J. Phys. Chem. 1983, 8 7 , 1596-1600
1598
concentration samples. The same holds for the values of Icpt,/K and while the quotient of SDDQ over the number n of samples shows a decreasing tendency. The trend of the K values is presented in Figures 2-4 for the combinations 8-H/3-Me, 7-Me/3-Me, and 3-Me/l-Me. Here and in the following discussion the variation in K of the combination 8-H/l-Me resembles that of 8-H/3-Me (Figure 2), and that of 7-Mell-Me resembles that of 7Me/3-Me (Figure 3). The uppermost plot in Figure 2 confirms the errors in the low-concentration shifts. Stepwise omission of the low-concentration samples makes K approach the most probable value of 0.115 L/mol without reaching it. The same holds for the uppermost plot of Figure 3, although in this case the decrease in K soon reaches a plateau near the most probable value (about 20% higher). In Figure 4 the general decreasing trend of K can be recognized in the uppermost plot as well, but for this combination (3Me/ 1-Me) the shift differences are much smaller than for the other combinations (compare the values of Icpt,+/K in Table VII). The influence of outlying shift values is therefore much stronger than in the other combinations. Consequently, the trend interruption caused by particularly large shift difference errors (samples 5 and 9) is striking. The influence of the outlying sample 17 was analyzed by repeating the preceding computations with omission of sample 17. The second (intermediate) plots in Figures 2-4 show the corresponding dependence of K. The approach to K = 0.115 L/mol is improved. This approach to K = 0.115 L/mol is improved further when the computation is repeated with omission of samples 15 and 17. This is shown by the bottom plots in Figures 2-4. For the combinations 7-Me/3-Me, 7-Me/ 1Me, and 3-Me/l-Me the most probable value of K is virtually matched. For the last combination sample 9 was
eliminated in addition to samples 15 and 17. The computed parameters corresponding to the last point of each bottom plot are as follows (K, Icpt,+/K, a2,01-p, SDDQIn, dimensions as usual in this paper, n is the number of data): &H/3-Me, 0.201,93.8, 1.04, 0.015; 8-H/l-Me, 0.195, 103.3, 2.06,0.013; 7-Me/3-Me, 0.122, 122.2, 0.60,0.024; 7-Me/lMe, 0.122, 132.2, 1.62, 0.057; 3-Me/l-Me, 0.131, 9.7, 1.03, 0.011. An analysis of this kind may be helpful when one evaluates K from rather scattering and uncertain shift values. The high sensitivity of the AUS correction to experimental errors is recognizable even with the very good caffeine-benzene shift data of ref 1. Application of the same omission procedure to shift difference data formed from series 1 of ref 1 (compare Table VII) yields Figure 5, again with a good congruence between the combinations 8-H/3-Me and 8-H/l-Me (not shown) as well as between the combinations 7-Me/3-Me and 7-Me/l-Me (not shown). The comparatively stronger error sensitivity of the combination 3-Me/l-Me is caused probably by the smallness of Icpt,+/K and of the shift differences. As for the demonstrated influence of experimental errors in the shift difference method one should consider a possible influence of variation in the concentration of the internal reference. We were made to realize this aspect by one of the reviewers. Perhaps, a part of some experimental errors in ref 9 might be caused by holding neither this concentration nor [A,,] sufficiently constant. Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft. This support is gratefully acknowledged. We thank one of the reviewers and Professor Milton Tamres, Ann Arbor, for many suggestions which helped to improve the manuscript. Registry No. NBASbenzene, 65646-04-0; DNBSbenzene, 3101-95-9.
Rate Constant for the Gaseous Reaction between Hydroxyl and Propene Roland H. Smith School of Chemistry, Macquarie University, North Ryde, New South Wales 2113, Australia (Received: June 15, 1982)
Discharge flow with resonance fluorescence monitoring of hydroxyl has been used to measure the rate constant for OH + C3H6at five temperatures in the range 255-458 K. A t 298 K the rate constant k l is (1.9 f 0.3) X cm3s-l where the quoted error includes both systematic and statistical components. While it has been established that at 298 K pressures of 0.9 and 3 torr are in the limiting high-pressure region for this addition reaction, the strongly negative temperature dependence observed at these pressures, described by either k , = 1.59 X exp(1470/T) cm3 s-l (with 18% accuracy) or k l = (2.3 X (T/300)-*.*cm3 s-l (with 25% accuracy),has been used t o infer that at the higher temperatures these pressures are within the falloff region. Results are compared with previous measurements.
Introduction Three recent flash photolysis measurements of the rate constant for the reaction C3H6+ OH product (1)
-
have produced values of 1011kl/(~m3 s-l) at 298 K which agree with one another: 2.51 f 0.25 by Atkinson and Pitts,' (1) R. Atkinson and J. N. Pitts, J . Chem. Phys., 63, 3591 (1975).
0022-3654/83/20871596$01.50/0
2.56 f 0.12 by Ravishankara et a1.2 (both groups using resonance fluorescence), and 2.46 f 0.28 by Nip and Paraskevopo~los~ (using resonance absorption). However, three earlier discharge flow measurements of 10llkl disagree with one another and two are significantly different (2) A. R. Ravishankara, S. Wagner, S. Fischer, G. Smith, R. Schiff, R. T. Watson, G. Tesi, and D. D. Davis, Int. J. Chem. Kinet., 10,783 (1978). (3) W. S. Nip and G. Paraskevopoulos, J . Chem. Phys., 71, 2170
(1979).
