Reaction rates of atomic oxygen with straight chain alkanes and fluoromethanes at high temperatures

Volume 204, number 3,4

19 March 1993

CHEMICAL PHYSICS LETTERS

Reaction rates of atomic oxygen with straight chain alkanes and fluoromethanes at high temperatures Akira Miyoshi a, Kenji Ohmori b, Kentaro Tsuchiya c and Hiroyuki Matsui a ’ Department ojReaction Chemistry. The Universityof Tokyo, 7-3-I Hongo, Bunkyo-ku, Tokyo 113, Japan b Research Instilutefor Scientific Measurements, Tohoku University,2-l-l Katahira, Aoba-ku, Sendai 980, Japan ’ NationalInstitute for Resources and Environment, 16-3 Onogawa. Tsukuba 305, Japan Received 29 October 1992; in final form 10 December 1992

Rates of reaction of atomic oxygen (‘P) with straight chain alkanes (C&5) and fluoromethanes (CHP and CHF,) have been measured at temperatures above 850 K by a laser flash photolysis-shock-tube technique coupled with atomic resonance absorption spectrometry. Measured rate constants agreed well with a recent TST calculation for O+CHa and O+CzH,. However, a smalldeviation from the TST calculation was found for 0+ C,HI and larger alkanes. Preferable modified Anhenius expressions for these reactions are presented. A good Evans-Polanyi correlation was found for the reactions investigated in the present study.

1. Introduction Reactions with atomic oxygen (3P) are important primary steps of hydrocarbon oxidation in combustion systems [ I]. The reaction of 0 + CH4 has been studied extensively up to 2200 K and several hightemperature measurements have -been reported for 0 t C2H6 [ 2,3 1. However, no (or very limited) experimental information is available for the reactions of larger alkanes above 700 K [ 2,3]. Recently, Cohen and Westberg evaluated and recommended the rate constants for 0 + alkanes up to 2000 K [ 31. Because of the lack of experimental data at high temperatures, they used transition-state theory (TST) to extrapolate low-temperature data [ 41, The main purposes of the present study are: ( 1) providing direct rate data at high temperatures, and (2) evaluating the validity of the TST calculation. The lack of high-temperature data for these reactions is mainly due to the experimental difficulty in the conventional shock-tube technique, in which oxygen atoms are generated by the thermal decomposition of N20, which is, however, slower than the reactions of interest and, in some cases, also slower than the thermal decomposition of large alkanes. Under such conditions, observations become insensitive to the reactions of interest and side reactions cannot be

neglected. The development of (laser) flash photolysis-shock-tube technique [ 5-71 enabled us to overcome these difficulties, since the oxygen atoms can be generated in a very short time scale at arbitrary temperature ranges (in principle). In the present study, using this technique, rate constants have been measured for the reactions of atomic oxygen with straight chain alkanes, 0+CH,+OH+CH3,

(1)

OtCzH6+OH+CzH5,

(2)

0 t CSHB+OHt C,H, ( l-C3H7 or 2-&H,) ,

(3)

0+ I~-C~HI,,+OH+C,H,

( l-C4H9 or 2-C4H9) ,

(4) 0tn-CSH,2+OH+CSH,, (I-C,H,,,2-CSH,,,or3-C,H,,),

(5)

and with fluoromethanes, OtCH3F-+OH+CH,F,

(6)

0+CHF,+OH+CF3,

(7)

at temperatures above 850 K. Experimental results are compared with the TST calculation. The effect of

0009-2614/93/$ 06.00 D 1993 Elsevier Science Publishers B.V. All rights reserved.

241

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chain length of alkanes and tlte effect of fluorine atom substitution are discussed.

2. Experimental A 5 cm inner diameter, 4 m long diaphragmless stainless-steel shock tube was used for present experiments. Details of the apparatus have been described elsewhere [ 71. Sample gas mixtures of an atomic oxygen precursor and a reactant (alkane or fluoromethane) diluted in Ar were irradiated by an ArF excimer laser ( 193 nm ) after 100 ps delay to the arrival of reflected shock wave at the observation port. Oxygen atoms were generated by the photolysis of SOr or NO, S02fhu(

193 nm)-+O+SO

NO+hz~( 193 nm)-+O+N.

