Kinetics catalytic

The presence of several rate processes occurring in series leads to the development of complex rate expressions, often described as Langmuir-Hinshelwood kinetics. Before going on, we need to separate the chemical steps from the mass transfer steps (a mass transfer step is one in which the species moves into position to react but does not undergo a chemical change). In this section, we consider only the chemical steps that lead to the development of a Langmuir-Hinshelwood rate expression we reserve the mass transfer issues for the following section. 

Because we have three consecutive reactions occurring in series (steps 3,4, and 5 from above), the development of the overall rate expression can be fairly complex. However, the procedure provides a general expression that is well known and fairly common. Once the more detailed expression can be obtained, simplification can provide a more manageable form for use in engineering calculations. 

Let s start by considering a catalytic reaction that is carried out in the gas phase over a solid catalyst. We write the overall reaction as 

According to our description above, this reaction must occur through three separate steps (adsorption, surface reaction, desorption), so we can write a chanical eqnation for each step. 

In order to use this rate expression, we require the concentration of component A adsorbed on the catalyst surface. This is obtained by assuming that the adsorption reaction is in pseudo-steady state. This means that the rate of the forward reaction 

Consider the reaction of a molecule that takes place on a solid catalyst surface. This reaction simply involves converting one form of the molecule into another in other words, it is an isomerization reaction. However, the reaction in question takes place only on the catalyst surface and not without the catalyst. 

When we analyze a reaction of this kind we find that at least two steps are involved. The first is called adsorption and is reversible. Adsorption is the transfer of a molecule from the bulk phase, either the gas or liquid, to the solid surface. The adsorption process is reversible and takes place without any change in the molecule. Like any reversible process, adsorption comes to equilibrium. Because no change occurs in the molecule, the rate of approach to equilibrium is very rapid and occurs essentially instantaneously. Once this occurs then the molecule on the surface can react to product. We can break the problem down into the adsorption equilibrium and the reaction rate of the adsorbed molecule. Take the isomerization to be first order on a surface concentration of species A and consider the reaction to be irreversible. The adsorption equilibrium steps take place by the interaction of the molecule in the bulk phase with a so-called adsorption site on the solid surface. The adsorption site is the locus of points on the surface that interact directly with the molecule. 

Once B is formed, it too undergoes adsorption and desorption. The desorption carries B from the surface and into the bulk fluid phase. The rate of this reaction is first order in the surface concentration of A and first order in the concentration of surface sites. It follows a simple kinetic rate law  

The surface concentration is difficult to measure, so we need to reexpress it in terms of the bulk phase concentration of species A. To do this we take advantage of the fact that the molecules adsorb and desorb so quickly that they come to equilibrium rapidly with the surface sites. Therefore we can express the surface concentration in terms of the equilibrium. The equilibrium gives rise to the following relationship for the surface concentration of A in terms of the bulk concentration of A  

We can substitute this expression into the rate expression for the reaction. This leads to this rate in terms of the bulk phase concentrations  

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The systematic use of classical catalytic kinetics is always a useful approach in modeling (Boudart 1986). Even if these models do not reflect the true mechanism in the case of structure-sensitive catalysts, they are a formally correct representation of the observed facts. As Boudart sees it in the case of structure-insensitive reactions, it can also be the real thing. 

Some G proteins are slow GTP hydrolases with turnover numbers around two per minute, others such as Ras are only marginally catalytic. Kinetic experiments in solution have shown that in both cases the most likely mechanism... 

Catalytic kinetic resolution can be the method of choice for the preparation of enantioenriched materials, particularly when the racemate is inexpensive and readily available and direct asymmetric routes to the optically active compounds are lacking. However, several other criteria-induding catalyst selectivity, efficiency, and cost, stoichiometric reagent cost, waste generation, volumetric throughput, ease of product isolation, scalability, and the existence of viable alternatives from the chiral pool (or classical resolution)-must be taken into consideration as well... 

This is the same case with which in Eqs. (2)-(4) we demonstrated the elimination of the time variable, and it may occur in practice when all the reactions of the system are taking place on the same number of identical active centers. Wei and Prater and their co-workers applied this method with success to the treatment of experimental data on the reversible isomerization reactions of n-butenes and xylenes on alumina or on silica-alumina, proceeding according to a triangular network (28, 31). The problems of more complicated catalytic kinetics were treated by Smith and Prater (32) who demonstrated the difficulties arising in an attempt at a complete solution of the kinetics of the cyclohexane-cyclohexene-benzene interconversion on Pt/Al203 catalyst, including adsorption-desorption steps. 

The LHHW kinetics represent a large oversimplification but, nevertheless, constitute a first step in quantifying catalytic kinetics. 

This type of isotherm is more realistic for describing chemisorption at intermediate 0a values but quickly leads to mathematically cumbersome or intractable expressions with many unknown parameters when one considers coadsorption of two gases. One needs to know how -AHa is affected both by 0A and by the coverages of all other adsorbates. Thus for all practical purposes the LHHW kinetics represent even today the only viable approach for formulating mathematically tractable, albeit usually highly inaccurate, rate expressions for catalytic kinetics. In Chapter 6 we will see a new, medium field type, approach which generalizes the LHHW kinetics by accounting also for lateral interactions. 

