Individual adsorption isotherms from dilute solutions

3 Individual adsorption isotherms from dilute solutions 

Adsorption onto solids from dilute solutions is important in dyeing processes, detergent action and the purification of liquids by passing through adsorption columns. For a dilute solution, where solute (2) is dissolved in solvent (1), it is generally assumed that (xi = 1) and (x2 = 0) in Equation (720), so we can write 

For this derivation, n is not assumed to be zero, but only (n x2) is very small in magnitude. The n term can be related to the excess concentration of the solute on the solid-solution surface 

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The adsorption from binary solutions on sohd adsorbents in general and on activated carbons in particular is discussed in Chapter 3. The nature and types of adsorption and adsorption isotherms from dilute solutions and from completely miscible binary solutions are described. The composite isotherm equation is derived. The shapes and classification of composite isotherms and the influence of adsorbate-adsorbent interactions, the heterogeneity of the carbon surface, and the size and orientation of the adsorbed molecules on the shapes are examined. The thickness of the adsorbed layer and the determination of individual adsorption isotherms from a composite isotherm are also described. 

For type a curves the Intercept n° may be interpreted as n°, that is the real value of n° In a complete layer from which all 1 Is expelled (n = 0). This is the plateau value attained by the individual Isotherm of 2, Indicated by the dashed curve In fig. 2.23. When an assumption Is made about the molecular cross-section from n° the specific surface area can be obtained. In principle, this method Is not different from finding from, say the plateau In a Langmuir Isotherm, the only difference being that horizontal Langmuir plateaus (for adsorption from dilute solution) are replaced by linear upper parts, approaching zero at 1 (for excess adsorption from binary mixtures). 

Adsorption from solutions can be classified into adsorption of solutes that have a limited solubility (i.e., from dilute solutions) and adsorption of solutes that are completely miscible with the solvent in all proportions. In the former case, the adsorption of the solvent is of little consequence and is generally neglected. In the latter case, the adsorption of both components of the solution plays its part and has to be considered. The adsorption in such a systan is the resultant of the adsorption of both the components of the solution. The adsorption from such solutions is represented in the form of a composite isotherm, which is a combination of the isotherms for the individual components. 

Adsorption isotherms represent a relationship between the adsorbed amount at an interface and the equilibrium activity of an adsorbed particle (also the concentration of a dissolved substance or partial gas pressure) at a constant temperature. The analysis of adsorption isotherms can yield thermodynamic data for the given adsorption system. Theoretical adsorption isotherms derived from statistical and kinetic data, and using the described assumptions (see 3.1), are known only for the gas-solid interface or for dilute solutions of surfactants (Gibbs). Those for the system gas-solid are of a few basic types that can be thermodynamically predicted81. From temperature relations it is possible to calculate adsorption and activation energies or rate constants for individual isotherms. Since there are no theoretically founded equations of adsorption isotherms for dissolved surfactants on solids, the adsorption of gases on solides can be used as a starting point for an interpretation. 

There are certain conditions that must be fulfilled if Eqs. (2.2), (2.3) and (2.4) are to be used to calculate partition coefficients. The basic assumption is that the individual retention mechanisms are independent and additive. This will be true for conditions where the infinite dilution and zero surface coverage approximations apply or, alternatively, at a constant concentration with respect to the ratio of sample size to amount of liquid phase. The infinite dilution and zero surface coverage approximations will apply to small samples where the linearity of the various adsorption and partition isotherms is unperturbed and solute-solute interactions are negligible. The constancy of the solute retention volume with variation of the sample size for low sample amounts and the propagation of symmetrical peaks is a reasonable indication that the above conditions have been met. For asymmetric peaks, however, the constant concentration method must be employed if reliable gas-liquid partition coefficients are to be obtained [191]. It is difficult to state absolutely the conditions for which contributions to retention from the structured liquid phase layer can be neglected. This will occur for some minimum phase loading that depends on the support surface area, the liquid phase... 

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