J . Phys. Chem. 1994, 98, 9792-9800
9792
Kinetics of the Reaction between Hydroxymethyl Radicals and Hydrogen Atoms S. Dobe,*$+ T. BCrces,* F. Temps, H. Gg. Wagner, and H. Ziemer Max-Planck-Institut f i r Stromungsforschung, Bunsenstrasse 10, 0-37073 Gottingen, Germany Received: March 24, 1994; In Final Form: June 28, 1994@
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Kinetics of the reactions H (D) CHPOH (CD20D) were studied at room temperature using the fast flow technique coupled with laser magnetic resonance and electron paramagnetic resonance detections. Rate cm3 mol-' s-l units) were determined for the coefficients of 4.1 f 0.8, 8.1 f 1.1, and 4.8 f 1.6 (in overall reactions H CHZOH products (l), D CHzOH products (2), and D CD20D products (3), respectively. Branching ratios for OH formation were found to be 25 f 5% in reaction 1 and 23 f 10% in reaction 2. Formation of H atoms by H/D isotope exchange was found to account for %12% of reaction 2. On the basis of the kinetic results and simple theoretical considerations, the reaction between H atoms and hydroxymethyl radicals was suggested to occur to about 70% via direct disproportionation leading to formaldehyde formation and to about 30% via indirect mechanism through complex (CH30H)*. Under the conditions used, CH3 and OH were shown to be the products of the major channel of the complex-forming reaction path. Results determined for reaction H CH20H are compared with those obtained previously for CH3O. Implications for combustion systems are discussed briefly. H
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1. Introduction Investigation of the kinetics and mechanism of radicalradical reactions has long been a challenging task to both experimentalists and theoreticians.ls2 This is particularly so for reactions of two different free radicals which frequently lead to more than one set of reaction products. Experimental studies of such multichannel reactions require controlled production of two different radicals and, preferably, time-resolved measurements of the absolute concentrations of both the reactant radicals and products. The reaction between hydroxymethyl radical and H atom is a multichannel process for which only very little information is available. Besides, it belongs to an important and interesting group of interrelated elementary reactions occurring through the formation of vibrationally excited methanol molecule, (CH3OH)*. Reactions that belong to this group are, for instance, CH3 OH,3-6 'CH2 H20,7CH30 H,8 O('D) C&?sLo and, in a wider sense, also the thermal decomposition" and photodissociationlo of methanol. In these reactions of the "methanol family", (CH30H)* is formed with different energy content; moreover, the various systems under certain conditions can be converted into each other, e.g., CH3 OH CH2OH H == 'CH2 H20, etc. These features allow interesting comparisons to be made in experimental and theoretical investigations. The reaction of CH20H with H is also important from a more practical point of view for its significant role in the combustion of methanol, a widely regarded alternative automotive fuel or fuel additive.12-17 In combustion environment, hydroxymethyl radical is formed mainly by the attack of OH radicals on methanol. Its further fate is essentially determined by the reaction with 0 2 . However, H CH20H is one of the few processes that can compete with the reaction with 0 2 . The implication for flame modeling is that reaction H CHzOH could act as a chain-terminating step or could exhibit chain
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' Permanent address: Central Research Institute for Chemistry, H-1025 Budapest, Pusztaszeri ut 59-67, Hungary. Central Research Institute for Chemism. H-1025 Budauest. Pusztaszeri ut 59-67, Hungary. Abstract published in Advance ACS Abstracts, September 1, 1994 1 ,
@
0022-365419412098-9792$04.50/0
propagation behavior depending on whether the molecular products, H2 and CH20, or radicals are formed preferentially.18 In the present work the kinetics of the overall reactions
+ CH,OH - products D + CH,OH - products D + CD,OD - products H + CD,OD - products H
(1) (2)
(3) (4)
and the channel-specific reactions
+ CH,OH - OH + CH, D + CH,OH - OH + CH2D H
(la) (24
have been investigated at room temperature. Overall rate constants for reactions 1-4 and branching ratios for reactions la, 2a, and 2b were determined. On the basis of the kinetic results, a mechanism for the reaction between hydroxymethyl radicals and H atoms is proposed and the combustion implications are discussed.
