Langmuir and Hinshelwood

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. 

In remarkable progress of catalytic industry in 1930-1950s, a kinetic model was considered as a basis of reactor design. Langmuir and Hinshelwood... 

In heterogeneous catalysis the simplest equation that is used to describe the kinetics of a reaction of a single reactant is due to Langmuir and Hinshelwood [24], It bears the functional form... 

The nature of the adsorbed species during reaction is not always revealed by the kinetic data analyzed following the ideas of Langmuir and Hinshelwood. For instance, when the reaction is zero order, it appears that the active part of the catalyst surface is saturated with such species as reactants, products, or intermediate compounds, the adsorption being independent of the ambient gas pressures. The kinetic behavior does not tell which of them is really adsorbed. One of the merits of the adsorption measurements during the reaction is to provide such an identification. 

The second, proposed by Langmuir and Hinshelwood (Langmuir-Hinshelwood model), relies on a much more complex reaction. In this reaction the carbon monoxide is in adsorbed form. The equation of the reaction is then written ... 

This equation, the Langmuir-Hinshelwood equation, was first proposed by Langmuir and Hinshelwood in the 1920-30s for solid-catalyzed gas-phase reactions under the assumption that adsorption and desorption rates are high compared with rates of other chemical transformations on the catalyst surface. In this model, adsorption-desorption steps are considered to be at equilibrium. Later, Hougen, and Watson proposed a similar equation, the Hougen-Watson equation, for a reversible catalytic reaction, again under the assumption that the adsorption-desorption steps are at equilibrium. 

Langmuir and Hinshelwood assume that the surface reaction occtrrs between adsorbed gases in the following form ... 

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 ... 

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

It is pertinent here to emphasize that the Langmuir formulation of surface kinetics was restricted to those surface reactions in which the velocity of interaction on the surface was the rate-determining process. This condition was indeed fulfilled in the classic researches of Langmuir and in further developments by Hinshelwood, Rideal, Schwab and others. A 9... 

If step (1) is irreversible, = 0, we get an equation which starts to resemble those of Langmuir, and popularized by Hinshelwood ... 

Similar equations were written by Eley [204] for the exchange of N2 with N2 catalyzed by Fe or W, and mechanisms such as Eq. XVIII-33 have come to be known as Eley-Rideal mechanisms. Mechanisms such as that of Eq. XVIII-32 are now most commonly called Langmuir-Hinshelwood mechanisms (see... 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

Rate laws have also been observed that correspond to there being two kinds of surface, one adsorbing reactant A and the other reactant B and with the rate proportional to 5a x 5b- For traditional discussions of Langmuir-Hinshelwood rate laws, see Refs. 240-242. Many catalytic systems involve a series of intermediates, and the simplifying assumption of steady-state equilibrium is usually made. See Boudart and co-workers [243-245] for a contemporary discussion of such complexities. 

It is Langmuir-Hinshelwood in type, and the usually observed rate law is... 

Derive the probable rate law for the reaction CO + j02 = CO2 as catalyzed by a metal surface assuming (a) an Eley-Rideal mechanism and (b) a Langmuir-Hinshelwood mechanism. 

The desire to understand catalytic chemistry was one of the motivating forces underlying the development of surface science. In a catalytic reaction, the reactants first adsorb onto the surface and then react with each other to fonn volatile product(s). The substrate itself is not affected by the reaction, but the reaction would not occur without its presence. Types of catalytic reactions include exchange, recombination, unimolecular decomposition, and bimolecular reactions. A reaction would be considered to be of the Langmuir-Hinshelwood type if both reactants first adsorbed onto the surface, and then reacted to fonn the products. If one reactant first adsorbs, and the other then reacts with it directly from the gas phase, the reaction is of the Eley-Ridel type. Catalytic reactions are discussed in more detail in section A3.10 and section C2.8. 

Figure A3.9.1. Schematic illustrations of (a) the Langmuir-Hinshelwood and (b) Eley-Rideal mechanisms in gas-surface dynamics.

Rettner C T 1994 Reaction of an H-atom beam with Cl/Au(111)—dynamics of concurrent Eley-Rideal and Langmuir-Hinshelwood mechanisms J. Chem. Phys. 101 1529... 

The first step consists of the molecular adsorption of CO. The second step is the dissociation of O2 to yield two adsorbed oxygen atoms. The third step is the reaction of an adsorbed CO molecule with an adsorbed oxygen atom to fonn a CO2 molecule that, at room temperature and higher, desorbs upon fomiation. To simplify matters, this desorption step is not included. This sequence of steps depicts a Langmuir-Hinshelwood mechanism, whereby reaction occurs between two adsorbed species (as opposed to an Eley-Rideal mechanism, whereby reaction occurs between one adsorbed species and one gas phase species). The role of surface science studies in fomuilating the CO oxidation mechanism was prominent. 

Mechanistic kinetic expressions are often used to represent the rate data obtained in laboratory studies, and to explain quantitatively the effects observed in the field. Several types of mechanisms have been proposed. These differ primarily in complexity, and on whether the mechanism assumes that one compound that is adsorbed on the catalyst surface reacts with the other compound in the gas phase, eg, the Eley-Rideal mechanism (23) or that both compounds are adsorbed on the catalyst surface before they react, eg, the Langmuir-Hinshelwood mechanism (25). 

Over the usual hmited range of conditions, a power law rate equation often appears to be as satisfactory a fit of the data as a more complex Langmuir-Hinshelwood equation. The example of the hydrogenation of oc tenes is shown in Fig. l-2d and l-2e, and another case follows. 

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

The model is intrinsically irreversible. It is assumed that both dissociation of the dimer and reaction between a pair of adjacent species of different type are instantaneous. The ZGB model basically retains the adsorption-desorption selectivity rules of the Langmuir-Hinshelwood mechanism, it has no energy parameters, and the only independent parameter is Fa. Obviously, these crude assumptions imply that, for example, diffusion of adsorbed species is neglected, desorption of the reactants is not considered, lateral interactions are ignored, adsorbate-induced reconstructions of the surface are not considered, etc. Efforts to overcome these shortcomings will be briefly discussed below. 

The catalytic reaction of NO and CO on single crystal substrates, under ultra-high vacuum conditions, has been extensively studied. Neglecting N2O formation and CO desorption, the Langmuir-Hinshelwood mechanism of the NO + CO reaction can be described by the following sequence of steps [16,17] ... 

A dimer-dimer (DD) surface reaction scheme of the type (1/2)A2 + B2 B2A has been proposed in order to mimic the catalytic oxidation of hydrogen A2 is O2, B2 is H2, AB is OH and B2A is H2O. The model reaction proceeds according to the Langmuir-Hinshelwood... 

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