Kinetics of a Catalytic Reaction

We conclude the first part of this chapter with a kinetic example. We will derive, using the rate limiting step approach, the Langmuir-Hinselwood kinetics of a simple catalytic (isomerisation) reaction A B. 

This reaction occurs via the following steps A is adsorbed onto an active catalytic site, the adsorbed species AS undergoes a surface reaction to form 

BS and finally B is desorbed to free the active site that can now catalyse another cycle. We assume that the surface reaction is the slowest and therefore the limiting step. The kinetic expression we derive is valid only under this assumption and if the assumption changes, another expression needs to be derived. Since the surface reaction is the slowest step, we assume that all other reaction steps are so fast that they are at equilibrium. 

Slow surface reaction (rate-limiting step). kx, k2 are the kinetic constants of the forward and backward reactions. 

In the above mechanism, (g) shows that the respective species is in the gas phase and (s) in the solid phase (catalyst). We symbolise with C the concentrations in the gas phase and 6 the concentration in the solid phase, usually in units of mol g l. 

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Unraveling catalytic mechanisms in terms of elementary reactions and determining the kinetic parameters of such steps is at the heart of understanding catalytic reactions at the molecular level. As explained in Chapters 1 and 2, catalysis is a cyclic event that consists of elementary reaction steps. Hence, to determine the kinetics of a catalytic reaction mechanism, we need the kinetic parameters of these individual reaction steps. Unfortunately, these are rarely available. Here we discuss how sticking coefficients, activation energies and pre-exponential factors can be determined for elementary steps as adsorption, desorption, dissociation and recombination. 

How appropriate is the power rate law for describing the kinetics of a catalytic reaction ... 

In solving the kinetics of a catalytic reaction, what is the difference between the complete solution, the steady-state approximation, and the quasi-equilibrium approximation What is the MARI (most abundant reaction intermediate species) approximation ... 

A closed-loop experimental G/S batch system as sketched in Fig. P18.19 is used to study the kinetics of a catalytic reaction A 2R. Pure A is introduced into the systems and is circulated at 0°C and 1 atm at 10 cmVsec. The stream is analyzed from time to time with the following results ... 

The kinetics of a catalytic reaction is usually measured in a reactor under conditions relevant to the industrial process. The measured overall rates can then be fitted to a mathematical model, the macroscopic kinetics. This is extremely convenient for process design purposes. 

The observed rate will appear to be first-order with respect to the bulk reactant concentration, regardless of the intrinsic rate expression applicable to the surface reaction. This is a clear example of how external diffusion can mask the intrinsic kinetics of a catalytic reaction. In a catalytic reactor operating under mass transfer limitations, the conversion at the reactor outlet can be calculated by incorporating Equation (6.2.20) into the appropriate reactor model. 

Rel. (9) indicates that the kinetics of a catalytic reaction described by equation (7) does not depend on the concentration of the reacting gas (is of zero order as a function of gas concentration). For rel. (9) the evaluation of k is based on statistical thermodynamics applied to transition state theory for chemical reactions [12]. This theory shows that k has the following expression ... 

Consider a case where the true order of the surface reaction is 2 [according to Eq. (10-2)] but the rate is diffusion controlled, so that Eq. (10-3) is applicable. Experimental data plotted as rate vs would yield a straight line. If diffusion were not considered, and Eq. (10-2) were used to interpret the data, the order would be identified as unity—a false conclusion. This simple example illustrates how erroneous conclusions can be reached about kinetics of a catalytic reaction if external mass transfer is neglected, a... 

At the end of this section we conclude that modeling of the kinetics of a catalytic reaction essentially relies on the Langmuir concept, assuming uniform surfaces with periodic arrangements of equal adsorption sites without interactions between the adsorbed particles and a "hit and stick" model for the adsorption process. The microscopic observations as discussed in the... 

The use of quantum chemical data to simulate overall kinetics of a catalytic reaction will be illustrated using the Eindhoven Dynamic Monte Carlo code. 

