J. Phys. Chem. 1984, 88, 5583-5589
5583
A Theoretical Model of Hydrocarbon Formation from CO and H, R. C. Baetzold Research Laboratories, Eastman Kodak Company, Rochester, New York 14650 (Received: February 21, 1984; In Final Form: June 18, 1984)
A general model of hydrocarbon formation from metal-catalyzed CO and Hz reactions is presented. A conventional reaction scheme involving irreversible CO dissociation, hydrogenation, and chain growth by methylene insertion into surface alkyl groups is treated kinetically under steady-state reaction conditions. We estimated the rate constants for the individual steps from theoretically computed enthalpies of reaction of intermediate species using transition-state theory. Results consistent with and in explanation of experiment are obtained. Hydrocarbon rate laws in CO and Hzpartial pressures vary with metal type as in experiment. The activation energy for CO dissociation critically influences hydrocarbon chain growth even though hydrogenation of alkyl groups is the rate-limiting step of hydrocarbon formation.
Introduction Mechanisms1q2of hydrocarbon formation from carbon monoxide and hydrogen invariably are cast in terms involving species such as CH, ( x = 1-3), CO, H , or CNHzN+l( N = 2, 3, ...) adsorbed to a metal surface. Experimental evidence for the presence of such intermediates is scarce. Scarcer still is evidence for the actual participation of such intermediates in the dominant reaction pathway. Let us note, however, some of the important studies in these areas. Methylene (CH2) is produced from the decomposition of diazomethane (CH2N2)on Ru(001) and is detected by electron energy loss spectroscopy (EELS)., Likewise, a methylidyne species (CH) is detected from the decomposition sequence of ethylene (C2H4)above 500 K on the Pt( 111) surface: Both of these species have been detected on iron single-crystal surfaces after reaction and direct analysis under v a ~ u u m . In ~ addition to the spectroscopic studies there have been several chemical studies aimed at identifying intermediate s p i e s through their reaction with probe molecules.6 One such example is the evidence for methylene, shown by the formation of norcarane upon scavenging a Fischer-Tropsch reaction mixture with cy~lohexene.~ Organometallic compounds have provided a fruitful list of examples of stabilized CH, species* that may also be involved in the formation of hydrocarbons from CO and H2 on catalyst surfaces. Some are noted in Table I. In all of these studies, we note the general lack of direct proof for participation of a particular intermediate species under practical reaction conditions. Information describing the properties of these species would be helpful in understanding hydrocarbon catalysis. The purpose of this work is to compute the heats of reaction for various CH, intermediates proposed in Fischer-Tropsch reactions leading to hydrocarbon formation. These data are then analyzed to determine microscopic rate constants, which are in turn used in a kinetic model of hydrocarbon formation from C O and H2. A test of the results will involve how well the computed overall rate laws of hydrocarbon formation agree with experiment. We have recently shown that the interaction of radical, donor, and acceptor species, including saturated hydrocarbons, with transition-metal films may be treated with tight-binding-type ~alculations.~This work has shown the predominant acceptor ~
(1) Bell, A. T. Caral. Reo.-Sci. Eng. 1981, 23, 203. (2) (a) Henrici-Olive, G.; Olive, S.J. Mol. Catal. 1982, 16, 111. (b) Rofer-DePoorter, C. K. Chem. Rev. 1981, 81, 447. (c) Osterloh, W. T.; Cornell, M. E.; Pettit, R.J. Am. Chem. SOC.1982,104, 3759. (d) Muetterties, E. L.; Stein, J. Chem. Reo. 1979, 79, 479. (3) George, P. M.; Avery, N. R.; Weinberg, W. H.; Tebbe, F. N. J . Am. Chem. SOC.1983,105, 1393. (4) Koestner, R. J.; Van Hove, M. A.; Somorjai, G. A. J . Phys. Chem. 1983, 87, 203. (5) Erley, W.; McBreen, P.H.; Ibach, H. J . Catal. 1983, 84, 229. (6) Ekerdt, J. G.; Bell, A. T. J. Caral. 1980, 62, 19. (7) Baker, J. A.; Bell, A. T. J. Catal. 1982, 78, 165. (8) (a) Churchill, M. R.; Wasserman, H. J. Inorg. Chem. 1982,21, 825. (b) Steinmetz, G. R.; Geoffrey, G. L. J . Am. Chem. SOC.1981, 103, 1278.
