A resonance fluorescence kinetic study of oxygen atom+hydrocarbon reactions, V:O(3P)+neopentane (415–922 K)

Nineteenth Symposium (International) on C o m b u s t i o n / T h e C o m b u s t i o n Institute, 1982/pp. 3 9 - 5 0

A RESONANCE

FLUORESCENCE

KINETIC

STUDY

OF

OXYGEN

ATOM

+ HYDROCARBON REACTIONS, V: O(3p) + NEOPENTANE (415-922 K) J. V. MICHAEL, D. G. KEIL, AND R. B. KLEMM Brookhaven National Laboratory Upton, New York 11973 Absolute values of the rate constants for the reaction of O(3P) with neo-C~H~2 were determined directly with the use of the complementary techniques: flash photolysis (FP) and discharge flow (DF). The O-atoms were monitored via resonance fluorescence (RF) in both systems, allowing experiments to be carried out at very low [O]. Secondary reactions were averted in this way, and the rate data thus obtained were stoichiometry-free. The DF-RF experiments were performed over the temperature range, 427-922 K while those with the FP-RF apparatus were performed from 415-528 K. Over the common range of temperature the absolute rate constants were in excellent agreement. The:combined set of data from 415922 K is well described by kl = (1.52 --+ 0.28) • 10-1~ exp (-7143 • 196/RT) cm 3 molecule -~ s -l where R is expressed in cal mole -1 K-l and the errors are taken at the two standard deviation level (95% confidence). The bond energy-bond order (BEBO) method along with activated complex theory was applied to the title reaction, and satisfactory agreement with experimental rate constants was obtained.

Introduction

work was performed under excess [O] conditions, and the attenuation of ueo-CsHlz as a function of distance (time) was measured. Using this procedure they assumed the system to be free from stoichiometric corrections because it is unlikely that the parent hydrocarbon could be reformed by any process or could react competitively with reaction products. However, the Herron and Huie study required an accurate knowledge of absolute [O] for precise absolute k 1 determination. The present study was carried out with two well known methods both of which utilize atomic resonance fluorescence detection of O(3P). These are flash photolysis-resonance fluorescence (FP-RF) and discharge flow-resonance fluorescence (DF-RF). With both techniques [O] attenuation as a funtion of time is measured in the presence of excess neoC~H12. However, the detection technique is sufficiently sensitive that secondary depletion of atoms by homogeneous reaction with products is not significant. Indeed, experiments are performed to show this, thus demonstrating that the present results are free from stoichiometric corrections. We present results from measurements over the range in temperature of 415-922 K. The primary goal of this study is to compare the present results with those of Herron and Huie, 4 particularly over the common range of temperature in the two studies. In addition, the results of a theoretical calculation using the BEBO-ACT method are presented.

Increasing interest in hydrocarbon combustion has prompted renewed work on chemical mechanisms for high temperature hydrocarbon oxidation. t'~ In the past two to three years, several O(zP) + RH reaction rate constants have been determined in this laboratory over substantial ranges of temperature (-400-1100 K) in an attempt to further define the rate behavior for application in high temperature combustion. In this paper we give results for the reaction O(3P) + neo-CsH12 ~ (CH3)3CCH2 + OH

(1)

To date there have been only two absolute reaction rate studies of reaction (1). Wright3 obtained a value of 3.0 • 10- 15 cm3 molecule- 1 s- 1 at 303 K. Herron and Huie 4 report the only temperature d e p e n d e n t study: k l = (1.0 - 0.4) x 10 -1~ exp(-5802 + 278/RT)cm 3 molecule -1 s -1 (here and throughout the paper R is expressed in cal mole- 1 K- 1), They have determined the rate behavior from 276-597 K by means of the discharge flow-mass spectrometric (DF-MS) technique. The This work was supported by the Division of Chemical Sciences, U.S. Department of Energy, Washington, D.C., under Contract No. DE-AC0276CH00016. 39

40

ELEMENTARY REACTIONS II

Experimental

Results and Discussion

The rate constant for reaction (1) was studied by two direct and complementary techniques: (1) Flash Photolysis-Resonance Fluorescence (FP-RF); 5,6 and (2) Discharge Flow-Resonance Fluorescence (DFRF). v'8 Both techniques have been utilized in this laboratory in previous investigations, s-t~ so only a brief description will be given here. The FP-RF apparatus was used for rate measurements at five temperatures ranging from 415 to 528 K. The photodecomposition of O z with k > 160 n m (suprasil cutoff) served as the source of O-atoms. With this wavelength discrimination, the photodecomposition of the reactant, neo-CsHlz, was minimized. Pre-formed mixtures of buffer gas (80% Ar and 20% Nz) and 0 2 along with variable amounts of neo-CsH12 were flowed slowly ( - 1 - 5 cm s -1) through the reaction cell. This procedure replenished the cell contents between photoflashes, and therefore, no reaction product was allowed to build to levels sufficient to perturb the temporal profile of O-atoms. Also the presence of N2 served to rapidly deactivate the photolysis product, O(1D), to ground state O(aP) atoms. 1~ The DF-RF apparatus was used for rate measurements from 427 to 922 K, so the range of temperature overlap between the two techniques is substantial. O-atoms were generated upstream from the thermostated flow reactor by passing Oz diluted in the He carrier gas through a microwave discharge. Alternatively, atomic oxygen was generated by titrating N-atoms, produced from N2, with NO which was also introduced upstream from the flow reactor but downstream from the discharge. The latter procedure allowed for precise calibration, and also, when the NO was introduced through the movable probe, for the determination of the rate constant for wall destruction of O-atoms. After flow tube treatment with dilute HF, typical values of k w = 5 s -1 were readily obtained at any temperature. The sensitivity for detection of O atoms is about 109 atoms cm- 3 at a signal to noise ratio of one. Most experiments were performed with 5 x 101~ [O]o_< I x 10lz atoms cm -3. Neo-CsHIz was obtained from the API Research Project 588 (Carnegie-Mellon University) and was of greater than 99.997% purity. Gas chromatographic analysis revealed no detectable impurities, so the API purity certification is conservative. All other reagents except NO were of research grade and were used without further purification. O z was MG Scientific (99.995%); He, Ar, and N z were from Matheson (99.9999%, 99.9995%, and 99.9995%, respectively). NO was obtained from Matheson (99.0% purity) and was outgassed and vacuum distilled from 90 to 77 K before use. Only the middle one third was retained.