0 1983 American Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 9, 7983
Gaseous Reaction between Hydroxyl and Propene
from the above consensus: 1.7 f 0.4 by Morris, Stedman, and Niki4 (using mass spectrometry), 0.50 f 0.17 by Bradley, Hack, Hoyermann, and Wagnel.5 (using ESR), and (0.5 f O.l)/n by Pastrana and Carr6 (using resonance absorption) where n is the stoichiometric coefficient, with in all probability n > 1. An earlier flash photolysis resonance fluorescence measurement by Stuhl' also differed from the later consensus, producing 10"kl = 1.45 f 0.22 cm3 s-l at 298 K. Discharge flow with resonance fluorescence monitoring of hydroxyl has now been used to reexamine the reaction in order to try to resolve the discrepancies among the discharge flow values and that between them and the later flash photolysis values, and in particular to try to determine whether a pressure falloff effect is partially responsible for the discrepancies. Ever since Morris et ala4detected adducts in the reactions OH + C2H4and OH C3H6,it has been generally believed that the first step in the reaction between OH and propene is an addition reaction. confirmation of the negative temperature dependence obtained by Atkinson and Pitts' was also sought. Because of the importance of the reaction in photochemical smog formation, accurate values of kl are required.
+
Experimental Section The 3.0 cm i.d., 30 cm long, phosphoric acid coated Pyrex flow tube had a fixed fluorescence detector at one end, a fixed hydroxyl source at the other (H atoms + excess NO,), and a movable multiholed inlet for admittance of propene. The flow tube was thermostated by fitting either a copper jacket for circulating liquid (at lower temperatures) or an electrically heated copper tube furnace (for higher temperatures). An interference filter (A, = 309 nm), an EM1 9789QA photomultiplier, and photon counting equipment were used to measure fluorescence. Sensitivity was typically 500 counts per second for 10" radicals cm9 with the ratio of fluorescence to the sum of scattered light plus dark current being approximately 15 for 10" ~ m - ~ . Carrier gas (helium) flow rates were determined by measuring pressure drop across a calibrated capillary (using an MKS Baratron series 170 capacitance manometer). Flow rates for other gases, propene, NO2,H,, often used mixed with helium, were measured by diverting the flow into a known volume and recording pressure rise as a function of time, again using the capacitance manometer. Flow rate measurements were reproducible to better than 0.5% and accurate to approximately 2%. Each day before any measurements were performed the flow tube was conditioned by passing through it a high concentration of OH (1 X 1012-3 X lo', ~ m - for ~ ) 1-2 h. The proportionality constant relating fluorescence signal to OH concentration was usually determined daily by measuring the fluorescence signal when to a large excess of H atoms a small known flow of NO, was added through the movable inlet positioned to allow H NO, OH NO to go to virtual completion without any significant loss of OH by wall reaction so that [OH] = [NO,]. The wall constant for OH removal, k,, was then determined by measuring under these same conditions the fluorescence signal as the distance between fluorescence cell and NO, inlet was increased: values for k, were in the range 8-20
+
-
+
S-1.
(4)E.D.Morris, D. H.Stedman, and H. Niki, J. Am. Chem. SOC.,93, 3570 (1971). (5)J. N. Bradley, W. Hack, K. Hoyermann, and H. G. Wagner, J. Chem. SOC.,Faraday Trans. I , 69,1889 (1973). (6)A. V. Pastrana and R. W. Carr, J. Phys. Chem., 79,765 (1975). (7)F. Stuhl, Ber. Bunsenges. Phys. Chem., 77,674 (1973).
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Helium (99.99%) was purified by passage through molecular sieve, NO, (Matheson) by freezepumpthaw cycles until a pure white solid was obtained, and propene (Matheson C.P. grade) by trap-to-trap distillation with rejection of first and last 25% fractions. Results and Discussion Kinetic experiments were performed with [C3H6] >> [OH], where [OH], is the hydroxyl concentration at the most distant upstream point to which the propene inlct was moved in the particular experiment. Fluorescence was measured as a function of x , the distance of the C3H6inlet from the fluorescence cell, with propene both present, [OH],P, and absent, [OH]:. On the assumption that OH is removed only by a first-order wall reaction and a pseudo-fmt-order reaction with propene, the pseudo-first-order rate constant, k f , is given b p kf = -U
d In [OH],P dx
+ U
d In [OH],O dx
where u is the average linear flow velocity. The contribution of the second term fo k f was only 0.3-3 5-l. Values of k; measured in this study ranged from 30 to 330 s-l, ti being 900-2400 cm s-l though most frequently 1300-1500 cm s-l. Plots of In [OH],P vs. x were linear generally for two to three half-lives. Viscous pressure drop through the reaction zone was always less than 3 % . The pressure used for calculating flow velocity u, rate constants k f , and propene concentration was the value at the midpoint of the reaction zone and was calculated from the measured pressure by A p / l = 8qu/P where q is the viscosity coefficient and r the radius of the flow tube. Axial diffusion was allowed for as explained by Kaufmang by using
kf = kf(1 + k,'D/u2) where kf is the corrected rate constant and D the diffusion coefficient estimated from the data of Marrero and Masonloto be 700 cm2torr s-'/P at 298 K with values at other temperatures calculated from D T112. The correction term kfD/u2was usually 1-3% but never greater than 7%. As a check on radial diffusion, the parameter D / k f r 2was calculated: generally it was greater than unity (and always > 0.5) so that, as shown by Poirier and Carr," radial diffusion was sufficiently fast to preserve plug flow so that negligible error (
