Isotherm sorption, equilibrium

To evaluate the sorption capacity of the biomass, biosorption isotherms of R016 were obtained at different solution pHs. The initial concentration was varied from 0 to 5000 mg L, which resulted in different final dye concentrations after the sorption equilibrium was achieved. 

The data of Loukidou et al. (2004) for the equilibrium biosorption of chromium (VI) by Aeromonas caviae particles were well described by the Langmuir and Freundlich isotherms. Sorption rates estimated from pseudo second-order kinetics were in satisfactory agreement with experimental data. The results of XAFS study on the sorption of Cd by B. subtilis were generally in accord with existing surface complexation models (Boyanov et al. 2003). Intrinsic metal sorption constants were obtained by correcting the apparent sorption constants by the Boltzmann factor. A 1 2 metal-ligand stoichiometry provides the best fit to the experimental data with log K values of 6.0 0.2 for Sr(II) and 6.2 0.2 for Ba(II). 

The working capacity of a sorbent depends on fluid concentrations and temperatures. Graphical depiction of sorption equilibrium for single component adsorption or Binary ion exchange (monovariance) is usually in the form of isotherms [nt = nt(c,) or n,(p,) at constant T] or isosteres [p, = p,(T) at constant n,]. Representative forms are shown in Fig. 16-1. An important dimensionless group dependent on adsorption equilibrium is the partition ratio [see Eq. (16-125)], which is a measure of the relative affinities of the sorbed and fluid phases for solute. 

Construction and use of adsorption isotherms from equilibrium sorption data has been employed by numerous researchers to describe adsorption of organic pollutants on a solid matrix [131-137]. An isotherm represents a relation between the amount of solute (i.e., the pollutant of interest) adsorbed per unit weight of solid adsorbent (i.e., soil, sediment) and the solute concentration in solution at equilibrium. 

In conclusion, the different shapes of isotherms describing equilibrium distributions of a contaminant, between geosorbents and aqueous or gaseous phases, depend on the sorption mechanism involved and the associated sorption energy. At low contaminant concentration, all models reduce to essentially linear correlation. At higher contaminant concentration, when sorption isotherms deviate from linearity, an appropriate isotherm model should be used to describe the retention process. 

Frontal analysis brings with it the requirement of the system to have convex isotherms (see Section 1.2.6). This results in the peaks having sharp fronts and well-formed steps. An inspection of Figure 1.3 reflects the problem of analytical frontal analysis— it is difficult to calculate initial concentrations in the sample. One can, however, determine the number of components present in the sample. If the isotherms are linear, the zones may be diffuse. This may be caused by three important processes inhomogeneity of the packing, large diffusion effects, and nonattainment of sorption equilibrium. 

Sorption isotherm curves are graphical relationships showing the partitioning between solid and liquid form where mass adsorbed per unit mass of dry solids (S) is plotted against the concentration (C) of the constituent in solution. K is the sorption equilibrium constant N is a constant describing the intensity of sorption. The linear sorption isotherm can be expressed as follows ... 

The equilibrium data [28] was used to evaluate p for the system. A heat of adsorption of 14.9 kcal/mole was estimated for the system. Curves b and c, respectively, show the corresponding uptakes for external film heat transfer control and isothermal sorption using the same k as in curve a. 

Equilibrium between solution and adsorbed or sorbed phases is a condition commonly used to evaluate adsorption or sorption processes in soils or soil-clay minerals. As previously stated, equilibrium is defined as the point at which the rate of the forward reaction equals the rate of the reverse reaction. Two major techniques commonly used to model soil adsorption or sorption equilibrium processes are (1) the Freundlich approach and (2) the Langmuir approach. Both involve adsorption or sorption isotherms. A sorption isotherm describes the relationship between the dissolved concentration of a given chemical species (adsorbate) in units of micrograms per liter (pg L 1), milligrams per liter (mg L-1), microequivalents per liter (pequiv L-1), or millimoles per liter (mmol L-1), and the sorbed quantity of the same species by the solid phase (adsorbent) in units of adsorbate per unit mass of adsorbent (solid) (e.g., pg kg-1, mg kg-1, peq kg-1, or mmol kg 1) at equilibrium under constant pressure and temperature. Sorption isotherms have been classified into four types, depending on their general shape (Fig. 4.13) ... 

Many studies indicated that in the presence of DOM, the metal sorption capacity decreased markedly for most soils, and the effect on the calcareous soil was greater than on the acidic sandy loam. Figure 10.4 shows the metal sorption equilibrium isotherms onto soils with or without the addition of 400 mg C/l of DOM. The equilibrium isotherms could be better depicted according to the linear Freundlich equation with the high value for the correlation coefficient of determination (r2) ... 

