Monomolecular catalytic reaction

So the product, R, of the electrochemical reduction reacts in the solution with an electroinactive oxidizer, Ox, to regenerate O, etc. If Ox is present in large excess, the chemical reaction is pseudo-first-order in R and O. For thermodynamic reasons, Rc can only proceed if the standard potential of the redox couple Ox/Red is more positive than that of O/R. Then, for Ox to be electroinactive, it is required that its electroreduction proceeds irreversibly, in a potential range far negative to the faradaic region of the 0/R reaction. Thus, Ox being stable for reasons of the slow kinetics of its direct reduction, it can be said that, in the presence of O, it is being catalytically reduced. 

A well-known example is the reduction of hydrogen peroxide catalyzed 

Many other examples are mentioned in refs. 11 and 147. Worth mentioning is the peculiar example where a reducible complex, Ag(CN), is regenerated by a reaction between the liberated cyanide ions and colloidal AgBr present in the solution [148]. 

The first reduction wave in the d.c. polarogram of oxygen is increased in the presence of the enzyme catalase [11]. This is caused by the dismutation of the produced hydrogen peroxide into oxygen and water (H202 = H20 + i 02 ). 

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Thus, we have derived the fundamental equation (1), since the term in the first brackets of Equation (11) may be considered as the constant fc,j and the second exponential function, owing to its rapid decay, may be neglected if h > 1 RT, whereas the first one may be neglected if h < 1 /RT. Equation (14) holds also for other cases of monomolecular catalytic reactions. 

The balance equations of pseudohomogeneous reactors with catalytic reaction and activity changes were developed under the simplifying assumptions [3], The monomolecular catalytic reaction... 

Immobilizing the catalyst on the electrode surface is useful for both synthetic and sensors applications. Monomolecular coatings do not allow redox catalysis, but multilayered coatings do. The catalytic responses are then functions of three main factors in addition to transport of the reactant from the bulk of the solution to the film surface transport of electrons through the film, transport of the reactant in the reverse direction, and catalytic reaction. The interplay of these factors is described with the help of characteristic currents and kinetic zone diagrams. In several systems the mediator plays the role of an electron shuttle and of a catalyst. More interesting are the systems in which the two roles are assigned to two different molecules chosen to fulfill these two different functions, as illustrated by a typical experimental example. 

Strictly speaking, mechanisms for heterogeneous catalytic reactions can never be monomolecular. Thus they always include adsorption steps in which the initial substances are a minimum of two in number, i.e. gas and catalyst. But if one considers conversions of only surface compounds (at a constant gas-phase composition), a catalytic reaction mechanism can also be treated as monomolecular. It is these mechanisms that Temkin designates as linear (see Chap. 2). 

In studies of catalytic reactions, linear (monomolecular) mechanisms are observed in the following two cases. 

Calculation of the Adsorption Enthalpy of n-Paraffins in Nanoporous Crystalline and Ordered Acid Catalysts, and Its Relation with the Activation Energy of the Monomolecular Catalytic Cracking Reaction... 

As an example of a unimolecular decomposition reaction, we study the monomolecular catalytic cracking reaction of //-paraffins in high-silica acid zeolites or other crystalline or ordered acid porous materials, in this section [97-102],... 

Within the framework of the transition state theory [112,113], the observed activation energy, Eobs, for a monomolecular catalytic process in the heterogeneous case is Eobs = E0 + A//ads [act. complex], where E0 is the energy of the reaction without a catalyst and A//.lds act. complex] is the adsorption enthalpy of the activated complex [114], In the monomolecular cracking of n-alkanes catalyzed by... 

The kinetic expressions derived by Antipina and Frost have general applicability to monomolecular heterogeneous catalytic reactions which occur on a uniform surface. The expression can be made to describe the cracking of synthin or decomposition of octene over silica-alumina as well as hydrogen disproportionation of gasoline and cracking of gas oils over the silica-alumina. Numerous other applications are discussed. 

