J. Phys. Chem. 1984, 88, 5020-5025
5020
is a skeletal e mode. There are 10 skeletal modes that qualify as promoting [a2, bl, and b2) in C,. The absence of isomer effects in Cr(NH3)4X2complexes is evidence against the involvement of skeletal promoting modes. Ligand-localized promoting modes would be subject to the same low symmetry as accepting modes and little or no cis-trans isomer difference would be expected for such modes. 2T, Emitters. In quadrate fields, 2Tlsplits into 2E and 2A2and the 2E(ZT1)component is the lowest in some complexes.I2 When the tetragonal distortion is either very small or very large, the mixing between the components of 2E and 2Tl is small and the description of the emission as ZEand 2T, is a good approximation. Near the crossover between 2E(2T,) and ZA,(ZE),ZB,(2E),the emission will be of mixed character. The 2T1emitters are distinguished from the ZEemitters by the emission band position and breadth,12 an indication of a larger horizontal displacement. The sensitivity of the energy gap and/or A M to small structural changes is exemplified by the very different, , ,X in trans-Cr(NH3).,Fzf (707 nm) and trans-Cr(en)2F2+(773 nm). This larger Stokes shift may be the reason for the faster relaxation in the en complex. Similarly, the increasing k,, in the sequences Cr(NH3)50H2t < t r a n ~ - C r ( N H ~ ) ~ ( 0 H ) C Br- > Cl-,24 the trend expected for H,. Neither Cr(NH3)5Xnor CrN4X2complexes exhibit a similar trend (Table 11). Instead, the order is C1- > F > Br- > I-. When complete interaction between the 30 configurations is invoked, the interplay between the diagonal energies and spin-orbit coupling in the off-diagonal elements would destroy any simple relation between doublet-quartet mixing and spin-orbit coupling.22,25 Furthermore, the need to include vibronic mixing into the calculation, as discussed above, further complicates the matter. Acknowledgment. We are grateful to 0. Mransted for a gift of the C r ( ~ y c l a m ) ( H , O ) ~complexes ~+ and to F. Galsbral for providing salts of Ir(II1) used as host crystals. Registry No. Cr(NH3)2', 14695-96-6; Cr(en)33c, 15276-13-8; tr~ns-Cr(NH,)~F~+, 3 1253-66-4;cis-Cr(NH3),F2', 58864-86-1;transCr(en)2F,t, 24407-74-7; c i ~ - C r ( e n ) ~ F ~22432-37-7; +, trans-Cr(NH3),CI2', 22452-49-9; cis-Cr(NH3),CI2', 60917-71-7; trans-Cr(en),CI2+, 14403-88-4;ci~-Cr(en)~Cl~', 14482-74-7;trans-Cr(NH,),(H20)23+,36834-73-8; cis-Cr(NH,),(H,O),", 42402-01-7; trans-Cr(en),(H20)?', 17993-12-3; ~is-Cr(en)~(H,O),'+,22432-36-6; transCr(en)2Br2+, 17993-14-5; ci~-Cr(en)~Br~+, 20631-53-2; trans-Cr(NHS)d(OH),+,51266-65-0;cis-Cr(NH,),(OH),', 57349-68-5;transCr(en)2(OH)2t,22334-52-7; ~is-Cr(en)~(OH)~+, 22432-35-5; trans-Cr(NH3),(H2O)CI2', 19052-43-8;C ~ S - C ~ ( N H , ) ~ ( H ~ O 19544-03-7; )CI~~, tr~ns-Cr(NH~)~(0H)C1+, 9 1670-49-4;C~S-C~(NH~)~(OH)CI+, 9173993-4; fr~ns-Cr(NH,)~(H~0)(0H)~+, 31564-04-2; tr~ns-Cr(en)~(H~O)(OH)2t, 62728-44-3;trans-Cr(en),(H20)F2', 28101-89-5; cis-Cr(en),(H20)F2', 34431-44-2; tr~nr-Cr(en)~(OH)F',85826-81-9; ~is-Cr(en)~(OH)F', 91739-94-5; trans-Cr(en),ClF+, 42476-29-9; cis-Cr(en),CIF+, 62792-40-9. (24) Thomas, T. R.; Watts, R. J.; Crosby, G. A. J . Chem. Phys. 1973,59,
m.m..1
LILJ.
(25) Flint, C. D.; Mathews, A. P.;O'Grady, P. T. J . Chem. SOC.,Faraday Trans. 2 1911, 73, 655.