,

(8)

(9)

When NO was used as a precursor, its concentration was kept high enough so that the reaction NtNO+OtN2

(10)

completes much faster than the reactions to be measured. The laser light was introduced to the shock tube through a suprasil quartz window located at the end of the shock tube. The intensity of the laser light was varied from 0.6x lOI to 3.1 x 1016photons cme2 so that the initial concentrations of oxygen atoms were kept smaller than one fifteenth of that of the reactants. Under such conditions, the estimated contribution of secondary reactions (e.g., OtOH, O+CH,, etc.) was less than 10%. Atomic resonance absorption spectrometry (ARAS) was used to monitor the 0( ‘P) atom concentrations. A microwave discharge of 1% 0, in He was used as a light source. Triplet resonance lines around 130.6 nm were separated with a 20 cm monochromator and detected by a solar-blind photomultiplier (Hamamatsu R976). Transient ARAS signals were recorded with a storage oscilloscope. An example of an oscillogram trace of ARAS signal is shown in fig. 1. After a correction for the nonLambert-Beer behavior of the ARAS signal [ 7 1, the time profiles of the oxygen atom concentration were fitted to a single exponential function with a leastsquares method. In some ARAS signals shown in fig. 242

-300 -x0

-100

0

mxo3334005006007M)

Time I J.IS Fig. 1. An example of an ARASsignal. Sample gas: n-butane (60.1 ppm)/SO1 (204 ppm)/Ar; PI=50 Torr; temperature=968 K; laser intensity = 1.7x 1016photonscmm2.

1, the absorption did not decay to the zero level, mainly because the Iater part (2 400 ps) of the signal was influenced by the reflected compression wave from the contact surface. However, blank tests (without laser light) showed that the rise of baseline absorption was negligibly small (smaller than 5% of the peak absorption) during the time region used for the analysis (typically O-200 us). Ar and O2 (Nihon Sanso; 99.9999% and 99.99%, respectively) were purified by passing a trap kept at - 120°C. n-pentane (Wako Chemicals; 99%), n-butane (Takachiho; 99.5%), and CHFX (PCR; 99%) were purified with trap-to-trap distillation. SOz, NO, methane, ethane, propane (Takachiho; 99.0%,99.9%, 99.95%, 99.7%, 99.9%, respectively), and CH3F (PCR; 99%) were used as delivered. All errors indicated with experimental values are at the level of two standard deviations.

3. Results Measured rate constants as well as the experimental conditions are summarized in table 1. No systematic difference was indicated between two precursor molecules (SO, and NO). At temperatures above 1250 K, an unexpected rise of absorption was found in ARAS during the measurements for reaction (7). The cause of this is not clear, but it may be the absorption of the products of subsequent reactions. The measurements were limited below 1330 K, where this

Table I Summary of measurements Temp. (K)

for O+alkane/fluoromethane Rate constant (IO-‘* cm3 molecule-’

OtCH,

980 1098 1219 1234 1367 1374 1399 1404 1522

OtClHh

938 967 1101 1111 1152 1172 1177 1192

0 t C,H,

0+&H,,

Otn-C5H,2

7.36kO.47

[RH] b,

110 101 30 100 81 30 80 76 70

867 154 154 867 154 154 154

50 42

264 151

30 30

151 264 151 151 264 151

30 30 30 30 50

154 154

939 1111 1133 1152 1153 1196 1223 1247 1263

11.8f2.1 11.8? 1.1 12.5k2.4 15.4+ 1.4

50 50 30 50

16.OIL3.9 16.9k2.7 17.9k4.1 28.924.0

30 30 30 27

896 931 968 1020 1080 1118 1138

21.220.5 18.8kO.5 24.3kO.7 26.8f0.9 32.5? 0.9 43.0+_ 1.2 35.5f2.5

66 59 50 45 36 31 31

60.1 60.1 60.1 60.1 60.1 60.1

852 942 1002

21.6d10.6 25.2* 0.5 29.9kO.9 28.0? 1.0 26.6kO.8 35.3f5.6 30.8f0.9 44.62 1.2 43.4* 1.2 41.5&0.9 26.121.4 27.22 1.5 30.2f 1.3 3l.lk1.8 43.7f2.1 46.9rf: 1.9

50 50 so

98.6 98.6 98.6

32 50 32 42

98.6 186 98.6 186 186 98.6 98.6 36.3 36.3 36.3 36.3 36.3 36.3

1034 1040 1061 1071 1117 1127 1141 900 950 967 1003 1091 110.5

PrC’

(ppm)

[Pr] *) (ppm)

s-‘)

