OH Chemiluminescence in the 0
+ C2H4System
2493
Use of a Mathematical Model and Experiments to Determine the Mechanism and Rate Constant of OH Chemiluminescence from Oxygen Atom Attack on Ethylene Barbara B. Krleger" Department of Chemical Engineering, University of Washington, Seattle, Washington 98 195
and Ralph H. Kummler Department of Chemical and Metallurgical Engineering, Wayne State University, Detroit, Michigan 48202 (Received April 26, 1977) Publlcation costs assisted by the National Science Foundatlon
The reaction mechanism for the chemiluminescence of OH (electronic and vibrational transitions) generated by the complex reaction sequence initiated by oxygen atom attack on ethylene has been modeled numerically through the solution of simultaneous differential equations involving 164 processes and 30 species. The temporal behavior of the OH(9-4, 9-3, 8-3, 8-2, 7-3, 7-2, 6-2, 5-1, and 4-0) vibrational transitions observed as chemiluminescence was monitored using photon counting techniques in a discharge flow tube experiment at 1 Torr total pressure. Use of the mathematical model to design experiments permitted identification of the reaction CHO + 0 CO OH(u) as the only contributor to the observed signals. The rate constant for the production of OH(u = 9) was experimentally determined as 6 (+4) X cm3/molecule s. The major loss mechanism was identified as 0 + OH(u = 9) products and the rate constant determined to be 3 (+2) X lo-" cm3/molecule s.
-
+
-
Introduction The OH Meinel emission, OH transitions in the nearinfrared and visible, have been observed in H + O3sysThis emission has also been observed in 0 + hydrocarbon (HC) systems by Krieger et al.' In the former case the vibrationally excited OH is produced directly in the primary reaction step. In 0 + HC systems, and in particular in 0 + ethylene systems, the ground state chemistry is well d o ~ u m e n t e d and ~ - ~leads ~ to OH via a multitude of paths. The species CH3, CHO, H, HOz, 03, CH2,02, and H2C0can all be involved. It was the purpose of this work t o determine the mechanism and rate constants for the production of vibrationally excited OH(u = 4-9) from the reaction of 0 + C2H4 In complex reacting systems under study in discharge flow tube experiments a t low pressure, often more than one elementary step may contribute to the production or loss of the species under study. T o unambiguously conclude which of the elementary steps is producing the species and to measure its rate coefficient, the experiment must be designed to minimize the rate of alternate production pathways. In order to predict experimental conditions in which a single rate or elementary step was dominant for the 0 + C2H4system, a mathematical model to be described herein was used to allow examination of the rates of competing reactions. The corresponding experiments were performed t o determine the effect of [O,], initial composition, total pressure, and time on reaction rates and to aid in defining the mechanism. Once the mechanism was determined, the quantitative experiments to yield the rate constants for the production of OH(u = 9) were performed. Mathematical Model and Experimental Design Reaction Model. The model consisted of a large number of probable steps in the mechanism for the reaction of oxygen atoms and ethylene. The model considered 30 species (and some excited states) given in Table I. The species were chosen on the basis of preliminary optical identification of t h e emission spectra found e~perimentallyl~ and on the extensive mass spectrometric data of Niki et al., Kanofsky et al., Herron and Penzhorn,
TABLE I: Species Considered in 0 + C,H, Kineticsa
Species Inert: A, He
State
Species CHO CHO'
0 H
CHO* CH3 CHZ HZ 0 HzO' H,O" HO,
0 2 0 2 "
HZ CH CH*
co CO'
co* OH OH' OH" OH* CO,
X('nld A( *Z+)
H,CO* H,CO* CZH,
g(3A"(A,)j &'A"(A,))
X References 34, 35, 50-52. Vibrationally excited. Meinel u = 1-3. e Higher energy viMeinel u = 4-9. brational modes (stretching). f Lower energy vibrational modes (bending). X(lXg+)
a
and Washida e t aL9-l4 In addition to reaction, several processes such as radiation from an excited species, collisional transfer of energy, and radial diffusion loss of radical species were modeled. The complete list of reactions considered in the model are presented in Appendix I (see paragraph a t end of text regarding supplementary material). The first criterion for including a reaction in the model was published evidence verifying the reaction mechanism and rate constants. Evaluated rate constants and branching ratios were used when available.16 Only those reactions that were exothermic or essentially thermoneutral %t300 K were included. If the heat of reaction of an elementary step was greater than the energy of some excited state of the products, additional reactions to form the excited products were included. The reaction product containing a newly formed bond was judged to be the The Journal of Physical Chemistty, Voi. 81, No. 25, 1977
B. B. Krieger and R. H. Kummler
2494
TABLE 11: Experimentally Determined Diffusion Parameters for H and 0 Atomsa Pressure, Species Matrix Torr k d , b S-’
0 H 0 H
a
Argon Argon Helium Helium References 15 and 25.
