1808
J. Phys. Chem. 1982, 86, 1808-1815
are able to influence the electronic nature of the ?r system. Normal Mode Assignments. Low-Frequency Region. Normal coordinate calculations have appeared for several metallooctaalkylporphyrins.36 These models should most closely approximate the mesoheme group of cytochrome c. When one examines the results for the potential energy contributions of various internal coordinates to the modes, one finds that in the frequency range 250-400 cm-' many modes have as the major contributor (20-80%)3to the potential energy distribution a coordinate described as pyrrole carbon-substituent group in-plane wagging. Since the symmetry is D&, these coordinates contribute to modes of Alg, A,, Blg, B , and E, symmetry. If one assumes, however, that the ?errocytochrome c symmetry of C, applies (Table 11), one finds numerous A' modes (totally symmetric representation for the C, point group) which would be resonance Raman active and polarized. Such a correlation is detailed in Table III, where calculated modes for copper(I1) octamethylporphyrin and nickel(I1) octaethylporphyrin are tabulated along with the observed modes for ferrocytochrome c. If the effective symmetry is assumed to be C,, one can account for the appearance of the low-frequency resonance Raman spectrum of native ferrocytochrome c. Since these substituent in-plane wagging coordinates contribute to a much lower degree to the potential energy distribution of higher-frequency modes, the high-fequency spectrum is relatively unperturbed from that expected for a fourfold symmetric chromophore. Protein-Induced Symmetry Lowering. The pH-induced changes in the low-frequency resonance Raman spectrum of ferrocytochrome c indicate that the effective symmetry of the heme iron is higher above pH 13 than in the pH range 7-12. This is consistent with reported protein structure changes22for ferrocytochrome c above about pH
12 which indicate a more open heme crevice, accessible to small ligands, such as CO and CN-, which can then displace an endogenous protein axial ligand. The heme is also reported to be more easily autooxidizable at high pH. We postulate that the symmetry lowering due to the pyrrole substituents is most effective for the tightly enclosed heme group of native ferrocytochrome c. Especially the anchoring of the heme by thioether linkages to the protein chain at the 2 and 4 positions of the heme periphery, as well as its rigid positioning in a tightly wound heme crevice, lead to an unusually effective expression of the asymmetry of the ring substituents in mixing with other modes. In effect, there truly are a t least three substituents of very different effective mass or which exhibit significant variation in force constant for in-plane wagging. As the pH is raised above 13, the protein relaxes its anchoring effect in the peripheral substituents, allowing the effective symmetry to be much higher and resulting in a decrease in the number and intensity of observed resonance Raman active modes. The persistence of a band near 347 cm-', which is observed for metalloporphyrinsand corresponds to one of the few calculated low-frequency totally symmetric modes in Dahsymmetry, is consistent with this picture. In effect, at high pH the protein allows the heme to relax to a limiting higher symmetry structure.
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this work, and to the National Institutes of Health (grant no. GM 27065), the Research Corp., the City University of New York PSC-BHE Research Award Program, and the Queens College Biomedical Research Support Award Program for additional support. We also thank Dr. Max Diem for this kind gift of data handling programs.
Kinetics of the Reaction of Hydroxyl Radical with Methane and with Nine Ci- and F-Substituted Methanes. 1. Experimental Results, Comparisons, and Applications Kyu-Man Jeongt and Frederlck Kauhnan' Department of Chembtry, Unlverstty of Pittsburgh, Ptttsburgh, Pennsylvank, 15260 (Received: October 22, 198 1; I n F/ml Form: December 1 I , 198 1)
The rates of reaction of OH with CH4and with all nine C1- and F-substituted methanes that contain at least one abstractable H atom are measured over wide temperature ranges (mainly 250-480 K)by the discharge-flow method under strictly comparable experimental conditions. Curvature is found in all but one Arrhenius plot, that of CHF, which is slower reacting and was studied over a smaller temperature range. Optimized threeparameter expressions require a temperature exponent, n,of 2.0-2.2. They are reduced to Arrhenius A's and E's centered at 300 K. Substantial variation is found in the A's for related compounds, less so in the E's which correlate roughly with the bond energy of the abstracted C-H. The results are compared with all published data, and their use in atmospheric science and combustion is briefly discussed. They represent the experimental basis of a test of transition-state theory in the following paper.
Introduction The reactions of OH are extraordinarily important in atmospheric chemistry and in combustion science. The strength of the HO-H bond (Do"= 118 kcal mol-', 5.12 'Gulf Research and Development Co., Pittsburgh, PA 15230. 0022-3654/82/2086-1808$01.25/0
eV) helps lower the energy barrier of H-abstraction reactiom, and the strength of (2-0 bonds and ultimate Stability of co and coz provide reaction Paths for OH addition to unsaturated compounds and for oxidative degradation. Consequently, OH rather than 0 or O3 is the principal initiator for oxidation processes in the atmosphere and in 0 1982 American Chemical Society
Kinetics of Reaction of Hydroxyl Radical
The Journal of Physical Chemistry, Vol. 86, No. 10, 1982 1809
Experimental Section
dtRH Coupling
T NO2
Flguro 1. Diagram of apparatus.
