Equilibrium adsorption diagram

The present paper deals with the threedimensional diagram for description of the equilibrium adsorption of O2/N2 mixtures on clinoptilolite. This diagram shows the dependence of the amount adsorbed on the total pressure, as well as the equilibrium concentration of the gas mixtures. Adsorption from binary mixtures involves theoretical and experimental problems. Ruthven s and Loughlin s works (7,8) provide much detail and they succeed in describing fully enough the complicated systems, but all at the expense of considerable characteristic constants used and elaborate computation. The experimental... 

Operating diagram for single-stage equilibrium adsorption. 

This line is shown in Figure 8.1.44(b) along with the equilibrium adsorption curve ufagainst Wis the column end compositions are also identified. Such a diagram may be utilized to determine the minimum adsorbent to gas flow rate ratio, (u/ /u/ ,"), when the operating line and the... 

The classical approach for discussing adsorption states was through Lennard-Jones potential energy diagrams and for their desorption through the application of transition state theory. The essential assumption of this is that the reactants follow a potential energy surface where the products are separated from the reactants by a transition state. The concentration of the activated complex associated with the transition state is assumed to be in equilibrium... 

A graph of the proportion 9 against the (equilibrium) concentration of adsorbate is also called an isotherm. (This dual usage of the word can cause some confusion.) A typical adsorption isotherm is shown in the schematic diagram in Figure 10.2, and shows how the proportion 9 of occupied sites increases quite fast initially as the concentration [capsaicin] increases. Above a certain concentration of adsorbate, however, the amount of capsaicin adsorbed does not increase but remains constant. In this example, the maximum value of 9 is about unity. In other words, all the possible adsorption sites are bonded to a molecule of capsaicin - but only if the concentration of the capsaicin is huge. 

Individuals of multicomponent mixtures compete for the limited space on the adsorbent. Equilibrium curves of binary mixtures, when plotted as x vs. y diagrams, resemble those of vapor-liquid mixtures, either for gases (Fig. 15.5) or liquids (Fig. 15.6). The shapes of adsorption curves of binary mixtures, Figure 15.7, are varied the total adsorptions of the components of the pairs of Figure 15.7 would be more nearly constant over the whole range of compositions in terms of liquid volume fractions rather than the mol fractions shown. 

Figure 5. Adsorption of hafnium on 0.20 grams of glass beads after 20 hours (O) and 71 hours (%) as a function of the equilibrium solution concentration. The corresponding pH values are given in the diagram...

The presence of mixed surfactant adsorption seems to be a factor in obtaining films with very viscous surfaces [411]. For example, in some cases the addition of a small amount of non-ionic surfactant to a solution of anionic surfactant can enhance foam stability due to the formation of a viscous surface layer, which is possibly a liquid crystalline surface phase in equilibrium with a bulk isotropic solution phase [25,110], In general, some very stable foams can be formed from systems in which a liquid crystal phase is present at lamella surfaces and in equilibrium with an isotropic interior liquid. If only the liquid crystal phase is present, stable foams are not produced. In this connection foam phase diagrams may be used to delineate compositions that will produce stable foams [25,110],... 

FIGURE 6 (a) Equilibrium isotherms and (b) dimensionless equilibrium diagram showing distinction between favorable, unfavorable, and linear systems. (Reprinted with permission from Ruthven, D. M. (1984). Principles of Adsorption and Adsorption Processes, copyright John Wiley Sons, New York.)... 

For multicomponent systems, the expression for y here employed may be shown equivalent to that involved in the cluster diagram technique (6), which is currently being employed in a variety of problems. The present derivation shows that the starting expressions satisfy the thermodynamic consistency relation embodied by the adsorption isotherm. It is, however, important to observe that any direct application of these alternative rigorous approaches, which is of necessity of an approximate nature, leads to some violation of the complete internal equilibrium conditions. Similarly, calculations of surface tension which employ the adsorption equation as a starting point invariably violate mechanical equilibrium in some order of approximation. 

In case of binaiy systems, co-adsorption was performed using three different initial mixtures - being equimolar (Z/ = Zz = O.S) and rich in component 1 and 2 (respectively Z/ = 0.85 and Z = 0.15) - whose molar ratio were formerly checked. The selectivity of adsorbent rn/2) was either directly represented in an X-Y isobaric equilibrium diagram, or determined using the following equation, where Xi and K are die adsorbed and gas phase molar fraction of f component, and plotted versus total amount adsorbed Qtad-... 

The GC route is particularly attractive for it requires no a priori information on the polymer. With the exception of X-ray measurements, most methods of measurement involve a comparison of some property of the polymer, such as density, with that of the totally amorphous or crystalline material. Furthermore neither the mass of polymer in the column nor the flow rate of carrier gas need to be measured since a ratio of retention volumes is computed in Eq. (21). It should be added, however, ttiat for the successful application of the method it is essential that the measured retention volumes correspond effectively to equilibrium bulk sorption, both above and below. Low molecular weight compounds are known to exhibit apparently similar discontinuities in retention diagrams at their melting points but this is to be ascribed to a change in retention mechanism, from surface adsorption for the solid to bulk sorption for the liquid stationary phase. For a detailed discussion of retention characteristics of low molecular weight substances near their transition temperatures the reader is referred to a recent review by McCrea (8J). 

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