the experimental data.
1 1 1 1 kd
30 340 60 360
* f
?:
i
10 40 10 40
is a least-squares fit to
Scheme I Rate coefficient H t O(+M)-t OH(+M) O + HO,-tOH+ 0,
HtH0,-OH+OH H+O,-rOH+O, OH,, + OH, -r OH,! t OH,ff CH, + 0, -r OH -t CHO CHtO,-rOH+CO CHO
+ O-r
OH t CO
Ref
1.6E- 37 33 1.5E- 11 44 1.8E- 11 16,43 2.6E- 11 5,6,24 {gas kinetic to est;54 1.OE - 1 3 1.OE- 12 est L O E - 12 est 1.1E-10 13
(1) (2) (3) (4) (5) (6) (7) (8)
excited p r ~ d u c t .Reactions ~ were also included to describe the collisional transfer of energy between excited states.” The set of differential equations resulting from the analysis of the complete kinetic mechanism was solved with the aid of “Kenesha Computer Code for Reaction Kinetics”,18 which employs the Runge-Kutta-Merson technique. This technique has been specially adapted to solve stiff equations by the use of the steady-state approximation. Flow Process Model. Several flow processes such as diffusion and expansion were also modeled by the flow tube code. Since experimental values of the pressure drop at a given total pressure were available, a linear pressure drop was assumed and, at each time bite, the concentrations were reduced by an incremental expansion from the pressure at the previous distance (time). A second flow process included in the computer code was the loss of atomic and excited species due to radial diffusion. Although the effects of diffusion on concentration profiles have been the topic of several p a p e r ~ , l ~a - ~ ~ somewhat different approach was used in this study since the species under study were vibrationally excited species which could be expected to have very high deactivation rates a t the wall. The species continuity equation with homogeneous first-order reaction and radial diffusion was solved to obtain an analytical solution. The details of this solution appear in Krieger15 and Smith.25 This solution predicted an apparent decay constant which compared favorably to the experimentally determined decay constant ZERO POINT ENERGY for 0 atoms and H atoms. The results (Table 11) were then used in the mathematical model. Figure 1. Schematic diagram indicating energy levels of OH and the Thermal Effects. Thermal effects from the exothermic energy of reaction (exothermicity)for reactions in the 0 4- C2H4system. reactions were not included in the model due to the dilute concentrations used. The calculated temperature effect instantaneous rate meter provided an analog signal to a chart recorder. in the extreme case is less than 3% change over the entire Residence time (velocity) measurements were made by 8-10-ms reaction time. No correction was applied to experimental data to account for heating.15 observing the time delay in a pulse of emitting species at successive windows triggered by the pulsed microwave Experimental Section discharge reference. For comparison, the average velocity Apparatus. The experimental system has been dewas calculated from the pressure drop.26,27A finite difscribed in detail e l ~ e w h e r e .Briefly, ~ ~ ~ ~ the system consisted ference solution to the continuity equation with reaction of a steady state discharge flow tube at 1 Torr total and Poiseuille flow showed this procedure to be adequate pressure in argon and helium into which 0 atoms and CzH4 in describing the residence time distribution of the species were introduced. For certain experiments, two microwave in the reactor.15>21!25 The gas velocity resulted in reaction discharge inlet streams were employed, one producing times of about 1-10 ms in 95% argon and 0.5-5 ms in 95% atomic oxygen, the other, atomic hydrogen in helium. helium. Absolute intensity measurements were made using Their concentrations were determined by titration and by the NO 0 actinometric ~ t a n d a r d . ~ ~ - ~ l the intensity of the separate reaction with N0.24925 Comparison of Experimental Observation and A photon counting detection system was used to Model Predictions measure the radiation from excited species through radially The calculations using the mathematical model indiviewing quartz windows. The wavelength dispersion was cated that the reactions shown in Scheme I for the proprovided by an 0.25-m Jarrell-Ash Ebert-type monoduction of OH(u = 9) in the 0 CzH4 system have chromator with a 50-500-pm slit centered over the window substantial rates at some experimental conditions. perpendicular to the flow. A thermoelectrically cooled These mechanisms are plotted vs. their exothermicity RCA C31034A photomultiplier tube with sensitivity from in Figure 1. Ultimately, we must account for the pro2000 to 9000 A measured the chemiluminescence. Pulse duction of vibrational levels as high as, but no higher than counting of the photomultiplier tube output was accomu = 9, as shown in Figures 2 and 3. These figures illustrate plished with Canberra Nuclear electronics and a Canberra
+
+
The Journal of Physical Chemistty, Vol. 81, No. 25, 1977
OH Chemiluminescence in the 0
+ C2H4 System
2495
TABLE 111: Comparison of Selected Reaction Rates in the Absence and Presence of Reactant Molecular Oxygena Rate
[O,] = 3.3 x 1015molecule/cm3 No initial [ O,] 3.1E + 06c 2.2E t 06 H t 0 + M - OH + Md 1.4E t 15 1.4E + 13 CHO + 0, CO + HO, 5.8E + 13 7.5E + 11 0 + HO, 0, + OH(u < 6 ) 6.OE + 14 6.2E + 12 H + HO, OH + OH(u d 4)e 1.6E + 12 4.1E + 09 H + 0, 0, + OH(u = 9)f 3.3E + l o b 8.8E + l o b OH(v) + OH(u) OH(u') + OH(u") 3.8E + 12 3.1E + 10 CH, + 0, CHO + OH(u > 9 ) 2.7E + 10 4.0E + 09 CH + 0, CO + O H ( u > 9 ) 1.8E + 14 1.6E + 14 0 + CHO- CO + OH(u d 9 ) (Experimentally achieved by (Experimentally achieved by N, discharge, 0, discharge) N+NO=O+N,) Upper bound on this rate a Basis system: P , = 0.95 Torr, [C,H,], = 1 mTorr, [O], = 4 mTorr, reaction time = 4.3 ms. using a gas kinetic rate constant, Units of rate are molecule/cm3 s. Reference 33. e Reference 32. Reference 6. Reaction
-+
-+
-+
-+
-
-+
-+
0
3 0,
0, 0
0.
Q
0 ,
.r
ilI
- i
I i
,
41
5
" 3 6800
7200
7800
8400
WAVELENGTH, ANGSTROMS Flgure 2. Corrected intensity vs. wavelength spectrum for 0 atoms
reacting with
C2H4.