0022-3654/84/2088-5583$01 .50/0
mode of these species when adsorbed to infinite surfaces, in accordance with perturbation model analyses'O and more general considerations of surface phenomena." These calculations have shown a significant three-center M-C-H interaction, in accord with earlier cluster calculations12 for Ni-CH,. The cluster calculations also indicated a strong analogy between CH, species on surfaces and in organometallic compounds. In addition, recent c a l c ~ l a t i o n sfor ~ ~CH, adsorbed to Pt( 111) films have determined the preferred site of adsorption for fixed metal-carbon distances. Under this assumption the site of coordination on Pt( 1 11) was found to complete tetravalency for C for the hydrocarbon fragment. This work also considered adsorption on cluster models. Some obvious caution must be noted in contemplating quantitative evaluations of heat of adsorption of Fischer-Tropsch intermediate species. Our computational theory is qualitative, so unless a good form of calibration is used, only trends will be meaningfully computed. Secondly, we lack a good source of geometrical information concerning the adsorbed species. Part of this information will be deduced from bond lengths in organometallic clusters. Finally, we note an intrinsic difficulty in attempting to compute accurately reaction coordinates of adsorbed species. Some type of procedure would be highly desirable as a source of activation energy parameters. A rather crude method will be used here. We will proceed, with the reservations noted above, to evaluate heats of various reaction sequences on the metal surface. When possible the results will be compared with reaction data in organometallic compounds to gauge the reliability of these results. The procedures9 developed for computing heats of adsorption of hydrocarbon species on five-layer metal films will be used as described in Appendix 1,
Results and Discussion CH, Adsorption Energies. Let us consider hydrocarbon species CH, ( x = 0-3) chemisorbed to metal films. The site of chemisorption considered on the (1 11) fcc metal surface is C,,as expected for radical adsorbates. There is little experimental evidence for the sites of CH, adsorption. The C,, site of fcc (1 11) metals is expected for C H adsorption, on the basis of experimental4 electron diffraction data for C-CH3. No similar data exist for CHI or CH3, although a theoretical analysis13suggested bridging and on-top sites, respectively, on Pt(l11). It is unclear how to (9) (a) Baetzold, R. C. J. Am. Chem. SOC.1983,105,4271. (b) Baetzold, R. C . Solid State Commun. 1982, 44, 781. (10) (a) Shustorovich, E. M. J . Phys. Chem. 1983, 87, 14. (b) Shustorovich, E. M. Solid State Commun. 1982, 44, 781. (1 1) Shustorovich, E. M.; Baetzold, R. C.; Muetterties, E. L. J. Phys. Chem. 1983,87, 1100. (12) Gavin, R. M., Jr.; Reutt, J.; Muetterties, E. L.Proc. Narl. Acad. Sci. U.S.A. 1981, 78, 3981. (13) Minot, C.; Van Hove, M. A,; Somorjai, G. A. Surf. Sci. 1982, 127, 441.
0 1984 American Chemical Society
5584
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984
Baetzold
TABLE I: Experimental and Theoretical Values of Hydrocarbon Species
species C CH CH2 CH3 CH4
C radius,“ 8, C-Fe dist, 8, 1.89 1.93
0.60 0.67 0.77 0.77
organometallic compd Fe6C(CO) HFe4($-CH)(C0),2d
C-M dist, 8,
Q,8
1.85 1.90 1.97 Fe(cl-CH3)(r-CO)(~5-C~H,)2(cl-CH~(Ph2)~)e 2.07
2.11
eV
gas-phaseb H-CH,I energy, eV
Q? eV 7.45 6.77 4.57 2.89 0.17
6.58 5.96 3.99 2.52 0.17
3.47 4.2 4.9’ 4.4
‘Pauling, L. “The Nature of the Chemical Bond”, 3rd ed.; Cornell University Press: Ithaca, NY, 1960. bHerzberg, G. “Molecular Spectra and Molecular Structure”; Van Nostrand: Princeton, NJ, 1967; Vol. 3. cBradley,J. S.; Ansell, G. B.; Hill, E. W. J . Am. Chem. SOC.1979, 101, 7417. dBeno, M. A.; Williams, J. M.; Tachikawa, M.; Muetterties, E. L. J. Am. Chem. SOC.1981, 103, 1485. ‘Dawkins, G. M.; Green, M.; Orpen, A. G.; Stone, F. G. A. J . Chem. Soc., Chem. Commun. 1982, 41. /Planar gas-phase structure. *Nd = 9.2. *Nd = 7.2.
I
( 1 1 ) Surface
C CH CHZ
CH,
5L
,
M-C = 1.858 M-CH : 1.90 M-CH, : I 9 7 M-CH, = 2.07
I
9
,H
H
H H i,
Nd
Figure 1. Computed heat of adsorption Q plotted vs. Nd for adsorption of CH, species to a hypothetical fcc (1 11) surface in the C,, site. Nd is
the number of d electrons per surface transition-metal atom. apply this analysis to variable metal-carbon distances as a function of site or carbon valence. Thus, we considered only the C,, site in this work. Our method of calculation is not expected to predict the metal-radical bond lengths, so covalent radii and bond lengths in organometallic compounds must be used to fix these values. Table I shows these data as well as the actual bond lengths used. Note that the carbon radius expands as the carbon valence decreases. This trend is nicely seen in the data for organometallic compounds of iron, where data for C, CH, and CH3 ligands are available. Based upon an average metallic radius of 1.3 A and the carbon radius, the meta1-C bond lengths in Table I were used. Computed heats of adsorption of these species at different transition-metal d occupations are shown in Figure 1. As expected, the early transition metals have a greater heat of adsorption for these radical species than the late transition metals. As radicals, all of these species withdraw electrons from the d orbitals of the metal surface. The species more unsaturated at carbon have the greatest effect. These features are a consequence of the variation of Fermi level, which decreases within a transition-metal series on moving toward the right. The small decrease in metallic radius upon moving from early to late transition metals in a given series does not change the shape of Figure 1 but only slightly reduces its curvature. Since our calculations are aimed at changes that occur in a transition series rather than with one specific element, this effect is not major to our objectives. Heats of Reaction. Let us consider the task of computation of enthalpy changes for successivehydrogenation of surface carbon. Direct computation is not yet possible. Instead, we will devise a thermodynamic cycle employing experimental data on gas-phase enthalpy of reaction and the experimental heat of H ad~orption.’~ These data are combined with calculated heats of adsorption to yield the heat of reaction. The strength of the C-H bond in CH, species in the gas phase has been measured spectroscopically15 (see Table I). We wish (14) Muetterties has pointed out the near constancy of the heat of H, chemisorption on various well-ordered transition-metal surfaces as in: Muetterties, E. L.; Wexler, R. L. Sum. Prog. Chem., in press.
