0

Finally, we should like to point out that one must carefully distinguish between a fit of experiments and a theoretical prediction. It is certainly possible to fit the recombination rate coefficients, which are approximately linear functions of T, by an~ two parameter representation (Many RRKM-models will do, since they contain at least this number of free parameters). However, to obtain good theoretical predictions in the long run, one should try to develop detailed models w h i c h correspond as closely as possible to physical reality (e.g. the statistical adiabatic channel model).

REFERENCES 1. M. QUACK a.'~DJ. TRoE, Ber. B unsenges, physik. Chem. 79, 170 (1975). 2. W. L. HasE, J. Chem. Phys. 64, 2442 (1976).

D. B. Olson, University1 of Texas, USA. We have measured the rate of ethane decomposition from 1500 to 2200 K at total densities of 2 x 10 -6 tool cm -a using the laser schlieren technique in incident shock waves. These pressure-dependent rate data are strongly curved on an Arrhenius graph, showing an increase of two decades in the falloff from the accepted high pressure rate over this temperature range. Preliminary corrections of these dat a to high pressure limiting rate constants were performed using the falloff data of Gliinzer et al., 1 extrapolating to lower densities using a bimolecular approximation, and to higher temperatures using the equation t~ = PI ( T2 / T1) s, where S =- E ~ib/ RT. The results obtained in this manner agree very well with the ethane decomposition rate 2 extrapolated from 950 K and with the present methyl recombination rate constant.

REFERENCES 1. GIS~ZER, K., QUACK,M., aNDTrloE, J.: Chem. Phys. Lett. 39, 304 (1976). 2. LIN, M. C., Ar
2115 (1967). Authors" Reply. It is gratifying that your dissociation data are in agreement with our recombination and dissociation measurements. Since you have used a very rough extrapolation procedure, it would be interesting to obtain a careful extrapolation of your data to the high pressure limit, e.g. by the method of ref. 37 in our paper.