combustion. Furthermore, the fast reactions of OH with other catalyst species such as 0,,NO,, and C10, in ozone photochemistry give that radical a central role in the chemistry of the stratosphere. Its well-characterized spectrum,' ease of generation by chemical reaction2 or by vacuum-UV photolysis, and sensitive detection by resonance fluorescence or laser-induced fluorescence make it the most widely studied reactant in radical-molecule reaction~.~ Recent concern regarding tropospheric and stratospheric pollution has stimulated research on hydrocarbon and halocarbon abstraction and addition reactions using well-developed flash photolysis or discharge-flow laboratory techniques. Unfortunately, much of this work has been confined to answer narrow questions, e.g., to provide rate parameters for specific reactions over small temperature ranges as input to computer models. Yet, the need for fundamental rate data in many fields of application is so extensive that piecemeal laboratory measurements should be accompanied by broader experimental and theoretical studies. We need to ask how well we understand the rate of a given reaction and its temperature dependence, how well we could predict it by use of reaction rate theory, and, if these questions seem overly ambitious, at least how well we may predict the effects of systematic structural changes such as halogen substitution near the reaction site on an ab initio basis. It is the combination of all of these needs, viz., providing input parameters for computer model calculations of the pathways of several naturally occurring and man-made compounds as well as testing reaction rate theory in a series of reactant molecules, that prompted us to do the work described in this and the following paper. The reaction rates for H abstraction by OH from CH, and from all nine C1- and F-substituted methanes (two with three H's, three with two H's, and four with one H) were measured over the widest temperature range accessible in our apparatus (usually about 250-480 K). The results were examined for precision and accuracy, compared with other published data and with each other, and discussed in the context of atmospheric chemistry and combustion. Finally, in the following paper, they are compared with the predictions of transition-state theory in its thermochemical kinetics variant4 including some sensitivity analysis, the too often neglected equivalent of experimental error analysis. (1)G. H.Dieke and H. M. Crosswhite, J. Quant. Spectrosc. Radiat. Transfer, 2, 97 (1962). (2)F.P.Del Greco and F. Kaufman, Discus. Faraday Soc., 33,128 (1962). (3) R. Atkinson, K. R. Darnall, A. C. Lloyd, A. M. Winer, and J. N. Pitta Jr., Adv. Photochem., 11, 375 (1979). (4) S. W. Benson, "Thermochemical Kinetics", 2nd ed., Wiley, New York, 1976.
Apparatus. The discharge-flow resonance fluorescence apparatus shown in Figure 1is similar to that used in some earlier studies.6 The Pyrex flow tube, 170 cm long and with 2.54-cm i.d., is connected at its downstream end to a stainless-steel fluorescence cell. The 90-cm section of the flow tube upstream of the fluorescence cell is surrounded by a cooling jacket and electric heating mantle which allows the temperature to be maintained from 200 to 500 K to about f l K along the 50-cm reaction zone traversed by the movable injector. The temperature is monitored by three external, fixed iron-constantan thermocouples and by a fourth internal, movable one that is retracted during OH decay measurements. The flow tube pressure is measured at two ports (Figure l),and, since the Poiseuille pressure drop is small, -1.3% for 1 = 50 cm at an average flow velocity of -1000 cm s-l and 3-torr pressure, a mean value for the reaction zone is used in the data analysis. The OH resonance lamp is a microwave discharge in He at 2.2 torr saturated with H 2 0 at atmospheric pressure (Raytheon Microtherm, 2450 MHz, 2040-W forward power). A 4-cm diameter quartz lens (5-cm focal length) focuses the resonance radiation on the entrance slit of a grating monochromator (McPheraon, Model 218). The signal is detected by a photomultiplier (EM1 9789 QA) at the exit slit of the monochromator in the current mode (Keithley Model 417 picoammeter) and displayed on a strip chart recorder (Hewlett-Packard Model 7100B). The noise level in the stable, scattered background signal corresponds to [OH] N 1.8 X loQ~ m - ~ , The [OH] measurement is calibrated by adding known amounts of NO2 to excess [HI produced upstream in a microwave discharge in He containing about 10 ppm of H2. The NO2 addition point (Figure 1) is about 50 cm upstream of the reaction zone so that there is ample time for the vibrational Telaxation of OH (u = 1,2) produced in the H + NO2reaction by collisions with H or NO2or the tube surface. The small flows of NOz required for quantitative OH measurements are obtained from a mixture of 0.5% NO2 in He prepared in a 2-L bulb. In OH + RH rate measurements a slight excess of NO2 is added to the Hcontaining gas stream. For measurements of the surface removal rate constant, k,, of OH, the NO2stream is added through the movable injector. Initial [OH] upstream of the injector is normally about 5 X loll ~ m - ~ . The 230-cm long injector tube, 0.3-cm o.d., consists of a Pyrex downstream and stainless-steel upstream section connected by a short piece of Teflon tubing. Its outside surface is coated with H3P04as is the flow tube, and they are baked at 450 K in a stream of OH as described earlier.s*6 This reduces k, to an acceptably low range of 5-20 s-l. Reactant flow rates are measured by the pressure increase in an evacuated volume into which the reactant flow is diverted. The stainless-steeltransducers (Validyne, Model DP7, *0.2 psi) used there and in the measurement of flow tube pressure are calibrated against an oil manometer. Gaseous reactants are added at an upstream pressure of 1atm using oil bubblers whereas liquid reactants (CH2C12,CHC13) are added from bulbs immersed in constant-temperature baths. Reactant Purification. Several of the reactants had to be further purified to remove fast-reacting impurities, particularly olefinic compounds whose reaction with OH usually has a negative temperature dependence and would thereby falsify low-temperature results. CHI (Matheson, (5) J.-S. Chang and F. Kaufman, J . Chem. Phys., 66, 4989 (1977). (6)U. C. Sridharan, B. Reimann, and F. Kaufman, J . Chem. Phys., 73,1286 (1980).