2. Experimental Section Rate coefficients for the overall processes and for product formation have been measured by using a flow discharge (FD) system with laser magnetic resonance (LMR) detection of radicals and electron paramagnetic resonance (EPR) detection of atoms. Both detection methods utilize the Zeeman effect to achieve transitions between energy levels in the far-infrared and microwave region, respectively. For a general discussion of the FDLMR and FDEPR techniques, the seminal works of Howard and Evenson19 and Westenberg and deHaas,*Orespectively, are referred to. The kinetic apparatus employed in the present study is shown schematically in Figure 1. The flow reactor was constructed of fused silica and had an internal diameter of 4.0 cm and overall 0 1994 American Chemical Society
Reaction
39, 1994 9793
Diaphragm Figure 1. Fast flow-LMR/EPR apparatus.
length of 70 cm. Its inner surface was coated with halocarbon wax in order to reduce heterogeneous wall effects. The flow tube was equipped with a movable quam injector to achieve time resolution. The flow reactor is connected downstream to an LMR spectrometer and below that to an EPR spectrometer. The LMR spectrometer consists of a far-infrared laser optically pumped by a COz laser and the LMR sample region which is located intracavity between the pole caps of an electromagnet. The magnet is movable vertically, thus providing a homogeneous magnetic field for either the LMR or the EPR measurements. More details of the LMR spectrometer2' and the LMFU EPR combination22have been presented elsewhere. Helium served as the carrier gas in the experiments. Most of the gas flows were regulated by Tylan mass flow controllers. Smaller flows were measured by timed pressure rise in known volumes and were regulated by needle valves. The pressure in the reactor was measured using a calibrated pressure transducer (MKS Baratron). CH20H radicals were produced inside the injector by the spatially separated reactions F HC1 C1 HF and C1 CH30H CH20H HCl. The reactants HCl and CH30H were introduced through perforated loop inlets into the injector in slight excess which assured complete conversion of F to C1 and C1 to CH20H. Fluorine atoms were generated by passing F2 (highly diluted in He) through an alumina-lined microwave discharge. CD20D radicals were obtained from CD30D in a similar way to that of CH20H. The reactions described above proved to be convenient clean sources of CHzOH and CDzOD without the formation of the isomeric methoxy radicals. Hydrogen and deuterium atoms were generated in microwave discharges of Hz/He and D2/He mixtures, respectively, and entered the reactor through a side arm. The CH20H and CD20D radicals were detected with the LMR spectrometer in the form of HO2 and D02, respectively. Hydroperoxyl (and deuterioperoxyl) radicals were produced in the absorption volume of the laser tube by the fast conversion reaction, CHZOH (CD20D) 0 2 CH20 (CD20) HO2 (D02), by admixing the effluent gases from the reactor with an excess of 0 2 . The advantage of the detection of the hydroxymethyl isotopomers after conversion to H02D02 lies in the by far better LMR detection sensitivity for the latter. Furthermore, the LMR spectrum of CDzOD is not known yet. Details of the
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applicability of the indirect detection method have been discussed in ref 23. OH formation was also monitored with the LMR technique in the present study. During the OH measurements, 0 2 was replaced by Ar. The following LMR parameters were applied (in parentheses the FIR laser gases and polarizations are given): HO,: A = 163 pn (CH,OH, a),Bo = 0.25 T (ref 24) DO,:
A = 433 pn (HCOOH, n),Bo = 0.09 T (ref 25)
OH: A = 163 pn (CH,OH,
G),
Bo = 0.37 T (ref 26)
Detection of H and D atoms was accomplished by the EPR spectrometer utilizing the transitions at v = 8.9 GHz klystron frequency and Bo = 0.32 and 0.34 T magnetic flux densities, re~pectively.~~ For the EPR measurements, 0 2 was also added to the gas flows in order to improve sensitivity via increased spin-spin relaxation.28 Sensitivity limits of the LMRlEPR detections (at signal-to-noise ratio of 1) were 5 x lo8, 1 x lo9, 1 x lo8, 5 x IO9, and 1 x 1O'O cm-3 for HOz, D02, OH, H, and D, respectively. Several calibration procedures based on gas titrations were applied to determine absolute concentrations for the atoms and radicals. The EPR detection sensitivities for H and D were obtained by adding a known amount of NO2 to an excess of H and D atoms, respectively. Special care was taken to assure a stoichiometry close to unity.Z8b,29The EPR calibration factors for H and D proved to be very reproducible; therefore, they were checked only occasionally. Daily calibrations were performed, however, to obtain absolute CHzOH and OH concentrations. As described above, CHzOH and CDzOD were detected by the LMR in the form of HO2 and DO,, respectively. This method has facilitated the implementation of wellestablished gas titrations based on r e a c t i o n ~ ~ ~ , ~ ~
F
+
+ Hz02-
HF
+ HO,
and
+ C H 2 0 -HF + CHO CHO + 0, -.HO, + C O
F
D6bC et al.