Pressure Dependence of the Rate Constants for the Reactions of C,H, and C3H8with OH Radicals at 295 K Th. Klein, I. Barnes, K. H. Becker,* E. H. Fink, and F. Zabel Physikalische Chemie/Fachbereich 9, Bergische Universitat- Gesamthochschule Wuppertai, D 5600 Wuppertal, West Germany (Received: October 24, 1983; In Final Form: April 17, 1984)
-
-
The pressure dependence of the rate constants for the reactions CzH4 + OH products ( k , ) and C3H6(propene) + OH products ( k 2 ) was measured at 295 K by using a relative rate method in a 420-L reaction chamber. Synthetic air and argon were applied as diluent gases in the pressure range 1.3-1000 mbar. The H 0 2 N 0 2 / N 0system was used as a "dark" source of OH radicals. k l shows falloff behavior below about 250- and 500-mbar total pressure in synthetic air and argon, respectively. k2 exhibits falloff behavior below about 50-mbar total pressure of synthetic air and argon. The limiting high-pressure rate constants as obtained from a falloff curve analysis are kI,- = (8.5 h 0.6) X cm3 molecule-l s-l and k2,- = (3.0 f 0.2) X lo-'' cm3 molecule-' s-I using the reaction n-hexane + OH products as reference with k = 5.64 X cm3 molecule-' s-l. Falloff parameters are presented which allow the calculation of kl for M = He, Ar, air and k2 for M = Ar, air between 1.5 and 1000 mbar at 295 K.
-
Introduction The OH radical is an important intermediate in atmospheric chemistry and combustion processes. Extensive efforts have been made to determine the rate constants of OH radical reactions under atmospheric conditions including the influence of temperature and total pressure.l Accurate kinetic data obtained over ( 1 ) Atkinson, R.; Darnall, K. R.; Lloyd, A. C.; Winer, A. M.; Pitts, J. N.,
Jr. Adu. Photochem. 1979, 11, 3 1 5 .
a wide range of experimental conditions are necessary for modeling the atmosphere. Rate constant determinations and product analysis for OH reactions of atmospheric interest have mostly been carried out by using absolute methods at low pressures where the chemistry of the system is normally fairly well characterized. In recent years relative rate studies using large reaction chambers have been developed where reliable rate data can be obtained even in complex chemical systems under atmospheric conditions. Both saturated and unsaturated hydrocarbons are significant constituents of the urban and rural atmosphere and there is a
0022-365418412088-5020$01.50/0 0 1984 American Chemical Society
Pressure Dependence of Rate Constants
The Journal of Physical Chemistry, Vol, 88, No. 21, 1984 5021
general agreement that the photochemical degradation of hydrocarbons is primarily initiated by reaction with OH radicals. The reaction of OH radicals with alkanes proceeds by H-atom abstraction. In contrast, for unsaturated hydrocarbons an initial electrophilic addition of the OH radical to the .rr-bond system is expected to dominate, at least for the less complicated alkenes and aromatics.' Such a mechanism leads to a complex dependence of the overall reaction rate constant on pressure and temperature. Previous studies on the reactions
C2H4+ OH C3H6
+ OH
kl
kl
products
(ref 2-19)
(1)
products
+
(ref 3, 4, 6, 7, 9, 10, 12, 19-31) (2) have mostly been made in limited ranges of pressure and temperature. Although the results on kl and k2 show considerable scatter, a dependence on total pressure is well established for k , and discernible for k,. The pressure-dependent studies were all made by using absolute rate techniques with rare gases as the third body. U p to now measurements in synthetic air as the diluent have been performed only at atmospheric pressure by using relative rate methods. Since both reactions are of tropospheric importance and are often used as reference reactions in relative rate measurements, a more accurate knowledge of the pressure dependence of k , and k2 is of interest. The present work describes the measurement of kl and k2 relative to the rate constant for the reaction n-hexane + OH products at 295 K over the pressure range 1.5-1000 mbar using synthetic air and argon as diluent gases.