Figure 2. Adsorbed CH, reaction intermediates for successive hydrogenation reactions. C(g)
+
H(g1
lac C(a)
laH +
H(d
6.E
CH ( 9 ) b C H
-A HI
CH (0)
-AH, = B E + QCH - O H - Q c
-
Figure 3. Thermodynamic cycle used to compute the enthalpy of the
surface reaction C + H
CH.
TABLE 11: Computed Enthalpy Changes and Activation Energies for Hydrocarbon Reactions (kcal/mol)
AH, AH2 AH3
AH4
reaction C+H-+CH CH+H+CHZ CH2 + H CHj CH3 + H CH, CH,+ CH,-C,H, CzH5+ H-C,H6
ending transition metal AH AE -4 11 17 4 17
middle transition metal
AH -2 15 16 6 0 0 21 22 8 4 22 21 0
AE 0 18 2 24 6 24
to combute the heats of the surface reactions shown in Figure 2. A thermodynamic cycle, as exemplified for C H in Figure 3, is used for each species. Here the calculated heats of CH, adsorption QCH,will be used along with the experimental gas-phase C-H bond energy and experimental heat of hydrogen adsorption to give the heat of reaction. We use 2.7 eV (62 kcal) for the latter quantity, which Muetterties has noted to be almost constant across a transition-metal series.I4 Using this procedure and correcting for the planar15 gas-phase geometry of CH3, which is computed (15) Herzberg, G. “Molecular Spectra and Molecular Structure”;Van Nostrand: Princeton, NJ, 1967; Vol. 3.
Hydrocarbon Formation from C O and H2 CONVENTIONAL REACTION SCHEME
co
c +o 2H CH
CH2
CH3
CH,
CH2
f
kg
CH,
.
C2H5
k
CH, t ~
2
4+ ~ 5 C3H7 C2H6
Figure 4. Conventional reaction scheme of CO and H2to form hydrocarbons. Rate and equilibrium constants are defined.
here to be 0.5 eV more stable than pseudotetrahedral, we arrive at the AHi values in Table 11. Note that we have considered ending transition-metal elements (Nd = 9.2, nickel column) and middle transition-metal elements (Nd = 7.2, iron column) in arriving at these values. This classification is rather arbitrary because of these many factors involved in simulating different Nd values. Previously? we demonstrated how the Fermi level and the d energy level may be systematically varied to simulate changes in Nd. We consider the enthalpy change on forming ethyl radical from methyl and methylene. In the gas phase we compute 4.8 eV for this reaction. Then, using the values in Table I with a thermodynamic cycle similar to that in Figure 3, we compute the energies in Table 11. Rate Constants. Let us consider the rate constants k = k,,c-m/RTfor surface hydrogenation reactions. The preexponential part was determined by transition-state theory16 as described in Appendix 2. The second parameter needed to specify the rate constants is the activation energy term. This cannot be calculated directly since a full knowledge of the reaction coordinate is needed. This task is beyond the scope of our present computational tools. Instead, we have used an equation of the type used by Evans and Polanyi” AEi = AHi + x (1) where the activation energy values AEi are related by the same linear constant to the enthalpy values AHi. This procedure is crudely consistent with the Hammond postulate,l8 which similarly links activation energy and enthalpy change for a like series of compounds. The exact specification of x will be shown later. Reaction Mechanism. We now consider hydrocarbon formation on a metal surface. A conventional reaction scheme involving CO dissociation prior to hydrogenation is considered. This mechanism (Figure 4) has been discussed by Bell’ where the limiting forms of the kinetics have been determined. We consider CO dissociation to be irreversible, with rapid removal of 0 from the surface (reactions with H or C O are known). Hydrogenation of alkyl fragments is taken to have a rate independent of chain length;
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 5585 however, the model could be readily extended to rates dependent on chain length. Steady-state kinetics are solved to give the concentrations of surface species. This leads to a set of nonlinear equations, which must be solved iteratively. Some of these equations are shown in Appendix 3. An initial guess, based upon methanation kinetics, is made for the first cycle of calculation. A convergence of 0.001% between successive cycles for CH2 and CH3 surface concentrations if the criterion for solution and requires 30-100 cycles. The first problem to be treated is the adsorption of Hz and CO from the gas phase. It was first assumed that CO and H compete for the same sites on the catalyst surface. Under this assumption, we found methanation rate laws with much too strong an inverse CO partial-pressure dependence (e.g., p(CO(g))-2) to be consistent with experiment. A model employing C O and H adsorption on independent sites is necessary to fit the methanation kinetics. One site contains only CO, and the other contains C, H, and all other hydrocarbon species. The steady-state concentration of 0 is assumed to be negligible compared to that of the dominant species. The relevant equations are