Identification of OH transitions.
the observed spectrum and the absolute population distributions, respectively. From Figure 1,we can conclude that only reactions 1, 4,and 6-8 are sufficiently energetic to produce OH(u = 9) directly. Other mechanisms could be coupled with a vibrational pumping mechanism such as (5) to produce OH(u = 9), and thus we did not rule them out in the preliminary screenings. The model predictions for the rates of reaction of each of these mechanisms are given in Table 111, both including and excluding molecular oxygen. We can draw several conclusions from these rates. First, 0 + HOz = O2+ OH (2) is potentially an important OH production mechanism in the presence of O2 due to the large rate of CHO + O2 = CO H02, the HOz formation reaction.61 However, the OH produced by (2) does not contain a new bond and therefore it is not expected to be vibrationally excited. The comparable reaction with H atoms, reaction 3, would also be potentially important in an O2 containing system and is known to produce OH(u < 4).32 To produce the observed absolute concentration of OH(u = 9) from these lower vibrational levels requires a rate constant for ( 5 ) exceeding gas kinetic. Upper limit calculations to the pumping rate via vibration-vibration exchange can be made as illustrated in Table I11 by applying a gas kinetic rate constant. Clearly, vibrational pumping is a very minor mechanism. This is substantiated by the fact that no OH(u = 10) has been observed in H + 03 Thus, we can eliminate any mechanism not energetic enough to produce OH(u = 9). Table I11 also leads us to the conclusion that reactions involving CH and
I
I
7 9 UPPER V I E STATE
1
II
+
Flgure 3. Absolute concentration of OH' vs. vibrational level for 0 C2H4. The populations in this figure have been divided by the [HC] and [O]atom concentrations to put them on a comparable basis. Reaction time 1-2 ms; 1 Torr total pressure; O2 was discharged.
N, Discharge
OWH4
+
WAVELENGTH, NM
+ C2H4spectrum obtained in a N2discharge to one obtained in an O2discharge system. Reaction time, -5 ms; 1 Torr total pressure. Figure 4. Comparison of 0
CH2with 0 2 are too slow to be important when molecular Oz is excluded as a reactant. Finally, Table I11 suggests that there is only one OH(u = 9) production mechanism 0 + CHO = CO + OH(u = 9), which is independent of the molecular oxygen concentration in these experimental regimes. Experiments were conducted to test the calculations in Table 111. Direct discharge of molecular oxygen provided a source of oxygen atoms in 02,while discharge of N2and The Journal of Physical Chemistry, Vol. 81, No. 25, 1977
B. 6.Krieger and R. H. Kummler
2496
titration of N atoms with NO provided a source of oxygen atoms in the absence of 02.The experimental spectra in Figure 4 confirm the fact that the observed intensities in an N2 discharge as well as an O2 discharge are virtually identical. Hence, we can rule out H 03,CH + 02,and CH2 + O2 both quantitatively and qualitatively as sources of OH(u = 9) in this system. For H 0 2 experiments, two microwave discharge inlet streams were employed, one producing atomic oxygen, the other, atomic hydrogen. Atomic hydrogen concentrations were also determined by titration and by the intensity of the separate reaction with N0.24126With these two discharges, reactions 1-3 could be experimentally investigated. The procedure was to create H 0 2 in the upstream discharge and allow it to react with 0 and H atoms downstream (the rate constant for its production, H + O2 + M = H 0 2 + M, is known).16 Experiments were conducted with reactants in reactions 1-3 in concentrations equal to or greater than those found in the 0 + C2H4system. In each case, the observed spectra did not show the characteristic Meinel band emission in the absence of C2H4.I5 The remaining production mechanism for OH(u = 4 9) in the C2H4 + 0 reaction is CHO + 0 -+ OH(u < 9 ) t CO A H = -74.3 kcal/mol (8) This candidate mechanism shows the following characteristics that corroborate its being the OH(u = 9) production mechanism consistent with experimental results: The reaction will occur in an 021free environment, meeting the requirement that the OH chemiluminescence appear in an N2 discharge + NO experiment. The CHO concentration is sufficiently high to produce the observed OH(u) concentrations with reasonable rate ~ 0 n s t a n t s . lThe ~ formyl radical concentration can be predicted accurately since the rate constants for its production and loss are well established.13J4 This mechanism would show a linear dependence of the OH(u) emission on [C2H4],as observed experimentally for sufficiently low HC (or sufficiently excess 0 atoms).16 The energetics are appropriate to produce vibrationally excited hydroxyl radical in the ninth vibrational The 0 to H bond is the new bond being formed in the reaction and therefore would be expected to contain the energy of reaction as vibration. During development of the model, provision was made to predict the reaction rates in the 0 H2C0 system. Since calculations and experiments with 0 + H2C09show substantial production of CHO, the OH Meinel emission should be observed from this reaction as well. The following reaction sequenceg~10 has been put forth
+
-
+
0 t H,CO
--f
CHO
+ OH
0 t CHO+ CO + OH 0 + O H - + 0, t H
A H = -25 kcal/mol A H = -74 kcalimol
The experiment of reacting 0 atoms with H2C0 was performed in an N2discharge to exclude molecular oxygen. The results in the form of an uncorrected spectrum are shown in Figure 5. When this figure is compared with Figure 4,also in N2,it can be seen that the emission from formaldehyde is the same as that from ethylene. The intensities are somewhat different due to the slower rate of reaction of formaldehyde (1/5 that of ethylene). Due to the absence of the CH3 radical in the above mechanism for 0 H2C0, there are insignificant concentrations of H atoms produced. Likewise, since O2 was excluded by using
+
The Journal of Physical Chemistry, Vol. 81, No. 25, 1977
84 m.00
lW.00
8W.00
8UO.W
8b.00
9io.00
!&OO
WAVELENGTH, NM Figure 5. Intensity vs. wavelength spectrum for 0 atoms reacting with formaldehyde. (Atomic oxygen formed by adding NO to N atoms formed from an N, discharge.) Reaction time, -5 ms; 1 Torr total pressure.
Scheme I1 Rate coefficient 0 + C,H,
Ref
8.1E - 1 3 cm3/s l O , l l , ( 9 ) 39 0 t CHO -+ OH(u = 9 ) + CO This work (8) 0 t CH, H,CO + H 1.2E - 10 cm3/s 1 4 (10) 0 t OH(u = 9 ) .-L products This work (11) -+
CH, t CHO
-f
Wall
OH(u = 9 )
OH
100 s"
15
(12)
OH
300 s-'
35
(13)
products
2.OE - 10 cm3/s 1 3
(14)
radiation
OH(u = 9 )
0 + CHO-
all paths
an N2 discharge to create 0 atoms, these experiments again preclude H O3 as a source of the OH(u) chemiluminescence.
+
