Langmuir adsorption isotherm assumptions

In this assumption, the singlet oxygen adsorption on a surface may be considered a quasistationary process and described by the Langmuir Adsorption Isotherm. Then the equilibrium constant is... 

The basic assumption of the Langmuir adsorption isotherm is that the adsorbed molecules do not interact. This condition is not always fulfilled for adsorption, particularly on electrodes. The Frumkin adsorption isotherm includes interaction between molecules in the adsorption film,... 

Two assumptions essential to obtain Eqs. (82) or (84) are (i) the hetaeron adsorption has an asymptotic limiting value, and (ii) complexes between the eluite and hetaeron form in the mobile phase. The Langmuir adsorption isotherm is used here because it is simple to manipulate mathematically and because most data on the adsorption of detergents used as hetaerons are reported to obey this relationship as determined directly (207, 209) or from analyses of its effect on chromatographic retention ( 4). 

What are the assumptions implicit in the Langmuir adsorption isotherm ... 

The Langmuir adsorption isotherm can be derived [134,417] using the statistical thermodynamics techniques discussed in Chapters 8 and 9. The assumptions necessary are basically the same as were used in deriving the Langmuir adsorption isotherm in Section 11.4.1. That is, adsorption is assumed to occur on a fixed array of surface sites there is assumed to be no interaction between adsorbed species the particular sites that are filled are assumed to be random and adsorbed species are immobile, corresponding to a chemisorbed species. 

Theory of Vapor-Particle Partitioning of PAH Compounds in the Atmosphere. Yamasaki et al. (64) treated semivolatile PAHs as inherently vapor-phase materials, existing in the particle phase only because of their tendency to sorb on nonvolatile materials. Under this assumption, the proportion in each phase should vary with the available surface area for sorption and with the ambient temperature. They assumed that sorption followed a Langmuir adsorption isotherm, requiring that there be only a low fractional coverage of the particulate matter with semivolatile material. In this case, competition for sorption sites can be ignored. At equilibrium, the rate of sorption equals the rate of evaporation. They derived this relationship ... 

To illustrate the analogy more clearly, it is necessary to consider the derivation of the Langmuir adsorption isotherm. We can incorporate the above assumptions into an equilibrium expression which equates the rate of adsorption racis to that of desorption rdes of gas molecules of type J. The desorption rate is directly proportional to the fraction of monolayer sites occupied /, and is expressed as... 

The Langmuir adsorption isotherm is based on the characteristic assumptions that (a) only monomolecular adsorption takes place, (b) adsorption is localised and (c) the heat of adsorption is independent of surface coverage. A kinetic derivation follows in which the velocities of adsorption and desorption are equated with each other to give an expression representing adsorption equilibrium. 

A final area of difficulty is in the application of data analysis to specific models of adsorption isotherms. This difficulty results from the fact that different models for adsorption isotherms generate plots of surface versus dissolved concentration that have characteristic shapes. If a plot of observational data results in a curve with a shape similar to that generated by a model, this result is often taken as proof that the particular model applies. Unfortunately, this assumption has been made for situations where many of the basic requirements of the model are violated in the system under study. The Langmuir adsorption isotherm model has suffered considerable abuse by geochemists in this regard. It should be remembered that "shapes" of adsorption isotherms are far from proof that a specific model applies. 

A frequently used adsorption model that allows for adsorption in multilayers has been introduced by Brunauer, Emmett and Teller [10] and is known as the BET equation. With the exception of the assumption that the adsorption process terminates at monolayer coverage, these authors have retained all the other assumptions made in deriving the Langmuir adsorption isotherm. Hence all objections to the application of the Langmuir equation apply here, too. 

Competitive Langmuir Adsorption Isotherm When two or more substances can be adsorbed on a surface, the so-called competitive isotherms are applied. The Langmuir isotherm was improved for the adsorption of two gases by Markham and Benton (1931). Of course, the four assumptions of Langmuir isotherms are valid here, too. The surface-adsorbed quantity of component 1 is... 