OH = [ K ~ ( H Z ( S ) ) I ’ /-~ OH ( ~ - Cod i
(2)
where 0, is the surface fraction of species x and CiOiis the surface fraction of all species other than H and CO. Here, C O occupies a site and does not compete with other surface species for this site. Based upon experimental facts, this result is plausible. C O is known to bond end-on or bridge two metal atoms on transition-metal surfaces, whereas atomic adsorbates prefer the site of highest c o ~ r d i n a t i o n . Thus, ~ ~ H or the radical CH, species could bind at the threefold site on (1 11) surfaces with C O binding at the end-on or bridging site. Further theoretical work is needed to put this result on a better footing, but the lead provided by this analysis seems real. In all of our model calculations, independent H and CO sites are assumed. A recent analysiszb of hydrocarbon, CO, and H surface species on Fe( 100) has assumed independent H and C O sites, based upon the experimental observation that CO does not displace H adsorbed previously. Also, we note that earlier mechanismsz1~2z for C O hydrogenation have proposed surface nonhomogeneity to justify different adsorption sites for CO and hydrogen. The model assuming independent H and CO sites probably holds only over some limited range of the possible concentrations of H or CO. Thus, as long as the surface fraction of H is small (typical reaction condition), the relation holds. However, if the surface fraction of H becomes large, the independent-site model will probably become inadequate. In addition to the model discussed above, various modifications were considered that allowed the carbon and hydrocarbon species to compete for the same sites occupied by undissociated CO. Although this treatment changes some quantitative details, the computation agrees with experimental methanation rate laws as long as H and C O occupy different sites. In the independent models the concentration of each type of site per unit area was varied from C, = 1 X 1015-2 X 1015sites/cm2 as estimated from close-packed metal density. Clearly, this is a simplification, since C, might be different as a function of surface geometry or composition. The heats of adsorption of H2 and C O on metal surfaces are important parameters in this calculation. It is particularly important to choose values for these parameters appropriate to the metal surface under reaction conditions rather than clean conditions. Experiments20b,chave shown much lower heats of adsorption of H2 and C O on nickel and iron surfaces at high coverages or on surfaces containing C than on clean surfaces. For (19) Muetterties, E. L.; Rhcdin, T. N.; Bond, E.; Brucker, C. F.; Pretzer, W. R. Chem. Rev. 1979, 79, 91.
(16) Moore, W. J. “Physical Chemistry”, 3rd ed.; Prentice Hall: Englewood Cliffs, NJ, 1963. (17) Evans, M. G.; Polanyi, M. Trans. Faraday SOC.1938, 34, 1 1 . (18) Hirsch, J. A. “Concepts in Theoretical Organic Chemistry”;AUyn and Bacon: Boston, MA, 1974.
(20) (a) Benziger, J. B.; Madix, R. J. SurJ Sci. 1982, 115, 279. (b) Benziger, J. B.; Madix, R. Ibid. 1980, 94, 119. (c) McCarty, J. G.; Madix, R. J. Ibid. 1976, 54, 121. (21) Vannice, A. M. J . Catal. 1975, 37, 462. (22) Boudart, M. AIChE J . 1972, 18, 465.
5586 The Journal of Physical Chemistry, Vol. 88, No. 23, 1984
Baetzold TABLE III: Effect of CO Decomposition Activation Energy on Methanation Rate Laws at 250 O C , 0.75 atm of H2,and 0.25 atm of
co
AE, kcal 15 13 11 9 Pd/Si02 Ir / AI2O3 Pt/A1203 Pd/AlzOp Fe/A1203 Rh/A1203 Ni/AI20, C0/A1203 Ru/A1203
2
4
6
PL.
PTO
0.82 1.15 1.35 1.50
0.08
-0.10 -0.31 -0.38
CHd turnover no. 7.5 x 10-4 1.2 x 10-3 4.7 x 10-4 3.4 x 10-4
Vannice's Experiments (Ref 21) 0.15 0.71 0.10 0.96 0.03 1.03 0.03 1.03 -0.05 1.14 -0.20 1.04 -0.31 0.77 -0.48 1.22 -0.6 I .6
8
X (kcall
Figure 5. Methane turnover number (s-l) at 250 OC, 0.75 atm H2, and 0.25 atm CO as a function of x in the equation AE, = AH, x. AH, is the computed enthalpy term for various steps in carbon hydrogenation (see Table I), and AE,is the corresponding activation energy. Data are plotted for an ending transition-metal atom.