Since resonance fluorescence is such a sensitive technique, it was possible to perform all experiments under pseudo-first-order conditions. With either apparatus the [neo-CsH12]/[O]o ratios were always greater than 200. Therefore, with reaction (1) as the only removal process, O-atoms are expected to exhibit a logarithmic decay, as a function of reaction time, that is linearly dependent on kl[neo-CsH12]. However, before such an assertion can be made, other processes that could possibly perturb [O] have to be ruled out. In the present case, impurity levels are too low to cause significant perturbations. Also, as noted earlier, no products accumulate, and therefore, the only possible perturbing influences on [OJ are the initially formed radicals from the photoflash (FPRF experiment), the wall reaction (DF-RF experiment), or primary products from reaction (1) (both FP-RF and DF-RF experiments). The last possibility can be assessed by utilizing variable [O]o in otherwise identical experiments. This is accomplished in the FP-RF experiment with variable flash energy and in the DF-RF experiment by discharging larger concentrations of O 2 (or N 2 + NO). Initial experiments with the FP-RF apparatus revealed a small but detectable flash energy effect particularly at T < 458 K. For example a definite increase in the first order decay constant at 458 K was noted at flash energies greater than 40 J. Similar behavior was noted at the other temperatures, and therefore, care was taken to establish the lower range of flash energies over which no variation, outside experimental error, occurred. Under these low flash energy conditions, the depletion of [O] is then given by: ln([O]J[O]o) = -Kt,

(I)

where JOlt and [O]o are the O atom concentrations at time = t and time = 0, respectively, and are proportional to fluorescence counts. K is the experimental first-order decay constant and is determined from linear least squares analysis of the logarithm of fluorescence counts against time. Even with no secondary complications, K is still a composite since atoms can be removed by three processes: reaction (1); termolecular recombination with 02; and diffusion out of the viewing zone which is determined by the intersection volume of the photoflash, resonance lamp beam, and detector solid angle. The latter two loss terms were determined simultaneously (as K') and directly in experiments where [neo-CsH12] = 0. Thus, K' = kr[O2][M] + Kdiffu~ion, and then,

(II)

R E S O N A N C E F L U O R E S C E N C E K I N E T I C STUDY ~

41

TABLE I Rate data for the reaction of O(3P) with n e o p e n t a n e from flash photolysis-resonance fluorescence experiments

T/K

Neopentane/ mTorr

528

Oz/Torr

Pr~/Torr

3.00 100 3.03 100 3.03 100 3.03 100 3.00 50 2.98 50 2.98 50 0.60 30 142.6 0.60 30 142.6 0.60 30 142.6 0.60 30 -+ 1.6) • 10 -14cm 3 molec ~ s -~ -4.01 100 70.4 4.00 100 70.4 4.00 100 101.0 4.02 100 101.0 4.02 100 -0.40 100 136.6 0.40 100 136.6 0.40 100 136.6 0.40 100 -6.01 100 214.6 5.97 100 214.6 5.97 100 2.01 100 475.3 2.00 100 -+ 1.2) • 10 -14 cm a molec -1 s -~ -3.00 50 107.3 2.98 50 107.3 2.98 50 107.3 2.98 50 107.3 2.98 50 +- 0.34) • 10 -x4 cm 3 molec -1 s -l -4.01 100 101.0 4.02 100 101.0 4.02 100 -+ 1.36) • 10 -14 cm 3 molec -1 s -l -4.01 100 70.4 4.00 100 101.0 4.02 100 -+ 0.80) x 10 14 cm 3 molec-i s-1 --

44.3 44.3 44.3 -107.3 107.3 -

(k~)c = (18,4 498

-

(kl) c = (11.0 458

(kl) ~ = (5.65 440

(kl) ~ = (4.56 415

(k~)~ = (2.69

-

-

F.E./J

KS/s -l

kl s • 1014/ cm3molec -l s -1

57-60 17 34 73 46 27 60 94-98 60 98 135

62 207 206 218 94 479 469 137 605 613 594

_+ -+ -+ -+ _+ _+ _+ _+ -+ -+ _+

2 2 10 6 4 18 15 4 21 9 11

-17.9 -+ 0.5 17.8 -+ 1.6 19.3 -+ 1.0 -19.6 -+ 1.1 19.1 +- 1.0 -17.9 -+ 1.0 18.8 -+ 0.5 17.5 -+ 0.6