1810
Jeong and Kaufman
The Journal of phvsical Chemistty, Vol. 86, No. 10, 1982
UHP) was passed through a molecular-sieve (Fisher, M513) trap at 195 K to remove higher hydrocarbons. CH3C1 (Matheson, >99.5%) was passed through a glass-wool trap a t 195 K and then through a molecular-sieve trap at 195 K. CH3F (Matheson, >99.0%, containing SiF4and CH3OCH3 impurities) was first bubbled through two towers of 98% H2S04, through H20, and then treated as CH3C1 above. Gas-chromatographic analysis indicated >99.7 % purity and no detectable CH30CH3. CH2C12(Fisher, >99.0%) and CHC13 (Dow Chemical, special sample, >99.99%, amylene, 40 ppm) were extracted with 98% H2SO4, washed with 10% NaHC03 and 10% NaCl solutions, dried over anhydrous CaC12, and fractionally distilled through a 10-in. long Vigreaux column under N2. The purified samples were stored a t 77 K in the dark. Gas-chromatographic analysis indicated >99.98% for CHZCl2and >99.999% for CHC13. The analyses of the other, specially purified samples were as follows: CH2F2 and CHF3 (Allied Chemical) >99.97% and >99.9%; CH2ClF (FC-31, E. I. du Pont de Nemours, Freon Products Laboratory) >99.9%, 268 ppm CHClF2,146 ppm CClJ?, 46 ppm CHC12F,21 ppm CH2ClZ; CHClzF (FC-21, E. I. du Pont de Nemours, as above) >99.66%, 2553 ppm CHC1F2,643 ppm CH,ClF; CHClF2 (FC-22, E. I. du Pont de Nemours, as above) >99.88%, 1029 ppm CHC12F, 63 ppm CHF3, 28 ppm CHzF2. He carrier gas (Air Products, HP) was passed through a molecular-sieve trap (Fisher, M-513) at 77 K. Hz (Matheson, UHP) was used without further purification. NOz (Matheson, 99.5%) was purified by several fractional crystallizations until colorless crystals were obtained, and stored in a 2-L darkened bulb. Procedure and Data Analysis. All experiments were carried out under pseudo-first-order conditions, [RH] >> [OH], in the often used fixed radical source, fixed detector, movable reactant addition configuration. In the plug flow approximation the first-order rate constants, k' -o(d in [OH]/&), and the desired bimolecular rate constant, k = k'/[RH]. Corrections for axial and radial diffusion' are quite small (52%) and will tend to cancel in the comparison among different reactions. Surface reaction effects cancel completely (a) if the added reactant does not affect k , and (b) if the effect of the variable surface area of the movable injector can be neglected. This latter perturbation is easily taken into account. Letting k , be the constant wall reaction rate constant due to the flow tube surface and letting the variable injector wall rate constant be k,' -0 In ([OH],/[OH]o) = k,(xD - ~ 0 + ) k,'(xi - ~ 0 + ) k'(xD - xi) where xi is the injector position, xo is the source position, and xD is the detector position. The working equation now becomes o(d In [OH],/dxi) = k' - k W where x increases from xo to xD. The injector surface recombination thus contributes a small term of opposite sign to that of the gas reaction, because it is largest when reaction time is smallest, when the injedor is pushed nearly to the detection cell. In practice, k,' is measured routinely by monitoring [OHID as a function of injector position when He rather than reactant is added. Since k , = yCA/4V in simplest approximation,' where y is the probability of OH removal per surface collision, I? = (8RT/ T M ) ~ 'is~ the molecular velocity of OH, A is the surface area, and Vis the volume of the flow tube, the contribution of the injector to A is ri/ro as large as that of the flow (7) F.Kaufman, B o g . React. Kinet., 1, 1 (1961).
100
-VI
c
z1
0
5
IO
0
I 0
__I
I
I
I
I
I
I
IO
20
30
40
50
Injector D i s t a n c e , cm Figurr 2. Plots of log [OH] vs. injector distance. RH = CHCI,; T = 370 K; [CHCI,] indicated in figure.
Figure 3. Plots of k' vs.
[CHCI,] at various temperatures.
tube walls, i.e., k,' N 1-3 s-l. The more serious problem (a) of k , dependence on added RH, e.g., the possibility of a second-order surface reaction of OH with RH, is treated indirectly through the dependence of k' on [RH]. Although the contribution of a second-order, surface-reaction term is indistinguishable from that of the gas-phase reaction in a single experiment, it should have two observable consequences: (i) an inverse dependence on flow tube radius such as was checked in recent studies of the OH + H20zreaction6 and (ii) a saturation effect in the event of a rapidly reversible surface reaction that should lead to a large positive intercept at [RH] = 0 in the k' vs. [RH] plot. The constant slope of that plot at large [RH] could then be identified as the desired rate constant, k, for the gas-phase reaction. This latter complication was carefully monitored, and experiments with large intercepts (an uncommon occurrence) were rejected as indicating surface contamination. Moreover, a qualitative argument can be made against strong adsorption effects of halogen-substituted methanes on H3P04-coatedPyrex surfaces. Typical plots for [OH], vs. xi and for k' - k,' vs. [RH] are shown in Figures 2 and 3. Experimental parameters enter the calculation of k as follows. For k' = -d(d In [OH]/&), d = 760+J'/(273aroZP) where & (cm3s-l, STP) is the total flow rate and P (torr) is the average pressure ) by in the reaction zone. [RH] (molecules ~ m - is~ given
Klnetics of Reaction of Hydroxyl Radical
The Journal of Physlcal Chemistry, Vol. 86, No. 10, 1982 1811
