1866
Kern et ai.
The Journal of Physical Chem;stty, Vol. 82, No. 17, 1978
Comparative Rates of Exchange behind Reflected Shock Waves. I. ciao co2vs. 13co C O , ~
+
+
A. F. Bopp, R. D. Kern, Jr.,* T. Niki, and
D. E. Wilbanks
Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70 122 (Received April IO, 1978) Publication costs assisted by the National Science Foundation
The rate of exchange of carbon monoxide with carbon dioxide was studied over the temperature range 306C-4115 K by analyzing the gas from the reflected shock zone at 2 0 - ~ intervals s with a time-of-flight mass spectrometer. Separate mixtures containing 2% Cl8O-2% COPand 2% 13CO-2% COz each diluted with inert gas were sampled dynamically in order to measure the time dependence of a major product, m/e 46 or mle 45. The time dependence was determined to be nonlinear for both mixtures. However, the rate of formation of m/e 46 exceeded that of mle 45 over the range covered. Computer simulation of the respective product profiles using the appropriate atomic mechanism failed to account for the total amount of exchange conversion observed. A molecular mechanism involving excitation of reactants prior to the transition state leading to exchange is proposed. Two molecular channels involving three and four center transition state geometries participate.
Introduction Previous work on the exchange of carbon, oxygen, and nitrogen atoms a t high temperatures utilized the single pulse t e c h n i q ~ e and ~ - ~ the dynamic analysis of reacting gases by a time-of-flight (TOF) mass spectrometeraka The results from the single pulse and the TOF work for the self-exchange of carbon monoxide3,' and of nitrogen'@were shown to be compatible over a wide temperature range. The formation of exchange product was not in agreement with the predictions of an atomic mechanism and in both systems the proposed mechanism consisted of a series of energy transfer steps preceeding the transition state exchange complex. Earlier TOF investigation of the exchange of l8OZwith C0,5COz, and SO: were induced by the addition of NzO. The resulting exchange products were argued to be formed via an atomic mechanism and the rate constants for the three-center atom exchange steps were shown to be in agreement with rate constants obtained a t much lower temperatures. The purpose of this work is to study the exchange of CO with COz by using different isotopes of carbon monoxide, namely, 13C0 and Cl80. The mechanism for atomic exchange of these two species with COz is quite different and the rate constants for a computer simulation of the reaction are available. Secondly two possible geometries for the transition state molecular exchange complex can be separated for the formation of 13C02and l80CO, thereby allowing assessment of the relative importance of two molecular pathways.
Experimental Section The apparatus and procedure for the experiments performed have been described previou~ly.~One important change is the acquisition of a Tektronix 4662 digital plotter to assist in the reading of the mass spectral peak heights. The height of a particular peak is determined by positioning a cross hair over a scribed base line and sending the plotter coordinates to the computer. Repeating this process a t the top of the peak eliminates much of the data reduction effort. The 4662 is also used to plot the refined data for a run. The plots shown herein were drawn by the 4662. Isotopic 13C0 and Cl80 (each 90% enrichment) were purchased from Stohler Isotope Chemicals and were used without further purification. Matheson Research Grade 0022-365417812082-1866$01 .OO/O
Ne-1% Ar was used as the diluent. Matheson C 0 2 (99.5% min) was subjected to bulb-to-bulb distillation before it was used. Mixtures containing 2% 13C0-2% CO2-96% diluent and 2% P 0 - 2 7 ~coz-96% diluent were prepared by measuring the reactant pressures with a WallaceTiernan 0-10-in. H 2 0 differential pressure gauge and the total mixture pressure with a Wallace-Tiernan 0-400-in. HzO gauge. The mixtures were stored in Pyrex bulbs and allowed to stand 24 h before use. Each mixture was analyzed by the TOF and found to be free of impurities to a t least the background level. A calibration mixture which contained 25 ppm OZ-diluent balance established the magnitude of the background signal. Hydrogen was used as driver gas. All experiments were performed a t an initial pressure of 5 Torr. Typical observation times were on the order of 500 ps.
