Adsorption equilibrium isobar

The reader will find adsorption equilibrium relationships presented in any of three typical forms. The form of equilibrium most frequently presented is the isotherm, the partial pressure as a function of the loading at a given constant sorbent temperature. An isobar implies a chart of the loading as a function of the temperature while the partial pressure of the sorbate is held constant. 

The adsorption equilibrium is characterized by the concentration of the adsorbate in the gas phase and the corresponding equilibrium load of adsorbate adsorbed by the solid. Adsorption equilibrium may be represented by three graphical methods adsorption isotherms, adsorption isobars and adsorption isosteres (Figs. 1-33 and 1-34) ... 

FIGURE 113. Equilibrium isobars (a) and isosteres (b) showing temperature and pressure dependence of equilibrium adsorption capacity for water on 4A sieve. (Courtesy of W. R, Grace/... 

Fig. 7.5 The three representations of adsorption equilibrium of gas on solid at constant temperature (isotherm), constant pressure (isobar) and constant adsorbed amount (isoster)...

Figure 17.4. Equilibrium data for the adsorption of ammonia on charcoal1 10) (a) Adsorption isotherm (b) Adsorption isobar (c) Adsorption isostere...

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 threedimensional diagram for N2 and O2, for various mixtures, is shown on Figure 3. Cuts at constant total pressure give isobars, an example of which is given in Figure 4, and represents ability of adsorption of each sorbate at different equilibrium con-... 

The Chreedimensional diagram obtained could serve both theoretical and technological computations concerning oxygen enrichment of air on K-clinoptilolite. It is a basis for determining of adsorption isobars, fictitious and real isotherms, as well as thermodynamic data for adsorption from binary C /Nj mixtures. Freundlich and Henry constants (for the real adsorption isotherms) correlated with the equilibrium concentration are useful for computation of the amounts adsorbed at arbitrary partial pressures and equilibrium concentrations. 

Adsorption Isotherm The mathematical or experimental relationship between the equilibrium quantity of a material adsorbed and the composition of the bulk phase at constant temperature. The adsorption isobar is the analogous relationship for constant pressure, and the adsorption isostere is the analogous relationship for constant volume. See also Bru-nauer-Emmett-Teller Isotherm, Langmuir Isotherm. 

The adsorption of oxygen on unpromoted manganese ore and catalyst No. 55 (silver-promoted) was studied over the temperature range —18 to -f-140 C. Isobars for an oxygen pressure of 610 mm. are shown in Fig. 1 and resemble those frequently reported for the case of van der Waals adsorption at low temperatures, followed by activated adsorption at higher temperatures, except for the sharp rise near 80°C. with the promoted catalyst and near 100 C. with the unpromoted catalyst. If the isobars above these temperatures actually represent equilibrium values, it is difficult to agree with Roiter et al. when they ascribe this phenomenon... 

In the case of multilayer formation, it is useful to express the coverage degree by 6 = V/Vm where denotes the volume of the adsorbed substance in a monolayer. Adsorption and desorption can be described as well as the kinetic and equilibrium process. Equilibrium is described by the general condition /( , p, T) = 0. The process is described either at a constant pressure (adsorption isobar) or constant temperature (adsorption isotherm). The most simple adsorption isotherm after Freundlich and Langmuir is based on the equilibrium... 

An adsorption isotherm is the relationship at constant temperature between the partial pressure of the adsorbate and the amount adsorbed at equilibrium. Similarly an adsorption isobar expresses the functional relationship between the amount adsorbed and the temperature at constant pressure, and an adsorption isostere relates the equilibrium pressure of the gaseous adsorbate to the temperature of the system for a constant amount of adsorbed phase. Usually it is easiest from an experimental viewpoint to determine isotherms. The coordinates of pressure at the different temperatures for a fixed amount adsorbed can then be interpolated to construct a set of isosteres, and similarly to obtain an isobaric series. 

In practice, the experimental adsorption data are usually represented in the form of adsorption isotherms because investigation of the adsorption process at constant temperature is most convenient. Furthermore, the theoretical analysis of adsorption data for certain assumed models usually arrives at adsorption isotherms and not isobars or isosteres. The adsorption bar is determined less frequently, and the direct measurement of an isostere is rare. Adsorption isobars are sometimes useful in ascertaining the adsorption mechanism in a particular system and to determine whether more than one type of adsorption is involved. Adsorption isosteres, on the other hand, are often used for calculating heats of adsorption from adsorption measurements at two or more temperatures, using the Clasius-Clapeyron equation. In an adsorption isotherm, it is usual to express the amount adsorbed in millimoles, or milliliters, of the gas or vapor at NTP per gram of the adsorbent. Because the three types of equilibria (i.e., the isotherm, the isobar, and the isostere) are equilibrium functions, it is possible to obtain one relationship from the another. For example, from adsorption isotherms for a given system at several temperatures, the isobars and isosteres can be obtained. Similarly, isotherm can be obtained from isobars and isosteres. 

Adsorption capacity. Adsorption capacity is defined as gaseous quantity adsorbed by unit weight of catalyst, and is often recorded as Vstp- It can determine the relationship between adsorption capacity and pressure (Isotherms) at fixed temperature or fixed pressure (Isobar), but usually isotherms are used, that is, the equilibrium relation between pressure and the adsorption capacity (isothermal equation). 

When both components of a binary gas or vapor mixture are separately adsorbed to roughly the same extent, the amount of either one adsorbed from the mixture will be affected by the presence of the other. Since such systems are composed of three components when the adsorbent is included, the equilibrium data are conveniently shown in the maimer used for ternary liquid equilibria in Chap. 10. For this purpose it is convenient to consider the solid adsorbent as being analogous to liquid solvent in extraction operations. However, adsorption is greatly influenced by both temperature and pressure, unlike liquid solubility, which is scarcely affected by pressure under ordinary circumstances. Equilibrium diagrams are consequently best plotted at constant temperature and constant total pressure, and they are therefore simultaneously isotherms and isobars. 

As an example of the influence of the adsorption temperature, the equilibrium data for water (H2O) adsorbed at T = 303, 353 and 423 K on a H-BEA zeolite specimen (outgassed at T = 873 K) are illustrated in Fig. 1.6. In Fig. 1.6a the three volumetric isotherms are reported (for experimental and samples details vide infra Sect. 1.4) as far as the equilibrium pressure Phio increases, the adsorbed amounts also increase more or less steeply according to the adsorption temperature. In Fig. 1.6b the amounts adsorbed at a constant equilibrium pressure (pnio = 6 Torr) are plotted against the adsorption temperature giving rise to an adsorption isobar (nods vs. Tads)- Note that... 

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