Determination of Rate Constants The preceding discussion has shown that kformation and klosshas served to quantify and, in this case, simplify what is an otherwise very complex system. With this knowledge, we could then determine the production and loss rate constants for OH(u = 9). Absolute intensity measurements were obtained from spectra such as Figures 2 and 4 as described p r e v i o ~ s l y . ~Although ~ - ~ ~ this yielded absolute population distributions for OH(u = 4) through OH(u = 9) as shown in Figure 3, the mathematical model showed that the complex processes such as vibrational quenching (hu 2 1) and radiation contributed to the formation of vibrational states OH(u = 8) to OH(u = 1). Thus, OH(u = 9) was the only state formed directly and exclusively by chemical reaction and the rate constant determination focused on this species. The procedure used to uncouple the kformationand hloss of an intermediate is described in Washida et al.13J4 Briefly, the concentrations of reactants are reduced to levels that allow the observation of the approach to steady state concentrations during the residence time in the flow tube. The experimental conditions for these experiments were predicted by the model. Consider the simplified mechanism shown in Scheme 11. From this mechanism the differential equation describing the OH(u = 9) concentration is
d[OH(v = 9)] / d t = k,[CHO] [O] - ( k l l [ o 1 + S)[OH(U= 911
(1)
OH Chemiluminescence in the 0
+ C2H4System
2497
TABLE IV: Rate Constant Determinations of k , , for the Reaction 0 + OH(u = 9) = Products (cm3/s) ~~
~
[HCI / [O1 2.63 2.87 1.67 1.26 1.74 1.38 2.13 3.80 1.08 3.00 1.60 3.20 2.00 4.00 14.20 0.90 2.05 0.96 0.50 0.50 1.45 5.20 1.20 0.48 0.96
a
t, 2.3863 - 11 4.8023 - 1 2 7.5733 - 1 2 1.511E - 11 1.6073 - 11 1.2753 - 11 1.587E - 11 3.0633 - 11 4.108E - 11 2.5463 - 11 2.2693 - 11 1.9683 - 11 3.5493 - 11 3.041E - 11 1.9973 - 11 1.470E - 11 1 . 2 3 6 3 - 11 9.9193 - 1 2 8.614E - 1 2 1 . 2 8 8 3 - 11 1.417E - 11 2.088E - 1 3 1.193E - 11 2.0443 - 11 2.515E - 11
t2
~
ba
t3
7.6163 - 11 6.597E - 11 4.7933 - 11
8.2213 - 1 3 1.5943 - 11 1.711E - 11 2.2503 - 11 1.906E - 11 1.511E - 11 1.593E - 11 4.3583 - 11 4.0423 - 11 3.5073 - 11 3.517E - 11 2.6443 - 11 6.09E - 11 8.7273 - 11 2.962E - 11 2.0893 - 11 2.0253 - 11 2.578E - 11 1.746E - 11 3.137E - 11 1.723E - 11 8.200E - 1 2 8.340E - 1 2 3.4403 - 11 3.0993 - 1 2
3.025E - 11 2.399E - 11 6.7803 5.358E 3.9313 2.608E 2.2033 -
11 11 11 11 11
4.9583 - 11 2.797E - 11
3.310E - 11
3.207E - 11
Weighted mean k , , = 3.3E - 11 Determination at ti corresponding to times in Figure 6.
+
where S = h12 kI3. According to Washida et al.13J4
(11) [CHOI = [CHOl,s(1- exp(-k14[01 t ) ) where [CHO],, denotes the steady state concentration [ CHO1ss = (hg/k14) [ C21141 It can be shown that
X
(111)
X
X
X X
- kS[Ol [CHOIS, A where A = hll[O] + S.
(IV)
Dividing the solution to differential eq I (assuming constant [O]) by eq IV and substituting eq I1 for [CHO] we obtain
Ae-kl4 lo 1 t [OH(u = 9)] = 1 - e-At + [OH(u = 9)Iss k14[01- A
where A = hll[O] + S. The assumption of constant [O] atoms for the residence times of these reactions was investigated with the model and is valid to within experimental error of the [ O ] concentration measurement at these low 1 e ~ e l s . l ~ Although eq V appears complicated, there is only one unknown, hll. This rate constant was solved for and the tabulated results appear in Table IV. One representative data set is shown in Figure 6 in which a correction for pressure drop and 0 atom depletion was applied. Determination of ks and Fractional Yield of OH( v = 9) The value of kg,the rate constant to produce OH(u = 9) from the reaction of CHO 0, was determined from
+
1
.04 .06 .08 .IO TIME,SEC(xlO') Figure 6. Intensity of the OH( Y = 9-4) transition as a function of time .02
0
for the reaction 0
+ C2H4.