27-41 4 7 6 11 32-57 14 36 73 32-36 32 46 49-60 63

58 209 215 266 283 39 328 349 335 82 541 534 52 926

_+ _+ -+ _+ _+ _+ -+ +_ _+ • • • • -+

2 6 3 7 14 2 14 16 5 1 44 36 2 120

38-41 8 17 22 29

77 200 206 209 204

+ • _+ + _+

1 4 6 20 10

27-32 5 9

67 -+ 1 166 • 17 170 -+ 20

-4.47 -+ 0.81 4.65 +- 0.95

23-27 5 4

77 +- 1 124 -+ 2 136 _+ 8

-2.87 -+ 0.18 2.51 + 0.38

11.1 11.5 10.6 11.5 10.9 11.7 11.2 11.0 10.9 9.5

--+ -+ -+ -+ --+ -+ -+ -+ -+ -+-

0.6 0.4 0.5 0.8 0.6 0.7 0.3 1.1 0,9 1.3

m

5.44 5.70 5.84 5.61

+ -+ +-+

0.22 0.31 0.93 0.49

~Diluent gas was 80% Ar and 20% N~. S"Diffusion" data are averages of 3 or m o r e replicate runs. Errors for K are standard errors of linear least squares fits in most cases; however, a few runs w e r e analyzed graphically. E r r o r s in kl are propagated from standard errors in K's and concentration. ~Average at each t e m p e r a t u r e , the errors are estimated to be two standard errors (i.e., 95% confidence). K = kl[neo-CsH12] + K'

(III)

The bimolecutar rate constant for reaction (1) can then be calculated by r e a r r a n g e m e n t of Eq. (III),

k 1 = (K - K ' ) / [ n e o - C s H J .

(IV)

Table I lists the individual values of K, K', and the derived k 1 values at five t e m p e r a t u r e s ranging from

42

ELEMENTARY REACTIONS II 24

I

I

I

I

I

I

I

I

2.0

5.0

cence counts, d is the distance from the reactant inlet to the detector, and v is the linear flow velocity. The experimental first-order decay constant, kobs, was obtained by linear least squares analyses of first-order plots according to Eq. (V). The diffusion corrected first-order constant, kc, was then calculated by the equation,

T 2O ,v16 "6 E

~ t2 o

o ~.

8

-'G'

k~ = kobs(1 + kobsD/v2),

Q.

<-~- 4 0.2

0.5

1.0

I0.0

[0]0/IOII otoms cm -5

FIG. 1. Values of the apparent rate constants, k]pp, with the DF-RF apparatus for O(3p) + neoCsHx~ as a function of [O]o. T = 470 K, PT = 1.90 Torr, v = 990 cm s-L The limiting low [O]o rate constant is 7.1 x 10-14 cm3 molecule -1 s-L The abcissa is logarithmic for clarity of display. 415-528 K. Since these results were obtained under limiting low photoflash energies and with flows which were sufficient to replenish the cell contents between flashes, we assert that secondary complications were not contributing. The derived bimolecular rate constants then refer only to reaction (1). The temperature dependence of these results from linear least squares analysis at the one standard deviation level is, k 1 = (1.78 +- 0.69) x 10-1~ exp(-7268 +-. 302/RT) cm 3 molecule -1 sec -1. Initial experiments with the DF-RF apparatus also revealed decay constant sensitivity to [O]o. The results were strikingly similar to those found in the FP-RF experiments. Typical results are shown in Fig, 1 where the apparent bimolecular rate constant is plotted against the logarithm of [O]o. At [O]o ~ 1012 atoms cm -3 the apparent bimolecular rate constant is higher than the unperturbed value by more than a factor of two. Also distinct nonlinearities in first-order plots were noted for these high [O]o experiments. This behavior clearly supports the FP-RF results and suggests that a fast secondary reaction between O-atoms and a product radical from reaction (1) can become important at high [O]o. Whatever that reaction may be, its perturbing effect can clearly be eliminated at [O]o 5 x 101~atoms cm -3. Similar experiments at each temperature established the [O]o upper limit that could be used before secondary complications become significant. All experiments were then carried out under these low [O]o conditions. Depletion of [O] can then be attributed to reaction (1) and wall reaction in the DF-RF experiments. The kinetics obey a pseudo-first-order rate law and the temporal behavior of [O] is given by, ln[O]a = -kob~(d/v) + ln[O]o,

(V)

where [O]a and [O]o are proportional to fluores-

(VI)

where D is the diffusion coefficient for O-atoms in He. s'l~ Generally the maximum correction amounted to less than ~15%. Then k~ is related to k I through kc = kl[neo-CsH12 ] + Akw,

(VII)

where Ak w is the difference betwen wall termination constants for O-atom removal with and without added neo-CsH12. The bimolecular rate constant, kl, was determined from linear least squares analyses of the data according to Eq. (VII), and the results are given in Table II. Three determinations of k 1 were made with the "ON/OFF" method originally described by Westenberg and deHaas. 11 With this method the attenuation of [O] is given by ln([O]a/[O]~) = - kob~(d/v)

(VIlI)

where [O]~ and [O]a (both proportional to fluorescence counts)are measured at probe distance, d, without and with neo-CsH12 being present, respectively. The method eliminates the wall reaction process from the analysis. Examples of data plotted according to Eq. (VIII) are given in Fig. 2 where strict first-order behavior is noted over one and a half to three decay lifetimes. The observed firstorder decay constants are obtained from linear least squares analyses of such plots, and the resulting values are corrected for diffusion according to Eq. (VI). The k c values are then plotted against [neoCsHlz] as shown in Fig. 3, and the linear least squares slope is then k 1 since, kc = kl[neo-CsH12 ].