-
Experimental Section All experiments were carried out in a 420-L cylindrical Duran glass reaction chamber with Teflon-coated aluminum end flanges which has been described in detail e l s e ~ h e r e .n-Hexane ~~ was (2) Greiner, N. R. J . Chem. Phys. 1970, 53, 1284. (3) Morris, E. D., Jr.; Stedman, D. H.; Niki, H. J . Am. Chem. SOC.1971, 93, 3570. (4) Stuhl, F. Ber. Bunsenges. Phys. Chem. 1973, 77, 674. ( 5 ) Smith, I. W. M.; Zellner, R. J . Chem. SOC.,Faraday Trans. 2 1973, 69, 1617. (6) Bradley, J. N.; Hack, W.; Hoyermann, K.; Wagner, H. Gg. J. Chem. SOC.,Faraday Trans. 1 1973, 69, 1889. (7) Pastrana, A. V.; Carr, R. W., Jr. J . Phys. Chem. 1975, 79, 765. (8) Davis, D. D.; Fischer, S.; Schiff, R.; Watson, R. T.; Bollinger, W. J . Chem. Phys. 1975, 63, 1707. (9) Gordon, S . ; Mulac, W. A. Int. J. Chem. Kinet. Symp. I1975, 289. (10) Cox, R. A. Int. J. Chem. Kinet. Symp. I1975, 379. (11) Howard, C. J. J . Chem. Phys. 1976, 65, 4771. (12) Lloyd, A. C.; Darnall, K. R.; Winer, A. M.; Pitts, J. N., Jr. J . Phys. Chem. 1976,80, 789. (13) Atkinson, R.; Perry, R. A.; Pitts, J. N., Jr. J . Chem. Phys. 1977, 66, 1197. (14) Overend, R.; Paraskevopoulos, G. J. Chem. Phys. 1977, 67, 674. (15) Farauharson. G. K.: Smith. R. H. Aust. J . Chem. 1980. 33. 1425. (16) Atk&son, R.; Aschmann, S. M.; Winer, A. M.; Pitts, J. N., Jr. h t . J . Chem. Kinet. 1982, 14, 507. (17) Bartels, M.; Hoyermann, K.; Sievert, R. Symp. (Int.) Combust.,
[Proc.] 1982, 19, 61. (18) Tully, F. P. Chem. Phvs. Lett. 1983, 96, 148. (19) Zellner, R.; Lorenz, K.J . Phys. Chem. 1984, 88, 984 (20) Simonaitis, R.; Heicklen, J. Int. J . Chem. Kinet. 1973, 5, 231. (21) Gorse, R. A,; Volman, D. H. J . Photochem. 1974, 3, 115. (22) Atkinson, R.; Pitts, J. N., Jr. J . Chem. Phys. 1975, 63, 3591. (23) Ravishankara, A. R.; Wagner, S.; Fischer, S.; Smith, G.; Schiff, R.; Watson, R. T.; Tesi, G.; Davis, D. D.Int. J . Chem. Kinet. 1978, 10, 783. (24) Nip, W. S.; Paraskevopoulos, G. J . Photochem. 1978, 9, 119; J . Chem. Phys. 1979, 71, 2170. (25) Hoyermann, K.; Sievert, R. Ber. Bunsenges. Phys. Chem. 1979,83, 933. (26) Cox, R. A,; Derwent, R. G.; Williams, M. R. Enuiron. Sci. Technol. 1980, 14, 57. (27) Atkinson, R.; Carter, W. P. L.; Winer, A. M., Pitts, J. N., Jr. J . Air Pollut. Control Assoc. 1981, 31, 1090. (28) Barnes, I.; Bastian, V.; Becker, K. H.; Fink, E. H.; Zabel, F. Chem. Phys. Lett. 1981, 83, 459. (29) Barnes, I.; Bastian, V.; Becker, K. H.; Fink, E. H.; Zabel, F. Atmos. Enuiron. 1982, 16, 545. (30) Ohta, T. J . Phys. Chem. 1983, 87, 1209. (31) Smith, R. H. J . Phys. Chem. 1983, 87, 1596.
used as the reference hydrocarbon in all measurements. The concentration-time behavior of the hydrocarbons was monitored by G C (Hewlett-Packard Model 5710 A, FID, stainless steel column packed with Porasil C). The concentrations of the hy~ . semdrocarbons were on the order of lOI4 molecules ~ m - The istable peroxynitric acid H 0 2 N 0 2(PNA) in the presence of N O was used as the source of OH radicals. P N A was prepared by the heterogeneous reaction of concentrated H202(85%) with NO,, as previously de~cribed.,~ In a standard experiment 0.13-0.33 mbar of the PNA-containing gas mixture was introduced into the reaction chamber through a gas handling system. Such gas mixtures contained typically 20%PNA, with impurity levels of 10% H N 0 3 , 15% H20 (estimated), 15% NO,, and 10% H202(estimated). 