Sorption rate parameter, equation

Practically any experimental kinetic curve can be reproduced using a model with a few parallel (competitive) or consecutive surface reactions or a more complicated network of chemical reactions (Fig. 4.70) with properly fitted forward and backward rate constants. For example, Hachiya et al. used a model with two parallel reactions when they were unable to reproduce their experimental curves using a model with one reaction. In view of the discussed above results, such models are likely to represent the actual sorption mechanism on time scale of a fraction of one second (with exception of some adsorbates, e.g, Cr that exchange their ligands very slowly). Nevertheless, models based on kinetic equations of chemical reactions were also used to model slow processes. For example, the kinetic model proposed by Araacher et al. [768] for sorption of multivalent cations and anions by soils involves several types of surface sites, which differ in rate constants of forward and backward reaction. These hypothetical reactions are consecutive or concurrent, some reactions are also irreversible. Model parameters were calculated for two and three... 

In a study achieved by Memon et al. [16] the sorption of carbofuran and methyl parathion on treated and untreated chestnut shells has been studied using high performance liquid chromatography. In this study, the maximum sorption of methyl parathion and carbofuran onto chestnut shells was achieved at a concentration of 0.38.10 and 0.45.10" mol.dm respectively. Adsorption isotherms depicted a better fitting with the Langmuir isotherm. The results of sorption energy obtained from the Dubinin-Radushkevich isotherm pointed out that adsorption was driven by physical interactions. The kinetics of sorption follows a first-order rate equation. The thermodynamic parameters AS and AG indicate that the sorption process is thermodynamically favourable, and spontaneous, whereas the value of AH shows the exothermic nature of sorption process for methyl parathion and endothermic nature of carbofuran. The developed sorption method has been employed in methyl parathion and carbofuran in real surface and ground water samples. The sorbed amount of methyl parathion and carbofuran may be removed by methanol to the extent of 97-99% from the surface of chestnut shells. 

Figure 6. Pressure dependence of diffusion coefficients calcuiated from permeation ( -), sorption ((,)) and desorption (A) rate curves for CO2 in PI2080. 9 is average vaiue of diffusion coefficients from sorption and desorption rate curves at same pressure. The soiid iine is caicuiated from Equation 14 using parameters 0 in Tabie 1. The dotted line is calculated from Equation 15 using parameters in Table 1.

The multisite approach was previously described by Sjovall et al. [27] and investigated by Skarlis et al. [22]. The proposed model describes the storage of NH3 on a Cu-zeolite by including four different surface sites (i) a metal site where a single molecule of NH3 can be stored, (ii) a second metal site where up to three molecules of NH3 can be adsorbed, (iii) an acid site, and (iv) a site for physi-sorption. The mathematical expressions for the adsorption/desorption reaction rates of each site is the same as the single-site approach which was previously discussed (Eqs. 13.21—13.23). The parameters of the above-mentioned set of equations need to be estimated for each of the four surface sites. 

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