(IX)

The T = 869K "ON/OFF" results are shown specifically in Fig. 3 along with other results which were obtained by means of Eq. (VII). The reason for the comparison between the "ON/OFF" method and that described by Eq. (VII) is to experimentally show the unimportance of the wall reaction process in comparison to reaction (1). This is demonstrated further in Table II where nearly all linear least squares intercepts, Ak w, are within two standard deviations (95% confidence) of zero regardless of the method of analysis, Eq. (VII) or Eq. (IX). The low wall activity indicated by these reaction experiments corroborates our direct measurement of k w

RESONANCE

FLUORESCENCE

KINETIC

STUDY

43

T A B L E II R a t e d a t a f o r t h e r e a c t i o n o f O(3P) w i t h n e o p e n t a n e f r o m d i s c h a r g e f l o w - r e s o n a n c e fluorescence experiments"

T/K 922 •

PT/Torr 1b

2.41 •

0.01

v / c m s -1 3420 •

7

Neopentane/1014 m o l e c u l e c m -3

kc/s -~

0.28 0.82 1.24 1.81 2.46

94-+ 241 • 358 • 5 4 2 -+ 680 •

4 10 8 15 17

3 3 9 6 -+ 14

0.35 0.58 1.02 1.46 1.92 2.05 2.55

138 223 377 533 653 740 885

-+ +-+ • + •

2 3 9 10 12 18 20

3 0 2 8 -+ 14

0.26 0.47 0.81 1.27 1.98 2.57

80 141 248 379 618 749

-+ • + -+ • ~

1 4 2 17 9 20

3 2 5 5 -+ 2 0

0129 0.92 1.31 1.79 1.89 2.48

75 228 330 456 468 616

-+ • -+ +• -+

2 3 3 12 25 6

3074 •

14

0.49 1.36 2.01 2.69 3.45

65 220 312 419 514

-+ + -+ • -+

3 6 10 11 10

3 2 1 6 -+ 11

0.27 1.02 1.41 2.23 2.87 3.54

61 223 311 484 638 758

• -+ • + -+ •

2 4 5 10 15 14

kl = ( 2 . 7 4 • 0 . 2 0 ) x 1 0 - ' 2 c m 3 m o l e c -1 s -1 Ak~ = 2 0 • 31 s - ' 917 •

0

2 . 1 8 -+ 0 . 0 1

kl = ( 3 . 3 8 -+ 0 . 1 6 ) • Ak~ = 2 7 • 2 5 s -~ 908 •

0

10 -12 c m 3 m o l e c - l s -1

1 . 5 6 -+ 0 . 0 0

kl = ( 2 . 9 6 -+ 0 . 1 6 ) x 10 -12 c m a m o l e c -1 s -1 Akw = 6 -+ 24 s -~ 869 •

Ib

kx = ( 2 . 4 8 • Akw = 3 • 813 •

2.33 •

0 . 0 6 ) x 10 -lz c m 3 m o l e c -~ s -1 10 s

0b

kl = ( 1 . 5 2 •

0.01

2 . 3 7 -+ 0 . 0 1

0.11) •

10 -12 c m 3 m o l e c - l s -1

Ak~ = 3 -+ 2 4 s - t 809 •

0

kl = ( 2 . 1 6 • 0 . 0 6 ) • Ak~ = 4 -+ 15 s -1

2 . 5 5 -+ 0 . 0 0

1 0 -12 c m 3 m o l e c - t s - l

44

ELEMENTARY

REACTIONS

II

T A B L E II (continued) R a t e d a t a f o r t h e r e a c t i o n o f O(3P) w i t h n e o p e n t a n e f r o m d i s c h a r g e f l o w - r e s o n a n c e fluorescence experiments

T/K

v/cm s -1

PT/TOrr

7 7 3 --- 0

2.26 •

0.01

Neopentane/1014 m o l e c u l e c m -1

kc/s -1

2975 •

45

0.68 1.20 2.02 2.74 3.40 4.32

111 200 309 424 531 632

----• • •

4 5 6 10 10 9

2633 •

11

0.87 1.56 2.09 2.44 3.43 4.87

101 190 249 287 399 547

• -+ +• • +

2 3 2 2 5 7

2 6 2 3 +-- 2 7

1.07 2.38 2.38 3.06 4.03 4.95 6.19

70 151 156 216 270 333 443

-+ • • -+ -+ --•

3 6 2 3 2 3 6

1331 •

5

0.50 0.73 1.48 1.51 1.74 2.32

36 55 104 110 128 167

--• • +--•

2 2 2 1 1 2

1 2 9 2 --- 4

0.79 1.60 2.53 3.28 3.65

33 65 100 133 149

--+ • +-----

1 2 1 1 2

2390 •

1.78 3.48 5.06 6.11 7.90 9.64

65 129 202 239 288 350

• • • + --+ •

2 2 3 5 4 2

kl = i l . 4 5 • 0 . 0 8 ) x 1 0 12 c m 3 m o l e c ~ s 1 Ak~ = 21 --- 2 2 s -1 730 + 0

1.52 •

kl = (1.11 -+ 0 . 0 4 ) • Akw = 14 • 12 s -1 690 •

2

0.00

1 0 -lz c m 3 m o l e c - l s -1

1 . 9 8 --- 0 . 0 1

kl = ( 7 . 2 0 -+ 0 . 4 4 ) x 10 -13 c m 3 m o l e c - l s - l Akw = - 1 3 - 1 7 s - i 6 4 9 +- 1

kl = ( 7 . 1 7 -+ 0 . 2 8 ) • Akw = 1 • 4 s -1 6 2 1 +- 2

kl = (4.05 • 0 . 1 5 ) • Ak~ = 0 • 4 s -1 6 0 1 -+ 1

kl = ( 3 . 6 2 -+ 0 . 3 0 ) • Ak~ = 8 -+ 18 s -1

2.09 •

0.01

10 13 c m 3 m o l e c - I s-1

2.41 •

0.00

10 -13 c m 3 m o l e c -1 s - l

1.97 •

0.01

10 -1~ c m 3 m o l e c - l s 1

23

RESONANCE

FLUORESCENCE

KINETIC

STUDY

45

T A B L E II (continued) R a t e d a t a f o r t h e r e a c t i o n o f O(3P) w i t h n e o p e n t a n e f r o m d i s c h a r g e f l o w - r e s o n a n c e fluorescence experiments a