TABLE I : Rate-Constant Data for Reactions of OH with CH, and Nine Substituted MethaneP
reactant
K
1oi4k, cm3s-l
CH,
278 297 339 389 419 473
0.557 i 0.054 0.789 f 0.049 1.78 f 0.12 3.47 i 0.23 5.49 f 0.35 10.2 i 0.7
CH,C1
247 293 332 363 401 426 483 292 330 356 368 385 416 455 480 251 292 323 342 384 415 455 250 295 323 348 399 438 486
2.03 f 0.15 3.95 f 0.26 6.68 i 0.46 8.74 f 0.58 12.8 f 0.9 16.3 i 1.3 25.4 f 2.0 1.40 i 0.09 2.50 i 0.18 3.86 f 0.33 4.76 i 0.31 5.48 i 0.66 8.56 i 0.66 13.1 i 1.1 16.0 f 1.1 9.59 i: 0.69 15.3 i 0.95 20.8 f 1.4 27.6 f 1.9 35.2 ? 2.4 45.0 i 2.9 60.9 f 3.8 2.76 f 0.18 4.94 i 0.30 6.60 i 0.40 8.85 i 0.55 14.0 f 0.9 17.2 f 1.1 25.4 i: 1.7
CH3F
CH,Cl,
CH,ClF (FC-31)
a
temp,
10-14(concn range), ~ m - ~ reactant 7.36-62.7 1 5.O-88.5 6.7 1-48.1 3.34-17.4 2.42-18.2 2.34-11.1 2.32-14.2 1.78-17.8 1.23-12.1 1.46-10.5 1.01-8.16 0.737-6.26 0.7 90-6.15 6.54-53.3 4.05-18.3 1.75-18.2 1.62-15.6 1.75-14.8 2.52-14.3 0.909-7.15 1.05-7.16 0.7 43-9.2 1 0.434-7.52 0.764-3.77 0.418-2.53 0.493-2.20 0.435-2.08 0.348-1.91 2.52-26.4 2.39-19.0 2.17-15.0 0.905-14.3 0.749-11.0 0.698-8.83 0.652-4.03
temp,
1014k,cm3s-l
10-14(concn range), cm-,
250 298 336 384 432 464 492 249 298 339 370 411 466 487 250 295 315 354 392 433 483
0.429 f 0.038 1.12 i 0.075 2.10 f 0.14 4.34 f 0.27 7.27 f 0.46 9.51 i 0.66 14.1 i 1.2 5.51 f 0.41 10.1 i 0.65 16.0 i 1.0 23.2 f 1.6 30.8 f 2.0 44.8 f 2.7 55.0 f 3.9 1.88 i 0.14 3.37 f 0.22 4.25 i 0.27 5.85 i 0.36 7.86 i 0.48 10.5 f 0.65 14.8 f 1.0
10.1-111 6.34-63.2 6.48-35.8 2.37-17.7 1.72-14.9 1.90-1 1.7 2.31-8.49 2.60-11.9 0.972-7.97 0.866-4.9 3 0.741-3.97 0.519-2.98 0.408-2.09 0.372-2.01 7.53-32.6 2.28-25.9 2.06-20.4 2.00-18.7 2.27-14.7 1.63-13.0 0.976-8.00
CHClF, (FC-22)
293 327 360 391 436 482
0.483 i 0.032 0.768 f 0.048 1.08 i 0.075 1.79 i 0.14 2.75 f 0.18 4 . 3 9 f 0.27
11.7-106.0 13.0-88.5 7.88-76.1 6.91-54.3 4.36-48.2 2.84-26.0
CHF,
387 410 428 447 465 480
0.169 i 0.237 f 0.331 f 0.448 i 0.546 i 0.719 i
43.3-297 43.8-177 32.0-176 28.0-131 25.0-177 20.6-102
K
CH,F,
CHC1,
CHC1,F (FC-21)
0.011 0.017 0.027 0.029 0.036 0.045
Error limits are l o .
@&P/(@TR7')where $RH (cm3s-l, STP) is the flow rate of RH, N = 6.02 X is Avogadro's number, and T (K) is the temperature of the experiment. The combination of the expressions for k' and k shows the latter to be proportional to q$TS/(&Pr,Z) where S = d In [OH]/& is the slope of the semilog [OH] vs. x: plot (Figure 2). This is particularly important in error analysis where the propagation of independent errors can be estimated by akV/k = [(2a&p/'#JT)' + (a,,/@RH)'
+ (2aT/T)' + + (~,/S)~I'/~
(~u,/P)' + (2ar,/r0)'
Conservative estimates of the precision of the experimental variables were used, i.e., 2%, 2%, 1%,1%,and 1% for the first five ay/ Y values at the single standard deviation level in the order of the ukv/k expression. u,/s was determined by least-squares fits of the In [OH] vs. X plots and found to be 5 2 % , making ahv/k about 6%. The total random error, of each k(7') was then set equal to [(UkV)' + (akRH)'I1/' where ahRH is the least-squares error of the k' vs. [RH] plots as determined by computer fit. a h T ranges from 6% to 8.2% for all but 3 of 68 experimental rate constanta for the 10 reactants studied, and those three were 8.7%, 9.7%, and 12% at single standard deviation. In most cases ahRH is much smaller than 6% and ahT is dominated by the estimated uncertainty of measured flow rates, temperature, and pressure. Systematic errors due to transport effects, secondary reactions, impurities, surface effects, etc., are likely to be small (515%) but cannot be ruled out. Some cancellation can be expected in the cross comparison of different RH + OH reactions. Arrhenius parameters are determined from a weighted least-squares fit using a computer program by Dye and
Nicely.8 Since most Arrhenius plots showed curvature (concave upward), computer fits to the three-parameter expression k = BT" exp(-E'/RT) were also evaluated. The errors of these interdependent parameters are very large, e.g., un/n 0.6, ag/B 8, aE?/E' 1, and, even though n was consistently found to be near 2.0 (see below), it was instructive to test the reality of this curvature in the following manner. Least-squares fits were calculated for modified three-parameter expressions with the value of n held fixed in each fit, but varied stepwise from 0 to 2.5. The average standard deviation of the experimental k from that calculated by the modified three-parameter expression was seen to decrease by about a factor of 2 from n = 0 (Arrhenius) to n = 2. This test supports the use of three-parameter expressions, particularly for the comparison among different OH + RH reactions where kinetic data were collected over somewhat different temperature ranges.
-
-
-
Results and Discussion The measured rate constants for all 10 compounds at all temperatures (six to eight per compound) are shown in Table I along with l a error estimates (see above), [RH] ranges, and number of measurements, a total of 609 experiments. Figure 4 shows the Arrhenius diagrams for all compounds. The k's span about 2.5 orders of magnitude from CHF3, the slowest, to CH2C12,the fastest. Table I1 lists best-fit Arrhenius A and E values, three-parameter expressions, and modified Arrhenius parameters centered at T = 300 K calculated from the three-parameter ex(8) J. L. Dye and V. A. Nicely, J. Chem. Educ., 48, 443 (1971).