0.692kO.052 1.62f0.05 1.83&0.37 2.91f0.15 3.62kO.25 5.40f0.93 6.82f0.26 5.69kO.27 9.52kO.31 3.49 f0.47 3.77kO.85 7.51?1.16 6.50+0.81 11.3k2.5 11.1+1.0 8.32+0.66 12.92 1.0

a) PI (Torr)

30 30 32 67 60 58 53 50 42

SO2 so2 SO2

50.0 105 105 50.0 105 105 105

1.1 1.2 2.9 1.2 1.0 2.9 1.4 I.0 1.5

so2 so2 so2

50.0 50.0 50.0 50.0

2.9 2.9 2.9 2.9

so2

50.0 50.0 50.0 50.0

2.9 2.7 2.9 2.7

so* so2 so2

so2 SO2

so*

a

so2 so2 SO2

207 200 207

so2 so2

199 207

so2 so2 so2 so2 SO2

199 200 199 207

60.1

105 105

Laser intensity (10’6 photons cm-*)

100

50.0 100 50.0 50.0 50.0 100

3.0 3.0 3.0 2.9 3.0 3.0 3.0 3.0 3.0

so2

204 204 204 204 204 204

1.3 1.4 1.7 1.8 1.9 2.6

so2

204

1.2

284 284 284 284 143 284 143 143

1.4 2.9 1.5 1.5 3.1 3.0

so*

so2

so2 so2 so2 so2 so2

so2 so2 so2 so2 so2 so2 so2 so2 332 so2

NO NO NO NO NO NO

50.0 100

284 284 1430 1430 1430 1430 1430 1430

3.1 3.1 1.5 3.0 2.6 2.5 2.5 2.5 2.5 2.9

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CHEMICAL PHYSICS LETTERS

Volume 204, number 3,4 Table 1 Continued Temp. (R)

Rate constant ( 10-‘2cm3

molecule-’ O+CH,F

0+CHF3

P, a’

[RH] b,

(Toa)

(PPm)

Pr C)

[Pr] d, (rwm)

s-‘)

2.33 k 0.20 2.71 kO.25 3.22k0.41

999 999 999 999 999 999 999 999 999

1354 1447 1568

3.54f0.28 3.52kO.40 3.02 f0.48 5.12kO.50 5.66 k 0.90 6.56 + 0.61

30 30 30 30 30 30

500 999 999 500 999 999

956 974 1005 1047 1085 1142

0.0224+0.0019 0.0487 k 0.002 I 0.0313f0.0027 0.0630 2 0.0050 0.094lk 0.0037 O.l28+0.008

51 60 50

6130 6130 6130 6130 6130 6130

1211 1270 1328

0.204+0.018 0.418iO.028 0.427 k 0.047

43 38 33 31 31 30

0.570+0.138 1.0210.15 0.874f0.115 0.767+0.159 1.84kO.15 1.68k0.17

1152 1239 1267 1271 1304 1319

(10’6

photons cm-‘) 44 40 40 50 40 30 40 30 30

923 985 991 999 1140 1143

Laser intensity

6130 6130 6130

NO NO NO NO NO NO NO NO NO NO

2570 2570 2570 2570 2570 2570 2570 2570 2570 2480

2.6 1.5 2.5 2.6 2.6 2.5 2.6 1.4 1.3 1.1

NO NO NO NO NO

2570 2570 2480 2570 2570

1.4 0.6 1.1 0.6 1.3

SO2 SO2 SOZ

201 201 201

1.2 I.0 1.0

so2 SO2 SC% SO2 SO2 SO2

201 201 201 201 201 201

1.0 1.2 1.0 1.2 1.2 1.0

a1 Total pressure in the test section (I Torr= 133.322 Pa). b, Concentrations of alkane or fluoromethane in the test section. c) Precursor molecules used as oxygen atom source. d, Concentrations of precursor molecules in the test section.

absorption did not affect the analyses of the O-atom decay profile. To ensure the validity of the measurements for O+alkane, thermal decomposition of alkanes, reactions ( 1 1)-( 15) below, must be carefully considered because the subsequent reactions ( 16)-( 19) (see below) rapidly consume oxygen atoms, CH,+M-+CH,+H+M,

(11)

CzH, +M+2CH, +M ,

(12)

&HO tM-+CH3+CzH5+M,

(13)

n-C4HrotM-tCH3+n-CaH,+M,

244

(Ida)

n-C,H,, +M-+2CzH5 +M ,

(14b)

n-C5Ht2 tM+CH3 t n-C,H, +M ,

(15)

0 t CH3-+products ,

(16)

0 t CzH5-*products ,

(17)

Otn-C3H,-+products,

(18)

O+n-C4Hg +products .