9794 J. Phys. Chem., Vol. 98, No. 39, 1994 300
Usually the F/CH20/02 calibration method was applied, but occasional cross-checks using the reaction F H202 provided identical calibration factors of H02. DO2 calibrations were made with deuterioformaldehyde. The LMR sensitivities for OH were obtained by one or both of the reactions
+
F
+ H 2 0 - OH + HF
(H,O in excess)
-
(H in excess)
and H
+ NO2
OH
+ NO
The two methods supplied calibration factors which agreed within 15%. All gases were of the highest commercially available punties (He, 99.9999%; 02,99.998%; HC1,99.9990%; Hz, 99.9999%; D2, 99.7%; all from Messer-Griesheim). CH30H and CD30D (both of “Uvasol”, 299% quality from Merck) were degassed prior to use. H2CO and D2C0, required for the HO2 and DO2 calibrations, respectively, were produced by pyrolyzing paraformaldehyde as described p r e v i o u ~ l y . NO2 ~ ~ (Messer-Griesheim, 98%) was purified by low-temperature bulb-to-bulb distillation. All substances were used as 1- 10% mixtures premixed in He.
,w
100
I 0
20
10
30
10i3[H]or[D] / mol cm-’ Figure 2. Pseudo-first-order rate coefficient plots vs H and D atom concentrations.
corrections had to be applied also to allow for the consumption of D atoms during the course of the reaction. The maximum overall correction amounted to +13%. The bimolecular rate constants were obtained from plots of the corrected kist values vs [HI or [D]. Two of such plots are presented in Figure 2. The H and D concentrations considered were averages of EPR measurements carried out at the highest and lowest positions of the movable inlet during a kinetic run to allow for the small losses of H and D atoms on the surface of the inlet. The data 3. Results points obeyed straight lines with zero intercepts within the Experiments were carried out at T = 296 f 2 K and at an experimental uncertainties, and the LSQ analyses supplied the overall pressure of P = 1.5 f 0.1 mbar. The average linear bimolecular rate coefficients. The results are summarized in flow rate was in the range of u = 21-23 m s-l. All Table 1. The error limits given are the maximum uncertainties measurements were performed under pseudo-first-order condibased on the observed statistical errors and the estimated tions with more than 10-fold excess of H or D atoms over the systematic uncertainties. These error limits are thought to be hydroxymethyl radicals. The initial CH20H and CD20D valid at the 95% confidence level. Because of technical reasons, concentrations were of the order of (2-9) x mol ~ m - ~ . only an upper limit could be obtained for k4. Heterogeneous wall losses of transient species were found to 3.2. Branching Ratios. Branching ratios for reactions H be similar to those found in other fast-flow experiments; Le., CH20H and D CH20H were determined in separate kinetic k,” x k: x 2 s-1, k:H20H x k y X 40 s-l, and k? % 15 s-l runs. In the presence of excess H (or D), the consumption of were the typical wall rate constants. A total of 31 kinetic hydroxymethyl radicals and the buildup of the product OH experiments were performed to obtain the overall rate constants. radicals were monitored by LMR technique. For the case of The product branching ratios were determined in nine separate the D CH20H reaction, the buildup of H atoms was also runs. measured (with EPR) as a function of reaction time. In order 3.1. Overall Rate Coefficients. The overall rate coefficients to obtain the branching ratios for the underlying elementary for reactions 1-4 were determined by monitoring with the LMR reactions, Le., for reactions la, 2a, and 2b, calibrations for the technique the depletion of CH20H (or CD20D) along the CHzOH, OH, and H concentrationswere carried out as described reaction distance. The usual pseudo-first-order evaluation in the Experimental Section. Representative concentration vs scheme was applied. Thus, for example, the consumption rate time profiles are shown in Figures 3 and 4. The observed time of hydroxymethyl radicals in reaction 1 can be given by histories of CH20H, OH, and H concentrations were analyzed by computer simulation^^^ to determine the rate coefficients kla, k2a9 and k2b. As a first step in the simulations, larger sets of reactions