T/K 600 •

Px/Torr 0

3 . 5 7 --- 0 . 0 1

k 1 = (3.54 • 0.36) • Ak~ = 2 3 • 2 4 s -~ 556 •

0

kl = ( 2 . 7 4 • Ak = 7 _ _ _ 6 s 556 -

0

Neopentane/1014 m o l e c u l e c m -3

1 3 0 6 --- 6

1.22 2.86 4.17 6.17 7.16 8.95 9.54

56 127 176 254 279 316 371

+ • • --• -----

5 1 2 4 6 6 7

0.01

1163 •

5

1.69 2.54 3.64 5.18 5.27 6.94

53 74 108 151 154 194

--• + -+ • •

2 3 1 3 2 2

1177 •

5

1.67 3.99 5.57 6.78

46 110 138 145 169

• • -+

1 3 2 1 1

15

2.26 3.96 8.23 8.73 14.3

36 54 112 112 191

• • ---

1 1 4 3 5

1 0 0 4 + 12

2.83 6.16 8.47 11.3 14.4 17.1

28 57 79 93 113 139

--• --• •

1 2 1 4 1 3

9 8 6 + 12

3.21 6.54 8.85 11.3 14.0 17.2

27 55 73 82 103 124

-----+ + +---

2 1 1 3 1 6

10 -13 c m 3 m o l e c -1 s -~

2.08 •

0.00

5.22

kl = ( 2 . 4 3 •

0.22) •

kc/s -1

1 0 -13 c m 3 m o l e c -1 s -1

2.03 •

0.12) • -1

v/cm s -1

10 -13 c r n 3 m o l e c -1 s -1

h k ~ = 9 -+ 11 s -1 5 1 5 -+ 0

2 . 0 7 -+ 0 . 0 1

kl = ( 1 . 2 9 --- 0 . 0 8 ) • Ak~ = 4 • 7 s -1 471 •

0

469 •

0

k~ = ( 6 . 7 7 Akw=9_+6s

10 -13 c m 3 m o l e c - l s -l

1 . 9 1 -4- 0 . 0 1

k 1 = (7.45 • 0.70) • Ak~ = 10 --- 8 s 1

10 14 c m 3 molec-X s - i

1.88 •

0.58) • -~

1085 •

0.00

10 -14 c m 3 m o l e c -1 s -1

46

ELEMENTARY REACTIONS II TABLE II (continued) Rate data for the reaction o f O(3P) with neopentane from discharge flow-resonance fluorescence experiments"

T/K

Pr/Torr

v/cm s -I

427 --- 2

1.64 - 0.00

1749 -+ 49

Neopentane/1014 molecule cm -3 6.65 11.5 19.2 30.8

k J s -1 30 41 67 107

- 1 -+ 1 -+ 3 +-- 6

k I = (3.26 --- 0.32) x 10 -14 cm 3 molec -1 s -1 Ak, =6__+ 6 s -1 "Standard deviations in kc are at the lcr level, and in kl and Ak,. at the 2or level. bON/OFF mode (see text).

5 s -1. In addition to variations of [O]o, the effects of variable O 2 were examined. O 2 free experiments were carried out with the N + NO titration technique. No effects of O2 could b e documented (outside of experimental error) if [O]o was maintained at less than - 5 • 101~ atoms cm -3. We therefore assert that the values of the bimolecular rate constants in Table II refer to reaction (1). The temperature dependence of these

-0

~-

~- -e....._

'

'

results from linear least squares analysis at the one standard deviation level is, kl = (1.56 -+ 0.18) • 10 -1~ exp ( - 7 1 9 1 --- 135/RT)cm a molecule -1 s -1. A comparison between the Arrhenius parameters from the present FP-RF and DF-RF results, even at the one standard deviation level, shows virtually exact agreement. Both sets of data can then be taken as one, and, as shown in Fig. 4, the combined results exhibit good linearity on the Arrhenius plot form 415-922 K. On linear least squares analysis, the combined results give the Arrhenius expression, k 1 = (1.52 --+ 0.28) • 10 -1~ exp ( - 7 1 4 3 -+ 196/RT) cm a molecule - I s -1. This result has the errors expressed at the two standard deviation level (95% confidence). Also shown in Fig. 4 are the two results from

600

T

c

400

-5 200

-4

0

I0

20

50

d/crn

FIG. 2. Typical first order decay plots for relative [O] as a function of d in the " O N / O F F " neo-CsHl2 experiments (DF-RF apparatus). T = 869 K, PT = 2.33 Torr, v = 3255 cm s -1. In units of,1014 molecules cm-*, [neo-CsHl2] is: 0 - - 0 . 2 9 ; []--0.92; O--1.31; T--1.79; V--1.98; and A--2.48. k~ = (2.48 -+ 0.06) • 10 -~2 cm 3 molecule -~ s -~ (see Fig. 3).

0

0

2

4 6 8 I0 [2 14 [neo-C5Hi2]/1014 molecule cm- 3

16

18

FIC. 3. Plots of corrected first-order decay constants, kc, for O(aP) + neo-CsHl~ (DF-RF apparatus). ~7 T = 469 K, Pr = 1.88 Torr, v = 9 8 6 c m s-~; O - - T = 566 K, PT = 2.03 Torr, v = 1163 cm s -~, O~ free; [] = T = 690 K, Pr = 1.98 Torr, v = 2623 cm s-l; 0---869 K, PT = 2.33 Torr, v = 3255 cm s -1, " ' O N / O F F " method. Slopes give the. k~ values in Table II.

