Hinshelwood Kinetics

We have thus far written unimolecular surface reaction rates as r = kCAs assuming that rates are simply first order in the reactant concentration. This is the simplest form, and we used it to introduce the complexities of external mass transfer and pore diffusion on surface reactions. In fact there are many situations where surface reactions do not obey simple rate expressions, and they frequently give rate expressions that do not obey simple power-law dependences on concentrations or simple Arrhenius temperatures dependences. 

Surface reactions are in principle multistep processes, and previously we saw how diffusion to the surface of a porous pellet or diffusion within the pores of a pellet can lead to rate expressions with rate coefficients much different than k . However, so far all were first order in the reactant partial pressure. 

Another reason for describing surface reaction kinetics in more detail is that we need to examine the processes on a microscopic scale. While we are interested primarily in the macroscopic description of catalytic reactor behavior, we cannot do this intelligently until we understand these processes at a molecular level. 

We wiU need to describe concentrations of species in the gas or liquid above the catalyst surface as well as adsorbed on the surface. 

Another convention in catalytic reactions at surfaces is to use the partial pressure Pj rather than the concentration Cj in describing densities in the bulk phase above catalyst surfaces, although there are of course many situations where the reactants and products are in the liquid phase. These are simply related for ideal gases by the expression Cj = Pj/RT. 

Interestingly, this is also a good description of many (but not all) homogeneous catalysis and biocatalysis reactions. Here the reactant or the substrate first coordinates to the metal complex or to the enzyme, then a reaction occurs. Finally, the product dissociates from the catalyst and diffuses back into the solution. 

Equation (2.23)—(2.25) show the three steps in this cycle and their corresponding differential rate expressions. 

This leads to some complicated differential equations which are usually solved numerically. To simplify things, let us assume that the surface reaction (Eq. (2.24)) is the rate-determining step, while the adsorption and the desorption steps are at equilibrium (i.e., the net change in Eqs. (2.4) and (2.6) is zero). In this case, Eq. (2.26) apply, where KA and / Pj are the adsorption equilibrium constants for A and B, respectively. 

Substituting these values in the rate-determining step gives Eq. (2.27). 

Before going further, let us see if Eq. (2.28) agrees with chemical intuition. The rate of the isomerization A - B increases when [A] is higher, as well as when there are more free active sites. Moreover, the rate equation is symmetric with respect to A and B. Indeed, this is what one would expect for this catalytic isomerization. 

The first step in any catalyzed reaction is the activation of the substrate by adsorption on the catalyst as represented by Eqn. 7.1, where M is an active site on the catalyst, S is a substrate molecule, and P is the product. In such situations the rate of the reaction will depend on the amoimt of S adsorbed on the catalyst, that is, on the concentration of M-S as shown by Eqn. 7.2. 

While it is generally recognized that, as described in Chapter 3, a catalyst surface is composed of a number of different types of surface sites with varying adsorption and reaction characteristics, this model is not easily used for kinetic analyses. Instead, it is assumed that every surface atom on the catalyst is capable of adsorbing a substrate molecule, that they all do so with equal energy, and that there can be only one substrate molecule adsorbed on each surface atom. The amount of the substrate, S, added to the reaction mixture is known, but the amount of S adsorbed on the catalyst as M-S is not. However, the total number of surface atoms, Mo, can be determined by procedures such as those discussed in Chapter 2 so the number of atoms on which a substrate is adsorbed can be written as in Eqn. 7.3. 

In this case R is generally expressed as an areal turnover frequency (TOP), the number of molecules reacted per unit time per unit surface area. If the catalytic process follows this model the rate, R, will be related to [S] as shown in Fig. 7.1. The rate is first order at low values of [S] and decreases to zero order as [S] increases. By analogy, [M-S] is expected to be small when S is weakly adsorbed and the reaction should be first order. When S is strongly adsorbed a larger value for [M-S] should result and the reaction will be zero order. 

Unimolecular reactions of this type, though, are generally of little synthetic interest. Most synthetically useful catalytic reactions involve an interaction between two adsorbed species to give the product. In such cases Eqn. 7.1 must be expanded to Eqn. 7.9, 

Following the line of reasoning used for the unimolecular process Eqns. 7.11 and 7.12 can be developed,  

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Solid Catalyzed Reaction The pioneers were Langmuir (J. Am. Chem. Soc., 40, 1361 [1918]) and Hinshelwood Kinetics of Chemical Change, Oxford, 1940). For a gas phase reaction A + B Products, catalyzed by a solid, the postulated mechanism consists of the following ... 

Boudart (1956) and Weller (1956) discussed the applicability and need of Langmuir-Hinshelwood kinetics to describe the rate of industrially... 

It is well known that photocatalytic oxidation of or nic pollutants follows Langmuir-Hinshelwood kinetics[6]. Therefore, this kind of reaction can be represented as follows. 