Results The mass spectral data were fit to the following equation 1 - fco,/fco,, eq = e x p ( - W
(1)
where fco, is the mole fraction of the exchange product. For the formation of mle 45, fco, was calculated according to the formula fco, = 45/(44 + 45) (2) where 44 and 45 are the peak heights. Experiments on the mixture which produced mle 46 as the major exchange product revealed minor amounts of the double exchange product mle 48 formed during the course of the reaction. The mole fraction equation was fco, = 46/(44 + 46 48) (3)
+
The mole fraction of COz a t equilibrium was determined by observation of the plateau obtained and by a statistical mechanical calculation. The value employed was 0.46. All of the runs displayed a nonlinear growth of the product mole fraction. The time dependence exponent z in eq 1 was determined by plotting the In In of the lefthand side of eq 1 vs. In t. The best value for z was 2 for f45 and 1.5 for f46 production. The fit of the data for two runs a t approximately the same temperature is displayed in Figures 1 and 2. In all runs where the temperatures were comparable, it was clear that the growth of f46 exceeded that of f4&. 0 1978 American Chemical Society
Exchange Rates behind Reflected Shock Waves
1
T,, K 3060 3065 3220 3283 3310 3367 3378 3406 3463 3471 3553 3565 3618 3637 3691 3736 3826 3841 3872 3910 3933 3957 4114
T I M E CUSEC>
Figure 1.
S
Reaction profile for
1867
TABLE 11: Rate Constants for the Production off,,"
0'61 0.4
The Journal of Physical Chemistry, Vol. 82, No. 17, 1978
fd5 at 3723 K
0'1
106h' 10bp, mol ~ m ' ~ p s - " 5 0.844 0.542 0.874 0.824 1.37 1.39 1.32 1.30 1.50 1.65 2.09 2.47 2.33 2.38 2.64 2.94 2.75 3.09 4.13 3.17 3.28 6.08 5.30
2.233 2.234 2.267 2.280 2.285 2.296 2.299 2.304 2.314 2.316 2.381 2.333 2.342 2.345 2.354 2.362 2.37 6 2.378 2.383 2.389 2.392 2.396 2.418
cm3 s-l.5
3.78 2.43 3.85 3.62 5.99 6.04 5.77 5.64 6.49 7.13 8.97 10.6 9.94 10.2 11.2 12.4 11.6 13.0 17.3 13.3 13.7 25.4 21.9
" The mixture consists of 2% C1*O,2% CO,, 96% diluent; PI = 5 Torr.
0.2
I
y
9 . 4 j
E A 8
3073 2.236 0.505 2.26 3125 2.247 1.56 6.94 1.83 8.11 3169 2.257 2.22 9.74 3288 2.281 2.283 1.17 5.12 3297 1.19 5.21 3343 2.292 2.296 2.20 9.56 3367 3376 2.298 1.59 6.92 3408 2.304 3.04 13.2 3474 2.317 5.07 21.9 3480 2.318 2.61 11.3 3509 2.323 3.37 14.5 3516 2.324 6.63 28.5 3543 2.329 3.29 14.1 3596 2.338 5.04 21.6 3671 2.351 4.91 20.9 3695 2.355 6.44 27.3 3702 2.356 5.02 21.3 3705 2.356 7.23 30.7 3723 2.359 5.52 23.4 3820 2.375 6.93 29.2 3847 2.379 6.47 27.2 3893 2.386 8.82 37.0 3904 2.388 9.47 39.7 3977 2.399 15.9 66.4 4010 2.403 7.98 33.2 a The mixture consists of 2% I3CO, 2% CO,, 96% diluent; P, = 5 Torr.
The rate constants h' were calculated for all of the runs and are listed in Tables I and I1 along with the reflected shock zone gas density p5. Although no experiments were performed to determine any of the order exponents, h' was divided by p 5 to yield the rate constant k . The Arrhenius
,2L6LLL
8 .0 8
188
288
388
488
588
T I M E CJASEC)
Comparison of experimental f45 profile (solid line) and computed atomic mechanism (dotted line) at 3543 K. Figure 3.
parameters for the two mixtures yielded the following results: hd5 = 1016.33&0.38 exp(-66.7 f 6.1/RT)
h,, =
1013.94i0.18 exp(-48.9
f 3.O/RT)
where k45 has units of cm3 mol-' s-' and k 4 6 has units of cm3 mol-I s - ~ . ~The . activation energy is expressed in kcal mol-'.
Discussion An atomic mechanism was formulated to simulate the f45 reaction profile using the following steps. The program used for the calculation has been described previously.1° COZ + M + CO 0 + M (a) 0 + coz = co + 0 2 (b) O2 + M = 2 0 + M (4 13co o + M + 1 3 ~ 0+~M (d)
+
+
l3CO + o2= 13C02+ 0 (e) The results of the calculations yielded f45 profiles which did not account for the amount of product observed. A typical comparison is depicted in Figure 3. The amount
The Journal of Physical Chemistry, Vol. 82, No. 17, 1978
1868
0'61
Kern et al.
