Application of Ideal Adsorbed-Solution Theory

Example 5 Application of Ideal Adsorbed-Solution Theory 

Consider a binary adsorbed mixture for which each pure component obeys the Langmuir equation, Eq. (16-13). Let n = 4 mol/kg, n2 = 3 mol/kg, Kipi = K2p2 = 1- Use the ideal adsorbed-solution theory to determine nx and n2. Substituting the pure component Langmuir isotherm 

Other approaches to account for various effects have been developed. Negative deviations from Raoult s law (i.e., y, 1) are frequently found due to adsorbent heterogeneity [e.g., Myers, AIChE J., 29, 691 

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Example 5 Application of Ideal Adsorbed-Solution Theory. 16-16... 

Predictions of adsorption equilibria by ideal-adsorbed-solution theory are usually satisfactory when the specific amount adsorbed is less than a third of the saturation value for mono-layer coverage. At higher adsorbed amounts, appreciable negative deviations from ideality are promoted by differences in size of the adsorbate molecules and by adsorbent heterogeneity. One must then have recourse to Eq. (14.123). The difficulty is in obtaining valnes of the activity coefficients, which are strong functions of both spreading pressnre and temperatnre. This is in contrast to activity coefficients for liquid phases, which for most applications are insensitive to pressure. This topic is treated by Talu et ai. ... 

Unfortunately, the available experimental results suggest that the column saturation capacity is often not the same for the components of a binary mixture, so Eq. 4.5 does not account accurately for the competitive adsorption behavior of these components [48]. A simple approach was proposed to turn the difficulty (next subsection). Although it is applicable in some cases, more sophisticated models seem necessary. Numerous isotherm models have been suggested to solve this problem. Those resulting from the ideal adsorbed solution (IAS) theory developed by Myers and Prausnitz [49] are among the most accurate and versatile of them. Later, this theory was refined to accormt for the dependence of the activity coefficients of solutes in solution on their concentrations, leading to the real adsorption solution (RAS) theory. In most cases, however, the equations resulting from IAS and the RAS theories must be solved iteratively, which makes it inconvenient to incorporate those equations into the numerical calculations of column dynamics and in the prediction of elution band profiles. 

There are several methods available that allow the prediction of mixture isotherms based on general single-component information. An application can significantly reduce the necessary number of experiments. The most successful approach is the ideal adsorbed solution (IAS) theory initially developed by Myers and Prausnitz (1965) to describe competitive gas phase adsorption. This theory was subsequently extended by Radke and Prausnitz (1972) to quantify adsorption from dilute (i.e., also ideal) solutions. 

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. 

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