Langmuir-Hinshelwood rate law

If reaction XVIII-42 is the slow step, the Langmuir-Hinshelwood rate law is... 

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. 

To determine Km and Vmax, experimental data for cs versus t are compared with values of cs predicted by numerical integration of equation 10.3-3 estimates of Km and Vmax are subsequently adjusted until the sum of the squared residuals is minimized. The E-Z Solve software may be used for this purpose. This method also applies to other complex rate expressions, such as Langmuir-Hinshelwood rate laws (Chapter 8). 

A global rate expression for CO methanation over a nickel catalyst is given by Lee (1973) and Vatcha (1976). They report that a Langmuir-Hinshelwood rate law of the form... 

Problem 9.5 Considering reaction between A and B catalyzed by a solid there are two possible mechanisms by which this reaction could occur. The first is that one of them, say A gets adsorbed on the solid surface and the adsorbed A then reacts chemically with the other component B which is in the gas phase or in solution and is not adsorbed on the surface. The second mechanism is that both A and B are adsorbed, and the adsorbed species undergo chemical reaction on the surface. The reaction rate expression derived for the former mechanism is the Rideal rate law and that for the second mechanism is the Langmuir-Hinshelwood rate law. Obtain simple derivations of these two rate laws. 

Both the Rideal and Langmuir-Hinshelwood rate laws are based upon the Langmuir adsorption equation, which is applicable for gas-solid as well as liquid-solid systems where diffusion of the sorbate to the solid surface is not rate limiting (generally true). The basic assumption of the Langmuir adsorption is that adsorption occurs at adsorption sites and all these sites are equivalent. For gas-solid systems, the rate of adsorption, fo, of the gas A is proportional to the gas pressure, pa, and the number of vacant sites, i.e.. 

Consequently, we see that for heterogeneous reactions, Langmuir-Hinshelwood rate law s are preferred over power law models. 

Ziegler-Natta catalyst systems being mostly heterogeneous in nature, adsorption reactions are most likely to occur in such polymerizations and feature in their kinetic schemes (Erich and Mark, 1956). A number of kinetic schemes have thus been proposed based on the assumption that the polymerization centers are formed by the adsorption of metal alkyl species on to the surface of a crystalline transition metal halide and that chain propagation occurs between the adsorbed metal alkyl and monomer. In this regard the Rideal rate law and the Langmuir-Hinshelwood rate law for adsorption and reaction on solids assume importance see Problem 9.4). 

Preliminary kinetic studies have been performed. The Langmuir-Hinshelwood rate expression was used to correlate results of experiments as it was indicated by the shape of kinetic curves (see Fig. 6). However, the reaction order with respect to hydrogen appeared to be dependent on temperature, while activation energy depends on pressure (9.6 kJ/mol at 11 bar and 35.5 kJ/mol at 21 bar). Therefore the rate of benzaldehyde consumption was approximated using the following simple power law equation ... 

Table 3.4 Comparison of Power-Law and Langmuir-Hinshelwood Rate Equations...

Ref. 205). The two mechanisms may sometimes be distinguished on the basis of the expected rate law (see Section XVni-8) one or the other may be ruled out if unreasonable adsorption entropies are implied (see Ref. 206). Molecular beam studies, which can determine the residence time of an adsorbed species, have permitted an experimental decision as to which type of mechanism applies (Langmuir-Hinshelwood in the case of CO + O2 on Pt(lll)—note Problem XVIII-26) [207,208]. 

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.)... 

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. 

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. 

By combining surface-reaction rate laws with the Langmuir expressions for surface coverages, we can obtain Langmuir-Hinshelwood (LH) rate laws for surface-catalyzed reactions. Although we focus on the intrinsic kinetics of the surface-catalyzed reaction, the LH model should be set in the context of a broader kinetics scheme to appreciate the significance of this. 

Propose a rate law based on the Langmuir-Hinshelwood model for each of the following heterogeneously catalyzed reactions ... 

The Michaelis-Menten equatioa 10.2-9, is developed in Section 10.2.1 from the point of view of homogeneous catalysis and the formation of an intermediate complex. Use the Langmuir-Hinshelwood model of surface catalysis (Chapter 8), applied to the substrate in liquid solution and the enzyme as a colloidal particle with active sites, to obtain the same form of rate law. 

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 ... 

Rate data of the reaction for the synthesis of phosgene, CO + Cl2 = C0C12, over activated carbon are given. Although a Langmuir-Hinshelwood mechanism may be preferred, a power law rate is asked for. 

When a simple, fast and robust model with global kinetics is the aim, the reaction kinetics able to predict correctly the rate of CO, H2 and hydrocarbons oxidation under most conditions met in the DOC consist of semi-empirical, pseudo-steady state kinetic expressions based on Langmuir-Hinshelwood surface reaction mechanism (cf., e.g., Froment and Bischoff, 1990). Such rate laws were proposed for CO and C3H6 oxidation in Pt/y-Al203 catalytic mufflers in the presence of NO already by Voltz et al. (1973) and since then this type of kinetics has been successfully employed in many models of oxidation and three-way catalytic monolith converters... 

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