were compiled, which were then reduced by standard sensitivity techniques.34bThe reduced mechanisms are presented in Table or, with the premise that the wall activity is the same in the 2. Included in the table are the normalized fiist-order sensitivity presence and absence of H atoms,32by coefficients, SCH~OH, SOH,and SHwhich represent the percentage uHO? change in CH20H, OH, and H concentrations, respectively, for ’+H1st Z -ln-=kl the percentage change of the given k. The sensitivity coefHO2 U S-H ficients show that the solutions of the kinetic differential equations of the H CH20H reaction system are by far the where S y 2 and &!$ are respectively the amplitudes of the most sensitive to those rate coefficients which were treated as HO2 LMR signals with and without added H, z is the length of fitting parameters. Other k values that have smaller influence on the solutions either are reliably known from the literature or the reaction zone, u is the average flow velocity, and k:st is the are wall rate coefficients which were determined experimentally pseudo-first-order rate constant. The semilogarithmic decay in the present study. The situation is less satisfactory concerning plots, constructed according to eq 11, provided good straight the D CH20H reaction system. Here, the fast reactions OH lines, indicating the validity of the pseudo-first-order kinetics. D H OD (16) and CH2D D CHD2 H (17), with The pseudo-first-order rate coefficients were obtained as linear least-squares slopes and were corrected for axial diffusion and uncertain rate coefficients, play a relatively important role, viscous pressure drop as In the case of reaction 2, especially in H atom formation and also in OH consumption.
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Reaction between Hydroxymethyl Radicals and H
J. Phys. Chem., Vol. 98, No. 39, I994 9795
TABLE 1: Summary of Overall Rate Coefficient Determinations reaction [HI or [D], mol kl", H D D H
+ CH20H-products (1)
-
6.9-30.7 7.3-30.0 18.2-40.0
+ CHzOH products (2) + CDzOD-products (3) + CD20D - products (4)
s-l
k(296 K) f 2a, 1013cm3mol-' 4.1 f 0.8 8.1 f 1.1 4.8 f 1.6 56
31-160 70-245 82-203
TABLE 2: Room Temperature Rate Coefficients, k, and Sensitivity Coefficients, Estimation reaction (A) Reaction System H CHzOH H + CHZOH CH3 + OH (la) H CHzOH products ( l')b 2CH20H products ( 5 ) OH CH3OH CH20H HzO (6) OH + HCl Hz0 + Cl(7) OH CHzOH products (8) OH CH3 products (9) CH3 CHzOH products (10) CH20H wall products (11) OH wall products (12) H wall products (13)
+ + + - + + + + -(B) Reaction System D + CHzOH D + CHzOH - CHtD + OH (2a) D + CH20H - CHDOH + H (2b) D + CHzOH- products (2')c H + CHzOH - CH3 + OH (la) H + CHzOH - products 2CHzOH -products OH + CH30H - CHzOH + H20 (6) OH + HCl - HzO + OH + CH20H- products CHzOH- wall products (11) OH - wall products H - wall products (13) D - wall products (14) 4-CHID - products (15) OH + D - H + OD CHzD + D - CHDz + H (17)
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ref
1.0 1013 3.1 x 1013 9.0 x 10'2 5.0 x 10" 4.8 x 10" 2.4 x 1013 1.8 x 1013 1.2 1013 40 15 2
varied varied 35 36 36 37 4 37 this work this work this work
-0.22
varied varied varied this work this work 35 36 36 37 this work this work this work this work 4 38 estimatedd
-0.09 -0.08 -0.48
1013 1013 1013 1013 1013 10l2 5.0 x 10" 4.8 x 10" 2.4 x 1013
( l')b
(5)
Cl(7) (8)
40
15 2 2 1.8 x 1013 7.8 x 1013 1.1 1014
(12)
OH
(16)
5
2
for Reactions Used in Parameter
k, cm3mol-' s-l, s-l
2.0 x 1.0 5.1 x 1.0 3.1 x 9.0 x
no. of expts 11 13
s-l
-
SCH~OH
SH
SOH
0.87 -0.31 -0.03 -0.14
-0.61 -0.06 0.04
0.02 -0.01
-0.05
-0.04 -0.01
-0.01 -0.19
-0.09 -0.09 -0.01
0.01
0.17 0.64 0.54
0.84 -0.06 -0.47 0.01
0.04
-0.01
-0.01 -0.01
-0.02 -0.01 0.01
0.04
-0.02
-0.04
-0.06 -0.01 0.01 -0.01 -0.11 -0.01
-0.02 -0.02
-0.10 -0.08
+
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'Normalized fiist-order sensitivity cogfficients, e.g., sij = a In s / a In kj, calculated for 8 and 4 ms reaction times for the H CHzOH and D CHZOHreaction systems, respectively. S values not given are less than lf0.01). Reactions other than (la): kl, = kl - kl,. Reactions other than (2a) and (2b): kz, = k2 - kza - kzb. Estimation based on ref 39.