1812
The Journal of Physical Chemistry, Vol. 86, No.
IO, 1982
Jeong and Kaufman
TABLE 11: Arrhenius and Three-Parameter Expressions for OH k(T) = Ae-E/RT
reactant
10IZA,cm3 s-I 5.59 f 3.51 t 8.18 f 5.73 t 2.44 f 4.40 f 5.65 i 1.21 t 1.28 f 3.02 i
CH, CH,Cl CH,F CH,CI, CH,CIF CHF, CHCI, CHC1,F CHClF, CHF,
' Error limits are lo.
1.50' 0.55 0.66 0.74 0.32 0.37 0.40 0.13 0.33 0.29
+ RH k(T) = A300e-E3"/RT
k(T) = BTne-E'/RT E', kcal s-' K-" n mol-'
10'*B,cm3
E, kcal mol" 3.92 f 0.20a 2.61 * 0.11 3.75 * 0.06 2.08 i 0.09 2.28 f 0.09 3.52 f 0.06 2.35 i 0.05 2.10 t 0.08 3.32 t 0.19 5.79 f 0.09
6.27 4.22 1.86 6.68 2.64 7.31 1.69 1.22 1.28
2.00 1.97 2.22 2.00 2.00 1.95 2.18 2.00 2.00
10'2A300, E"', kcal cm3 s-l mol-
2.51 1.19 2.21 0.763 0.912 2.26 0.821 0.672 1.88
4.17 2.30 5.41 4.44 1.76 3.48 3.76 0.81 0.85 1.44b
3.70 2.36 3.53 1.96 2.10 3.42 2.12 1.86 3.07 5.26b
n is assumed to be 2.00.
TABLE 111: Rate Parameters and Comparison with Published Results for the Reaction of OH + CH, 1Ol5k, cm3 s-l T, K 10IZA,cm3 s-' E , kcal mol-' T range, K 17.9 10.8 t 2.5 9.15 f 0.47 7.5 i 0.1 7.9 t 0.5 26.1 ?: 2.7 54.8 i 1.7 6.5 * 0.3 9.5 i 1.4 8.8 i 0.7 7.50 8.04
t f
0.60 0.99
298 300 295-302 298 298 38 1 416 295f 2 296 298
83.2 5.5 * 0.8 2.36 t 0.21 3.83 * 0.20
5.00 3.77 3.40 3.66
298-423 i
0.10
t
0.04
295-498 240-373 292-426
* 0.18
298 298
ref 11 12 13 15 14 17
300-500
16 18 19
298-1020 269-473
20 this work
pressions by A3O0= B(300e)"and E3@' = E'+ 300nR for the present discussion and for comparison with transition-state theory in the following paper. Although the standard deviations in A and E are fairly large, it is probable that the relative magnitude of A and E is somewhat more reliable than these errors indicate. The errors of the Am and Ejoo values are about a factor of 1.5-2 smaller than those of A and E. It should be understood that Am and P are "local" values, strictly applicable only at, e.g., 300 f 50 K . Comparison with Published Data. The comparison with other published results is given in the following tables in necessarily abbreviated form considering the large amount of cited work. The reader is also referred to review articles3 and to critical evaluations, particularly recent ones by NASAQand CODATA'O connected with the needs of atmospheric chemistry programs. However, these latter evaluations cover mainly those RH important in atmospheric photochemistry. OH + CH,. As Table I11 shows, 11absolute measurements, including this one, may be cited.'+*O Excluding ~
~
~~
(9)NASA, JPL, Pasadena, CA, 1981,JPL Publication 81-3. (IO) D. L. Baulch, R. A. Cox,R. F. Hampson, Jr., J. A. Kerr, J. Troe, and R. T. Watson, J . Phys. Chem. Ref. Data, 9,295 (1980). (11)D.G. Horne and R. G. W. Norrish, Nature (London),215,1373 flBf371 \___ ,_ .
(12)W. E. Wilson and A. A. Westenberg, Symp. (Int.) Combust., [Proc.], 11, 1143 (1967). (13)N. R. Greiner, J. Chem. Phys., 53, 1070 (1970). Res. (14)J. J. Margitan, F. Kaufman, and J. G. Anderson, Geophys. . . Lett., 1, 80 (1974). (15)D. D. Davis, S. Fischer, and R. Schiff, J . Chem. Phvs., 61. 2213 (1974). (16) R. Overend and G. Paraskevopoulos, Can. J. Chem., 53, 3374 (1975). (17)S. Gordon and K. Mulac, Znt. J . Chem. Kinet. Symp., 1, 289 (1975). (18) C. J. Howard and K. M. Evenson, J. Chem. Phys., 64,197(1976). (19)R.Zellner and W. Steinert, Int. J. Chem. Kinet., 8,397 (1976). (20)F. P. Tully and A. R. Ravishankara, J. Phys. Chem., 84,3126 (1980).
10-l~
I
I
I
2.0
3.0
4.0
IOOO/T Figure 4. Arrhenlus diagram for all 10 OH i- RH reactions.
