Adsorbed Langmuir isotherm

Adsorbent Langmuir Isotherm Parameters Freundlich Isotherm Parameters Thermodynamic Parameter... 

For adsorbed hydrocarbons, the adsorption—desorption process can be thought of as a reaction and the adsorption isotherm as a description of the reaction at equihbtium. For the Langmuir isotherm,... 

Consider a binary adsorbed mixture for which each pure component obeys the Langmuir equation, Eq. (16-13). Let n = 4 mol/kg, nl =. 3 mol/kg, Kipi = K2P2 = 1. Use the ideal adsorbed-solution theory to determine ni and n. Substituting the pure component Langmuir isotherm... 

The bi-Langmuir model (Equation (2)) or tri-Langmuir model, the sum of two or three Langmuir isotherms, correspond to models that assume the adsorbent surface... 

The assumptions made to derive the Langmuir isotherm (Eq. 2.7) are well known Energetic equivalence of all adsorption sites, and no lateral (attractive or repulsive) interactions between the adsorbate molecules on the surface. This is equivalent to a constant, coverage independent, heat (-AH) of adsorption. 

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. 

We start by noting that the Langmuir isotherm approach does not take into account the electrostatic interaction between the dipole of the adsorbate and the field of the double layer. This interaction however is quite important as already shown in section 4.5.9.2. In order to account explicitly for this interaction one can write the adsorption equilibrium (Eq. 6.24) in the form ... 

We now examine what happens to the modified electrochemical Langmuir isotherm (Eq. 6.36) when AO is created only by the presence of the adsorbate j, i.e. in absence of any coadsorbing ionic species. Substituting equation (6.49) into equation (6.36) and expressing AO via the Helmholz equation (5.16) one obtains ... 

In essence, we have used the Langmuir isotherms for the adsorbing and desorbing species. By substituting the coverages into the rate expression for the ratedetermining step we obtain... 

Here we consider a simple Langmuir isotherm where an atom A is in equilibrium with adsorbed A on the surface. 

To understand the chemisorptive property of lr/ln/H-ZSM-5 in a comparison with that of ln/H-ZSM-5, the chemisorption data were analyzed in detail. The data shown in Fig. 3 are relatively well fitted to the Langmuir isotherm, as shown in Fig. 5. From these relations, the equilibrium constant (K) and the amount of NO2 adsorbed at saturation (Vo) were determined according to the following equations ... 

Often, mnltistep reactions are enconntered where a reactant j first becomes adsorbed on the electrode, then is converted electrochemically (or chemically) to a desorbing prodnct. We shall consider the case where the electrochemical step involving adsorbed particles is rate determining. With a homogeneons electrode surface and without interaction forces between the adsorbed particles [i.e., in conditions when the Langmuir isotherm (10.14) can be apphed], the assumption can be made that the rate of this step is proportional not to the bulk concentration Cy j but to the surface concentration Aj or to the degree of surface coverage 0 hence. 

Electrochemical reaction rates are also influenced by substances which, although not involved in the reaction, are readily adsorbed on the electrode surface (reaction products, accidental contaminants, or special additives). Most often this influence comes about when the foreign species I by adsorbing on the electrode partly block the surface, depress the adsorption of reactant species j, and thus lower the reaction rate. On a homogeneous surface and with adsorption following the Langmuir isotherm, a factor 10, will appear in the kinetic equation which is the surface fraction free of foreign species 1 ... 

One of the simplest nonlinear isotherm models is the Langmuir model. Its basic assumption is that adsorbate deposits on the adsorbent surface in the form of the monomolecular layer, owing to the delocalized interactions with the adsorbent snrface. The Langmuir isotherm can be given by the following relationship ... 

With the adsorbate concentration low enough, the Langmuir isotherm transforms into the linear equation and becomes the simplest isotherm of adsorption, as described by Henry s law. 

From the asymmetrical concentration profile with front tailing (see Figure 2.4b), it can correctly be deduced that (1) the adsorbent layer is already overloaded by the analyte (i.e., the analysis is being run in the nonlinear range of the adsorption isotherm) and (2) the lateral interactions (i.e., those of the self-associative type) among the analyte molecules take place. The easiest way to approximate this type of concentration profile is by using the anti-Langmuir isotherm (which has no physicochemical explanation yet models the cases with lateral interactions in a fairly accurate manner). 

The second example is the extraction of Ni(II) with 2-hydroxy oxime. 2-Hydroxy oxime including 5-nonylsalicylaldoxime (P50) [15], 2-hydroxy-5-nonylacetophenone oxime (SME529) [16], and 2-hydroxy-5-nonylbenzophenone oxime (LIX65N) [17], are widely used as commercial extractants of Ni(II), Cu(II), and Co(II) in hydrometallurgy. These extractants are adsorbed at the interface even in their neutral forms following the Langmuir isotherm,... 

The limited number of free sites for the adsorbed substance on the surface is considered by the Langmuir isotherm,... 

Sorption and desorption are usually modeled as one fully reversible process, although hystersis is sometimes observed. Four types of equations are commonly used to describe sorption/desorption processes Langmuir, Freundlich, overall and ion or cation exchange. The Langmuir isotherm model was developed for single layer adsorption and is based on the assumption that maximum adsorption corresponds to a saturated monolayer of solute molecules on the adsorbent surface, that the energy of adsorption is constant, and that there is no transmigration of adsorbate on the surface phase. 

Derivation of the Langmuir Equation— Adsorption of a Single Species. The kinetic approach to deriving a mathematical expression for the Langmuir isotherm assumes that the rate of adsorption on the surface is proportional to the product of the partial pressure of the adsorbate in the gas phase and the fraction of the surface that is bare. (Adsorption may occur only when a gas phase molecule strikes an uncovered site.) If the fraction of the surface covered by an adsorbed gas A is denoted by 0Ay the fraction that is bare will be 1 — 0A if no other species are adsorbed. If the partial pressure of A in the gas phase is PA, the rate of adsorption is given by... 

The Langmuir Equation for the Case Where Two or More Species May Adsorb. Adsorption isotherms for cases where more than one species may adsorb are of considerable significance when one is dealing with heterogeneous catalytic reactions. Reactants, products, and inert species may all adsorb on the catalyst surface. Consequently, it is useful to develop generalized Langmuir adsorption isotherms for multicomponent adsorption. If 0t represents the fraction of the sites occupied by species i, the fraction of the sites that is vacant is just 1 — 0 where the summation is taken over all species that can be adsorbed. The pseudo rate constants for adsorption and desorption may be expected to differ for each species, so they will be denoted by kt and k h respectively. 

In addition to the assumptions implicit in the use of the Langmuir isotherm the following assumption is applicable to all Hougen-Watson models the reaction involves at least one species chemisorbed on the catalyst surface. If reaction takes place between two adsorbed species, they must be adsorbed on neighboring sites in order for reaction to occur. The probability of reaction between adsorbed A and adsorbed B is assumed to be proportional to the product of the fractions of the sites occupied by each species (0A9B). Similar considerations apply to termolecular reactions occurring on the surface. 

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