+
example, the heat of C O adsorption on a carbided Ni surface is 12 kcal/mol, compared to 30 kcal/mol, the low-coverage value on the clean surface. For H2, no adsorption was observed at room temperature on the carbided Ni surface. In our calculations, AHa = -12 kcal/mol and A",,= -8 kcal/mol were used throughout. Computed Rates. Now we are ready to consider computation of methanation rates and determination of the linear constant x in eq 1 . Activation energies are computed by adding a linear constant to the AH term and observing the effect on the overall turnover numbers. Thus, the overall turnover number is scaled to experimental values. Figure 5 shows that adding 4 kcal to the AH value for ending transition-metal elements gives a turnover number s-I, which agrees with experimental methanation turnover numbers for these elements.*' A similar procedure led to 2 kcal for use with the middle transition-metal elements, as shown in Table 11. The turnover number is defined here as the number of product molecules formed per catalyst surface atom per second. One additional parameter needs to be specified to begin our computations. This is the activation energy for CO decomposition. Table I11 shows calculated results for several empirical values of this parameter along with the turnover number and the reaction order for C O and H2.The C O reaction order decreases and the H2 reaction order increases as the C O activation energy for decomposition decreases. The computed reaction orders agree well with the experimental reaction orders of VanniceZ1shown in the bottom part of the table. The trends track one another well, except for the experimental data for Ni. Positive orders in C O result in the smallest positive orders in H2 and vice versa. This behavior, obtained without deliberate fit of parameters, suggests a good modeling of methanation. Only some of the Vannice data are listed in Table 111; they were chosen to be representative but do not reflect effects of support or catalyst concentration on the reaction order, which may influence the Ni data. The reason for negative CO reaction order is found from this analysis. Increasing surface C O increases surface C but decreases surface H. The latter has a higher positive reaction-order dependence. The activation energy for methanation may be computed by fit of the calculated turnover numbers to an Arrhenius-type equation. This procedure gives 27.5 kcal/mol for the activation
10-41
, c2
,
, c4
,
, c6
Carbon chain length
Figure 6. Turnover numbers for hydrocarbon formation at 250 OC, 0.75 atm H,,and 0.25 atm CO plotted logarithmicallyvs. carbon number for various values of the activation energy for CO decomposition. These plots give the smallest slope at the smallest AE value. Data are for a middle transition-metal element.
energy of middle transition-metal elements and 23.1 kcal/mol for ending transition-metal elements. Those values agree well with experimental data reported by Vannice.21 The thermodynamics of hydrocarbon formation is only partially treated in this work. This treatment includes only competitive effects in the forward reaction. A complete thermodynamic treatment requires treatment of all back-reactions and would introduce the need for additional parameters, which are not well in hand. As a consequence, all reaction data are reported near a total calculated pressure of 1 atm. Effect of CO Decomposition Activation Energy. The activation energies of C O decomposition in Table I11 are less than the activation energies for hydrogenation of carbon in Table 11. Thus, considering preexponential terms and surface concentrations, CO decomposes more easily than C is hydrogenated. This model result is in complete accord with recent experiments of BiloenZ3et al., leading further credence to this model. The rate of C O dissociation significantly influences the surface concentration of C, H, and CH, species. As the CO dissociation rate increases, surface C concentration increases while the surface concentrations of H and all of the CH, species decrease. This behavior determines a dependence of the hydrocarbon chain-length distribution on the activation energy for CO dissociation. Figure 6 shows the turnover numbers computed for various hydrocarbon chain lengths at various CO decomposition activation energies. It is apparent that longer chains are formed when CO can decompose more easily. Since CO decomposition occurs more (23) (a) Biloen, P.; Helle, J. N.; Sachtler, W. M. H.AIChE J . 1979, 58, 95. (b) Biloen, P.; Sachtler, W. M. H. Adv. Cutul. 1982, 30, 165.
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 5587
Hydrocarbon Formation from C O and H2 TABLE IV Typical Surface Concentrations on Transition Metals at 250 'C, 0.75 aim of Hl,and 0.25 atm of COO
soecies
co H C CH C H ~ CH,
C2H5 C3H7
late transition metalb 5.5 x 1014 1.9 x 1014 9.6 X 1.1 x 1.7 x 8.9 x 5.0 X 2.8 X
10l2 1015 (1.2 x 1 0 9 109 (1.7x 109) 1010 (8.9x 1010) 1O'O 1O'O
middle transition metalC 4.1 x 1014 1.3 x 1014 6.4 x 1013 1.3 x 1015 (1.4x 1015) 2.1 x io8 (2.0 x 108) 1.0 x 109 (1.1 x 109) 6.3 X 3.8 X
lo8 lo8
Concentration unit is atoms/cm2. Computed equilibrium concentrations in parentheses for CH, CH2, and CH,. bCO activation energy for dissociation is 1 1 kcal/mol. cCO activation energy for dissociation is 9 kcal/mol. (I
easily on the middle transition-metal elements than on the ending transition-metal the former would be expected to form the longest hydrocarbon chains. This effect is in accordance with the dependence of C O dissociation activation energy on metal position in the periodic table. Bell' recently discussed this effect, based upon an analysis of bond energy/bond order calculations of MiyazakLzs This chain-length effect is generally found in experiment, since Co and Fe form long chains, whereas Ni is a methanation catalyst.23 Thus, the model offers a possible explanation of why longer hydrocarbon chains are formed on the middle transition-metal elements. We assume in this analysis that the primary variable reflecting differences from metal to metal in controlling hydrocarbon chain length is the rate of CO decomposition. Heats of CO and H, adsorption remain approximately ~ o n s t a n t " ~on ' ~ traversing a transition-metal series. The variations in activation energy (rate constants) for carbon hydrogenation or chain growth computed for different Nd values in Table I1 do not lead to significantly different hydrocarbon chain-length distributions. The value of the chain-growth rate constant could significantly influence the hydrocarbon distribution. However, our calculations did not show a significant variation of the chain-growth rate constant with metal type. Moreover, even if the chain-growth rate constant varied significantly with metal type so as to explain the chain-length distribution, this parameter would not influence the methanation rate laws, in contrast to the behavior we observed in Table I11 for C O decomposition rate constants. Thus, it is believed that the C O decomposition rate is the most important parameter in controlling hydrocarbon chain length. The effect of potassium promoters on increasing hydrocarbon chain length can also be explained by the changes in C O dissociation activation energy. Potassium decreases the activation energy for CO d i s s ~ c i a t i o n . This ~ ~ ~behavior, ~~ observed experimentally, is completely consistent with our observation of longer chain lengths for lower activation energy of C O dissociation (Figure 6 ) . Surface Concenlrations. Table IV lists representative values computed for the surface concentration of various species on typical late and middle transition metals, under reaction conditions. Clearly, C H is present in dominant concentration to the other CH, species and should be detectable experimentally at these concentrations. There is little hope of spectroscopically observing the other CH, species under reaction conditions with our present analytical techniques. We have also computed equilibrium concentrations of species for the equilibrium CH,
K*I +He CH,+i
x = 0-2
(3)
(K,) (HI (CHX-I) (CHx) = 1 + (K,)(H)(CH,-,)/C0 (24) Broden, G.; Rhodin, T.N.; Brucker, C.; Benbow, R.; Hurych, Z . Surf:
__
Rri 1976 . - . -59 - , - -591 -.