the steady state observations of the OM(u = 9) concentration. Solving for h8 from eq I11 and IV we obtain
ha=-- [OH] 'ss [C&I at high [O] or
Ilk 14
kg
at low [O] and long times. The absolute OH(u = 9) concentration was determined with the actinometric standard and the OH Einstein coefficients of M i e ~ . ~ ~ Table V presents the values of hg determined from the steady state OH(u = 9) concentrations at the last observation port as well as other steady state values at high [O]. The average of these values is 6E - 12 cm3/s with an uncertainty of +4E - 12. The value of the CHO concentration in eq IV was calculated from the steady state expression for its concentration13J4 and in the mathematical model. A computation of the value of [CHO] from the model agrees with the simple calculation to within The Journal of Physical Chemistry, Vol. 81, No. 25, 1977
B. B. Krieger and R. H. Kummler
2490
TABLE V: Determination of the Rate Constant for the Production of OH(u = 9 ) from the Reaction of 0 t CHO [HCl/[Ol 0.16 .~ 0.05 0.34 2.23 2.87 1.67 1.26 1.74 1.38 2.13 3.80 1.08 3.00 1.60 3.20
k , , cm3/s [HCI/[Ol 1.0123 - 11 2.00 4.00 1.288E - 11 14.20 8.910E - 1 2 0.90 3.803E- 1 2 2.05 3.0893 - 1 2 0.96 5.7613 - 1 2 0.50 4.286E - 1 2 0.50 5.3153 - 1 2 4.7223 - 1 2 1.45 5.20 6.8683 - 1 2 1.20 4.017E - 1 2 0.48 2.071E - 11 0.96 6.4483 - 1 2 3.65 7.7833 - 1 2 5.4343 - 1 2
k,, cm3h 7.481E - 1 2 6.1333 - 1 2 3.7193 - 1 2 6.366E - 1 2 5.2043 - 1 2 4,7643 - 1 2 6.2293 - 1 2 8.4093 - 1 2 3.5023 - 1 2 3.5643 - 1 2 4.721E - 1 2 6.2933 - 1 2 5.3923 - 1 2 3.9043 - 1 2
Average value = 6E - 1 2 ( t 4 E - 1 2 ) cm3/s
50%. The model considers secondary sources of CHO such as the reaction of H2C0 and 0 atoms to produce CHO as well as the 0 atom depletion. The value from the model was used here. When the rate constant for the production of OH(u = 9) from the reaction of CHO + 0 is ratioed to the total rate constant for the reaction, hi4 -+
CHO t 0
’
----t
all product^'^^'^
CO t OH
of OH(u = 9) been measured. It was felt that the upper limit to h12for infinitely fast deactivation a t the wall was an appropriate value (calculated as in Cleland and Wilhelm22and Ahumada and Michael23). The OH(u = 9) total radiative lifetime and A coefficients used in this mathematical model are calculated in M i e ~ . These ~~ calculations were compared35 to experimental measurements for some vibrational transitions and the agreement reported was good. However, the radiative lifetime of OH(u = 9) as discussed in Potter et al.37is larger than that reported in Mies. Since both h12 and h13 values used in calculating hll are upper limits to the rate coefficients, new values of these h’s would cause kll to increase. The combination of these uncertainties in the values used in eq V causes hll to be underestimated, perhaps, by as much as a factor of 4. To indicate the direction of the uncertainty, the value reported is a weighted average of the experimentally determined values and the standard deviation appears with a positive sign.15 The errors in he are the same since h8 is derived from kll using the steady state concentration of OH(u = 9). In addition, the p r ~ c e d u r eto l ~determine ~ ~ ~ ~ the absolute OH steady state concentration from the OH(9-4) transition spectrum underestimates the OH(u) due to the overlap from other transitions. In this study only the spectral region free from overlap was used. Thus, h8 is also reported with a positive standard deviation.