Horne and Norrish," whose results were very high probably because of their very large [OH], and Gordon and Mulac," who measured k only near 400 K, we may compare nine k's at room temperature. These values adjusted to T = 298 K average to (8.5 f 1.2) X cm3 s-l (single
The Journal of Physical Chemistry, Vol. 86,No. 70, 1982 1813
Kinetics of Reactlon of Hydroxyl Radlcal
TABLE IV: Rate Parameters and Comparison with Published Results for the Reactions OH reactant
1oi4k, cm' s-'
T,K
CH,Cl
3.6 f 0.8 4.4 f 0.5 4.29 f 0.21 4.10 f 0.68 3.95 f 0.52
296 298 298 297 29 3
1.6 f 0.35 2.18 t 0.18 1.40 * 0.18
296 297 292
CH,F
E, kcal mol-'
+ CH,Cl, CH,F
T range, K
ref
2.70 i: 0.30 2.18 f 0.07
298-422 240-400
2.61 f 0.11 3.51 * 0.55 k = (4.22 x 10-18)T'.97e-s99/T
247-483
18 22 23 24 this work
292-480
18 27 this work
10"A, cm' s-' 4.1 1.84 f 0.18
8.18 f 0.66 3.75 f 0.06 k = (1.86 x 10-18)T2.2Ze-1112/T
TABLE V: Rate Parameters and Comparison with Published Results for the Reactions OH t CH,Cl,, CH,ClF, CH,F, reactant 1014k,cm' s-l T,K 10"A, cm' s'l E, kcal mol-' T range, K ref CH,Cl,
15.5 f 14.5 f 11.6 f 15.3 f
CH,ClF (FC-31)
CHP,
3.4 2.0 0.5 1.9
296 299 298 292
3.7 f 0.6 4.21 f 0.41 3.5 f 0.7 4.10 f 0.68 4.94 f 0.60
296 298 293 297 295
0.78 f 0.72 f 1.17 f 1.12 f
296 298 297 298
0.12 0.10 0.14 0.15
4.27 f 0 . 6 2.17 f 0.16 5.73 f 0.74 2.08 f 0.09 k = (6.68 x 1 0 - ' 8 ) T 2 . 0 0 e - 3 " f l
245-375 251-455
2.84 3.19
2.50 f 0.10 2.62 f 0.20
245-375 273-373
2.44 f 0.32 k = (2.64 x
2.28
250-486
7.4 f 0.5
4 . 2 f 0.4
18 f
0.3 0.9
f
0.09
4.40 f 0.37 3.52 f 0.06 k = (7.31 x 10-18)Tl.9Se-l137/T
*
~~
f
25 26 24 this work
18
standard deviation), very good agreement among four flash photolysis and five discharge-flow studies that should put to rest any doubts concerning the absolute reliability of either method. Our own value adjusted to 298 K is 8.0 X W5cm3s-'. However, thisfine agreement does not extend to the reported Arrhenius parameters. Published A values range from 2.4 X to 5.5 X 10-l2cm3 s-' and E's from 3.4 to 3.8 kcal mol-'. This is mainly the consequence of curvature in the Arrhenius plots such that those studies carried out at lower average temperature obtained lower A's and E's and vice versa. The reality of this curvature is clearly shown in the two studieslgathat span the largest temperature range and also by ours. Comparing threeparameter expressions, Zellner and Steinert report (5.75 X 10-21)P*08 exp(-1010/T), but their highest temperature points seem scattered and too high. Zellner's2' best-fit expression of (2.57 X 10-18)P*13 exp(-1233/T) for several studies is in very good agreement with Tully and Ravishankara'sm (1.32 X 10-17)P*92 exp(-1355/T) covering the largest T range and with our (6.27 X 10-'8)P.oo exp(1263/ 7') notwithstanding the seemingly large differences in the B values that mainly reflect small differences in n. For example, the last three expressions reduce to Arrhenius Am values of 4.1 X 5.1 X 10-l2,and 4.2 X cm3 s-' centered a t T = 300 K, in the above order, and the corresponding E300 values are 3.72, 3.84, and 3.70 kcal mol-l. OH + CH3C1, C H P . Table IV lists five measurements for CH3C118*n-24 and three for CH3F.l8vZ6The agreement for the former adjusted to 298 K is very good, the average of the five km values being (4.1 0.3) X cm3 s-', but ~
18 22 23 this work
~~
(21)R.Zellner, J.Phys. Chem., 83,18 (1979). (22)R.A. Perry,R. Atkinson, and R. N. Pitts, Jr., J.Chem. Phys., 64, 1618 (1976). (23)D. D.Davis, G.Machado, B. Conaway, Y. Oh,and R. T. Watson, J. Chem. Phys., 65, 1268 (1976). (24)G. Paraskevopoulos,D. L. Singleton, and R. S. Irwin, J. Phys. Chem., 86,561 (1981). (25)R. T.Watson, G.Machado, B. Conaway, S.Wagner, and D. D. Davis, J. Phys. Chem., 81, 266 (1977).
293-429 25 0-4 9 2
28 27 this work
the three seta of Arrhenius parameters differ substantially, mainly because of the curvature and sparse coverage of the temperature range. For CH3F ours seems to be the first study of the temperature dependence. The three adjusted room-temperature values are in good agreement, k29s = (1.9 f 0.3) X cm3s-'. The Am and Ejoo values for the two reactions from our three-parameter expressions are 2.3 X and cm3s-' and 2.36 and 3.53 kcal mol-' for CH3Cl 5.4 X and CH3F, respectively. The difference between the A300 values is puzzling. OH CH2CZ2,CH2C1F,C H P P Table V summarizes the available rate data. For CH2C12,18~22~23 the fastest-reacting halocarbon, the average of the adjusted km8 values is (14.6 f 2.2) X cm3 s-', and the agreement among the two available Arrhenius expressions is very good. For CH2ClF (FC-31),18*-s the k m average is (4.2 f 0.6) X cm3s-', our value unfortunately being the highest (5.1 X 10-14),and the three sets of Arrhenius parameters agree fairly well. It should be noted, however, that the scatter of the A and E values run counter to the Arrhenius curvature explanation, since our temperature range extends higher than the other two, whereas our A and E are lower than the others. For CH2F218*27*2s the four adjusted k298average to give cm3 s-l. The lowest of these28is also (0.96 f 0.23) X connected with unusually high A and E values and is probably in error as seen below. The corrected A300and E300 for the three CH2X2compounds are 4.4 X 10-l2, 1.8 X 10-l2,and 3.5 X cm3 s-' and 2.0, 2.1, and 3.4 kcal mol-' in the above order, as obtained from the three-parameter expressions. The strong variation in Am is again unexpected. The trend of increasing E300with F-substi-
+
(26)V. Handwerk and R. Zellner, Ber. Bunsenges. Phys. Chem., 82, 1161 (1979). (27)W . S.Nip, D. L. Singleton, R. Overend, and G.Paraskevopoulos, J. Phys. Chem., 83,2440 (1979). (28)M. A. A. Clyne and P. M. Holt, J. Chem. SOC.,Faraday Trans. 2,75,582 (1979).
