Isothermal Langmuir kinetics

Isothermal Langmuir Kinetics and Film Resistance Models. 316... 

Equation 5.114 is formulated by analogy to the adsorption isotherm (Langmuir kinetics, see Equ. 2.55) using the sorption capacity as measurement for sludge activity... 

We should point out that the Langmuir kinetics given by expressions (1.11) and (1.12) which is often observed in experiment is as often violated. In numerous cases the data on adsorption kinetics follows the well-known Roginsky-Zeldovich-Elovich kinetics isotherm [47, 48]... 

When Should One Use the Frumkin-Temkin Isotherms in Kinetics Rather than the Simple Langmuir Approach ... 

Until now, we have focused our attention on those adsorption isotherms that show a saturation limit, an effect usually associated with monolayer coverage. We have seen two ways of arriving at equations that describe such adsorption from the two-dimensional equation of state via the Gibbs equation or from the partition function via statistical thermodynamics. Before we turn our attention to multilayer adsorption, we introduce a third method for the derivation of isotherms, a kinetic approach, since this is the approach adopted in the derivation of the multilayer, BET adsorption isotherm discussed in Section 9.5. We introduce this approach using the Langmuir isotherm as this would be useful in appreciating the common features of (and the differences between) the Langmuir and BET isotherms. 

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. 

By introducing a number of simplifying assumptions, Brunauer, Emmett and Teller (1938) were able to extend the Langmuir mechanism to multilayer adsorption and obtain an isotherm equation (the BET equation), which has Type II character. The original BET treatment involved an extension of the Langmuir kinetic theory of monomolecular adsorption to the formation of an infinite number of adsorbed layers. 

The adsorption of methylene blue by coir pith carbon was carried out by varying the parameters such as agitation time, dye concentration, adsorbent dose, pH and temperature. Equilibrium adsorption data obeyed Langmuir isotherm. Adsorption kinetics followed a second order rate kinetic model. The adsorption capacity was found to be 5.87 mg dye per g of the adsorbent. There was no significant change in the per cent removal with pH. The pH effect and desorption studies suggest that chemisorption might be the major mode of the adsorption process. 

The solid and liquid film linear driving force models can be written under the same general form of a second order Langmuir kinetic model [1]. We can insert the Langmuir isotherm equation q = qsbC)/ l bC)) in the partial differential equation of tire solid fihn linear driving force model (Eq. 14.3)... 

As mentioned above, the adsorption kinetics for a kinetic-controlled mechanism is given by the balance of surfactant adsorption and desorption fluxes to and from the interface and for the Langmuir kinetics this balance has the form of Eq. (4.15). The rate constants kad and kdes are functions of the activation energies adsorption and desorption and can be specified on the basis of the molecular kinetic [9, 120] or transition state theory [121]. Eq. (4.15) was applied to adsorption kinetics data of surfactants at the water/air interface by many authors, for example in [24, 39, 83, 97, 122, 123, 124, 125, 126, 127]. In these works, it was shown that the values of kad and kdes are not constant hut depend on the surfactant bulk, the degree of adsorption layer saturation, or its lifetime. To obtain better correspondence with the experimental data, some authors had assumed that the adsorption and desorption activation energies depend on the degree of adsorption layer saturation. These rather complicated kinetic equation are more or less empirical, although they transforms into a valid adsorption isotherm at equilibrium... 

The Mo adsorption process can be studied by using adsorption isotherms. Langmuir and Freundlich equations are the two major types of isotherms used to describe the Mo adsorption process. The Langmuir equation is based on the kinetic theory of gaseous adsorption onto solids, but is often used to model the adsorption of ions from solution (Ellis and Knezek, 1972). A common form of the Langmuir equation is... 

ABSTRACT Ephedra waste was modified by epichlorohydrin and diethylenetriamine to obtain aminated ephedra waste biosorbent. The factors affecting the adsorption efficiency, such as pH and contact time were investigated. The results showed that the optimum absorption conditions of aminated ephedra waste pH was 4.7 contact time was 3 h equilibrium was well described by Langmuir isotherms and kinetics was found to fit pseudo-second order type. According to the Langmuir equation, the maximum adsorption capacities of modified adsorbent for Cu + are 93.11 mg/g, which are higher than untreated adsorbent (17.61 mg/g). The aminated ephedra waste biosorbent had excellent absorbability toward heavy metal ions Cu f... 

Our library contains FRFs for four simple isothermal mechanisms Langmuir kinetics, film resistance model, micropore diffusion, and pore-surface model. For each mechanism, a short description with the model equations is given, together with the expressions for the first-order FRF Fx p(w), and two second-order FRFs, F2,pp(w, w) and F2,pp(w, —[Pg.293]

Equation 5.60 demonstrates the combination of Langmuir adsorption isotherm and kinetics which are first-order in the adsorbed species, and is called the Langmuir-Hinshelwood kinetic model. 

Kinetic characteristics of the deposition study of the deposition isotherms Langmuir type localized deposition on almost energetically equivalent deposition sites. Lateral Interactions are exerted between the adsorbed species. 

A. The Langmuir adsorption isotherm and kinetics of reactions on surfaces. Consider a molecule A coming from the gas phase and absorbed on an empty surface site S that then becomes occupied, A - - S A - S. The fraction of surface sites that are covered by A molecules is denoted B. (a) At equilibrium... 

Langmuir adsorption isotherm A theoretical equation, derived from the kinetic theory of gases, which relates the amount of gas adsorbed at a plane solid surface to the pressure of gas in equilibrium with the surface. In the derivation it is assumed that the adsorption is restricted to a monolayer at the surface, which is considered to be energetically uniform. It is also assumed that there is no interaction between the adsorbed species. The equation shows that at a gas pressure, p, the fraction, 0, of the surface covered by the adsorbate is given by ... 

The preceding derivation, being based on a definite mechanical picture, is easy to follow intuitively kinetic derivations of an equilibrium relationship suffer from a common disadvantage, namely, that they usually assume more than is necessary. It is quite possible to obtain the Langmuir equation (as well as other adsorption isotherm equations) from examination of the statistical thermodynamics of the two states involved. 

Langmuir-Type Relations For systems composed of solutes that individually follow Langmuir isotherms, the traditional iTuilti-component Langmuir equation, obtained via a kinetic derivation, is... 

As with the Langmuir adsorption isotherm, which in shape closely resembles Michaelis-Menten type biochemical kinetics, the two notable features of such reactions are the location parameter of the curve along the concentration axis (the value of Km or the magnitude of the coupling efficiency factor) and the maximal rate of the reaction (Vmax). In generic terms, Michaelis-Menten reactions can be written in the form... 

There are several reasons for deviations from the LHHW kinetics Surface heterogeneity, surface reconstruction, adsorbate island formation and, most important, lateral coadsorbate interactions.18,19 All these factors lead to significant deviations from the fundamental assumption of the Langmuir isotherm, i.e. constancy of AHa (and AHB) with varying coverage. 

Despite the already discussed oversimplifications built into the Langmuir isotherm and in the resulting LHHW kinetics, it is useful and instructive at this point to examine how a promoter can affect the catalytic kinetics described by the LHHW expressions (2.11) to (2.14). 

Such a model should be as simple as possible, without however missing any of the underlying thermodynamic and physicochemical factors which cause electrochemical promotion. In particular it will be shown that even the use of Langmuir-type adsorption isotherms, appropriately modified due to the application of potential (or equivalently by the presense of promoters) suffice to describe all the experimentally observed rules G1 to G7 as well as practically all other observations regarding electrochemical promotion including the effect of potential on heats of adsorption as well as on kinetics and reaction orders. 

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