Summary From this determination the fractional yield to produce the OH(u = 9) yield becomes OH(u = 9), the highest accessible vibrational level of OH within the exothermicity of the reaction 0 CHO, is ks = 6E-12 $ == 2.9% reasonably large. Integration of the total spectrum in the 1214 2.1E- 10 Au = 4,5, and 6 transitions of OH such as those shown in Figure 2 showed a “total” fractional yield to produce However, since the reaction is known to produce C02 and vibrationally excited OH from the original reaction rate H atoms as well as OH and CO, if the H + C 0 2 branch is of about 15%. The 15% is an estimate since the intensity eliminated from consideration a more representative value from OH(u = 1, 2, and 3) could not be measured within of the OH(u = 9) yield is given by the sensitivity region of the GaAs photocathode of the photomultiplier tube used in this work. Consideration of $=-- k 8 - 6E - 1 2 = 5% u = 1,2, and 3 would increase the “total” yield of OH(u) koH+CO 1.2E - 10 from the reaction of 0 C2H4. Thus, the production of using the branching ratio of Westenbure and d e H a a ~ ~ ~vibrationally excited OH is an important channel for the energy of the reaction 0 C2H4. h C O , t H /hOH+co = 0.73 f 0.15 The two rate constants, k8 = 6E - 12 and hll = 3E - 11 If the yield of OH(u = 9) is based on the branching ratio cm3/s describe the production and loss of OH(u = 9) in the reaction of 0 C2H4. The products of the reaction of Niki et al.1° 0 OH(u = 9) were not measured. This situation has a h C O , t H l k 0 H + C O = 0.25 direct parallel in the H O3 system studied by Charters et and Potter et al.4 The primary loss of OH’ in the the yield becomes H O3 system is interaction with O3 when the ozone is 6E - 12 in excess, just as the oxygen atoms are in excess in this = 3.5% work. Potter et ala4and Streit and Johnston6 have = 1.7E - 1 0 measured the rate constant for Discussion of Errors OH(u = 9 ) + 0, products Due to the large radial concentration gradients caused to be h = 7.7E - 12 cm3/s4to 1.1E - 11 cm3/s6 but they by high wall deactivation rates of excited species at a given state the products of the interaction were not measured. axial distance, an observation is biased toward the gases From this work the reaction of near the center of the flow tube. These gases have experienced a distribution of residence times (arising from OH(u = 9 ) + 0 products (11) laminar flow) less than that given by the observation k , , = 3 ( t 2 ) E - 11 cm3/s distance divided by the average v e l o ~ i t y . ~Thus, ~ > ~ the ~-~~ is faster than the O3 OH(u = 9) reaction as expected, observation time, t , in eq V can be overestimated by as and hll has nearly the same value as the rate constant for much as a factor of 2. The [O] can also be overestimated the reaction of 0 OH(u = 0), ground state OH by as much as a factor of 2 at the extremely low levels used in some experiments due to inadequate intensity for NO2 3.8 k (1.7)E- 11 to OH t 0 - 0, + H titration.15 The value of h12,the apparent radial diffusion 4.2(+1.7)E - 11 cm3/s loss of OH(u = 9) and its deactivation on the metal walls, as reported in NBS-CIAPl6 and Baulch et aL60 The inhas not been measured, nor has the diffusion coefficient 14
-+
co, t H
+
+
+
+
+
’
+
+
-+
-+
+
+
The Journal of Physical Chemlstry, Vol. 81, No. 25, 1977
OH Chemiluminescence in the 0
+ CpH, System
dicated uncertainty in the determination of hll is comparable to the uncertainty in the ground state reaction of OH and 0 atoms. Since the determination is a lower limit, the extreme value of 5E - 11 cm3/s would certainly be reasonable for the reaction of 0 OH(u = 9) which might be expected to be faster than the ground state reaction of 0 + OH. The rate constants obtained in this work should further the ability to model systems in which reactions of excited states of OH are prevalent such as chemical lasers, plasmas, or in the upper atmosphere. In such kinetic systems with several available excited states of a species, the complexity is multiplied by having to consider additional species and additional processes such as radiative and collisional transfer of energy. As shown here, the mathematical model offers a systematic way of segregating experimental conditions in which certain reactions rates are important or certain processes are unimportant. To be sure, at this stage, rate constants for excited state reactions are few, but estimates to upper bounds can be made which allow insight into the chemical mechanism. The model, in fact, offers the hope to the experimentalist that conditions are chosen in which competing reactions are minimized so that unambiguous rate coefficient measurements are obtained.
+
Supplementary Material Available: Appendix I contains a complete list of reactions considered, rate coefficients, and references (4 pages). Ordering information is available on any current masthead page. References and Notes (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17)
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The Journal of Physical Chemistry, Vol. 8 I , No. 25, 1977