r
0
5
10
15
20
t / ma Figure 3. Consumption of CHtOH and the formation of OH radicals in the reaction H + CH20H.
The preferred rate coefficient for reaction 16, k16 = 7.8 x I O l 3 cm3 mo1-I s-l, is that reported by Margitan et al.,38 which provided better fittings than the more recent value of Howard and Smith40 (k16 = 3.2 x 1013 cm3 mol-' s - l ) . A further increase in the assumed k16 value could further improve the agreement between calculated and experimental OH and H concentrations. In the computer simulations, a general problem associated with the experimental results obtained with the fast flow technique had to be taken into account. Namely, the reaction
0' 0
'0 4
8
12
t / ms Figure 4. Consumption of CHZOHand the formation of OH radicals and H atoms in the reaction D + CHZOH. The H atom profile is shifted toward shorter reaction time (see text).
time calculated from the flow rate of the carrier gas and the geometry of the reactor is a quantity which is not well defined. This does not affect the evaluation of the overall rate constants under pseudo-first-order conditions, but it hampers the comparison of the computed and experimental concentration profiles of the reaction products. A "standard" correction procedure is to determine the zero of the reaction time as the point where the straight lines obtained in plots of In [CH@H]+H and In [ C H ~ ~ H ] -vsH time cross. This yields a small correction of
D6bt et al.
9196 J. Phys. Chem., Vol. 98, No. 39, 1994 the absolute time scale from that determined simply by the injector position. In order to estimate the error caused in the rate parameters by the uncertainty in the reaction time, we have systematically varied the zero reaction time within a range corresponding to this uncertainty. It was found, in accordance with the expectations, that the estimated rate coefficients changed with the assignment of the zero reaction time; however, their ratios and thus the derived branching ratios were remarkably constant. We note furthermore that the computer simulations with the "standard" reaction time scale returned rate coefficients the sum of which agreed within 40% with the experimental pseudo-first-order overall rate coefficient determinations. In Figure 3, the concentration-time profiles for the H CH2OH system are presented. The agreement between calculation and experiment is indeed very good. The results of a typical experiment for the D CH20H system are displayed in Figure 4. Characteristic for this type of concentration profiles is the fast decline of the OH concentrations after a maximum has been reached. This behavior is only moderately well reproduced by the computer simulations. A probable explanation for the difference in the results of calculation and experiment is the uncertainty in the k16 value, as discussed above. In Figure 4, the time scale given refers to the CH20H and OH concentration profiles. The plot of the H atom concentrations corresponds to a time scale which is shifted toward longer reaction times since the EPR spectrometer is located downstream from the LMR monitoring port (cf. Figure 1). No attempt was made to obtain a plot corresponding to a common zero time, because of the uncertainties of the absolute reaction times. Instead, we took advantage of the fact that the H atom concentration at long reaction times reached a constant limiting value. This limiting H atom concentrationrather than the whole concentration-time profile was used in the simulations. The computer simulations provided the following branching ratios:
+
+
+
a reference reaction, C2Hs H. In this way a value of 3 x 1013 cm3 mol-' s-' was obtained for k l , which is about 30% lower than the present determination. Considering the error limits and the uncertainty of the rate constant of the reference reaction, the agreement is satisfactory. By comparison of the yields of the stable products, formaldehyde formation was found to be the main channel of the reactions amounting to about 75%. This is in accordance with our conclusion drawn from mechanistic considerations (see below). More recently, Heinemann-Fiedler and H ~ y e r m a n nad~~ dressed again the question of product formation in the CH30/ CH20H -I- H reaction systems applying the sensitive and versatile REMPI detection technique. Quantitative measurements of normal and deuterated hydroxymethyl and methyl radicals allowed the