Irreversible isotherm sorption kinetics

In recent years the Coal Research Laboratory has been investigating the kinetics and isotherm behavior of methanol sorption on coal (6, 7, 10) along with the sorption of other vapors on coal (6) and of polar vapors on swelling gels (9, 10). Methanol sorption was shown to be reversible on coal, and its sorption behavior supports the model of coal as a gel or mixture of gels in its physical structure. All indications (I, 6, 7) are that its interaction is with specific and a fixed number of sites for a particular coal sample. Although the sorption of methanol is reversible, coal exhibits sorption behavior which is interpreted in terms of an irreversible swelling of the coal gel upon initial exposure to methanol vapor. As a result of these studies, an isotherm and experimental rate equation for the sorption and desorption were derived that fit the observed data. The isotherm derived for methanol sorption on coal was ... 

For reversible interactions, the linear dynamic range is determined by that portion of the coating-analyte sorption isotherm (discussed in Section 5.4) that lies between the LOD and the saturation limit. For irreversible interactions, the LDR will depend on the sorption/reaction kinetics and the coating capacity. For practical reasons, it is desirable to have the widest LDR possible, although inexpensive microprocessors and associated memory make correction for minor nonlinearities straightforward. For an example of a wide linear dynamic range, refer to Figure 5.13. 

Figure 5. Schematic representation and equations defining the 2-box (top) and 3-box (bottom) kinetic models. X = dissolved metal Y, Yi and Y2 = reversibly sorbed metal on Freundlich sorption sites f = fraction of Freundlich sorption sites reaching equilibrium instantaneously K and n are the Freundlich-isotherm constants r and k are the reversible and irreversible rate constant, respectively Z = irreversibly sorbed metal. The subscript 0 in the mass balance equations denotes concentrations at time zero, and Cp = particle concentration. (Adapted from ref. 15)...

Should be pointed out to relatively high values of the sorption of n-CgFj g on Styrosorbs at low P/Pq values and irreversibility of the isotherms in the initial region. The latter may be attributed both to slight swelling of polymers in this sorbate and to retarded kinetics of the sorption of n CgFj g in the micropores present in these seunples. 

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