Laws Langmuir kinetics

In many practical situations, one is mainly interested in C t), which for most kinetics (power law, Langmuir-Hinshelwood, bimolecular reactions, etc.) can be accurately estimated or exactly calculated from the following simple expression... 

The kinetics of a coupled catalytic reaction can be well described by equations of the Langmuir-Hinshelwood type, since these are able to express mutual influencing of single reactions. Power-law equations are not suitable for this purpose. 

A reason for using microkinetics in heterogeneous catalysis is to have comprehensive kinetics and a transparent reaction mechanism that wonld be useful for re or design or catalyst development. Furthermore, in the long run, the exparimental effort to develop a microkinetics scheme can be less than that for a Langmuir-Hinshelwood (LH) or powa--law scheme because of the more fundamental nature of the reaction kinetics parameters. 

Hill-Langmuir equation and the application of the law of mass action to the kinetics of drug-receptor interaction ... 

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. 

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 ... 

Kinetic models proposed for sorption/desorption mechanisms including first-order, multiple first-order, Langmuir-type second-order, and various diffusion rate laws are shown in Sects. 3.2 and 3.4. All except the diffusion models conceptualize specific sites to or from which molecules may sorb or desorb in a first-order fashion. The following points should be taken into consideration [ 181,198] ... 

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... 

In general, the use of Langmuir-Hinshelwood-Hougen-Watson (LHHW)-type of rate equation for representing the hydrogenation kinetics of industrial feedstocks is complicated, and there are too many coefficients that are difficult to determine. Therefore, simple power law models have been used by most researchers to fit kinetic data and to obtain kinetic parameters. 

For a formal kinetic description of vapour phase esterifications on inorganic catalysts (Table 21), Langmuir—Hinshelwood-type rate equations were applied in the majority of cases [405—408,410—412,414,415]. In some work, purely empirical equations [413] or second-order power law-type equations [401,409] were used. In the latter cases, the authors found that transport phenomena were important either pore diffusion [401] or diffusion of reactants through the gaseous film, as well as through the condensed liquid on the surface [409], were rate-controlling. 

The permeation of a gas through a porous polymer is generally described by equations based on the kinetic theory of gases. The sorption isotherm described by Eq. 1 is concave to the pressure axis and is commonly observed for a penetrant gas in a glassy polymer. It is composed of Henry s law and Langmuir-terms [20] ... 

The kinetics of elementary reactions occurring at a solid surface cannot be described with anything near the accuracy available for gas and liquid phase reactions, and, as a consequence, it is often necessary to describe the kinetics of an overall reaction using power-law or Langmuir-Hinshelwood-... 

In reality however, situations also exist where a more complex form of the rate expression has to be applied. Among the numerous possible types of kinetic expressions two important cases will be discussed here in more detail, namely rate laws for reversible reactions and rate laws of the Langmuir-Hinshelwood type. Basically, the purpose of this is to point out additional effects concerning the dependence of the effectiveness factor upon the operating conditions which result from a more complex form of the rate expression. Moreover, without going too much into the details, it is intended at least to demonstrate to what extent the mathematical effort required for an analytical solution of the governing mass and enthalpy conservation equations is increased, and how much a clear presentation of the results is hindered whenever complex kinetic expressions are necessary. 

Similar to reversible reactions, the mathematical treatment becomes more complicated if a Langmuir-Hin-shelwood (Hougen-Watson) type kinetic expression is used. For the most simple case of an irreversible, monomolecular reaction A — products, the following rate law holds ... 

When reactants or intermediates are adsorbed, the rate of the reaction may no longer be related to the concentration by a simple law. This situation is best understood where a reactant is nonspecifically adsorbed in the outer -> Helmholtz plane. The effect of such adsorption on the electrode kinetics is usually termed the -> Frumkin effect. Physical and chemical adsorption on the electrode surface is usually described by means of an -> adsorption isotherm and kinetic equations compatible with various isotherms such as the - Langmuir, -> Temkin, -> Frumkin isotherms are known. 

Equation (28) has been called the Langmuir rate law [5], Certain special cases of this equation lead to a variety of different kinetic forms. For example, if all species are only slightly adsorbed, the denominator tends to unity and the reaction becomes simply first-order in each of A and B. On the other hand, if A (and P and Q) is weakly adsorbed and B strongly, the denominator reduces to K cB which converts the reaction into one that is first order in A but inverse first order in B. Strong adsorption of one of the reactants thus denies surface sites to the other reactant and effectively stifles the catalytic process. 

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