RESONANCE FLUORESCENCE KINETIC STUDY -I0

[

-'\\ \

r

O(Sp) +

r

neopentane

\\ \ \

3" 2

~-re E

~ -15

-15

I 2

I 3

\

I0 3 K/T

FIG. 4. Comparison of present kinetic results with those of others in Arrhenius form. O---FP-RF, this work (Table I); O--DF-RF, this work (Table II). Solid line with dashed extrapolation is the least squares fit to the combined results (Tables I and III. V----result of Wright. 3 A--A--Arrhenius expression of Herron and Huie. 4 the only other studies of reaction (1).3'4 Wright3 obtained a value of 3.0 • 10-15 cm 3 molecule -1 s -1 at 303 K. This result is shown as the single point in the Figure. The present result extrapolated to 303 K would give about one third of Wright's value, 1 x 10-15 cm3 molecule -1 s -1. The present results are also lower than those of Herron and Huie. 4 They report k1 = (1.0 --- 0.4) x 10 -1~ exp (-5802 --- 278/RT) cm 3 molecule -1 s -1. This expression is shown as the solid line between two points which define the temperature limits of the previous study. Clearly their A factor is statistically indistinguishable from the present value. The different rate behavior is attributable entirely to a lower activation energy than the one measured in the present work. The inferred discrepancy at their lowest temperature (276 K) with the present Arrhenius parameters would appear to be quite large, the present inference being only 0.13 of their measurement. But the comparison should properly be made over the same range of temperature. At our lower T limit, 415 K, our value is 0.3 times theirs, and at their high T limit, 597 K, our value is 0.5 times theirs. This comparison shows a discrepancy that is outside the combined errors of both studies and therefore appears to be real. The reasons for it are not at all clear since, as mentioned in the Introduction, the Herron and Huie study should have been free from stoichiometric corrections. However, we emphasize that the results of the present study were also stoichiometry free and that this condition was experimentally demonstrated here. In addition, two different and complementary methods were used in determining absolute values for kl(T), and a wider range in temperature was covered here than in any previous study. These points therefore suggest a high degree of confi-

47

dence in the present results. In addition to the thermal rate studies, the present results may be compared to the molecular beam results of Andresen and Luntz 12 who obtained a threshold energy, E o, for reaction (1) of 6.2 kcal mole -I. In deriving this result, they used the excitation functional form, (r r162(E c - Eo), where E c is the relative collision energy. With well developed models which relate threshold energies to activation energies, 13 we calculate for E o = 6.2 kcal mole -1 an activation energy varying from 6.8 to 7.8 kcal mole -1 for temperatures 400 K-900 K, respectively, The thermal value from the present study, 7.14 kcal mole -1, for 415 K-922 K, is in excellent agreement. Luntz and Andersen 14 have performed theoretical calculations (LEPS) with an assumed three atom model for the intermediate configuration. The potential barrier for reaction (1) was 7.5 kcal mole -I which implies, on zero point energy correction, an activation energy of 6.5 kcal mole -1. This is lower than measured here, and if an activated complex theory calculation is used, then the implied activation energy to be compared to experiment would be even lower since the theoretical A factor would exhibit some T dependence. We have also performed theoretical calculations with the BEBO method 15 for determining the activated complex configuration. The method has been applied to O + CH4 and O with several other saturated hydrocarbons including neo-CsH12. Activated complex theory calculations of the rate constants are then carried out. Full details of these calculations are given elsewhere. 16 The method predicts a potential energy of activation for reaction (1) of 8.21 kcal mole -1. Tunneling factors were included. The only arbitrariness in these calculations is in the barrier for internal rotation of the complex. Best agreement with experiment was obtained with the assumption of free rotation in the com: plex. Since there is T dependence from several sources in the pre-exponential factor, the computed rate constants exhibit curvature in an Arrhenius plot. The calculated values are generally larger than experiment being 1.8 times larger at 500 K and 1.2 times larger at 900 K. The near success of the method particularly at 900 K is encouraging because it may provide a rational means for extrapolating the rate constant to the combustion temperature regime.

REFERENCES 1. W. C. GARDTNERAND D. B. OLSON, Ann. Rev. of Phys. Chem. 31, 377 (1980). 2. C. K. WESTBROOKAND F. L. DRYER, Eighteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 18, 749 (1981).

48

ELEMENTARY REACTIONS II

3. F. J. WRIGrlT, Tenth Symposium (International) on Combustion, The Combustion Institute, Pittburgh, PA, 10, 387 (1965). 4. J. T. HERRON AND R. E. HULL, J. Phys. Chem. 73, 3327 (1969). 5. W. BRAUNAND M. LENZI, Chem. Soc. Faraday Discuss. 44, 252 (1967). 6. R. B. KLEMM AND L. J. Stief, J. Chem, Phys. 61, 4900 (1974), and references therein. 7. J. v. MICHAEL, AND J. H. LEE, Chem. Phys. Lett. 51, 303 (1977). 8. R. B. KLEMM, E. G. SKOLNIK AND J. V. MICHAEL, J. Chem. Phys. 72, 1256 (1980). 9. R, B. KLEMM, J. Chem. Phys. 71, 1987 (1979). 10. R. B. KLEMM, T. TANZAWA,E. G. SKOLNIKAND J. V. MICHAEL, Eighteenth Symposium (International) on Combustion, The Combustion In-