Despite the already discussed oversimplifications built into the Langmuir isotherm and in the resulting LHHW kinetics, it is useful and instructive at this point to examine how a promoter can affect the catalytic kinetics described by the LHHW expressions (2.11) to (2.14). 

The spillover effect can be described as the mobility of sorbed species from one phase on which they easily adsorb (donor) to another phase where they do not directly adsorb (acceptor). In this way a seemingly inert material can acquire catalytic activity. In some cases, the acceptor can remain active even after separation from the donor. Also, quite often, as shown by Delmon and coworkers,65 67 simple mechanical mixing of the donor and acceptor phases is sufficient for spillover to occur and influence catalytic kinetics leading to a Remote Control mechanism, a term first introduced by Delmon.65 Spillover may lead, not only to an improvement of catalytic activity and selectivity but also to an increase in lifetime and regenerability of catalysts. 

Table 4.2 lists the same catalytic systems but now grouped in terms of different reaction types (oxidations, hydrogenations, reductions and others). In this table and in subsequent chapters the subscript D denotes and electron donor reactant while the subscript A denotes an electron acceptor reactant. The table also lists the temperature and gas composition range of each investigation in terms of the parameter Pa/Pd which as subsequently shown plays an important role on the observed r vs O global behaviour. Table 4.3 is the same as Table 4.2 but also provides additional information regarding the open-circuit catalytic kinetics, whenever available. Table 4.3 is useful for extracting the promotional rules discussed Chapter 6. 

The kinetics and mechanism of this reaction have been studied for years on Pt films deposited on doped Zr02.15 It has been found that at temperatures above 280°C the open-circuit catalytic kinetics can be described quantitatively by the rate expression... 

The molecular interpretation of major topics in catalytic kinetics will be highlighted based on insights on the properties of transition-state intermediates as deduced from computational chemical density functional theory (DFT) calculations. 

Whereas it is very useful to relate reaction mechanistic proposals with catalytic kinetics, one has to be aware that DFT-predicted energies typically have an error of at least 10 kj moUh... 

Murzin, D. and Salmi, T. (2005) Catalytic Kinetics, Elsevier, Amsterdam. 

The search for better catalysts has been facilitated in recent years by molecular modeling. We are seeing here a step change. This is the subject of Chapter 1 (Molecular Catalytic Kinetics Concepts). New types of catalysts appeared to be more selective and active than conventional ones. Tuned mesoporous catalysts, gold catalysts, and metal organic frameworks (MOFs) that are discussed in Chapter 2 (Hierarchical Porous Zeolites by Demetallation, 3 (Preparation of Nanosized Gold Catalysts and Oxidation at Room Temperature), and 4 (The Fascinating Structure... 

Ab initio methods allow the nature of active sites to be elucidated and the influence of supports or solvents on the catalytic kinetics to be predicted. Neurock and coworkers have successfully coupled theory with atomic-scale simulations and have tracked the molecular transformations that occur over different surfaces to assess their catalytic activity and selectivity [95-98]. Relevant examples are the Pt-catalyzed NO decomposition and methanol oxidation. In case of NO decomposition, density functional theory calculations and kinetic Monte Carlo simulations substantially helped to optimize the composition of the nanocatalyst by alloying Pt with Au and creating a specific structure of the PtgAu7 particles. In catalytic methanol decomposition the elementary pathways were identified... 

Furthermore, the same methodology was used for an approach towards enantiopure PGFla (2-46) through a catalytic kinetic resolution of racemic 2-43 using (S)-ALB (2-37) (Scheme 2.10) [14]. Reaction of 2-35, 2-36 and 2-43 in the presence of 2-37 led to 2-44 as a 12 1 mixture of diastereomers in 75 % yield (based on malonate 2-36). The transformation proceeds with excellent enantioselectivity thus, the enone 2-45 obtained from 2-44 shows an ee-value of 97 %. 

Figure 3.1 shows a typical laboratory flow reactor for the study of catalytic kinetics. A gas chromatograph (GC, lower shelf) and a flow meter allow the complete analysis of samples of product gas (analysis time is typically several minutes), and the determination of the molar flow rate of various species out of the reactor (R) contained in a furnace. A mass spectrometer (MS, upper shelf) allows real-time analysis of the product gas sampled just below the catalyst charge and can follow rapid changes in rate. Automated versions of such reactor assemblies are commercially available. 

These assumptions are the basis of the simplest rational explanation of surface catalytic kinetics and models for it. The preeminent of these, formulated by Langmuir and Hinshelwood, makes the further assumption that for an overall (gas-phase) reaction, for example, A(g) +...- product(s), the rate-determining step is a surface reaction involving adsorbed species, such as A s. Despite the fact that reality is known to be more complex, the resulting rate expressions find wide use in the chemical industry, because they exhibit many of the commonly observed features of surface-catalyzed reactions. 

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