In later sections of this chapter the microscopic basis of the sticking coefficient will be returned to when the main aspects of chemical bonding on surfaces and the implications for the overall kinetics of a catalytic reaction are examined. 

From a theoretical point of view the study of the kinetics of coupled catalytic reactions makes it possible to investigate mutual influencing of single reactions and the occurrence of some phenomena unknown in the kinetics of complex reactions in the homogeneous phase. This approach can yield additional information about interactions between the reactants and the surface of the solid catalyst. 

In kinetic analysis of coupled catalytic reactions it is necessary to consider some specific features of their kinetic behavior. These specific features of the kinetics of coupled catalytic reactions will be discussed here from a phenomenological point of view, i.e. we will show which phenomena occur or may occur, and what formal kinetic description they have if the coupling of reactions is taking place. No attention will be paid to details of mechanisms of the processes occurring on the catalyst surface from a molecular point of view. 

In this chapter we will discuss the results of the studies of the kinetics of some systems of consecutive, parallel or parallel-consecutive heterogeneous catalytic reactions performed in our laboratory. As the catalytic transformations of such types (and, in general, all the stoichiometrically not simple reactions) are frequently encountered in chemical practice, they were the subject of investigation from a variety of aspects. Many studies have not been aimed, however, at investigating the kinetics of these transformations at all, while a number of others present only the more or less accurately measured concentration-time or concentration-concentration curves, without any detailed analysis or quantitative kinetic interpretation. The major effort in the quantitative description of the kinetics of coupled catalytic reactions is associated with the pioneer work of Jungers and his school, based on their extensive experimental material 17-20, 87, 48, 59-61). At present, there are so many studies in the field of stoichiometrically not simple reactions that it is not possible, or even reasonable, to present their full account in this article. We will therefore mention only a limited number in order for the reader to obtain at least some brief information on the relevant literature. Some of these studies were already discussed in Section II from the point of view of the approach to kinetic analysis. Here we would like to present instead the types of reaction systems the kinetics of which were studied experimentally. 

In zone R, all three phenomena that take place in the film are fast compared to the diffusion of the substrate from the bulk of the solution to the film-solution interface. The concentrations of both Q and A are constant through the film. The RDEV response is similar to that of a monolayer coating (Section 4.3.2), except that more catalytic material is present on the surface of the electrode (it is multiplied by the number of layers in the multilayered coating). A linear Koutecky-Levich plot is obtained from the intercept, from which the kinetics of the catalytic reaction can be characterized. 

The occurrence of kinetic instabilities as well as oscillatory and even chaotic temporal behavior of a catalytic reaction under steady-state flow conditions can be traced back to the nonlinear character of the differential equations describing the kinetics coupled to transport processes (diffusion and heat conductance). Studies with single crystal surfaces revealed the formation of a large wealth of concentration patterns of the adsorbates on mesoscopic (say pm) length scales which can be studied experimentally by suitable tools and theoretically within the framework of nonlinear dynamics. [31]... 

Inhibition of a catalytic reaction by impurities present may take place and sometimes this may have a temporary character. If it is permanent one cannot be mistaken in the kinetic measurements. Impurities that are more reactive than the substrates to be studied may block the catalyst if they react according to a scheme like that of Figure 3.7. Only after all inhibitor has been converted the conversion of the desired substrate can start. Another type of deactivation that may occur is the formation of dormant states, which is very similar to inhibition. Either the regular substrate or an impurity may lead to the formation of a stable intermediate metal complex that does not react further. There are examples where such intermediates can be rescued from this dormant state for instance by the addition of another reagent such as dihydrogen (Chapter 10, dormant states in propene polymerisation). 

The mechanistic evidence from relative kinetic data can be greatly enhanced when correlations with other independent quantities are constructed, and thus links between the catalytic processes and other phenomena are found. Boudart (7) was first to point out the possibilities of such correlations. When a relationship of a catalytic reaction to a noncatalytic chemical transformation is established in this way, the catalytic mechanism can be elucidated on the basis of analogy. Moreover, if the relationships are linear, the interpretation of their slopes yields additional information. 