Langmuir s research on how oxygen gas deteriorated the tungsten filaments of light bulbs led to a theory of adsorption that relates the surface concentration of a gas to its pressure above the surface (1915). This, together with Taylor s concept of active sites on the surface of a catalyst, enabled Hinshelwood in around 1927 to formulate the Langmuir-Hinshelwood kinetics that we still use today to describe catalytic reactions. Indeed, research in catalysis was synonymous with kinetic analysis... 

Hinshelwood Kinetic mechanism of reactions in heterogeneous catalysis... 

In Langmuir-Hinshelwood kinetics is it assumed that all species are adsorbed and accommodated (in thermal equilibrium) with the surface before they take part in any reactions. Hence, species react in the chemisorbed state on the surface. This is the prevailing situation in heterogeneous catalysis. 

Figure 2 depicts the dependence of N2 rate on Pco at fixed Pno= 0.52 k Pa for three different values of the catalyst potential. Vwr=+KXX) mV corresponds to the clean Pt surface (unpromoted rate) and Vwr=- 200 mV corresponds to a sodium promoted surface. Both CO2 and N2 rates exhibit Langmuir-Hinshelwood behaviour and as can be seen from Figure 2 for N2 rate, increased levels of Na result in a systematic increase in the CO partial pressure (P co) necessary for inhibition. The N2O rate also exhibits Langmuir-Hinshelwood kinetics, but the effect of increased Na is somewhat different in particular, high levels of Na tend to suppress the N2O rate and there is no systematic shift in P co-... 

Figure 3.52 Parity diagram based on Langmuir-Hinshelwood kinetics of the oxygen reaction rate [121].

GP 11] [R 5] Langmuir-Hinshelwood kinetics adequately describe the observed results as a parity diagram (Figure 3.52), comparing experimental with theoretical values (2.0-7.0 mmol 1 hydrogen 3.6 mmol oxygen 48-70 °C) [121]. 

Another problem which can appear in the search for the minimum is intercorrelation of some model parameters. For example, such a correlation usually exists between the frequency factor (pre-exponential factor) and the activation energy (argument in the exponent) in the Arrhenius equation or between rate constant (appears in the numerator) and adsorption equilibrium constants (appear in the denominator) in Langmuir-Hinshelwood kinetic expressions. 

Deactivating catalytic reaction with Langmuir-Hinshelwood kinetics in a completely mixed reactor. 

Lag in the system 509 Langmuir-Hinshelwood kinetics 321 Laplace transformation 80, 536 Latent heat of vapourisation 517 Least squares 112 Level control 509... 

Note the similarity to Langmuir-Hinshelwood kinetics.) The rate is expressed on the basis of the instantaneous number of solid carbon atoms, Nc. The rate r (measured at one gas composition) typically goes through a maximum as the carbon is converted. This is the result of a maximum in the intrinsic activity (related to the fraction of reactive carbon atoms, NCJNC) because of both a change in Nq> and a decrease in Nc. 

In the catalyzed gas-phase decomposition A - B + C, suppose A also acts as an inhibitor of its own decomposition. The resulting rate law (a type of Langmuir-Hinshelwood kinetics, Chapter 8) is ... 

The limitations of analytical solutions may also interfere with the illustration of important features of reactions and of reactors. The consequences of linear behavior, such as first-order kinetics, may be readily demonstrated in most cases by analytical techniques, but those of nonlinear behavior, such as second-order or Langmuir-Hinshelwood kinetics, generally require numerical techniques. 

The pioneers are Langmuir (JACS 40 2361, 1918) and Hinshelwood (Kinetics of ChemicaJ Change, 1940). 

Thermal decomposition of diethyl ether is postulated by Hinshelwood (Kinetics of Chemical Change, 1941) to proceed by the chain mechanism. 

Mann, Thurgood, and coworkers—Langmuir-Hinshelwood kinetic model for methanol steam reforming and WGS over Cu/Zn. Mann et al.335 published a complex Langmuir-Hinshelwood model for CuO/ZnO catalysts based on what one would encounter for a methanol steam reformer (MSR) for fuel cell applications. The water-gas shift rate, containing all MSR terms, was determined to be ... 

Wheeler, Schmidt, and coworkers—kinetic model for Pt/Ce at short contact times over medium to high T range. In 2004, Wheeler and coworkers422 reported on the water-gas shift reaction over Pt/ceria at short contact times (0.008-0.05 sec) for temperatures between 300 and 1000 °C. The reactant composition for CO, H2, and H20 was 1/2/4. A Langmuir-Hinshelwood kinetic model was used to adequately fit the medium and high temperature shift data ... 

Based on Langmuir-Hinshelwood kinetics the rate expression for a first order reaction (A —> R) that is surface reaction-controlled becomes equal to the following expression [2] ... 

Figure 7-25 Langmuir Hinshelwood kinetics for a unimolecidar surface-catdyzed reaction A products. The rate is first order in at low covauges aid zeroth orda at high coverage.

These rate expressions are for Langmuir-Hinshelwood kinetics, which are the simplest forms of surface reaction rates one could possibly find We know of no reactions that are this simple. LH kinetics requires several assumptions ... 

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