1814
Jeong and Kaufman
The Journal of Physical Chemistry, Vol. 86, No. 10, 1982
TABLE VI: Rate Parameters and Comparison with Published Results for the Reactions OH t CHCl,, CHCl,F, CHClF,, CHF, reactant CHC1,
CHC1,F (FC-21)
CHClF, (FC-22)
CHF,
a
lOI4k, cm3 s-'
10.1 f 1.5 11.4 f 0.7 10.1 f 1.3
T,K 296 298 298
2.6 f 0.4 2.7 f 0.3 2.88 f 0.24 3.04 f 0.11 3.9 f 0 . 2 3.39 f 0.86 3.52 f 0.44
296 298 298 296 298 297 298
0.475 f 0.048 0.34 f 0.07 0.48 f 0.05 0.425 f 0.028 0.46 f 0.08 0.33 t 0.07 0.458 f 0.058 0.475 i 0.063
297 296 298 296 293 294 297 298
0.02 f :;is 0.013 f 0.004 0.014 f 0.006 0.017O
296 296 430 298
Trange, K
ref
4.69 f 0.71 2.25 f 0.21 2.35 f 0.05 5.65 t 0.40 k = (1.69 x 10-l8)Tl*l8e-4l3/T
245-375 24 9-48 7
18 23 this work
1.75 1.87 f 0 . 2 1.16 f 0.17 4.79 f 0":;
298-4 2 2 245-375 241-396 293-4 13
18 22 25 5 28 24 this work
10I2A,cm3 s-'
E, kcal mol-'
2.49 t 0.30 2.47 f 0.05 2.13 t 0.08 2.8 f 0 . 2
250-483 297 -4 34 0.925 f 0.010 1.20 f 0.16 2.1 * 0.6 9.5 f
::;
3.13 f 0.14 3.29 f 0.08 3.54 t 0.30 4.6 f 0 . 4
1.28 f 0.33 3.32 f 0.19 k = (1.28 x 10-'8)T2.0Oe-946/T
3.02 t 0.29
5.79 f 0.09
293-482
29 18 25 5 26 28 24 this work
387-480
18 28 28 this work
250-350 253-427 263-373 294-426
Extrapolated value.
tution is in accordance with the increasing C-H bond strength, but mainly for the second F-substitution. OH CHC13, CHCZ2F, CHClF,, and CHF,. As Table VI shows, the three k298values for CHC1318*23 are in excellent agreement, (10.6 f 0.7) X cm3s-', and the two Arrhenius expressions are also in reasonable accord. For CHC1,F (FC-21)5J822924@~28 there is good agreement, (3.05 f 0.34) X lo-', cm3 s-l, among six measured values excluding that by Clyne and Halt,% whose k,A , and E are out of line. There is also reasonable agreement among four sets of Arrhenius parameters even though some of the temperature ranges are fairly small. CHClF2(FC-22) is an important refrigerant, and its OH reaction has been studied repeatedly.5~'8~24-26~28~2g Again the results reported by Clyne and H o l P are suspect and must be excluded. The seven adjusted kM values average to (4.6 f 0.5) X cm3 s-', and four of the five sets of Arrhenius parameters are in excellent agreement while onez6is somewhat higher. Lastly, for CHF3 the present data are the only quantitative ones available. The reaction is so slow at room temperature that Howard and Evenson's18 result is necessarily qualitative and Clyne and H o l P report no temperature dependence between 296 and 430 K even though this reaction has the largest activation energy of the 10 studied. Our Am values for the four halocarbons are 3.8 0.85 X 10-l2,and 1.44 X cm3s-', x 10-l2,0.81 X again a surprisingly varied set with lower values for unsymmetrical substitution just as in the preceding CHzX2 group. The trends in E300, i.e., 2.12, 1.86, 3.07, and 5.26 kcal mol-', are qualitatively predictable, but there is again little change in P at the f i t F-substitution (a difference of -0.26 kcal mol-' between CHC1, and CHC1,F just as that of +0.14 kcal mol-' between CHZCl2and CH2ClF is probably within experimental uncertainty), but sharp increases at the second and third. Returning to the general comparison of Arrhenius parameters, especially A300and E300from this study, what
+
(29)R.Atkinson, D.A. Hansen, and J. N. Pith, Jr., J. Chem. Phys., 63,1703 (1975).