(25)(a) Miyazaki, E.J. Curd. 1980,65, 84. (b) Miyazaki, E. Surf Sci. 1978, 71,741. (26)(a) Kelley, R. D.; Goodman, D. W. Surf. Sci. 1982, 123,2743.(b) Campbell, C.T.;Goodman, D. W. Ibid. 1982, 123,413. (27)Bonzel, H. P.;Krebs, H. J. Surf. Sci. 1982, 117,639.
TABLE V Parameters of the Calculation" atom Slater orbital -Ht,, eV metal 4s 5 4P 4 3d 10 C 2s 21.40 2P 9.40 H 1s 13.60
exponent 2.75 2.75 5.983 (0.5264)b 1.625 1.625 1.300
OM-M distance is 2.5 A. C-H distance is 1.1 A. WolfsbergHelmholz K 1.75,intramolecular; 2.0,adsorbate-metal; 3.0,metalmetal. * A linear combination of two Slater orbitals represents the d metallic orbitals. Coefficients are given in parentheses.
using an equilibrium constant calculated from the ratio of rate constants. Essentially, the deviation from equilibrium is very small, so that an equilibrium assumption to compute the surface concentration of C H 3 from C and H surface concentrations would not be too bad. Thus, the x value that we have used in eq 1 is not significant in determining the concentration of CH3. The rate-limiting step for methane formation in this model is hydrogenation of methyl groups. This point can be seen from comparison of the preexponential values in Appendix 2, activation energies of hydrogenation in Table 11, and the surface concentrations in Table IV. The rate constant for hydrogenation of methyl is smaller than for hydrogenation of any of the other CH, species, owing to its large activation energy. This value is such that C O dissociation (Table 111) also is not rate limiting. Summary. A first-stage model describing a mechanism of hydrocarbon formation from CO and H, has been presented. Rate constants were computed through transition-state theory and the use of computed surface enthalpy values for intermediates in Evans-Polanyi relationships to give overall kinetics of reaction. Good agreement of hydrocarbon formation in terms of rate laws and kinetics was obtained between theory and experiment. The large number of parameters involved in this model is a weakness or a strength of this analysis. The weakness derives from the large number of parameters that must be supplied. As experimental data become available, however, this can be turned to a strength. Clearly, the calculations used to derive the microscopic rate constants of hydrocarbon formation involve many approximations. The individual activation energy terms might vary considerably from those which might sometime be measured for one specific system. Nevertheless, these parameters do seem to reproduce a good amount of experimental data and provide support for the conventional reaction mechanism. Here also, some individual reaction steps that we have not considered in our initial treatment might be important in some particular systems. In this regard mention should be made of the kinetic analysis of H-assisted CO bond breaking as the rate-limiting step of methanation of Ptsupported alumina, silica, and titania.28 In addition, we have considered CH, adsorption only at the C3, metal site and have not permitted significant M-C-H interactions. Clearly, future work might consider some of these effects. Despite these reservations, we feel the results of this work apply in a general sense and are helpful to understand hydrocarbon formation.
-
Conclusions 1. The rate-limiting step in methanation is CH3 + H CH4, not co decomposition, 2. The species C H is calculated to be present in highest concentration of the CH, species [ x = 1-4). 3. The rate constinLfor C O decomposition determines hydrocarbon chain length. Longer chains form if the CO decomposes more rapidly. 4. Potassium promoters decrease the CO decomposition activation energy, which is consistent with an increased hydrocarbon length predicted from Our 5. Quantum-mechanical calculations can be applied to a surface reaction to describe the variations in catalytic with metal . -properties properties. (28) Vannice, M. A.; Twu, C. C. J . Cutul. 1983, 82,213.