"'"1
0.44
$
-
e: -1
0.2-
0
100
300
260
5e0
400
TIME (CISEC)
TIME (USEC)
Figure 4. Comparison of experimental f46 profile (solid line) and computed atomic mechanism (dotted line) at 3565 K.
Figure 5. Comparison of experimental profiles at 3100 K.
TABLE 111:
Arrhenius Parameters f o r C o m p u t e r Simulation Programa reaction
a
E*
ref
107.2 36.1 104.8 5.5 3.64 0.96 8.0 12.3
11 12 13 6 6 6 14 15
A 6.48 x 10-lo 7.59 x lo-'* 1.31 X 8.71 x 1 0 - 1 3 ~ 0 . 5 7.41 x 1 0 - 1 4 ~ 0 . 5 3.31 x 10-13~0.5 6.6 x 6.6 X lo-"
Units: A = c m 3 molecule" s-l;E* = k c a l m o l - ' .
of
f45 computed is contained in the baseline. There are several steps additional to (a)-(c) for the production of f46 and f48. The asterisk represents "0. 0 + c o * = o * + co (f) 0" + cot + co + 02* (g) (h) 02* + M + 0 O* M 0" + coz + 0 + c o , * (i) o* coz* + 0 c02** ci) o* + 02 + 02* 0 (k) C02* + M + CO* 0 + M (1) COz* M + CO O* M (m) C02** M + CO* O* M (n) 0 + c02* ?=co + 02* (0) 0 + c02* + 0 2 c o * (P) o* c02* + 02* + c o * (9) The amount of f46 produced by computer simulation was clearly insufficient a t lower temperatures but the gap was closed with increasing temperature as shown in Figure 4. The literature rate constants for the various reactions used in the simulation are listed in Table 111. All reactions which are identical except for isotopic identities are assigned the same rate expression after adjustment of preexponential factors for reactions with equivalent pathways (e.g., 1 and m) and equilibrium constants involving different symmetry numbers (e.g., i and j) were made. The time dependence exponent z was determined for each of the two atomic mechanisms using eq 1. The values obtained were 2.0 and 2.8 for f46 and f45 production, respectively. A comparison of the experimental results for fd5 vs. f46 reaction profiles is displayed in Figures 5-7. The plots were generated using the respective Arrhenius parameters, k45 and k46.
+
+
+ +
+
TIME CUSEC)
Figure 6. Comparison of experimental profiles at 3500 K.
+
+
+ + + + + + +
0.0
0
200
100
300
400
500
TIME OJSEC)
Flgure 7. Comparison of experimental profiles at 3900 K.
Consideration of a linear transition state complex as part of a molecular mechanism reveals that formation of f45 and fd6 is equally likely.
o=c=o..13c~o-,orc + 0=13c=o o=c=o. .CGO* + O E C + o = c = o * However, formation of a four-center complex leads to formation of f46 but not f45.
o=c=o :
0
:
~
~
o=c=o :
+
noexchange
1
3
: -+
*OEC
o=c=o* +
OSC
Since an atomic mechanism will not account for the amount of f45 or f46 produced a t the lower temperatures
Spectroscopy of Low Pressure Oxygen Discharge
The Journal of Physical Chemistry, Vol. 82, No. 17, 1978
and since f46 growth is greater than f45 over the range covered herein, it may be concluded that both transition state geometries are utilized. Simple subtraction of the amounts of f45 from f4at lower temperatures demonstrates this contention. For instance, a t 3100 K, the contribution from atomic channels a t 300 ps of reaction time amounts to for f 4 5 and 0.05 for f46. Subtracting the atomic contribution to f 4 6 a t 300 ps leaves an amount of f 4 6 which is twice that of f 4 5 . The conclusions drawn about the relative importance of atomic and molecular channels are definite although qualitative. Attempts to assess the differences quantitatively are not warranted. The choice of rate constants shown in Table I11 are thought to be reasonable and the “best”. However, other values for the dissociation of C 0 2 do exist.loaJ6J7 Using different values will change the amount of product formed from atomic pathways. The question of the effect of H atom impurities on the observed rates is important. Static analysis of the mixtures used herein did not reveal the presence of any hydrocarbon species that would introduce H atoms and thereby accelerate the exchange rate via the following reactions: H C02 F+ CO + OH (r)
+ CO* + OH H + O2
+
CO2* H F+ OH 0
+
(S)
(t) In order to assess the sensitivity of the computer profiles to impurity levels, initial concentrations of 10 and 100 ppm H atom were input and the product profiles were recalculated using the rate constants in Table 111. The profiles generated for 10 ppm addition a t 3100 K did not differ appreciably from the “clean” f45 and f a profiles. However, the presence of 100 ppm of H atom increased the atomic contribution to 5 X for f45 and 0.10 for f46 a t 300 y s of reaction time. The inclusion of these atomic impurity levels as initial contributions is an excessive measure but it does illustrate the sensitivity of the exchange rate to H atom concentrations.