a priori trends would chemical intuition suggest? Reaction path degeneracy alone would demand a proportional decrease from n = 4 to 3 to 2 to l in A300as the number of equivalent Hs, n, is decreased. The larger size and lower vibration frequencies of C1 compounds compared with their F or H counterparts should make the A values of chlorinated compounds relatively larger. These broad predictions are only roughly supported by our data. Although Am/n increases on average with increasing halogen substitution from 1.0 (CH,) to 1.3 (CH3X)to 1.6 (CH2Xz)to 1.7 (CHX3),its variation is large, i.e., 0.8 and 1.8 for CH3X, 0.9-2.2 for CH2X2,and 0.8-3.8 for CHX,. Furthermore, the pronounced decrease of A300/nfrom CH3Cl to CH3F and from symmetrical to unsymmetrical substitution in the CH2X2 and CHX3 cases does not correlate with physical parameters. The dipole moments, for example, are nearly equal for CH3C1and CH3F (1.87 and 1.85 D) and increase monotonically with increasing F-substitution in the other groups (1.60,1.82,and 1.97 D for CHzXz;1.01, 1.29,1.42, and 1.65 D for CHX,SO). A detailed comparison with theoretical prediction by transition-state theory is the subject of the companion paper. The range of E values for the 10 reactions is too small, from about 1.9 to 5.3 kcal mol-', and the reaction exothermicities, i.e., C-H bond strengths, are too uncertain to allow quantitative analysis. The C-H bond strengths increase from about 96 kcal mol-' in CHCl, to about 106 kcal mol-' in CHF, with 104 kcal mol-' in CHI being intermediate. The corresponding AHo2B8 for the OH + RH reactions therefore range from about -23 to -13 kcal mol-', i.e., the decrease in E3O0is about 0.39 of the increase in exothermicity. Heicklen3' has recently correlated rate constants of a large number of H-abstraction reactions by OH with C-H bond energies in a modified hard-sphere collision model. For our much smaller and more closely related group of reactants, we prefer to examine the preexponential factors in greater detail and avoid the less tractable problem of predicting (30)R.D.Nelson, Jr., D. R. Lide, Jr., and A. A. Maryott, Natl. Stand. Ref. Data Ser. (U.S., Natl. Bur. Stand.), 10 (1967). (31)J. Heicklen, Int. J. Chem. Kinet., 13, 651 (1981).
Kinetics of Reaction of Hydroxyl Radlcal
energy barriers even though they have a dominating effect on the magnitude of the rate constant. Applications in Atmospheric Chemistry and Combustion. CHI and CH3Cl are naturally occurring trace constituents of our atmosphere, whereas CH2C12,CHC13, CHC12F (FC-21), and CHClF2 (FC-22) are man-made compounds that are released into the atmosphere. For all of them the OH reaction is the principal removal process in both the troposphere and the stratosphere. In the mid to upper stratosphere CH, is also removed by reaction with O(lD) and C1. Approximate mole fractions in the troposphere are as follows: CH,, 1.7 X lo4; CH3C1, 6.5 X 10-lo; CH2C12, 4 X lo-"; CHC13, -1 X lo-"; CHClF2, 5 X lo-". For anthropogenic compounds, tropospheric removal is an important interception mechanism that prevents their transport into the stratosphere where the combination of long residence time and further breakdown (by reaction or solar photolysis) may add to the pool of catalytic ozone removal processes. The interested reader may wish to consult recent report^^^-^, on the present state of this problem. Because of its relatively slow OH reaction, the stratospheric CHI mole fraction is reduced to half its tropospheric value a t about 30-km altitude whereas the CH3Clmole fraction is down by a factor of about 20 at that altitude, in keeping with their relative rate constants. Similarly, the tropospheric concentration of CHC1F2 is larger than that of CH2C12even though the latter's release rate is nearly 1order of magnitude larger, a clear reflection of their very different rate constants. Thus, if an anthropogenic compound has reached steady state in the atmosphere, a knowledge of its release rate, tropospheric concentration, and k(T) provides an estimate of the average tropospheric [OH], and an imbalance between known source and sink strengths will suggest the presence of other processes. Since the rate of transport of a trace species into the stratosphere is roughly proportional to its tropospheric concentration which, in turn, is inversely proportional to its steady-state removal rate, the relevant k(7') information becomes a major input for stratospheric model (32) "Stratospheric Ozone Depletion by Halocarbons: Chemistry and Transport", National Academy of Sciences, Washington, DC, 1979. (33) 'Proceedings of the NATO Advanced Study Institute on Atmospheric Ozone", Report No. FAA-EE80-20, US Deptartment of Transportation, Washington, DC, 1980. (34) "The Stratosphere: Preaent and Future", NASA Reference Publication 1049, Washington, DC, 1979.
The Journal of Physi~alChemistty, Vol. 86,NO. 10, 1982 1815
calculations. In polluted, urban atmospheres, on the other hand, hydrocarbon oxidation initiated by OH attack gives rise to O3 formation in the presence of NO, mainly by R 0 2 or H02oxidation of NO to NO2,photolysis to NO + 0,and recombination of 0 with OF A wide variety of atmospheric processes is thus controlled by OH + RH reactions whose rates are here characterized and compared. The same is true in hydrocarbon combustion systems. In lean CH, mixtures, for example, the OH + CH, reaction is the major initiation even though the full mechanism may include up to -100 elementary reactions. The sensitivity of the overall combustion process to the rate constant of a particular step is difficult to predict without detailed computer calculation. Westbrook et alaa have shown that, even though CH3radicals are produced mainly by the OH + CHI reaction in lean CHI oxidation, the CH, loss rate is insensitive to its rate constant, because the steady-state OH concentration is inversely proportional to k and tends to cancel out the k dependence. Thus, substitution of Zellner and Steinert'slg three-parameter expression for Greiner's13 earlier Arrhenius parameters increases k 20-fold at 2000 K without greatly affecting the CH, consumption rate. This type of cancellation is, of come, not a general property of complex mechanisms and should not be cited as an argument against the importance of measuring rate parameters with good accuracy under well-controlled conditions. The growing use of elementary rate parameters in combustion studies has increased our need for high-temperature, higher-pressure rate measurements and for a framework of theory with well-defined predictive power. This latter point is put to a test in the following paper. Acknowledgment. This work was supported by the National Aeronautics and Space Administration under Grant No. 39-011-161. We are grateful to Mr. J. M. Isenbarger, Inorganic Chemicals Department, Dow Chemical, for the sample of high-purity CHC13 and to Mr. J. D. Baldo, Freon Products Laboratory, E. I. du Pont de Nemours and Co., for analyzed high-purity samples of FC-21, -22, and -31. (35) C. K. Weatbrook and F. L. Dryer, Symp. (Znt.)Combust., [fioc.], 18. 749 11981). '(36) C. K. Weatbrook, J. Creighton, C. Lund, and F. L. Dryer, J. Phys. Chem., 81, 2542 (1977).