stitute, Pittsburgh, PA, 18, 785 (1981). 11. A. A. WESTENBERG, AND N. DEHASS, J. Chem. Phys. 46, 490 (1967). 12. P. ANDRESENAND A. C. LUNTZ, J. Chem. Phys. 72, 5842 (1980). 13. (a) M. MENZINGERAND R. WOLFGANG, Angew. Chem. (Int'l. Ed.) 8, 438 (1969); (b) R. L. LEROY, J. Phys. Chem. 73, 4338 (1969). 14. A. C. LUNTZAND P. ANDRESEN,J. Chem. Phys. 72, 5851 (1980). 15. H. S. JOHNSTONAND C. PARR, J. Am. Chem. Soc. 85, 2544 (1963); H. S. Johnston, "Gas Phase Reaction Rate Theory," Ronald, New York, 1966. 16. J. V. MICHAEL, D. G. KEILAND R. B. KLEMM--to be published.

COMMENTS F. Kaufman, University of Pittsburgh, USA. In their BEBO calculations the authors continue to use Johnston's original values for the BEBO parameters even though more recent developments in rare gas interaction energies j as well as in bond distance and bond energies 2 have brought about changes in these values. Johnston's bond-energybond-order (BEBO) theory has as its base the appealing physical notion that the new bond "pays" for the breaking of the old such that the sum of the bond orders remains constant (and equal to unity for single bonds). By using the earlier, incorrect values of these parameters, the authors, in fact, deny the physical basis of the theory and make it entirely empirical rather than semi-empirical. This may be justifiable if it can be shown that the original parameters give better agreement with measured rate constants than the revised ones. Have the authors shown this? If not, what is their justification for denying the theory's fundamental assumptions? REFERENCES 1. R. M. JORDANAND F. KAUFMAN,J. Chem. Phys. 63, 1691 (1975). 2. R. D. GILLIOM, J. Chem. Phys. 65, 5027 (1976).

Author's Reply. Our BEBO calculations are so extensive that, for reasons of length, they could not be included in the full paper. However, I should like to answer your question anyway. The BEBO method represents a simple way to determine both configuration and energy at saddle

points. It had enjoyed unusual success in theoretical chemical kinetics, but Jordan and you I in 1975 redetermined the bond index parameters and simply destroyed all of the previous success. In 1976 Gilliomz reinstated the method and claimed better success than with the original Johnston-Parr bond index values. 3 If we use Gilliom's values on O + CH4 we find at the saddle point, ARc~ = 0.01 A, A Roll = 0.02 ,~, and AV = - 0 . 7 kcal/mole, fi-om the values obtained with the Johnston-Parr parameters. Therefore configurations are not much affected, but energy is. On the basis of new C-C bond distances Gilliom redefined the Pauling's constant and changed the triplet repulsion constant from 0.5 to 0.45. Since Pauling's rule is a more general correlation between bond length and bond order than just for CC bonds, the fix cannot be justified. I then believe that your original criticism of BEBO is still valid. But your criticism is only one of many that can be leveled against it. To illustrate, if one allows that the extensive POL-CI ab initio calculation of Walch and Dunning 4 on O + CH 4 gives the correct saddle point configuration, then I note through Pauling's rule that n~ + n2 = 0.77. This of course refutes the most fundamental assumption of the method, namely that bond order is conserved. Other points of criticism are the assignment of "chemists bond order" which is at best intuitive, the association of rare gas dimers as species with zero bond order, and the form of the triplet repulsion term. Johnston and Parr 3 anticipated all of the changes that have come about in the last 19 years. They wrote: "Although these calculations seem to have no adjustable parameters, the authors realize that the treat-

RESONANCE F L U O R E S C E N C E KINETIC STUDY ment is partially "adjusted" and do not take the interpretations (constancy of bond order; Pauling's bond-order relation; separability of energy between bonds 1, 2, and 3; activated complex theory; or separable one-dimensional tunneling factors) at all literally. . . . It is to be expected that further r e f n e m e n t s of Lennard-Jones parameters, values of Pauling's constant, and magnitude of the triplet repulsion will destroy some of the remarkable success of these calculations . . . . BEBO is then totally empirical and utilizes scaled input parameters. Other methods such as LEPS do the same thing. Even ab initio quantum mechanical calculations use scaling. Though these methods have been particularly good at structure prediction, even quite elegant calculations often give poor energy predictions. Then rules for energy scaling have to be used in order to recover experimental values. So there is not that much difference between scaling input parameters versus output parameters in order to correlate with measurements. What is important is how well do various techniques compare to one another and particularly to experimental results. Also can the method be used for predictions on reactions of a similar type (homologous series). That is the approach we have taken in our calculations of O + saturated hydrocarbons.

REFERENCES 1. R. M. JORDANand F. KAUVMaN, J. Chem. Phys. 63, 1691 (1975). 2. R. D. GILLIOM, J. Chem. Phys. 65, 5027 (1976). 3. H. S. JOHNSTON AND C. PARR, J. Am. Chem. Soe. 85, 2544 (1963). 4. S. P. WALCHAND T. H. DUNNING, JR., J. Chem. Phys. 72, 3221 (1980).

F. Kaufman, University of Pittsburgh, Pittsburgh, USA. The authors should be congratulated on their accurate rate measurements by two different experimental methods over a wide t e m p e r a t u r e range. I am surprised that their Arrhenius plots are entirely linear even though both theory and other experimental works shows curvature. Could the authors give a brief, quantitative account of how the usually small correction terms for axial and radial diffusion, surface recombination, viscous pressure drop, and, especially, development of parabolic velocity distribution (see Bron, J. Res. Natl. Bureau Stand., 1978) affect their results? Is it possible that there is an increasing correction factor with increasing temperature that would introduce the predicted Arrhenius curvature?