The Langmuir adsorption isotherm was developed by Irving Langmuir in 1916 from kinetic considerations to describe the dependence of the surface fractional coverage of an adsorbed gas on the pressure of the same gas above the adsorbent surface at a constant temperature. The Langmuir isotherm expression was re-derived thermodynamically by Volmer and statistically mechanically by Fowler. In his original treatment, Langmuir made several assumptions for his model ... 

From the above equations, models of different degrees of sophistication can be obtained. The simplest physically realistic one is that based on the assumption of equilibrium adsorption-desorption with linear Langmuir adsorption isotherm, which will be presented first, followed by the general non-equilibrium adsorption-desorption model. 

As we have seen, the Langmuir adsorption isotherm is based on the simplest of assumptions. Systems which obey the equation are often referred to as showing ideal... 

Derive the Langmuir adsorption isotherm (Eq. 4.1.8) under the assumptions that there are a finite number of free adsorption sites, the adsorption rate is second order in c and the available adsorption sites, and the desorption rate is first order in the material adsorbed. Show what the constant b represents. 

The saturation of all adsorption sites on the solid surface (6 = 1) is characterized by a plateau in the isotherm. The Langmuir adsorption isotherm is based on the following assumptions the surface is uniform and every adsorption site is equivalent to the others, the substrate surface is saturated when aU adsorption sites are occupied and monolayer formation has occurred, there are no interactions between the adsorbed particles. In general, physisorption isotherms show various shapes. These are, according to the lUPAC classification, types II and III which describe adsorption on nonporous or macroporous adsorbent with strong and weak gas-solid interaction, respectively. Type IV and V are adsorption isotherms which show typically capillary condensation with hysteresis loops and type VI isotherm shows stepwise multilayer adsorption. 

The changes in versus [M" ] were fitted to the Langmuir adsorption isotherm [43,46,49]. The Langmuir model is based on the assumptions that adsorption is limited to one monolayer that all surface sites are equivalent and the adsorption to one site is independent of the occupancy condition of the adjacent sites. The com-plexation equilibrium is given by ... 

For describing the kinetics of heterogenous catalytic reactions, the Langmuir adsorption isotherms are used mainly. We now derive them for associative, dissociative, and competitive adsorption. The main assumptions are the following ... 

Interestingly, while the adsorption of polyelectrolytes onto BaS04 does not conform to the usual assumptions of the Langmuir adsorption isotherm model, the Langmuir model nevertheless provides a good fit to these experimental results as it does in many other cases of polymer adsorption. The Langmuir adsorption isotherm can be written in linear form as shown in Equation 1. 

A set of equations derived from the model assumptions complemented by Langmuir adsorption isotherm was used by Shi et al. (2009) to describe experimental steady-state and transient performance of a PEMFC in the presence of adsorbed toluene species in the cathode airstream. The model allowed the authors to quahtatively describe air-side toluene contamination observed for four different current densities (0.2,0.5,0.75, and 1.0 A/cm ) and three different concentrations (1,5, and 10 ppm). 

Brunauer, Emmett, and Teller (1938) successfully extended the Langmuir adsorption isotherm applicable to monolayer adsorption to multilayer adsorption. While the assumptions made contain some serious deficiencies, the reproducibility of the BET method has made it the standard procedure for determining total surface area. In addition to the assumptions involved in the Langmuir adsorption, the BET method assumes that heats of adsorption for the multilayer adsorption are the same for the second and subsequent layers and are equal to the heat of liquefaction of the adsorbate. Adsorption and desorption rate constants are assumed to be the same for all layers except for the first layer, which is in contact with the... 

In the case of gas-phase adsorbate, the siuface coverage 9 is dependent on the gas pressure. Adsorption isotherms relay the surface coverage and the gas pressure (at constant temperature) the most known equation of this type is Langmuir adsorption isotherm. It is based on the following assumptions [6] ... 

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