It is very instructive to compare the kinetics and plausible mechanisms of reactions catalyzed by the same or related catalyst(s) in aqueous and non-aqueous systems. A catalyst which is sufficiently soluble both in aqueous and in organic solvents (a rather rare situation) can be used in both environments without chemical modifications which could alter its catalytic properties. Even then there may be important differences in the rate and selectivity of a catalytic reaction on going from an organic to an aqueous phase. TTie most important characteristics of water in this context are the following polarity, capability of hydrogen bonding, and self-ionization (amphoteric acid-base nature). 

The non-linear theory of steady-steady (quasi-steady-state/pseudo-steady-state) kinetics of complex catalytic reactions is developed. It is illustrated in detail by the example of the single-route reversible catalytic reaction. The theoretical framework is based on the concept of the kinetic polynomial which has been proposed by authors in 1980-1990s and recent results of the algebraic theory, i.e. an approach of hypergeometric functions introduced by Gel fand, Kapranov and Zelevinsky (1994) and more developed recently by Sturnfels (2000) and Passare and Tsikh (2004). The concept of ensemble of equilibrium subsystems introduced in our earlier papers (see in detail Lazman and Yablonskii, 1991) was used as a physico-chemical and mathematical tool, which generalizes the well-known concept of equilibrium step . In each equilibrium subsystem, (n—1) steps are considered to be under equilibrium conditions and one step is limiting n is a number of steps of the complex reaction). It was shown that all solutions of these equilibrium subsystems define coefficients of the kinetic polynomial. 

Similar considerations apply to processes occurring on the surface of the catalyst i.e., the rate of dissociation of ethyl radicals to ethylene molecules will be equal to the rate of the reverse reaction. An alternative method of describing the kinetic behavior of an exchange reaction is to treat it as an example of a catalytic reaction where the products inhibit the reaction as they compete on equal terms with the reactants for the available surface. 

The third example (Fig. 4.3-27) is a loop reactor with internal recycle, developed by G. Lull. This reactor can advantageously be used to study kinetics of heterogenous catalytic reactions at pressures up to 40 MPa and temperatures to 500°C. The internal recycle... 

The phenomenon of catalysis is a subject of chemical kinetics, as follows from Ostwald s definition of catalysis. Therefore, the accumulation of data on the kinetics of concrete catalytic reactions favors the progress of the theory of catalysis. 

As previously emphasized, the positive identification of the specific entities that participate in the rate-limiting step of a catalytic reaction is a matter of considerable difficulty. Aspects of this problem have been discussed by Knozinger et al. 67) and by Webb (66). Thus, the interpretation of kinetic observations for heterogeneous processes must include consideration of the following possibilities. (It is not intended to imply, however, that every heterogeneous reaction necessarily includes each effect mentioned.)... 

When the surface concentration of species Csoi cannot be considered as constant the analysis of the electrochemical response that arises from reaction scheme (6.X) becomes much more complex since the process is of second order and the value of the surface concentration of Csoi will be a function of the kinetics of the catalytic reaction and also of the mass transport (and therefore of the electrode geometry). Due to this higher complexity, only the current-potential response in CV will be treated with the additional simplification of fast surface charge transfer. 

Fig. 7.36 Effect of the electrode radius and the kinetics of the catalytic reaction on the forward and net (vtj dlsc) responses in SWV calculated from Eq. (7.73) for a disc electrode. sw = 50mV, A s = 5mV, t = 10ms(/ = 50Hz), K= 0, T= 298.15 K, and D = lCP5cm2s 1. The values of the electrode radius rd and /sw are indicated on the graphs. Dotted lines mark the potential values where V swv = V/swv,Peak/2- Reproduced from [60] with permission...

At present the kinetics of complex catalytic reactions is a field involving the application of, on the one hand, physicochemical methods that provide possibilities for the direct determination of intermediate concentrations, and, on the other, new ideas in mathematics and theoretical physics promoting the interpretation of complex steady- and non-steady-state behaviour. 

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