Znd. Eng. Chem. Res. 1992,31, 2497-2502
Robinson, C. J.; Cook, C. L. Low Resolution Mass Spectrometric Determination of Aromatic Fractions from Petroleum. Anal. Chem. 1969,41,1648-1564. Sullivan, R. F.; Boduszymki, M.M.; Fetzer, J. C. Molecular Transformations in Hydrotreating and Hydrocracking. Energy Fuels 1989,3,603-612.
Tiesot, B. P.; Welte, D. H. Petroleum Formation and Occurrence; Springer Verlag: Berlin, 1984; pp 379-403.
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Weekman, V. W. Lumps, Models, and Kinetics in Practice. Chem. Eng. B o g . Monogr. Ser. 1979, 75, Wei, J.; Prater, C. D. The Structure and Analysis of Complex Reaction Systems. Adv. Catal. 1962, 13, 203. Received for review October 28, 1991 Revised manuscript received March 25, 1992 Accepted July 13, 1992
Rate of Heterogeneous Catalytic Reactions Involving Ionic Intermediates Slavik Kasztelan Institut Franqais d u Pgtrole, B.P. 311,92506 Rueil-Malmaison, Cedex, France
A solution to the problem of the computation of the rate law of a catalytic reaction involving ionic intermediates and taking into account the ionic nature of the surface species is proposed in this work. It is shown that such a rate law is computable within the Langmuir-Hinshelwd-Hougen-Watson (LHHW) theory when an electric charge conservation equation is added to the usual set of equations. Using the approximation that the number of sitea equal the number of negative charges of the surface species and neglecting the contribution of the bulk, a rate law can be computed exactly. This is illustrated by considering four examples of catalytic reactions involving ionic intermediates, namely the isomerization of unsaturated hydrocarbons by Bronsted acids, the hydrogenation of unsaturated hydrocarbons involving the heterolytic dissociation of hydrogen, the generation of methyl radicals in methane oxidative coupling, and the partial oxidation of hydrocarbons, With no approximations the rate law obtained is complex and includes, in an intricate manner, several initial concentrations of surface and bulk species characterizing the catalyst. Introduction Rate laws for catalytic reactions performed by nonmetallic catalysts are often established using the LangmukHinshelwood-Hougen-Watson (LHHW) formalism (Yang and Hougen, 1950). For redox reactions, redox models such as the well-known Mm-van Krevelen model (1954)are also often used. Rate laws obtained using these different models have been found very useful for the analysis of experimental resulta of kinetic studies (Smith, 1982)although in each case the formalism suffers from a number of simplifications and, in particular, the assumption that all of the sites are equivalent. Nevertheless, the rather simple equations obtained using these models are superior to empirical power rate laws as they are based on a description of the reaction mechanism and of the catalyst even though both are not, in general, known in great detail. The various types of adsorption considered for the computation of LHHW rate laws are nondissociative or dissociative homolytic adsorption. Thus adsorbates are considered in the form of either a molecule, a fragment of a molecule, radicals, or atoms. However, a number of catalytic reactions on nonmetallic catalysts involve or are thought to involve ionic intermediates. Catalytic reactions involving ionic intermediatea can be eliminations, additions, or substitutions (Noller and Kladnig, 1976). A simple example is that of an olefin transformed into a carbocation by association with a proton of Bronsted acid catalysta such as zeolites. Thus a first way to generate an ionic intermediate on a catalytic surface is by an associative reaction of a reactant with a preexisting ionic surface species. Heterolytic dissociation is another means of generating ionic intermediates, namely one negative and one positive species on the surface. The heterolytic dissociation of a number of molecules has been shown or is thought to occur on nonmetallic polar catalysta. Hydrogen has been shown 0888-5885 f 92 f 2631-2497$03.00 f 0
to dissociate heterolytically on ZnO forming a hydride ion H- bonded to Zn2+and a proton associated with an oxygen anion forming a hydroxyl ion OH- also bonded to Zn2+ (Kokes and Dent, 1972). Olefins have been also found or proposed to dissociate heterolytically on a number of oxides giving r-allyl carbanion or r-allyl carbocation (Burwell et al., 1969;Stone, 1990). Other molecules may also dissociate heterolytidy upon adsorption on an oxide catalyBt such as H20 (Burwell et al., 1969). A third means of generating surface ionic intermediates is evidently by electron transfer from the adsorbed molecule to the catalyst or vice versa. This process is particularly important in oxidation reactions. The ionic nature of the adsorbed species on the catalytic surface is usually not taken into account in the computation of rate laws according to LHHW or redox models. Then, from both a fundamental and an applied point of view, it appears of importance to be able to express, in a simple way, rate expressions for catalytic reactions involving ionic surface intermediates where the ionic nature of the species is explicitly taken into account. The aim of this paper is to demonstrate that this can be done for a variety of catalytic reactions by adding an electric charge conservation equation to the classical method of computation of LHHW rate law. The method will be illustrated by selected examples of different reactions on nonmetallic catalyst involving heterolytic dissociation or electron transfer such as the isomerization of unsaturated hydrocarbons by Bronsted acids, the hydrogenation of unsaturated hydrocarbons via heterolytic dissociation, the generation of methyl radicals in methane oxidative coupling, and the partial oxidation of hydrocarbons. Results and Discussion Description of the Catalyst. A nonmetallic perfect oxide Mn+=02; with the cation symbolized by M and the 0 1992 American Chemical Society
2498 Ind. Eng. Chem. Res., Vol. 31, No. 11, 1992