Baetzold
5588 The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 TABLE VI: Equations Used To Compute Enthalpy Change of Surface Carbon Hydrogenation to Methane and Corresponding Enthalpy Expressions’ reaction -AH, kcal/mol 1 3 H d d + COW 48
-
--
H2OW + CH4W 3H&) 6Wa) CO(g) C(a) + O(a) 2H(a) + O(a) H2O(g) + 3 + 4 3H2(g) + co(g) H2O(g) + 4H(a) + c(a) 1 - 2 - 3 - 4 4H(a) + c(a) -+ CH,(g)
2 3 4 2
-
~ E -H~ E H - H Ec + Eo - ECO - ~ E -HEo ~ E -H~ E H -+ H Ec + EHiO 48 - ( ~ E -H~ E H - + H EC - ECO + EH20)
EH-H = 103 kcal/mol, Eco = 256 kcal/mol, E H ~ =O 220 kcal/mol, Ec = adsorption energy of carbon, Eo = adsorption energy of oxygen, EH = adsorption energy of hydrogen, g = gas phase, a = adsorbed. TABLE VII: AE, Total Enthalpy Change, for C(a) CH4M
metal Fe
En, kcal/mol
Ru
67 65
Rh
68 63 63
Ir
61
Ni
63 60 63
os co Pd Pt
+ 4H(a)
EC, kcal/mol 169
-
AE,
kcal/mol 44 15
148 155
34 18 2 24 18
159 143
149 159 134 144
preexponential may be estimated from the partition functions of surface H . Under this assumption we compute the following values for preexponentials. ko = 1
k ( i , l ) ; hydrogenation
cm2/(atom s)
X
i = 2-5
ko = 1
k(i,2);unimolecular decomposition
X
lOI3 s-I
i = 2-5
ko = 5
k,; CH2 insertion
X
k ( 1 , l ) ;CO decomposition
lop5cm2/(atom s)
ko = 5
X
lo9 s-l
It is noted here that the normal preexponential term for a unimolecular reaction is expected to be 1 X 1013 s-l, but we have used the value 5 X 1Olo s-l for loss of H from CH, ( x = 1-3). This smaller preexponential was necessary in order to obtain reasonable turnover numbers in accord with the other parameters. Decreased preexponential values might be caused by hindered motion of the C H , species as a result of interaction with other adspecies or other factors discussed in Appendix 5 . Preexponentials in Equilibrium Constants.
KO = 9.7 X
K,; C O adsorption
K,;H 2 adsorption
KO= 1.6
X
cm lo7 cm-I
Appendix 3 Steady-State Equations for Reaction Sequence in Figure 4 .
-1
3
6. A conventional reaction mechanism involving C O dissociation, carbon hydrogenation, and chain growth by methylene insertion into alkyl gives behavior consistent with observed kinetics of hydrocarbon formation from C O and H,. Acknowledgment. I am grateful to E. M. Shustorovich for many helpful conversations on this subject and to J. F. Hamilton for critical reading of the manuscript and helpful suggestions.
Appendix 1 Our method of calculation is exactly that which was discussed earlierg in connection with adsorption of saturated hydrocarbons to metal films. The parameters of the calculation, which is calibrated for first-row transition metals, are listed in Table V. The C 2p ionization level is decreased from earlier work, to prevent excessive charge flow for the radical species. Appendix 2 Let us consider the problem of determining the preexponential part of rate constants for surface hydrogenation reactions. Take the bimolecular surface reaction CH H CHI (2.1)
+
kg(CH2)(C2H5)
( C 3 H 7 ) = k(5,1)6,Co
+ k,OcoCo
6, = fraction of surface covered by species x
where K = Boltzmann’s constant, T = temperature, h = Planck’s constant, and Q, = partition functions for species x . The partition function can be written in terms of translational (qT),vibrational (qv), and rotational (qR) one-dimensional elements
=4
~
~
4
~
4
~ (2.3) ~
where the translational component is by far the dominant term.
-
lo8 atoms/cm
qR
-
10
qv
-
1
(2.4)
We consider H to be mobile on the metal surface and are unsure whether the C H , species are mobile or immobile. Under either condition eq 2.5 holds for the adsorbed species. Thus, the QCH,
%
QcH,+~
(3.7)
d ( C , H d / d t = ~ ( ~ , ~ ) O H C O ( C ~ H , )( 3 . 8 )
Co = 2 x
qT
kg(CH2)
+
From transition-state theoryI6
Q’cH~
t
x = 0-3
(2.5)
atoms/cm2
Appendix 4 Let us consider the enthalpy change for the overall reaction
AE
C(a)
+ 4Wa)
CH,(g)
(4.1)
The AH of this reaction can be computed for a wide variety of metals by using Miyazaki’s bond energy data for adatoms adsorbed to metals.25 He combined electronegativity concepts with experimental data for dissociative chemisorption heats to prepare a table of bond energies for C , 0, and H with various transition metals. At issue for our attention is the availability of an independent comprehensive source of data to compare with our calculations, rather than the techniques used by Miyazaki. The enthalpy change for reaction 4.1 is computed from a thermody-
J . Phys. Chem. 1984, 88, 5589-5593
namic cycle (see below from the bond energy data). Using the Miyazaki values of EH and Ec (Table VII) with the thermodynamic cycle (Table VI) leads to the enthalpy change ( A E ) for reaction 4.1 on various metals listed in Table VII. The value for Ni in Table VI1 agrees well with our computed value (sum of AH'S in Table 11) for the ending transition metals (18 kcal) as determined by an independent procedure. For the middle transition-metal elements, our computed value of 36 kcal compares well with the values 44 kcal for Fe or 34 kcal for Os but poorly with 15 kcal for Ru. This illustrates the difficulty of the broad generalizations we have used in an attempt to fit all elements. The analysis also points out the fact that hydrogenation of surface C to hydrocarbons is an uphill process energetically. This statement is true for most hydrocarbon-forming reactions. Generally, the energy barriers to be overcome are larger for the early and middle transition metals than for the ending transition metals. Appendix 5 Let us offer some comments concerning the mechanism treated in this work. We have considered a reversible sequence of hydrogenation steps of CH, ( x = 0-2) based upon the mechanism of Bell.' Bell noted that reversible steps were considered, since reversible reactions are observed in organometallic complexes involving these species. Further support for reversible reactions comes from methane decomposition reactions on Ni/Si02 catal y s t and ~ ~ ~on metal films.30 In these cases decomposition of methane to adsorbed C and H is observed, particularly when H concentration is low. Yet in some mechanisms, irreversible reaction steps are proposed, involving no CH, ( x = 1-3) decomposition. There may be some systems in which the back-reaction is negligible and the model treated here is not applicable. (29) Kuijpers, E. G. M.; Jansen, J. W.; van Dillen, A. J.; Gas, J. W. J . Catal. 1981, 72, 75. (30) Frennet, A. Catal. Rev.-Sci. Eng. 1974, 10, 37.