0, is also a byproduct of the P N A production and probably accounts for the missing 30% in the mass balance. In the gas phase, PNA decomposes to give H0, and NO,. Its thermal lifetime at room temperature and atmospheric pressure is about 10 s.32 However, due to the rapid reverse reaction, H 0 2 + NO2 H 0 2 N 0 2 ,the actual lifetime of P N A in the reaction chamber under these conditions is about 1 h. Hydrocarbons can be added to the system without disturbing this equilibrium as they are relatively unreactive ~ . ~ ~ of N O toward H 0 2 radicals at room t e m p e r a t ~ r e . ~Addition then results in a rapid conversion of H 0 2 to OH according to the OH + NO,, k = 8 X lo-', cm3 fast reaction H 0 2 N O molecule-1 s - ' . ~ ~Thus, the thermal decay of PNA in the presence of NO results in the formation of O H radicals which undergo further reactions. When hydrocarbons, R,, are present in the system, their primary degradation step is R, OH products. The experimental procedure was as follows: PNA, the hydrocarbons (by syringe injection), and the diluent gas were added to the reaction chamber and the degradation process was then initiated by syringe injection of an excess of N O to the system. The hydrocarbon concentrations were measured before and after NO addition by G C analysis. The reaction time varied from 1 3 to 20 min depending on total pressure. In all measurements, the samples were taken with a 5-mL gas-tight syringe accordihg2tb the following procedure: (1) The syringe was placed in the reactor sample port. (2) The plunger was pulled back to the 5-mL graduated line and a period of 10-30 s (depending on the pressure) was allowed for pressure stabilization between reactor and sample volume. (3) The gas-tight push-bottom valve on the syringe was closed. (4) The gas sample was injected into the GC. With this sampling technique reproducible results were obtained for kl and kz at total pressures between 1.5 and 1000 mbar. The precision of the measurements of the hydrocarbon concentrations decreased from about f5% at total pressures greater than 10 mbar to f 10% at 1.5 mbar. The chemicals had the following stated purities: argon (99.997 ~ 0 1 % ethene )~ (99.7 vol %), propene (99.98 vol %), n-butane (99.5 vol %), n-hexane (99%), NO, (98.0 vol %), N O (99.85 vol %), synthetic air (99.995 vol %), H202(85 ~ 0 1 % ) .All chemicals were used without further purification.
-
+
-
+
-
Results and Discussion If the loss process for a reactant R in the system is the reaction with O H R
+ OH
k
products
the reaction rate is represented by -(d[R] /dt) = k[R] [OH] Integration over the reaction time t leads to A In [R] =
j' k[OH] dt 1=0
(32) Graham, R. A,; Winer, A. M.; Pitts, J. N., Jr. J . Chem. Phys. 1978, 68, 4505. (33) Lloyd, A. C. Int. J . Chem. Kinet. 1974, 6, 169. (34) Graham, R. A,; Winer, A. M.; Atkinson, R.; Pitts, J. N., Jr. J . Phys. Chem. 1979,83, 1563. (35) Baulch, D. L.; Cox, R. A,; Crutzen, P. J.; Hampson, R. F., Jr.; Kerr, J. A.; Troe, J.; Watson, R. T. J . Phys. Chem. ReJ Data 1980, 9, 295; 1982,
11, 327.
5022 The Journal of Physical Chemistry, Vol. 88, No. 21, 1984
-
TABLE I: Summary of Experimental Results for the Reaction C2H4 OH Products at 295 K"
+
no. plmbar
1004.1f 7.3 534.0f 4.4 272.3f 4.8 132.9f 0.4 66.9f 0.3 27.5 f 0.5 14.1f 0.5 9.6f 0.1 5.5 f 0.1 2.8f 0.1 1.5 f 0.1 1000.2f 3.5 530.8f 0.8 264.2f 0.1 132.9f 0.4 93.2f 0.1 53.5 f 0.1 26.9i 0.1 13.5 f 0.1 9.5f 0.1 5.5 f 0.1 2.8f 0.1 1.5 f 0.1
Klein et al.
-
TABLE 11: Summary of Experimental Results for the Reaction C3H, OH Products at 295 K"
+
10'2kl/
of runs
(cm3 molecule-'
M = Synthetic Air 10 6 7 10 7 4 9 4 5 3 3 M = Argon 6
no.
8.06f 1.50 7.70f 0.70 7.68f 1.12 7.30f 0.78 6.96f 0.56 5.90f 0.32 4.97f 0.26 4.46f 0.58 3.64f 0.34 3.21 f 0.60 2.58f 0.56 8.45f 0.50 8.45f 0.48 7.76f 0.24 7.36f 0.36 6.63f 0.52 6.19f 0.24 5.20& 0.36 4.40f 0.66 3.86f 0.14 2.98 f 0.70 2.26 f 0.26 1.79f 0.34
3 5
5 3 3 3 3 2 3 3 2
plmbar
s-I)
101'k2/
of runs
(cm3 molecule-' s-l)
998.3f 7.2 590.5f 3.2 265.4f 0.7 92.9& 0.1 26.8f 0.1 13.5 f 0.1 9.5f 0.1 5.5 f 0.1 2.8f 0.1 1.5f 0.1
M = Synthetic Air 12 6 3 2 2 4 4 4 4 3
2.83 f 0.44 2.70f 0.22 2.73f 0.16 2.91 f 0.08 2.82f 0.16 2.63f 0.16 2.55f 0.18 2.46f 0.18 2.16 f 0.14 1.92f 0.24
1006.1 f b.5 530.1f 0.1 265.0f 0.1 133.0f 0.3 93.0f 0.1 53.2f 0.1 26.8f 0.1 13.5 f 0.1 9.5f 0.1 5.5 f 0.1 2.8f 0.1 1.5 f 0.1
M = Argon 2 2 4 2 2 3 4 3 4 4 2 4
2.86 f 0.26 2.84f 0.02 2.78f 0.10 2.80f 0.12 2.82f 0.10 2.76f 0.22 2.74f 0.08 2.54f 0.08 2.52f 0.22 2.33f 0.34 2.15f 0.22 1.90f 0.68
"Quoted error limits 2a.