anion represented by 02-is considered as the catalyst in this work. The different surface and bulk species of this catalyst are defined in this section. The electroneutrality of the catalyst is expressed by the following relationship: n[M]", = 2[02-]", (1) where [MI", and [O2-Iotrepresent the initial cation and anion concentrations of the solid, respectively. The cations will be separated into bulk Mb and surface cation M, hence [MI", = [MI"b + [MI0 (2) The symbol for a cation surface site will be M and the total surface site concentration will be [MI". All the sites M are taken as being equivalent and each surface species will be associated to one site. Similarly, the oxygens of the catalyst 0:- will be either bulk anions o b 2 - or Surface anions M-02-, hence [O2-]"t = [O2-]"b + [M-02-]" (3) In this work a free surface site is defined as an empty surface anion position (symbol "V") linked to one surface cation M. The symbol for the free surface site is therefore M-V. Many different species will coexist on the catalyst surface. There will be species with two formal integer electric charge such as the surface oxygen M a 2 - and species with one negative charge symbolized by M-Y; such as M-OH-, M-O*-, etc. Species with no formal electric charge such as an adsorbed reactant M-R or the unoccupied site M-V will be also present. In the following, the unoccupied site will be considered, by extension, as a surface species and called a vacancy although it does not contain electrons as the usual meaning of an anionic vacancy suggests. With the notation employed above, it can be seen that, in terms of global negative charge, the surface species M-Y; is equivalent to M--Yi or M-"-Y;@ (with a + /3 = 1)as the total negative charge of the group site-adsorbed species is unity. Thus in this work no distinction is made between different cases of partial charge repartition for the same species. However, this could be done by using the notation M-Yi+ and defining different partial charges -j3 of the species YcB. For redox reactions we shall consider that only one electron transfer occurs and that only oneelectron-reduced sites are formed. On the surface, the reduced site will either be a vacancy with one electron M-V- (Vo' in the Kroger-Vink notation) or a reduced cation M--V. In the bulk, reduced cations Mb'- may be found as well as a vacancy with one electron Vb'-. In addition to these species, bulk vacancy v b and bulk oxygen species Ob*-will be ab0 considered as example of defects. Computation of Rate Laws. The method of computing rate laws used in this work is that of the LHHW formalism (Hougen and Watson, 1943; Yang and Hougen, 1950). A set of elementary reactions is first written and one rate-determining step is chosen. Then the quasiequilibrium conetanta for all the reactant adsorptions ( K J , surface reactions (KsJ or exchange reactions between bulk and surface species W e i ) are written as functions of concentrations. Then a number of conservation equations have to be writtan. This is done in the following for the species which have been considered in this work. For the bulk, there will be the bulk cation site conservation equation: (4) [Ml'b = [Mlb + [M-lb and the anion site conservation equation:
[O2-]"b
[O"]b
+ [o'-]b + [VI, + [v'-]b
(5)
For the surface, the conservation equation of the total number of surface sites [MIo will be [MI" [M-VI + [M-02-] + [M-Y;] + [M-R] + [M-V-] + [M-O*-] + [M--VI (6) In order to solve this set of equations, an additional equation is needed. This equation is the negative charge conservation equation (Kasztelan, 1990, 1991): 2[O2-]"t 2[02-]b + [o'-]b + [v'-]b + [M'-]b + 2[M-02-] + [M-Y;] + [M-V-] + [M-O'-] + [M--VI (7) This set of equations can be solved as is usually done for classical LHHW rate law computation because there are as many unknown variables as there are equations. The rate law will be a function of the quasi-equilibrium constants Ki, Ksi, and Kei, the partial pressures Pi of all the reactants i, the kinetic constant k, and the initial concentrations of species and defects ([ ]") characterizing the catalyst. However, a complex formula of the form of eq 8 will be obtained for the rate law and a numerical solution may be required in most cases. r = kf(Ki,Ksi, Kei, Pi, [ 1") (8) To simplify the rate expression, a first approximation can be used, namely, that the bulk does not intervene in the reaction. Then the negative charge conservation equation becomes the surface negative charge conservation equation: 2[M-02-]" = 2[M-02-] + [M-Y;] [M-V-] + [M-OO-] + [M--VI (9)
+
In this case the rate law will be a function of two initial concentrations, [MI" and [M-O"]". Another approximation can also be made, namely, that the surface is either initially composed of half unoccupied sites M-V and half M-02- species or is composed of MOH- species only. In other words, the s u m of the negative charges of surface species equals the total number of surface sites, i.e. 2 [M-02-] " = [MI" (10) This approximation will make it possible to solve exactly the set of equations and the only parameter characteristic of the catalyst remaining will be [MI", the concentration of sites, as it is found in classical LHHW rate laws. Reactions Involving Heterolytic Dissociation. The heterolytic dissociation of one reactant on the surface during a catalytic reaction will create a perturbation of the surface array of M-02- anions and free sites M-V. For example, on a catalyst such as an acidic oxide, H20 may play an important role by adsorbing on Lewis acid sites M-V and then transforming these sites into Bronsted acid sites (M-O"H+) upon heterolytic diaaociation. When such a dissociation occurs for water, a species carrying formally a double charge, M-02-, is transformed into a species carrying a single charge M-OH- (equivalent to M#-H+). Simultaneously, a free site with no electric charge is converted to a species, M-OH-, Carrying a single charge. Such a change of the number of electrical charge of a surface species is usually not taken into account in classical kinetic models. Two examples will be taken to illustrate the method of computing rate laws of reaction involving heterolytic dissociation without electron transfer and with all the elementary steps of the reaction being surface processes.