49

Author's Reply. This is a very complicated question which is impossible to answer briefly and still be quantitative. With regard to the last points, we have taken considerable care to understand the experimental limits of the flow tube equipment due to hydrodynamic and surface recombination factors. In all experiments the Reynolds numbers are generally around 2 in which case the laminae are fully developed in small flow distances given by 1, = 0.277 a Re. 1 Since the flow tube radius a =1.2 cm, laminar flow is fully developed in a fraction of a centimeter at all flow velocities, densities, and viscosities used in this work. Mixing is similarly fast. With a simple one dimensional model we estimate that the reactant mixes completely in the flow within 3 - 4 cm at the higher pressures, higher temperatures, and faster flow velocities used in Table II. Poiseuille pressure drop is always measured in every experiment at two ports 67 cm apart. Depending on the flow conditions, the absolute pressure differences amounted to 0.1-0.4 torr for the experiments in Table II. However, the kinetic data were always obtained over a distance interval of ~20 cm (see Fig. 2) in which case the pressure drops were 0.03-0.1 torr. Thus, pressure drops were generally small (<~5% of the total pressure for all experiments). The pressure measured at the middle point for the kinetic distance range was used to calculate flow parameters and concentrations. Radial gradients are most affected by large wall recombination constants. In the full paper we point out that k~ was measured directly at all temperatures and was found to be quite low at 5 s -1. We did, however, make the usual correction for axial gradients (Eq. VI). Since the wall recombination constant is so low, Eq. VI should be valid as discusssed by Brown. 2 Brown has, however, given a more general two dimensional solution which takes into account the effects of the parabolic flow distribution with diffusion to and removal at the walls. Brown's conclusions for the case of small k~ agree completely with earlier results of Walker, 3 Aris, 4 Taylor, s and Mulcahy et alp where it is pointed out that with small k~ and homogeneous chemical reaction, Eq. VI is valid except that the effective diffusion coefficient becomes D + aZv2/48 D instead of D alone. We have used only the molecular diffusion coefficient in Eq. VI; however, we note that the additive factor contributes at most about 10% to the effective diffusion coefficient. Thus, this additive factor affects the corrected values through Eq. VI by about 1% even for the most extreme conditions. A point which you did not ask about but which we feel is an important consideration in flow tube work, has to do with the transition behavior between molecular and laminar flow. Though most

50

ELEMENTARY REACTIONS II

workers understand the limitations at higher pressures (small D), almost no one is concerned with this low pressure flow transition regime. This can result, in our opinion, to misapplication of the technique. Dushman ~ has discussed this point with Knudsen's result and gives the expression; F,/F = (0.1472 a l l + (1 + 2.507 a/L)/(1 + 3.095 a/L)) -t, where Ft and F are molecular and total flow conductances, respectively, a is the radius of the tube, and L is the mean free path of the flowing gas. Our criterion is that the fraction of molecular flow to total flow should not exceed 10-15%, and this is met for all the experiments in Table II. Evaluation of the equation shows that for He carrier gas, the fraction becomes large for P < 1.5 torr at higher temperatures whereas somewhat lower pressures can be tolerated at lower temperatures. However, it is always tenuous procedure to ever operate a He flow reactor u n d e r any conditions at pressures lower than about 1 torr. Therefore, our answer is that we do not believe that there is an increasing correction factor which could possibly explain the lack of curvature in the data. We are not as surprised as you are that the data follow the Arrhenius expression. Actually curves could be drawn through the data and still be within the claimed error (random and systematic) which is -+10-15% for any k(T) value. It is well known that in order to infer T dependence in A factors from experimental data, either the k(T) values have to be known with high accuracy or the range of T -~ values has to be large particularly for reactions with high activation energies. A factor of T dependence

can be seen for reactions with low activation energies with -+10% accuracy in k(T). A case in point is CI + CH4 ~ HC1 + CH3 where the activation energy is only about 2.7 kcal/mole. 7'8 So our view in the present case is that for the T -~ range and the k(T) accuracy, the data do not justify more complex description than the Arrhenius equation. Even though modelers desire analytical expressions that can be used for extrapolation to higher or lower temperatures, and even though all theories of chemical kinetics require T dependence in A factors, we cannot be sensitive to this desire a n d / o r requirement if the accuracy of the data does not allow it. Therefore our claim is simply that the Arrhenius expression is a good representation of the rate constant within -+10-15%, but only over the T range of the study. REFERENCES 1. S. DUSHMAN, "Scientific Foundations of Vacuum Technique," J. M. Lafferty, ed., Wiley, New York, 1962. 2. R. L. BROWN, J. Res. Nat. Bur. Stds. 83, 1 (1978). 3. R. E. WhLKEa, Phys. Fluids 4, 1211 (1961). 4. R. ARIS, Proc. Roy. Soc. A235, 67 (1956). 5. G. TAYLOR, Proc. Roy. Soc. A219, 186 (1953); (A225,) 473 (1954). 6. M. F. R. MULCAHYAND M. R. PETHARD, Aust. J. Chem. 16, 527 (1963). 7. D. A. Wr~rrOCK, J. H. LEE, J. V. MICHAEL, W. A. PaYNE, AND L. J. STIEF, J. Chem. Phys. 65, 2690 (1977). 8. M. S. ZAHNISER, B. M. BERQUIST, AND F. KAUFMAN, Int. J. Chem. Kin. 10, 15 (1978).