"Quoted error limits 2a. 10
If two or more reactants Ri are present in the system and assuming that the reaction with OH radicals is the only major depletion process and that there are no processes which regenerate the hydrocarbons, the following simple relationship holds:
A In [Ri] A In [Rj]
-=-
,
I
100 I
,
1000 plTorr I
c
k,
kj
Thus, the ratio of two reaction rate constants can be determined by simply measuring the relative amounts of the reactants Ri and Rjbeing consumed during the total reaction time. The relative rate constants measured in this work are given by
M
C2Hb + OH +products
-12 0
with kn.hexsne = (5.64 f 1.1) X lo-'' cm3 molecule-'^-^. The rate constant kn.henane was determined over the pressure range 1.5-1000 mbar relative to n-butane by using the same experimental procedure as for ethene and propene. The observed rate constant ratio was found to be pressure independent as would be expected and had a value of kn.hexane/kn.butane = 2.23 f 0.22, which is in good agreement with the recent value of 2.21 obtained by Atkinsen et a1.16 at 1000 mbar in air. From this ratio, the absolute value for kn-hcxane was obtained with kn.b,tane(295K) = 2.53 X cm3 molecule-' s-', which is the average of four temperature-corrected (with Ea = 4.6 kJ mol-' (ref 36)) absolute absolute rate measurements.3639 The quoted error for the ratio kn.hexane/kn.bUuneis the 2a error from 20 measurements in the range 1.5-1000 mbar, while the error limits assigned to kn-hexaneinclude also an estimated overall error of 10% for kn.butane. The rate constants kl and k , obtained over the pressure range 1.5-1000 mbar at 295 K in synthetic air and argon are summarized in Tables .Iand 11, lespectively. Products. In Figures 1 and 2 the data of C2H4 OH Table I are presented as log k l vs. log [MI plots. As can be seen kl exhibits a prominent falloff both in synthetic air and argon and
+
(36)Perry, R.A,; Atkinson, R.; Pitts, J. N., Jr. J. Chem. Phys. 1976, 64, 5314. (37) Greiner, N.R.J . Chem. Phys. 1970, 53, 1070. (38)Stuhl, F.Z. Naturforsch. A 1973, 28, 1383. (39) Paraskevopoulos, G.; Nip, W. S. Can. J . Chem. 1980, 58, 2146.
I 16
ki(p) = kn.hexane(A In [Ri]/A In [n-hexane])
I
I
I
I
-
20
17 18 19 log ~ ~ M l / m o l e c u l e~s r nI - ~
Figure 1. Dependence of kl on total pressure at 295 K for M = synthetic air. The solid line through the data points is the calculated falloff curve. The error bar represents the average 2a error of all individual data points. For a discussion of the data points in parentheses see text. 1000 plTorr
100
10 I
-12 0
I
16
I
I
I
17 18 19 log ICMIlmolecules ~ m - ~ )
I 20
-
-
Figure 2. Dependence of klon total pressure at 295 K for M = Ar. The solid line through the data points is the calculated falloff curve. The error bar represents the average 2u error of all individual data points. For a discussion of the data points in parentheses see text.