(19)

Concentrations of alkyl radicals were estimated under each experimental condition using published rate parameters for reactions ( 1l)-( 15) [ 1,8,9]. Then the consumption of oxygen atoms by alkyl radicals during the time region used for the analysis (0-2~, typically O-200 us) was evaluated using the rate con-

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CHEMICAL PHYSICS LETTERS

stantsfor reactions (16)-(19) [2,10,11] #l, which were assumed to be temperature independent. When the condition

K 1200

T I Sal

L400

IllI

I

1000

I

900

I

[0] consumed by radicals < o ol [ 0] consumed by alkane

’

was satisfied, the datum was considered to be reliable. The products of reactions ( 16)-( 19) may also react rapidly with oxygen atoms. Although the mechanisms for such subsequent reactions have not been established at high temperatures, a severe criterion ( < 0.0 1) was used for the evaluation to minimize the effect of the side reactions.

\

tC-141I 6

4. Discussion

4

I

7

I

l

0 T-t I

Arrhenius plots for reactions ( 1 )- ( 5) and for reactions (6) and (7) are shown in figs. 2 and 3, res’ The rate constant for reaction ( 19) was estimated by the correlation of reaction rate constants with the ionization potential of radicals [ 121with IP(n-C,HP)=8.01 eV.

lo-’

7

IIll

la0

T/K 1200

I

I

loo0

I

900

I

in

a5 10-l f 3 s lo-'

Fig. 2. Arrhenius plot for the O+alkane reactions. Present results: (0) OfCHd, (0) 0+C2Hs, (A) O+C,Hs, (A) O+n&HI,,, (Cl) O+n-CSHj2. Previousdata: (a) Mahmudet al. [ 131 (OtC2Ha), (---)Tanzawaetal. [14] (OtC,H,).Dottedlines indicate TST calculation by Cohen and Westberg [ 41, and full lines indicate results of the fitting of present data to simple Arrhenius expression.

I

I

9

I

10

4

I

11

I

1O-4K'

Fig. 3. Arrhenius plot for the O+fluoromethane reactions. Present results: (0) 0 tCHrF, (0) OtCHFI. Present results for 0+ CH4are indicated by a broken line for comparison. Full lines indicate results of the fitting of present data to simple Arrhenius expression.

spectively. For comparison, the results of the TST calculation [4] are also shown in fig. 2. Present results for 0 t CH4 agreed well with the TST calculation and with previous measurements [ 2,3]. Recent measurements for 0 + CzH6 by Mahmud et al. [ 141 are also shown in fig. 2. They agree well with present results. A steep rise of their rate constants above 1200 K may be due to the thermal decomposition of C2H, as discussed above. The results for 0 t C3Hsseem to agree with the measurements by Tanzawa et al. [ 141 while the overlapping temperature range is narrow. For reactions of O+n-C,HIo and Otn-&HI*, no previous measurement was found above 650 K. A small deviation from the TST calculation was found for the reactions of C3Hs and larger alkanes, although the discrepancy is smaller than the uncertainty factor ( = 2) in the TST calculation noted by the authors. Therefore, the parameters of the modified Arrhenius expression (k= AT” exp( - EJRT) ) for these three reactions were re-evaluated using the present results and previous low-temperature data [ 14-171 (table 2). For reactions (1) and (2), the parameters (A, n, E,) in table 2 are those evaluated by the TST calculation. Also, the simple Arrhenius expressions (k=Aexp( -EJRT)) for reactions (l)245

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19 March 1993

Table 2 Arrhenius parameters for 0+ RH reactions Reaction

k=AT”exp( -E,/RT)

k=A exp( -E,/RT) log,cd =I

Kl (k.Jmol-‘)

log,& ‘)

temp. range (R)

logid ‘)

n

J%

temp. range

(kJ mol-‘)

(K)

