Ideal adsorption solution theory

For multicomponent adsorption the most commonly used isotherm is the extended Langmuir isotherm (Eq. 18). Another, frequently used approach is the Ideal Adsorption Solution theory (IAS theory), which was developed by Prausnitz [53] and applied to mixtures of gases by, for example, Kaul [54] and Rees [52,55]. 

The basis of all models is the ideal adsorption solution theory (lAST) published by Myers and Prausnitz (Myers and Prausnitz 1965). The basic assumption is the equality of the chemical potential of the component / in the gas phase... 

Chapters 2 to 4 deal with pure component adsorption equilibria. Chapter 5 will deal with multicomponent adsorption equilibria. Like Chapter 2 for pure component systems, we start this chapter with the now classical theory of Langmuir for multicomponent systems. This extended Langmuir equation applies only to ideal solids, and therefore in general fails to describe experimental data. To account for this deficiency, the Ideal Adsorption Solution Theory (lAST) put forward by Myers and Prausnitz is one of the practical approaches, and is presented in some details in Chapter 5. Because of the reasonable success of the IAS, various versions have been proposed, such as the FastlAS theory and the Real Adsorption Solution Theory (RAST), the latter of which accounts for the non-ideality of the adsorbed phase. Application of the RAST is still very limited because of the uncertainty in the calculation of activity coefficients of the adsorbed phase. There are other factors such as the geometrical heterogeneity other than the adsorbed phase nonideality that cause the deviation of the IAS theory from experimental data. This is the area which requires more research. 

We have a total of 2N+1 equations in the ideal adsorption solution theory. Let us now apply this ideal adsorption solution theory to the usual case of adsorption equilibria, that is we specify the total pressure and the mole fractions in the gas phase and wish to determine the properties of the adsorbed phase which is in equilibrium with the gas phase. For such a case the number of unknowns that we wish to obtain is given in the following table ... 

The total number of unknown variables is 2N+1, which is the same as the number of equations given by the ideal adsorption solution theory thus the problem is properly posed. Once the total adsorbed amount is determined, the adsorbed phase concentration of the component i is ... 

For multicomponent systems obeying the ideal adsorption solution theory, the spreading pressure of the adsorbed mixture is n. The partial pressure of the species i in the gas phase is related to the hypothetical pure component pressure which gives the same spreading pressure n as that of the mixture according to the Raoult s law analogy ... 

The ideal adsorption solution theory presented in previous sections provides a useful means to determine the multicomponent adsorption equilibria. The procedure is simple and the method of calculation is also straight forward. The method, unfortunately, only works well when the adsorption systems do not behave too far from ideality. For example, adsorption of the same paraffin hydrocarbon gases on activated carbon can be described well by the IAS theory. However for systems... 

It is worthwhile to compare the predictions of the potential adsorption theory with those of the ideal adsorption solution theory, the lAST, described in Section IVA. Both theories use the same number of fitted parameters. Analysis of experimental data considered on the basis of the lAST has been performed in the original article [81]. The authors found a large discrepancy between lAST estimates and experimental data. The experimental activity coefficients of different components in binary adsorbates vary Ifom 0.412 to 1.054, whereas the LAST assumes their values to be unity. In order to improve the correlations, the Costa et al. [81] had to go from lAST to real adsorption solution theory, using the Wilson equation with additional binary interaction parameters for the adsorbate. This significantly increased the number of fitted parameters and decreased the predictivity of the correlation. 

The ideal adsorption solution theory described in Section IVA is the simplest approach to multicomponent adsorption from the point of view of the general thermodynamic theory of the surface phase. The lAST is comparable with potential adsorption theory by predictability. Both theories need the correlation of experimental data for pure components in order to estimate adsorption of mixtures. However, in general, the predictions of the two theories are different, as illustrated in Section IVD. Let us analyze assumptions on which the two theories may become similar. 

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