approaches, within error limits, the same limiting high-pressure value for both diluent gases a s p 2 500 mbar. This behavior can
Pressure Dependence of Rate Constants
-
The Journal of Physical Chemistry, Vol. 88, No. 21, 1984 5023
be explained by the following mechanism: CzH4 + O H
[CHZCHzOH]* [CHZCHZOH] *
+M
-+
CzH4
-
-+
[CHzCHzOH]* CH2CH20H (+X) products
10
[CHzCHZOH] *
+ OH
100
1000 p l T o r r
+
0 0
- 11.0
CHzCHzOH products
--+
(X = NO, NOz, OH, 02,etc.) (le)
Reactions 1a-c describe a simple recombination mechanism which can account for the observed pressure dependence of kl. In fact, the CHzCHzOH radical has been identified in the CzH4 + O H reaction mass spectrometrically by various group^.^,'^ Reaction Id represents possible contributions of pressure-independent reaction channels leading to HzCO and CH,CHO which have been investigated in detail at low total pressures ( 6 3 mbar) in helium by Bartels et al." Reaction l e corresponds to all, mostly bimolecular, reactions which prevent the C H z C H 2 0 H radical from a back-formation of C2H4. The mechanism represented by reaction l e has been studied by Niki and c o - w ~ r k e r for s ~ ~a gas mixture containing O2and NO and will not be specified for the reaction systems of the present study. Tentatively, a falloff curve analysis, based on the symmetrized reduced Kassel integral formalism developed by Troe and coworkers,"' hls been applied to the data at p > 5 mbar. According to this formalism the pressure dependence of the reduced rate coefficient k/k, may be represented at room temperature by
where ko, which is proportional to [MI, and k, are the limiting second-order rate constants for low and high pressures, respectively. The broadening factor Fc,,, was calculated for the formation of the adduct CHzCHzOH with the C-0 bond energy estimated by using group additivity rules.42 The falloff curves resulting with P,,, = 0.7 are shown by solid lines in Figures 1 and 2. The good agreement between the calculated and experimental falloff curves for both M = Ar and M = synthetic air suggests that the simple recombination mechanism la-c is sufficient to describe the experimental data above 5 mbar. The best fit to the data points was achieved with k1,, = (8.5 f 0.6) X
cm3 molecule-' s-'
kte(295 K)/[air] = (9.5?:$)
X loez9cm6 molecule-2 s-'
ktb(295 K)/[Ar] = (5.9:;:)
X
cm6 molecule-* s-'
The quoted error limits of kI,, essentially represent the 20 errors of the data points for both M = air and M = Ar near 1000 mbar. The error limits assigned to the kl,ovalues refer to the ranges of kl,ovalues which result from the best fit of the calculated reduced falloff curve to the experimental data points when k1,, is varied within the stated error limits. In order to obtain estimated overall error limits for kl a 20% error for kn.hexane as the reference rate constant should be included. From the data above 5 mbar, a rate constant ratio for the addition reaction in the limiting low-pressure limit for M = air and M = Ar of k;f;/k$, = 1.6 is obtained which compares favorably with the results for other recombination/dissociation reactions at room temperature (see Baulch et al.35for comparison) where values between -1 and -3 have been determined for ky6/k;fb directly from experiments in the low-pressure region. It should be. emphasized, however, that the low-pressure rate constant (40) Niki, H.; Maker, P. D.; Savage, C. M.; Breitenbach, L. P. J . Phys. Chem. 1978, 82, 135; Chem. Phys. Lett. 1981, 80, 499. (41) Luther, K.; Troe, J. Symp. (Int.) Combust., [Proc.] 1979, 17, 535. Gilbert, R. G.; Luther, K.; Troe, J. Ber Bunsenges. Phys. Chem. 1983, 87, 169. (42) Benson, S. W. "Thermochemical Kinetics", 2nd ed.; Wiley: New York, 1976.
16
17 18 19 l o g (CMl/rnolecules ~ r n - ~ )
20
Figure 3. Comparison of literature kl values near rwm temperature with the calculated falloff curves from this work (solid line: M = Ar, broken line: M = synthetic air). The data points are presented without error limits to simplify the comparison.
ratio derived above for M = air and M = Ar is valid only if the curvature of the falloff curves does not depend appreciably on the nature of collision partner. Below 5 mbar the experimental data points are higher as compared to the calculated falloff curve, the difference increasing with decreasing total pressure. This behavior probably originates, at least partly, from an increasing contribution of strong collision partners which are introduced into the r,,action chamber as impurities in the HOZNO, sample. For example, at total pressures of 1.5 and 2.8 mbar about 14% and 7%, respectively, of the collision partners are represented by M = HOzNOZ,HNO,, H20, HzOz,and NOz, as estimated from FTIR absorption measurements. The data points at the two lowest pressures may be corrected for the contributions of these strong colliders assuming that the curuature of the falloff curves is independent of collision partner. With these corrections the data points in parentheses in Figures 1 and 2 are lowered to within f3% of the calculated = HOzNOz imfalloff curves provided that a ratio of /C,,~(M purities)/kl,o(M = Ar) = 8 is used, which is a reasonable value for strong collision partners as compared to argon. For this reason, the data presented in Figures 1 and 2 are fully consistent with a recombination mechanism for reaction 1 between 1.5- and 1000-mbar total pressure. An alternative explanation of the discrepancies between the experimental data points at low total pressures and the calculated falloff curves would be that with decreasing pressure an increasing fraction of the total rate is represented by pressure-independent pathways. Within the error limits, the present data between 1.5 and 1000 mbar are consistent with an upper limit of k I7 X lo-', cm3 molecule-' s-I for all pressure-independent reaction channels. Figure 3 shows a comparison of the room-temperature