O+CHdC’ 0+C2HsC) O+C,Hs 0+ n-CdH,,

-9.08iO.46 -9.00?0.56 -9.29kO.58 -9.27kO.44

58.2f 11.0 44.7& 11.8 34.1+ 12.7 25.028.5

0.19 0.14 0.15 0.10

980-1520 940- 1190 940-1260 goo- I 140

- 17.09 -17.23 -18.07+0.27 -20.39LO.19

2.2 2.4 2.56f0.99 3.43kO.90

31.8 24.4 13.2t4.9 9.7k3.8

420-1520 500-l 190 300-1260 250-I 140

0+ n-CrH,t

-9.45k0.32 -9.55iO.20 -9.12kO.63

20.2k6.2 47.5 k4.5 81.7+ 13.2

0.11 0.12 0.21

850-I 140 920-1570 960-1330

-17.05+0.12

2.37kO.52

11.4t-2.2

250-l 140

O+CHJF O+CHFJ

a) A is in units of cm3 molecule-’ s-‘. b, Fis the uncertainty factor (at Zalevel) for the rate constants evaluated by the Arrhenius expression in specified temperature range. =) Parameters for the modified Arrhenius expression (A, n, E,) for these reactions are unchanged from results of the TST calculation 141 since the present measurements agree well with them.

(7) are listed, which are valid over the present experimental temperature ranges. For the reaction of 0 + CH3F, no other direct measurement has been reported. For 0+CHF3, a previous measurement at lower temperatures (390-620 K) [ 18] has been reported. Since rate constant measurements at lower temperatures are limited, the modified Arrhenius expression was not evaluated for these reactions. The observed rates of reaction were smaller than the TST calculations for C3Hs, but vice versa for n&H,, and n-CSH,,. The rate constant for 0 +CaHs becomes closer to that for 0+&H, when the temperature increases. This trend may be ascribed to a steric effect such that the secondary hydrogens of C3H, become difficult to be abstracted (i.e. masked by the primary hydrogens) at high temperatures due to large translational or internal energy, which was not treated in the TST calculations. In other words, the sum rule assumed in the TST calculations (i.e. the overall rate constants can be expressed by the sum of reactivity of primary, secondary and tertiary hydrogens calculated by TST) may not hold for the reactants with many reactive sites such as large alkanes at high temperatures. An empirical relationship between activation energy and enthalpy of reaction (Evans-Polanyi rule [ 191) has been tested for the reactions of OH +alkanes [ 201 and OH t fluoroalkanes 1211 at around room temperature. The Evans-Polanyi-type

246

rule was examined also for the reactions of 0 + allcanes [ 171. However, these reactions are much slower than OH t alkanes at low temperatures, and may have larger uncertainties. Thus, it seems meaningful to reinvestigate this rule for the reactions of 0 + alkanes at high temperatures. The E, for “secondary” hydrogen abstraction was evaluated as follows: By assuming the additivity rule [ 221, the rate constant for 0+ alkane can be expressed as a sum of the rate constants for O+each C-H bond in the alkane. Then the rate constants for secondary hydrogen abstraction for C3 and larger alkanes were estimated by subtracting the rate constants for C2Hs. By plotting these subtracted rate constants versus the number of the secondary hydrogen in alkanes, the rate constant for O-l-“one secondary C-H bond” was evaluated at each temperature. An Arrhenius plot for these rate constants gave the activation energy for “secondary” hydrogen abstraction (as an average for C3-Cs straight chain alkanes). As shown in fig. 4, a correlation between &, and AH was found for the reactions studied here at high temperatures. The diffcrencc between &( secondary) (17.2 kJ mol-i) and E,(primary) (44.7 kJ mol-‘) is large compared to that obtained at lower temperatures [2], E,(primary)=27.4 kJ mol-’ and E,(secondary)=20.3

kJ mol-‘.

This must be ra-

tionalized by detailed theoretical investigations, but it should be noted that the uncertainty in the

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CHEMICAL PHYSICS LETTERS

9 20 I/

b secondary

0”“““““’ -30 -20

-10

0

10

20

AH02g,I kJ nxd Fig. 4. Evans-Polanyi plot for the O+alkane/fluoromethane reactions. Straight line indicates the results ofa linear least-squares fitting. Thermochemical data are from refs. [ 23,241. For the evaluation of E, for “secondary” hydrogen abstraction, see text.

