Equilibrium isotherms Langmuir isotherm

Adsorption Isotherm The mathematical relationship between the equilibrium quantity of a material adsorbed and the composition of the bulk phase at constant temperature. See also Gibbs Isotherm, Langmuir Isotherm. 

Among the isotherms that portray the adsorptive equilibrium, the Langmuir isotherm, Freundlich and Dubinin-Raduskevich were cited. For the adsorptive kinetic models, stand out the Lagergren, in models of pseudo-first order and pseudo-second order. 

For noncoustaut diffusivity, a numerical solution of the conseiwa-tion equations is generally required. In molecular sieve zeohtes, when equilibrium is described by the Langmuir isotherm, the concentration dependence of the intracrystalline diffusivity can often be approximated by Eq. (16-72). The relevant rate equation is ... 

The chromatographic resolution of bi-naphthol enantiomers was considered for simulation purposes [18]. The chiral stationary phase is 3,5-dinitrobenzoyl phenyl-glycine bonded to silica gel and a mixture of 72 28 (v/v) heptane/isopropanol was used as eluent. The adsorption equilibrium isotherms, measured at 25 °C, are of bi-Langmuir type and were proposed by the Separex group ... 

For nonlinear systems, however, the evaluation of the flow rates is not straightforward. Morbidelli and co-workers developed a complete design of the binary separation by SMB chromatography in the frame of Equilibrium Theory for various adsorption equilibrium isotherms the constant selectivity stoichiometric model [21, 22], the constant selectivity Langmuir adsorption isotherm [23], the variable selectivity modified Langmuir isotherm [24], and the bi-Langmuir isotherm [25]. The region for complete separation was defined in terms of the flow rate ratios in the four sections of the equivalent TMB unit ... 

Table 9-3. Operating conditions for complete separation under Equilibrium Theory. Langmuir adsorption isotherms (see Fig. 9-8).

Adsorption, like extraction, depends on equilibrium relationships. Isothermal adsorption is projected by Langmuir isotherms. The model is shown in Figure 7.14, which is based on the linear model of the following equation ... 

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 ... 

The equilibrium isotherms were favorable type and the Langmuir equation represents our experimental data very well. 

For each step in quasi-equilibrium we can either start from the differential equations as before or immediately use the Langmuir isotherm ... 

If we assume equilibrium between adsorption and desorption we find the Langmuir isotherm. 

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 ... 

In the most simple case of ideal, energy homogeneous surface the adsorption equilibrium of non-interacting particles is described by the Langmuir isotherm [33] ... 

Sorption. Capture of neutral organics by non-living particulates depends on the organic carbon content of the solids (9). Equilibrium sorption of such "hydrophobic" compounds can be described by a carbon-normalized partition coefficient on both a whole-sediment basis and by particle size classes. The success of the whole-sediment approach derives from the fact that most natural sediment organic matter falls in the "silt" or "fine" particle size fractions. So long as dissolved concentrations do not exceed 0.01 mM, linear isotherms (partition coefficients) can be used. At higher concentrations, the sorptive capacity of the solid can be exceeded, and a nonlinear Freundlich or Langmuir isotherm must be invoked. 

This term is analogous to relative volatility or its reciprocal (or to an equilibrium selectivity). Similarly, the assumption of a constant separation factor is a useful assumption in many sorptive operations. [It is constant for the Langmuir isotherm, as described below, and for mass-action equilibrium with za = zh in Eq. (16-24).] This gives the constant separation factor isotherm... 

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) ... 

The arrows show the isotherm evolution for continual addition of dissolved Me. The initial isotherm with the slope of 1 (in the double logaritmic plot) corresponds to a Langmuir isotherm (surface complex formation equilibrium). [Me]S0 = solubility concentration of Me for the stable metal oxide [Me]p = solubility concentration of Me for a metastable precursor (e.g., a hydrated Me oxide phase). 

Note that while 0, 0, and 0. (as well as 0 , if an equilibrium between the three states exists) are simple Langmuir isotherms, the BI of the mixture 0 is not. 

The other component of molecular transport through zeoHte membranes is the equilibrium sorption strength between the molecule and zeoHte. In general, this information is reported in the form of adsorption isotherms, which are tabulated for many species and zeoHte structures [22]. For example, Langmuir isotherm commonly describes the adsorpHon behavior of molecules transporhng through MFI-type zeoHte membranes and can be represented by the foUowing equahons ... 

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