data on k l . The results from several earlier investigations have suffered from uncertain stoichiometric factors and are not included in Figure 3. The broken line and the full line represent the data from this work for M = synthetic air (from Figure 1) and M = Ar (from Figure 2), respectively. The rate constant k l for M = air at a total pressure of 1000 mbar from this study (8.1 X cm3 molecule-' s-' at 295 K) agrees, within error limits, with the corresponding values from Lloyd et al.I2 (7.5 X cm3 molecule-' s-'; with k = 2.6 X cm3 molecule-' s-' for the reference reaction n-butane + OH products) and from Atkinson et a1.I6 (8.5 X cm3 molecule-' s-') and is close to the extrapolated cm3 molecule-' high-pressure limit (kl,, = (8.5 0.6) X s-'). As these three studies have used relative rate methods where the results depend on the correct absolute value of kn.butane, it is important to realize that the pressure-dependent absolute rate
+
-
*
5024
The Journal of Physical Chemistry, Vol. 88, No. 21, 1984
measurements of Overend and Paraskev~poulos'~ ( M = SF, and CF4, 533 and 800 mbar), Atkinson et al.13 (M = Ar, 33-880 mbar), and Tully18 (M = He, 67-800 mbar) approach similar 7.9 X and 8.5 X lo-', cm3 k1,- values of 10.6 X molecule-' s-', respectively. The present falloff curve for M = Ar is in excellent agreement with the results of Atkinson et a l l 3 (33-880 mbar of Ar) and is consistent with the recent results of Lorenz and Zellner19 (4-133 mbar of Ar). The falloff curve for M = air is in reasonable agreement with the rate constant for M = N2 from Davis et a1.8 at 4 mbar. Most of the literature data on kl have been obtained with helium as the third body. From the three most recent investigations of Howard," Farquharson and Srnith,l5 and Tullyls a falloff curve results for M = He which parallels the falloff curves for M = Ar and for M = air from this work. Application of the same falloff treatment as described above for M = air and M = Ar to the data points of these three studies gives, by the method of least squares, cm3 a high-pressure limiting rate constant of k1,- = 8.5 X molecule-' s-' and a limiting low-pressure rate constant for M = H e which is lower by 48% as compared to that for M = Ar. The early measurements of Morris et al.3 at 1.3 mbar are possibly high due to the complex chedical*system involved (excess of OH, stoichiometry assumed to be 1). The results of Stuh14 may be slightly low due to adsorption of ethene on the metallic reactor walls, as has been argued by Ravishankara et aLZ3 The results of the pressure-dependent study of Davis et a1.,8 although being consistent with the above presentation within the combined error limits, does not fit very well to the suggested pressure dependence, leading to a limiting high-pressure rate constant which is probably low by -40%. Finally, the measurements of Overend and Para s k e v ~ p o u l o in s ~67 ~ mbar of H e with varying amounts (0.05-5 mbar) of water vapor are not consistent with the presentation given above. Their rate constant k l strongly increases with the water content, approaching a limiting high-pressure value of 1 X IO-'' cm3 molecule-' s-I for PHlo > 1 mbar, which is in line with other kI,-values. However, the rate constant for the lowest H20partial pressure which has been applied is -45% below the value which would be expected at 67 mbar from the falloff curve for M = He as discussed above. There is no obvious reason for this discrepancy. According to the preceding discussion a satisfactory picture is obtained from Figure 3 for the pressure dependence of reaction 1 between 1.5 and 1000 mbar for three different diluents: the rate constant k, is close to 8.1 X cm3 molecule-' s-l at 295 K in 1000 mbar of synthetic air. The pressure dependence of k , between 1.5 and 1000 mbar is adequately described by the reduced falloff expression of Troe et aL4' with the parameters kl,- = 8.5 X cm3 molecule-' s-l, Pee,,,, = 0.7, kl,o/[Ar] = 5.9 X cm6 molecule-2 s-l, and the,low-pressure third-body efficiencies represented by the ratio k;fb:kti:kTi = 1.6:1:0.5. Unfortunately, the results on k l as discussed above are not consistent with recent measurements on the product distribution of reaction 1. Bartels et a1.I7 determined a ratio of about 3 for the contributions of the pressure-independent and pressure-dependent pathways at a total pressure of 3 mbar in helium. On the other hand, a value of I 1 is obtained for this ratio when the total rate constant for M = H e at 3-mbar total pressure from cm3 molecule-' s-I) is combined with the Figure 3 (1.4 X upper limit for the sum of the rate constants of the pressure-incm3 dependent reaction channels from this work ( 1 7 X molecule-' s-'), Further measurements on the product distribution and/or the total rate constant of reaction 1 are necessary to clarify this discrepancy. C3H6+ OH Products. The observed rate constants k2 from Table I1 are presented in Figure 4 as log k2 vs. log [MI plots for both diluent gases. As can be seen k2 exhibits falloff behavior at pressures below 50 mbar. This pressure dependence indicates that an addition mechanism similar to the reaction of ethene with OH is occurring for the reaction of propene with OH radicals. No difference could be established between the measured k2 values for both diluent gases presumably due to the fact that the rate constants at the lowest pressure used in the present study are still not far from the high-pressure limit. The 1.5-mbar data point
-
Klein et al. 10
100
1000 p/Torr L
I
I L
t
1 I I 17 18 19 log (CMJ/rnolecules crn-3)
16
I
-
20
Figure 4. Dependence of k2 on total pressure at 295 K for M = Ar (m) and M = synthetic air (0). The solid line through the data points is the calculated falloff curve. The error bar represents the average 2u error of all individual data points. For a discussion of the data point in parentheses see text.