5589
We have treated unimolecular reactions leading to two product species without the need for an additional vacant site (S). Clearly, this is an approximation. The need for an additional site in
co + s
+
c+0
(5.1)
can be incorporated into the corrected pseudo-first-order preexponential factor (kocorr)by kOcOfr
ko(1 - C8,)
(5.2)
X
where the partition function for the surface site is taken as Coand the sum is over all adspecies except CO. Computations utilizing this approximation produce results similar to those discussed in this paper with a slightly smaller value for the CO decomposition activation energy (-2 kcal/mol smaller). For reactions of the type x = 1-3 CH, + S C,' + H (5.3) +
we have already noted the need for a preexponential factor reduced from the typical value 1 X 1013 s-l. The need for the bare site S may also be a factor responsible for this reduction. Clearly, this is an area for future work on this model. One final comment concerns our calculated result that surface C H is present in greater concentration than undissociated CO at 1-atm pressure as displayed in Table IV. Good spectroscopic evidence has been compiled23bto indicate that under reaction conditions undissociated CO is the dominant surface species. Although our computations agree with this result at pressures greater than 20 atm, perhaps our model or parameters could be improved to better describe the situation. One area for consideration concerns the possibility that C O dissociation may occur at a special site different from and in lower concentration than the sites for storage of undissociated CO. Clearly, this is a matter for further investigation. Registry No. CO, 630-08-0.
Cyclopentylperoxyl and Cyclohexylperoxyl Radicals in Aqueous Solution: A Study by Product Analysis and Pulse Radiolysis Henryk Zegota,' Man Nien Schuchmann, and Clemens von Sonntag* Max-Planck-Institut fur Strahlenchemie, 0-4330 Mulheim a.d. Ruhr, West Germany (Received: March 15, 1984; In Final Form: July 3, 1984)
Radiolysis of N 2 0 / 0 2 (4: 1 v/v) saturated aqueous solutions of cyclopentane generates cyclopentylperoxyl radicals which decay by a second-order rate process (2k = 1.5 X lo7 M-' 9')and give rise to the following products (G values in parentheses): cyclopentanone (1.7), cyclopentanol (0.81, glutaraldehyde (1.2), 5-hydroxypentanal (0.8),organic peroxidic material (OS), and H202(1.7); oxygen is consumed with G = 5.0. The corresponding data for cyclohexane solutions are as follows (2k = 1.2 X lo7 M-l s-l ): cyclohexanone (2.5), cyclohexanol (0.9), total aldehydes (0.8), organic peroxidic material (0.9), H202 (1.6), and oxygen uptake (4.0). During the bimolecular decay of the cycloalkylperoxyl radicals small amounts (G = 0.5) of H02. (H' + 0,s) are formed. It is proposed that in the rate-determining step a short-lived tetroxide is formed which breaks up by four main routes: (i) 02,cycloalkanol, and cycloalkanone, (ii) H202and two molecules of cycloalkanone, (iii) O2 and two w-formylalkyl radicals (from which the acyclic aldehydes are formed), and (iv) O2and two cycloalkoxyl radicals. The cycloalkoxyl radicals undergo a 1,2-H shift, a reaction which eventually leads to the formation of the intermediate 02;. In the cyclopentane system the fragmentation (mainly the concerted process iii) is the most important single process (40%) whereas in the cyclohexane system this route does not exceed 15%. A fragmentation of the acyclic radicals is not observed.
Introduction In the presence of oxygen most carbon-centered radicals are converted into the corresponding peroxyl radicals with near diffusion-controlled rates. Under natural conditions oxygen is widely present and peroxyl radical reactions are important environ-
mentally. The fate of peroxyl radicals has mainly been studied in nonpolar media or in the gas phase, and comparatively little was known until recently about their reactions in aqueous solutions. The results from systems that have been studied in our laboratory, e.g., the peroxyl radicals generated by the reaction of OH radicals and molecular oxygen with methane,2 e t h ~ l e n emethan01,~ ,~ eth-
(1) Permanent address: Institute of Applied Radiation Chemistry, Technical University, Lodz, Poland.
(2) Schuchmann, H.-P.; von Sonntag, C. Z.Naturforsch.8 1984, 398, 217.
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0022-365418412088-5589$01.50/0
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0 1984 American Chemical Society
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