& (secondary) obtained here is large because the additivity rule assumed here is a crude assumption. Also, it is only an approximation that the rate constant for 0+ C2H6 is equal to those for O+primary C-H sites in larger alkanes. The E, obtained here was found to correlate also with C-H stretching frequency of alkanes (2992, 2950, and 2920 cm-’ for CH4, C2Hs, and secondary C-H in C3H,) [25,26] and fluoromethanes (2974 and 3035 cm-’ for CH3F and CHF,) [ 27,281. Fluorine atom substitution to methane is known to decrease the C-H bond energy [D(C-H)298] at mono- and di-substitution but increase it at tri-substitution (D (C-H )298=438.6, 418.4, 422.6, and 444.8 kJ mol- ’ for CH4, CH,F, CH2F2, and CHF3, respectively) [ 23,241. This anomalous ordering has been questioned [ 291, but has been supported by an Evans-Polanyi-type correlation for the reactions of OH + fluoroalkane [ 211. The correlation of D( CH)zgs with E, found in the present study also supports the anomalous ordering of D( C-H)298.

References [ I] J. Wamatz,

in: Combustion chemistry, ed. W.C. Gardiner Jr. (Springer, Berlin, 1984) p. 197. (21 J.T. Herron, J. Phys. Chem. Red. Data 17 ( 1988) 967.

19 March 1993

131N. Cohen and K.R. Westberg, J. Phys. Chem. Ref. Data 20 (1991) 1211. [4] N. Cohen and K.R. Westberg, Intern. J. Chem. Kinet. 18 (1986) 99. [5 1J. Ernst, H. Gg. Wagner and R. Zellner, Ber. Bunsenges. Physik. Chem. 82 (1978) 409. [6] J.W. Sutherland and R.B. Klemm, Proceedings of the 16th International Symposium on Shock Tubes and Shock Waves, Weinheim (1988) p. 395. 171M. Koshi, M. Yoshimura, K. Fukuda, H. Matsui, K. Saito, M. Watanabe, A. Imamura and C. Chen, J. Chem. Phys. 93 (1990) 8703. [8] A.M. Dean, J. Phys. Chem. 89 (1985) 4600. [ 9] D.R. Blackmore and C. Hinshelwood, Proc. Roy. Sot. A 36 (1962) 36. [ 101I.R. Slagle,D. Sarzynski and Il. Gutman, J. Phys. Chem. 91 (1987) 4375. [ 111I.R. Slagle, D. Sarzynski, D. Gutman, J.A. Miller and C.F. Melius, J. Chem. Sot. Faraday Trans. II 84 (1988) 491. [ 121A. Miyoshi, H. Matsui and N. Washida, J. Phys. Chem. 93 (1989) 5813. [ 131K. Mahmud, P. Marshall and A. Fontijn, J. Chem. Phys. 88 ( I988 ) 2393. [ 14] T. Tanzawa, D.G. Keil and R.B. Klemm, presented at the 2nd Chemical Congress of the North American Continent, Las Vegas (1980) paper 281, Phys. Chem. Div. [ 15] S.P. Jewell, K.A. Holbrook and G.A. Oldershaw, Intern. J. Chem. Kinetics I3 ( 198I ) 69. [ 16 ] D. Saunders and J. Heicklen, J. Phys. Chem. 70 (1966) 1950. [ 171J.T. Herronand R.E. Huie, J. Phys. Chem. 73 (1969) 3327. [ 181J.L. Jourdain, G. LcBras and J. Combourieu, J. Chim. Phys. 75 (1978) 318. [ 19] M.G. Evans and M. Polanyi, Trans. Faraday Sot. 34 ( 1938) 11. [20] N. Cohen, Intern. J. Chem. Kinetics 23 (1991) 397. [2 I ] J.-P. Martin and G. Paraskevopoulos, Can. J. Chem. 6 1 (1983) 861. [22]F.P. Tully, J.E.M. Goldsmith and A.T. Droege, J. Phys. Chem. 90 (1986) 5932. [23] JANAF thermochemical tables, 3rd Ed., J. Phys. Chem. Ref. Data 14 (198.5) Suppl, 1. [24] D.F. McMillen and D.M. Golden, Ann. Rev. Phys. Chem. 33 (1982) 493. [25] D.C. McKean, J.L. Duncan and L. Batt, Spectrochim. Acta 29A (1973) 1037. [26] D.C. McKean, S. Biedermann and H. Biirger, Spectrochim. Acta 30A ( 1974) 845. [27] H.J. Bernstein, Spectrochim. Acta 18 (1962) 161. [28] A. Ruoff, H. Biirger and S. Biedermann, Spcctrochim. Acta 27A (1971) 1359. [29] J.A. Kerr, Chem. Rev. 66 (1966) 465.

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