1869
The observation of a nonlinear time dependence for product formation rules out a single bimolecular encounter for product conversion. The fact that use of a reasonable set of literature rate constants is unable to account for the amount of product conversion a t the lower temperatures of this study from atomic routes leads to the proposition that two molecular channels are also utilized. The process of molecular conversion is best explained by a series of steps in which rotational/vibrational energy is accumulated in a critical amount by reactants prior to the exchange stepss Both three and four center geometries contribute to molecular conversion.
Acknowledgment. Dr. A. M. Dean kindly provided us with a copy of his computer program. Mr. Gary Stack assisted with the calculations. References and Notes (1) (a) Paper presented at the 33rd Southwest Regional Meeting of the American Chemical Society, Little Rock, A&., Dec, 1977. (b) Support of this work by the National Science Foundation, Grant CHE-7608529,
is gratefully acknowledged.
(2) A. Bar-Nun and A. Lifshitz, J. Chem. Phys., 47, 2878 (1967). (3) A. Burcat and A. Lifshitz, J . Chem. Phys., 51, 1826 (1969). (4) H. F. Carroll and S. H. Bauer, J. Am. Chem. Soc., 91, 7727 (1969). (5) S. H. Garnett, G. B. Kistiakowsky,and B. V. OQady, J. Chem. phys., 51. 84 (1969). (6) T. C. Clark, S: H. Garnett, and G. B. Kistiakowsky, J . Chem. Phys., 52, 4692 (1970). (7) A. F. Bopp, R. D. Kern, and B. V. O’Qady, J. phys. Chem., 79, 1483 (1975). (8) J. M. Bopp, R. D. Kern, and T. Niki, J. phys. Chem., 81, 1795 (1977). (9) J. M. Brupbacher, R. D. Kern, and B. V. O’Grady, J . Phys. Chem., 80, 1031 (1976). (10) (a) A. M. Dean, J. Chem. Phys., 58, 5202 (1973); (b) Ph.D. Thesls, Harvard University, 1970. (11) J. H. Kiefer, J . Chem. Phys., 61, 244 (1974). (12) S. C. Baber and A. M. Dean, J . Chem. Phys., 60, 307 (1974). (13) W. D. Breshears, P. F. Bird, and J. H. Kiefer, J . Chem. Phys., 55, 4017 (1971). (14) W. T. Rawlins and W. C. Gardiner, Jr., J. Phys. Chem., 78, 497 (1974). (15) G. L. Schott, Symp. (Int.) Combust., [Froc.], 7%, 1968, 569 (1969). (16) T. C. Clark, S. H. Garnet, and G. 8. Kistiakowsky, J . Chem. Phys., 51, 2885 (1969). (17) W. A. Hardy, H. Vasatko, H. Gg. Wagner, and F. Zabel, Ber. Bunsenges. Phys. Chem., 78, 76 (1974).
Spatial and Temporal Emission Spectroscopy of a Radio-Frequency Capacitively Coupled Low Pressure Oxygen Discharge Ramon M. Barnes” and Richard J. Window Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 0 1003 (Received July 27, 1977; Revised Manuscript Received April 28, 1978)
Spatial and temporal emission spectroscopicmeasurements are reported for a low-power, rf capacitively coupled barrier discharge operated at reduced pressure in oxygen. Unique spatial distributions are recorded for 0 I and 0 I1 transitions, and the temporal relations between the rf field and emission from specific transitions of both 0 and O+ indicate a close phase correlation. In order to explain these observations, a model is proposed which does not depend upon the conventional view of a plasma sheath region and positive column in the discharge. Instead, the rf field accelerates the electrons near the wall in a swarm, which collides inelastically in a small volume at a fixed distance from the wall and produces the observed radiation patterns.
Introduction Brown examined theoretically the breakdown and maintenace of high-frequency discharges a d categorized them based upon the mechanism which dominates the electron dep1etion.l The four cases which apply include electron attachment, mobility and diffusion control, and
secondary electron resonance. In the electron-attachment-controlled mechanism, electron loss is dominated by reaction 1;whereas, in the mobility-controlled mechanism, e-
+ M + M -,M- + M
(1)
the mobility of electrons in the gas is large and the electric
0022-3654/78/2082-1869$01.00/00 1978 American Chemical Society
