Catalytic reactions rate equations

Most real reactors are not homogeneous but use catalysts (1) to make reaction occur at temperatures lower than would be required for homogeneous reaction and (2) to attain a higher selectivity to a particular product than would be attained homogeneously. One may then ask whether any of the previous material on homogeneous reactions has any relevance to these situations. The answer fortunately is yes, because the same equations are used. However, catalytic reaction rate expressions have a quite different meaning than rate expressions for homogeneous reactions. 

Overall Reaction Rate Equation of Single-Route Complex Catalytic Reaction in Terms of Hypergeometric Series... 

In this equation, if the rate of diffusion is faster than that of the catalytic reaction at the surface (ko kc), the Arrhenius plot of rr gives the apparent activation energy Ec of kc. This is the reaction-controlled condition. On the other hand, if the rate of the catalytic reaction is faster than that of diffusion (kc 2> kid, the Arrhenius plot of rr gives the characteristics of temperature dependence of ko. This is the diffusion-controlled condition. Under diffusion-controlled conditions, the transferred reactant decreases at once at the surface (Cs = 0) because of the fast catalytic reaction rate. The gas flow along the catalyst surface forms a boundary layer above the surface, and gas molecules diffuse due to the concentration gradient inside the layer in the thickness direction. As the total reaction... 

Let us analyze the structure of eqn. (70). Its numerator can be written as K+ [A] - K [B], where K+ = Aq 2 3 and K = k 1k 2k 3. In this form, it corresponds to the brutto-equation of the reaction A = B obtained by adding all the steps of the detailed mechanism with unit stoichiometric numbers. The numerator is a kinetic equation for the brutto-reaction A = B considered to be elementary and fitting the mass action law. The denominator accounts for the "non-elementary character due to the inhibition of the complex catalytic reaction rate by the initial substances and products. 

C.J. van Duijn, Andro Mikelic, I.S. Pop, and Carole Rosier, Effective Dispersion Equations for Reactive Flows with Dominant Peclet and Damkohler Numbers Mark Z. Lazman and Gregory S. Yablonsky, Overall Reaction Rate Equation of Single-Route Complex Catalytic Reaction in Terms of Hypergeometric Series A.N. Gorban and O. Radulescu, Dynamic and Static Limitation in Multiscale Reaction Networks, Revisited... 

In certain cases, the assumption of a pseudo-homogeneous catalytic mechanism might be valid [19], and the reaction rate equation would depend only on the concentrations in the liquid phase. 

Analysis of the luetic equations of stationary processes reveals that only the mechanism of classes characterized by elementary steps common to two or more reaction routes (Cf,x " code substituent) differ in terms of their equation. Thus, for example, eqns. (4) for the rate for a route do not contain encompassing cydes when applied to dasses A and and. hence, r — 0. More sped-fically, for the 3-l-B >2,2,2 mechanism (graph 7), the catalytic reaction rate for route I is given... 

Our experimental technique of choice in many cases is reaction calorimetry. This technique relies on the accurate measurement of the heat evolved or consumed when chemical fiansformations occur. Consider a catalytic reaction proceeding in the absence of side reactions or other thermal effects. The energy characteristic of the transformation— the heat of reaction, AH —is manifested each time a substrate molecule is converted to a product molecule. This thermodynamic quantity serves as the proportionality constant between the heat evolved and the reaction rate (Equation 27.1). 

Related to the concentration of the active sites, the concentration of the reactant at the catalyst is part of the reaction rate equation, hi order to be able to differentiate between extensive (concentration of adsorbed reactant species) and intensive (impact of the catalytically active site on the reactant molecule) factors, the reaction kinetic equation has to be known in detail and to be carefully analyzed or valuable information would be wasted. 

In any event, the practicing engineer may be confronted with the need to analyze experimental data for the purpose of developing a reaction rate equation for a catalytic reaction. These rate equations rarely follow elementary power law kinetics so that the describing equation may be anything but elementary. 

The left side of Equation 11.1 summarizes the enzyme-dependent terms the rate constant, characterizes the catalytic reaction rate under conditions of substrate saturation (at high glucose concentration in the example, reaction of mediator with reduced GOx is the rate-determining step). In general, is characteristic of a particular combination of enzyme, mediator, and substrate. 

M.Z. Lazman, G.S. Yablonskii, Overall reaction rate equation of single-route complex catalytic reaction in terms of hypergeometric series, Adv. Chem. Eng. 34 (2008) 47-102. 

Work in the area of simultaneous heat and mass transfer has centered on the solution of equations such as 1—18 for cases where the stmcture and properties of a soHd phase must also be considered, as in drying (qv) or adsorption (qv), or where a chemical reaction takes place. Drying simulation (45—47) and drying of foods (48,49) have been particularly active subjects. In the adsorption area the separation of multicomponent fluid mixtures is influenced by comparative rates of diffusion and by interface temperatures (50,51). In the area of reactor studies there has been much interest in monolithic and honeycomb catalytic reactions (52,53) (see Exhaust control, industrial). Eor these kinds of appHcations psychrometric charts for systems other than air—water would be useful. The constmction of such has been considered (54). 

Direct Chlorination of Ethylene. Direct chlorination of ethylene is generally conducted in Hquid EDC in a bubble column reactor. Ethylene and chlorine dissolve in the Hquid phase and combine in a homogeneous catalytic reaction to form EDC. Under typical process conditions, the reaction rate is controlled by mass transfer, with absorption of ethylene as the limiting factor (77). Ferric chloride is a highly selective and efficient catalyst for this reaction, and is widely used commercially (78). Ferric chloride and sodium chloride [7647-14-5] mixtures have also been utilized for the catalyst (79), as have tetrachloroferrate compounds, eg, ammonium tetrachloroferrate [24411-12-9] NH FeCl (80). The reaction most likely proceeds through an electrophilic addition mechanism, in which the catalyst first polarizes chlorine, as shown in equation 5. The polarized chlorine molecule then acts as an electrophilic reagent to attack the double bond of ethylene, thereby faciHtating chlorine addition (eq. 6) ... 

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

Chlorine atoms obtained from the dissociation of chlorine molecules by thermal, photochemical, or chemically initiated processes react with a methane molecule to form hydrogen chloride and a methyl-free radical. The methyl radical reacts with an undissociated chlorine molecule to give methyl chloride and a new chlorine radical necessary to continue the reaction. Other more highly chlorinated products are formed in a similar manner. Chain terrnination may proceed by way of several of the examples cited in equations 6, 7, and 8. The initial radical-producing catalytic process is inhibited by oxygen to an extent that only a few ppm of oxygen can drastically decrease the reaction rate. In some commercial processes, small amounts of air are dehberately added to inhibit chlorination beyond the monochloro stage. 

All catalytic reactions involve chemical combination of reacting species with the catalyst to form some type of inteniiediate complex, the nature of which is the subject of abundant research in catalysis. The overall reaction rate is often determined by the rate at which these complexes are formed and decomposed. The most widely-used nonlinear kinetic equation that describes... 

The development of methods for the kinetic measurement of heterogeneous catalytic reactions has enabled workers to obtain rate data of a great number of reactions [for a review, see (1, )]. The use of a statistical treatment of kinetic data and of computers [cf. (3-7) ] renders it possible to estimate objectively the suitability of kinetic models as well as to determine relatively accurate values of the constants of rate equations. Nevertheless, even these improvements allow the interpretation of kinetic results from the point of view of reaction mechanisms only within certain limits ... 

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