determination of a branching ratio of 30% for reaction la, in very good agreement with the present findings. In recent years, the reaction between methyl and hydroxyl radicals has been the subject of several experimental investigations which, in principle, can supply rate coefficients for reaction la, via the equilibrium constant, K1,. However, the rate of reaction CH3 OH CH2OH H (-la) is too slow to be studied at room temperature. Methanol formation is by far the dominating reaction channel of the CH3 OH Therefore, no kl, value can be derived for comparison in this way. At flame relevant temperatures, H CH20H formation in reaction CH3 OH becomes an important reaction channel. Unfortunately, however, the published k-1, values cover a wide range; e.g., at (or close to) 1500 K the following rate coefficients were reported (in cm3 mol-' s-' units): 1.9 x 1012,442.7 x 1012:5 5.1 x 1012:6 and 1.5 x 1013.47Thus, the kl, values which can be derived are also very uncertain. All one can say on the basis of the CH3 OH studies is that quite a large rate constant is expected for kla, indicating zero or small positive temperature dependence of reaction la. 4.2. Mechanism of the Reaction H CHIOH. The kinetic observations made here and in previous s t ~ d i e s ~show * , ~ ~the formation of various products in the reaction H CH20H, Le., the occurrence of a multichannel type of radical-radical Such processes can proceed in principle as direct reactions, via the formation of bound complexes (in our case via the formation of vibrationally excited (CH30H)* molecule) or by both mechanisms. Complex Mechanism. The detection of OH radicals as primary products of the reactions H CH20H and D CH2OH and the identification of H-atoms in the reaction D CH2OH provide evidence for a complex mechanism. The bound complex, (CH30H)*, when formed in reaction H CH20H possesses an excess energy of about 410 kJ/mol. Thus, it behaves like a chemically activated system4* that undergoes collisional stabilization (S), decomposition into products (D), or re-formation of the reactants (-C):
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(k,,/k1) x 100 = 25 f 5% (k2Jk2)x 100 = 23 f 10% (k2&) x 100 = 12% The quoted error limits are estimated 2 0 values. The simulations returned branching ratios in the range of 6-17% for reaction channel 2b. The proposed value of 12% is a compromise with significant uncertainty. Nevertheless, this value can be used to obtain a rough estimate for the rate of the reformation of the reactants in the reaction between H and CH2OH which occurs through an energized (CH30H)* complex (see later). Taking 5 kJ/mol for the difference between the zeropoint energies of C-H and C-D bonds:' one estimates that the significance of the re-formation of the reactants in the reaction H CH2OH is less than 3% of the overall process (cf. section 4.2).
+
+
+
+
+
H
(C) + CH20H e (CH30H)* (4)
I
(D)
decomposition products
(111)
(S) + M
4. Discussion
CH30H
4.1. Comparison with Literature Data. The results of two direct investigations of the kinetics of the reaction of H CH2OH and the deuterated analogues have been reported so far.42,43 Hoyermann et a1*: studied the reactions of isotopically labeled CH30 and CH20H radicals with H and D atoms, employing the fast flow method coupled with high-resolution mass spectrometricdetection. The overall rate coefficients were determined by comparing the rate of the reactions with that of
+
The energetics of the processes appearing in this reaction scheme is of primary importance in determining the kinetic behavior and the product distribution of the system. Therefore, the energy diagram, shown in Figure 5, has been constructed. Only spin-allowed processes and, with the exception of H CH30, only exothermic reaction channels were considered. Most of the required enthalpy data were taken from two sources, Le.,
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Reaction between Hydroxymethyl Radicals and H
t 400
J. Phys. Chem., Vol. 98, No. 39, 1994 9797
CW.rO+H (444.21
reaction
-
-
+
-- + -- + - CH,OH
1-
-E " . r
200
AJ-'
H + CHzOH (CHsOH)* (C) (CH>OH)*- H CH2OH (-C) -CH3+OH(Dl) H CH30 (D2) CHzO + HZ(D3) CHOH + Hz (D4) 'CHI HzO (D5)
r
Y
TABLE 3: Input Parameters and Results of the QRRK Calculations"
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(k/Xk,) x 100'
b
2 x 10l6
1
3 x 10l6' 6 x IOl5f 3 x loL3g 1 x lOI4
94
