Isothermic processes Langmuir isotherms

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. 

Pan et al. [34] used the nonlocal density functional theory (DFT) [35] and the three-process Langmuir model (TPLM) [36] to predict the adsorption heats of propane and butane on carbon and compared these results with experimental data determined from isotherms measured on BAX-activated carbon (Westvaco) in the 297—333 K temperature interval. Both models agreed in showing that the adsorption heat for butane was c. 10 kj/mol higher than that of propane at the same loading. The satisfactory agreement found prompted the authors to propose the use of the DFT method as it requires only one experimental isotherm in contrast with the numerous isotherms required by the classic technique. 

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.)... 

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,... 

This precipitation process can be carried out rather cleverly on the surface of a reverse phase. If the protein solution is brought into contact with a reversed phase, and the protein has dispersive groups that allow dispersive interactions with the bonded phase, a layer of protein will be adsorbed onto the surface. This is similar to the adsorption of a long chain alcohol on the surface of a reverse phase according to the Langmuir Adsorption Isotherm which has been discussed in an earlier chapter. Now the surface will be covered by a relatively small amount of protein. If, however, the salt concentration is now increased, then the protein already on the surface acts as deposition or seeding sites for the rest of the protein. Removal of the reverse phase will separate the protein from the bulk matrix and the original protein can be recovered from the reverse phase by a separate procedure. 

The saturation of the SHG response at high cation concentrations suggests that the process of complex formation at the membrane surface may be treated by a Langmuir-isotherm type analysis [24,27]. At constant temperature, the Langmuir equation is given by... 

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... 

Spirodela intermedia, L. minor, and P. stratiotes were able to remove Pb(II), Cd(II), Ni(II), Cu(II), and Zn(II), although the two former ions were removed more efficiently. Data fitted the Langmuir model only for Ni and Cd, but the Freundlich isotherm for all metals tested. The adsorption capacity values (K ) showed that Pb was the metal more efficiently removed from water solution (166.49 and 447.95 mg/g for S. intermedia and L. minor, respectively). The adsorption process for the three species studied followed first-order kinetics. The mechanism involved in biosorption resulted in an ion-exchange process between monovalent metals as counterions present in the macrophytes biomass and heavy metal ions and protons taken up from water.112... 

Regarding submerged plants, sorption of Cu(II) by Myriophyllum spicatum L. (Eurasian water milfoil) has been shown to be fast and fits isotherm models such as Langmuir, Temkin, and Redlich-Peterson. The maximum sorption capacity (c/lll l j ) of copper onto M. spicatum L. was 10.80 mg/g, while the overall sorption process was best described by the pseudo-second-order equation.115 Likewise, Hydrilla verticillata has been described as an excellent biosorbent for Cd(II). In batch conditions, the qmsx calculated was 15.0 mg/g. Additionally, II. verticillata biomass was capable of decreasing Cd(II) concentration from 10 to a value below the detection limit of 0.02 mg/L in continuous flow studies (fixed-bed column). It was also found that the Zn ions affected Cd(II) biosorption.116... 

The Langmuir adsorption isotherm provides a simple mechanistic picture of the adsorption process and gives rise to a relatively simple mathematical expression. It can also be used to obtain a crude estimate of specific surface areas. More important, from the viewpoint of the chemical engineer, it serves as a point of departure for formulating rate expressions for heterogeneous catalytic reactions. 

Many individuals have developed more elegant theoretical treatments of adsorption processes since Brunauer, Emmett, and Teller published their classic paper. Nonetheless, the BET and Langmuir isotherms are the most significant ones for chemical engineering applications. 

Poisoning is caused by chemisorption of compounds in the process stream these compounds block or modify active sites on the catalyst. The poison may cause changes in the surface morphology of the catalyst, either by surface reconstruction or surface relaxation, or may modify the bond between the metal catalyst and the support. The toxicity of a poison (P) depends upon the enthalpy of adsorption for the poison, and the free energy for the adsorption process, which controls the equilibrium constant for chemisorption of the poison (KP). The fraction of sites blocked by a reversibly adsorbed poison (0P) can be calculated using a Langmuir isotherm (equation 8.4-23a) ... 

If other ions affect the internalisation process via competition for the transport sites [3,5,14,15,37,52,69,93,97-99], then a reasonable starting point is to modify the Langmuir isotherms (3) to ... 

Predominantly, Freundlich s fitted adsorption isotherms computed by means of simple linear regression were proposed for the mathematical description of the process studied. Unlike the Langmuir equation, the Freundlich model did not reduce to a linear adsorption expression at very low nor very high solute concentrations, as above resulted. 

Data on the adsorption of caprylic acid on a hydrophobic (mercury) surface in terms of a double logarithmic plot of Eq. (4.13) Panel a) compares the experimental values with a theoretical Langmuir isotherm, using the same values for the adsorption constant B for both curves. Panel b) shows that the adsorption process can be described by introducing the parameter a, which accounts for lateral interaction in the adsorption layer. Eq. (4.13) postulates a linear relation between the ordinate [= log [0/ 1 - 0)] - 2a 0 / (In 10)] and the abscissa (log c). If the correct value for a is inserted, a straight line results. For caprylic acid at pH 4, a value of a = 1.5 gives the best fit. 

Ferrocene-based Linear Polymers. The first derivative that was studied from the electrochemical point of view was polyvinylferrocene (PVF). As illustrated in Figure 25, it displays a single oxidation process, which in some solvents is affected by problems of adsorption of the oxidation product (though not of the ideal Langmuir isotherm type discussed in Chapter 2, Section 1.6). 

Abstract Removal of catechol and resorcinol from aqueous solutions by adsorption onto high area activated carbon cloth (ACC) was investigated. Kinetics of adsorption was followed by in-situ uv-spectroscopy and the data were treated according to pseudo-first-order, pseudo-second-order and intraparticle drfiusion models. It was fotmd that the adsorption process of these compotmds onto ACC follows pseudo-second-order model. Furthermore, intraparticle drfiusion is efiective in rate of adsorption processes of these compoimds. Adsorption isotherms were derived at 25°C on the basis of batch analysis. Isotherm data were treated according to Langmuir and Freundhch models. The fits of experimental data to these equations were examined. 

In the mechanism of the anodic iron dissolution, described in this section, the formation process of the intermediate of ferrous hydroxocomplexes, Eqn. 9-21a, is in the quasi-equilibrium state so that the Nemst equation applies between the adsorption coverage, 6p oa-, of the intermediate FeOH [d and the overvoltage, t). Accordingly, for the range of relatively low coverages of adsorption to which Langmuir s adsorption isotherm applies, we obtain Eqn. 9-22 ... 

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