Thus, the approach to the stationary state of any simple (i.e., undergoing monomolecular or reduced to monomolecular transformations) reaction of the catalytic intermediates means the catalyst functioning at the minimal rate of energy dissipation in terms of the identical electric circuit. 

As most of the acid sites are located in pores of molecular size the rate and the selectivity of catalytic reactions depend not only on the intrinsic properties of the sites but also on the pore structure. A zeolite catalyst selects the reactant or the product by their ability to diffuse to and from the active sites (reactant and product selectivity). Steric constraints in the environment of the sites limit or inhibit the formation of intermediates or transition states (restricted transition state selectivity) [24,25]. The strong polarizing interaction between zeolite crystallites and adsorbed molecules leads to an unusually high concentration of the reactants in the pores. This concentration effect causes an enhancement of the rates of bimolecular reaction steps over monomolecular reaction steps [26]. 

For the overall rate of a catalytic reaction, this is an important conclusion because the rate of a catalytic reaction is proportional to the site occupancy and the rate constant of molecular activation, when the latter step is rate limiting. For a monomolecular reaction this follows from an elementary expression for the overall rate r ... 

The rate expression developed above is for a monomolecular catalytic process. There are also two types of bimolecular catalytic reactions. One proceeds by the reaction of an adsorbed A with a gas phase B ... 

SO far only been attained by Monte Carlo simulations. Figure 5 illustrates the situation due to the combined effect of diffusion and catalytic reaction in a single-file system for the case of a monomolecular reaction A B [1]. For the sake of simplicity it is assumed that the molecular species A and B are completely equivalent in their microdynamic properties. Moreover, it is assumed that in the gas phase A is in abimdance and that, therefore, only molecules of type A are captured by the marginal sites of the file. Figure 5 shows the concentration profile of the reaction product B within the singlefile system imder stationary conditions. A parameter of the representation is the probabiUty k that during the mean time between two jump attempts (t), a molecule of type A is converted to B. It is related to the intrinsic reactivity k by the equation... 

No catalytic reaction can be elementary as at least three steps are always involved adsorption ofthe reactant, surface reaction and desorption of the formed product. For a simple monomolecular reaction, for example, an isomerization, the steps involved are shown in Figure 2.15. 

The addition of Co and Mn acetates to the reaction mixture changes the general features of the products formation kinetics (1.19). Thus increases and acetophenone has been identified (AcP). The sum of the products exceeds by 7.3-fold that at cumene ozonolysis. OZ is obtained at the interaction of ozone with the benzene ring, and AcP is provided by the monomolecular decomposition reaction of RO"-radicals. Most likely the main role of Mn is in accelerating of these two reactions. The catalytic properties of the metal salts studied are confirmed by the ratio of the amount of the products formed in the catalyzed and noncatalysed processes per unit of absorbed ozone. At Co Mn=5 l this ratio becomes equal to 7.3 and is greater by about 6% than that in the absence of Mn. The cumene conversion is increased but the selectivity of the process is reduced. The contribution of OZ and ApC to the total sum of the products formed is 27%. The synergism of the simultaneous action of the both salts (Fig. 19) can be associated with the occurrence of the following reaction ... 

As we will discuss in the next section, it is of interest to analyze the meaning of the expression when the Langmuir adsorption expression for 9 is used. For a monomolecular gas-phase reaction, the expression for the catalytic reaction rate is... 

The rate of the monomolecular heterogeneous-catalytic reaction in the general case is given by the equation ... 

Reaction rates for the start-of-cycle reforming system are described by pseudo-monomolecular rates of change of the 13 kinetic lumps. That is, the rates of change of the lumps are represented by first-order mass action kinetics with the same adsorption isotherm applicable to each reaction step. Following the same format as Eq. (4), steady-state material balances for the hydrocarbon lumps are derived for a plug-flow, fixed bed catalytic reformer. A nondissociation, Langmuir-Hinshelwood adsorption model is employed. Steady-state material balances written over a differential fractional catalyst volume dv are the following ... 

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