--
10.5
f.;
m
c
'a,
2
U
E,
0
100
1000 p/Torr I D
I
I
-I-
d-
- 1
-
10
A
- 1 1 ,o
1
C3H6* OHSproducts
k2,w
6 . N
x
Y
-F - 11.5
1 I
16
a i ? : v L L O Y D et
COX et al.
I
E123 C263
01.
I
1
17 18 19 log ( C M l l r n ~ l e c u l e s ~ c r n ~ ~ )
-
20
Figure 5. Comparison of literature k2 values near roam temperature with the calculated falloff curve from this work (solid line).
has been put in parentheses as corrections due to the presence of 10% strong collision partners (HO2NO2,etc., see discussion on k l above) would lower the measured rate constant by 10%. A falloff curve analysis was applied to the data above 2 mbar as = 0.5 described for reaction 1. With an estimated value of P,,, for the reaction C3H6 OH M CH3CHCH20H+ M the best fit to the data points is obtained with
-
+
k2,- = (3.0 k,,,/[M]
-
8 X
+
-
* 0.2) X lo-''
cm3 molecule-] s-I
cm6 molecuk2 s-'
(M = air, Ar)
The k2,0value is subject to large uncertainties due to the broad range of possible extrapolations from the small experimentally observed falloff. The above k,,,/[M] value seems to be reasonable when it is compared with ko/[M] values for other recombination reactions leading to product molecules of comparable size (see In Figure 5 the literature data on k2 at T r ~ for e comparison). ~ ~ room temperature are compared with the results from this work. All measurements are in good agreement between 30 and 1000 mbar. Obviously, k2 is very close to the high-pressure limit in this pressure range and independent of the third body. For this reason, the average of all k2 values a t total pressures above 30 mbar might be the "best choice" at the present time for k2 at 1000 mbar and M = air: from the rate constants (in units of lo-'' cm3 molecule-' s-l) of the relative rate measurements of Lloyd et a1.I2 (2.61; with kn-butane = 2.69 X cm3 molecule-' at 305 K) and of this work (2.8) and of the absolute rate measurements of (43) Troe, J. J. Chem. Phys. 1977, 66, 4758.
J . Phys. Chem. 1984, 88, 5025-5031 Atkinson and Pitts22(2.51), Ravishankara et al.23(2.63), Nip and P a r a s k e v o p ~ u l o s(2.44), ~~ and Lorenz and ZellnerIg (3.0) an estimate of kz (298 K, M = air) = (2.7 f 0.3) X lo-" cm3 molecule-' s-l is obtained. At total pressures below 30 mbar, the k2 values differ by as much as a factor of 6. The measurements relative to the reaction C O OH CO, H20-21 have been omitted from Figure 5 , as the rate of the reference reaction subsequently proved to show a complex dependence on pressure and possibly also on the O2 partial pressure (see discussion in ref 35 for comparison). The low values of Bradley et a1.6 and Pastrana and Carr' can probably be discarded due to uncertainties in the stoichiometric factors n which they used to calculate k, from the measured nkz. Yet it is not understood why even their effective rate constants nk, are definitely low as compared to the falloff from the present work. In static experiments problems may arise from the adsorption of alkenes, and in particular of propene, on the walls of metallic reaction vessels, as has been discussed by Ravishankara et aLZ3 The low value of Stuh14 is possibly the result of such wall effects. Near 1.3 mbar, the falloff curve from the present work is in good agreement with the results of Morris et al.,3 Barnes et a1.,28and Smith,31 but only in poor agreement with the recent work of Zellner and Lorenz.lg The slight pressure dependence of k2 from this work and the much steeper pressure dependence as suggested from the work of Zellner and Lorenz are not consistent with the conclusion of Smith3' that k2 is already at the high-pressure limit
+
-
5025
near 1.3 mbar. However, the actual degree of falloff at pressures