Ind. Eng. Chem. Res., Vol. 31, No.11,1992 2499 Table I. Set of Elementary Reactionr for the Iromerization of Olefin R into P on a Bronsted Acidic Catalyst 1.1 R + M-OH- M-ORHKR 1.2 M-ORH- M-OPHrI80M 1.3 P + M-OH- = M-OPHKP 1.4 HzO + M-V + M-0'- * 2M-OHKHP
-
The first example (example 1)will be the isomerization of an olefin R by a Bronsted acid catalyst where heterolytic dissociation of water is considered. The second example (example 2) will be the hydrogenation of an unsaturated hydrocarbon where both hydrogen and water dissociate heterolytically Example 1. The isomerization of an olefin R is described by the set of elementary reactions reported in Table I. An alkyl carbocation RH+ is first formed by an associative adsorption of the olefin on a proton in reaction L1 where the notation used for the carbocation is M-ORHrather than M-Oa-RH+ in order to keep track of the global single negative charge of the surface species. Rearrangement of the adsorbed carbocation then occurs according to reaction 1.2, which is considered to be the rate-determining step. The isomerized olefin P can then desorb according to reaction 1.3. The adsorption of water is taken into account by reaction 1.4. For this set of elementary reactions, the conservation equation of the total number of surface sites [MIo is [ M a 2 - ] + [M-ORH-] + [MIo [M-VI [M-OPH-] + [M-OH-] (11) and the surface negative charge conservation equation is written 2[M-O2-I0 = 2[M-02-] + [M-OH-] + [M-ORH-1 + [M-OPH-] (12) A solution is obtained by making the approximation that the number of negative surface charge is equal to the number of sites (eq lo), hence
.
+
with ai = Kipi. This rate law has the classical form of a LHHW rate law and takes into account all of the reactants and in particular water. It can be easily found that if the water partial pressure is infinite, the Lewis sites are all converted into Bronsted si- and the concentration of site [MIo is equal to the proton concentration, [H+]O. Then the classical rate equation for proton-catalyzed isomerization is found:
Example 2. The example of the hydrogenation of an olefrn with heterolytic dissociation of hydrogen is yet another demonstration of the interest in accounting for the ionic nature of the surface species. For such a reaction, the feed contains the unsaturated hydrocarbon R, the hydrogen to be dissociated heterolytically, and H20 also dieeociated heterolytically. This example will illustrate a more complex case of a catalytic surface in interaction with two reactants which can dissociate heterolytically and generate a common species, here M-OH-. A two-step reaction scheme, reported in Table 11, is considered in this work starting with an associative adsorption of the olefin with a proton to form a carbocation RH+ (reaction E l ) , followed by the addition of an hydride ion (reaction 11.2). The latter reaction will be considered to be the rate-determining step. Evidently other reaction
Table 11. Set of Elementary Reactionr for the Hydrogenation of Olefin R with Heterolytic Disrociation of Hydrogen . -
R + M-OH-
11.1 11.2 11.3 11.4 11.5
-
M-ORHM-ORH- + M-HM-RHZ M-0" RH2 + M-V * M-RHP Hz + M-V + M-0'- * M-OH- + M-HHzO + M-V + M a 2 - 2M-OH-
+
KR
rHm
KRH~ KH2 KHP
schemes can be considered, such as a two-step hydrogenation through the addition of the hydride to form an alkyl carbanion RH-followed by the addition of a proton coming from an OH- group. A simplified rate law for this hydrogenation reaction is established as before using a charge conservation equation and making the approximation of the equality of the total number of surface sites and the total number of charges of the surface species. The obtained rate (eq 15) has again a form similar to a LHHW rate law. rm
~HM[M]OX ffRaH2cyH20
(aH2
+ a H , O ( l + a R ) + 2aH20"2(1 + aRH2)'/2)2
(15)
Hydrogenation with heterolytic dissociation of hydrogen is usually not considered for kinetic analysis of experimental results in the literature. It is then interesting to note that making the usual approximations for high-temperature reaction, Le., Kipi