Lewin and coworkers [255-260] developed an accessibility system based on equilibrium sorption of bromine, from its water solution at pH below 2 and at room temperature, on the glycosidic oxygens of the cellulose. The size of the bromine molecule, its simple structure, hydrophobicity, nonswelling, and very slow reactivity with cellulose in acidic solutions, contribute to the accuracy and reproducibility of the data obtained. The cellulose (10 g/1) is suspended in aqueous bromine solutions of 0.01-0.02 mol/1 for 1-3 h, depending on the nature of the cellulose, to reach sorption equilibrium. The diffusion coefficients of bromine in cotton and rayon are 4.6 and 0.37 x 10 cm /min, respectively. The sorption was found to strictly obey the Langmuir isotherm, which enables the calculation of the accessibility of the cellulose as follows ... 

The heat of adsorption may be calculated from a knowledge of the sorption isotherm at equilibrium by use of the Clausius-Clapeyron equation. 

Figure 10.8 Overview of hydrogen sorption equilibrium isotherms measured for Pd nanoparticles of different sizes, shapes, and stabilizers [44],...

Sorption Kinetics. The adsorption and desorption data were analyzed in terms of a model based on the following main assumptions. Micropore diffusion within the sieve crystals is the rate-controlling process. Diffusion may be described by Fick s law for spherical particle geometry with a constant micropore diffusivity. The helium present in the system is inert and plays no direct role in the sorption or diffusion process. Sorption occurs under isothermal conditions. Sorption equilibrium is maintained at the crystal surface, which is subjected to a step change in gas composition. These assumptions lead to the following relation for the amount of ethane adsorbed or desorbed by a single particle as a function of time (Crank, 4). 

The influence of sorbed moisture on chemical stability and the flow and compaction of powders and granulations is well established. The moisture content and hygroscopicity of excipients is particularly important as total product processing as well as finished product stability can be affected. Hygroscopicity, moisture-sorption isotherms, and equilibrium moisture content can be determined by thermogravimetric analysis and Karl Fisher titration methods. 

Figure 2 Sorption-desorption isotherm for mannitol. Sorption equilibrium moisture Desorption equilibrium moisture...

Natural surfaces generally are too complex to be characterized as having uniform solute interaction energies, however. It is therefore not unexpected that sorption equilibrium data for natural soils and sediments are rarely described adequately by the Langmuir model. Such data are commonly described more satisfactorily by the empirical Freundlich isotherm model, which has the form... 

Sousa et al [5.76, 5.77] modeled a CMR utilizing a dense catalytic polymeric membrane for an equilibrium limited elementary gas phase reaction of the type ttaA +abB acC +adD. The model considers well-stirred retentate and permeate sides, isothermal operation, Fickian transport across the membrane with constant diffusivities, and a linear sorption equilibrium between the bulk and membrane phases. The conversion enhancement over the thermodynamic equilibrium value corresponding to equimolar feed conditions is studied for three different cases An > 0, An = 0, and An < 0, where An = (ac + ad) -(aa + ab). Souza et al [5.76, 5.77] conclude that the conversion can be significantly enhanced, when the diffusion coefficients of the products are higher than those of the reactants and/or the sorption coefficients are lower, the degree of enhancement affected strongly by An and the Thiele modulus. They report that performance of a dense polymeric membrane CMR depends on both the sorption and diffusion coefficients but in a different way, so the study of such a reactor should not be based on overall component permeabilities. 

A large number of zeolite-gas systems have been investigated with respect to the sorption equilibrium. Some of the results described in the literature are of a more qualitative nature and cannot be evaluated quantitatively. Sorption isotherms are frequently described as rectangular, which means that measurements were made only at relatively high pressures where saturation is approached and that no information about the form of the isotherm was obtained. 

Several gas-zeohte systems that have been investigated quantitatively with respect to the sorption equilibrium and the form of the isotherms are listed in Table I the list is not exhaustive. The reproducibility of results obtained with the same sorbent seems to be very good, in general. However, results obtained with sorbents of the same structure and essentially the same composition, but from different sources, do not always agree. The following conclusions can be drawn from equilibrium measurements. 

The equilibrium relations that must be expected for a mixed sorbate, are relatively simple for localized sorbate particles on identical independent sites in a zeolite. The pure components (indices i, j) obey Langmuir isotherms, Eq. (11), and the sorption equilibrium of the mixture will be described by... 

Fundamentals of sorption and sorption kinetics by zeohtes are described and analyzed in the first Chapter which was written by D. M. Ruthven. It includes the treatment of the sorption equilibrium in microporous sohds as described by basic laws as well as the discussion of appropriate models such as the Ideal Langmuir Model for mono- and multi-component systems, the Dual-Site Langmuir Model, the Unilan and Toth Model, and the Simphfied Statistical Model. Similarly, the Gibbs Adsorption Isotherm, the Dubinin-Polanyi Theory, and the Ideal Adsorbed Solution Theory are discussed. With respect to sorption kinetics, the cases of self-diffusion and transport diffusion are discriminated, their relationship is analyzed and, in this context, the Maxwell-Stefan Model discussed. Finally, basic aspects of measurements of micropore diffusion both under equilibrium and non-equilibrium conditions are elucidated. The important role of micropore diffusion in separation and catalytic processes is illustrated. 

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