Adsorption isosteres

This equation, which represents an adsorption isostere—the relation between p and T for a given amount adsorbed—can be plotted from the isotherms for a series of temperatures. The value of tf is then immediately calculable from the slope of the isosteric plot. 

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

On the basis of experimental data for Ir, Rh and their alloys, the adsorption isotherms at different temperatures have been plotted (Figure 5a). The adsorption isosteres are obtained by the intersection of the adsorption isotherms at a specified... 

Another thermodynamic quantity, the isosteric heat of adsorption, can be calculated from the temperature dependence of the adsorption isotherm by obtaining the slope of the adsorption isostere and is defined by... 

The relationship between P and T for a constant adsorption amount M is called an adsorption isostere, which is used for calculating the isosteric heat of adsorption from the isotherm curves at various temperatures. 

Although the heat of adsorption or enthalpy change accompanying adsorption is directly obtained by calorimetry, it can conveniently be evaluated from the adsorption isostere. According to thermodynamics, the relationship between temperature T and pressure P under a state of -(J> phase equilibrium can generally be expressed with the Clausius-Clapeyron equation ... 

The heat of adsorption Qjso at each adsorption level is obtained from the temperature gradient of the pressure in the adsorption isostere. The heat of adsorption Qjso obtained thus is called the isosteric heat of adsorption. 

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. 

Furthermore, on polystyrene it was found that the adsorption of HPA in the low surface coverage region increased with increasing temperature, except at the isoelectric point (i.e.p.) of the protein where the adsorption appeared to be independent of the temperature. According to Clapeyron s law a positive value for (6r/6T) implies an endothermic adsorption process under isosteric conditions. Although with protein adsorption isosteric conditions are difficult to establish, the qualitative conclusion is that at pHf i.e.p. the adsorption enthalpy is positive. Hence, under those conditions, adsorption must be entropically driven. We will return to this subject in section 5. 

The adsorption isosteres for ethylbenzene (see Figure 18), adsorbed from a benzene/ethylbenzene mixture into H-ZSM-5, provided isosteric heats of... 

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) ... 

Fig. 1-34. Adsorption isobars (a) and adsorption isosteres (b) for water on a Baylith T144 molecular sieve (Na-form, 3 10 m) [4.23].

Adsorption Isobars The mole ratio of the adsorbate in the adsorbent Xi is plotted against the temperature at a constant partial pressure of the adsorbate Pi Adsorption Isosteres The temperature is plotted against the partial pressure of the adsorbate p,-. The parameter is the mole ratio Xi of the adsorbed substance in the adsorbent. (A logarithmic plot of the variables may be more useful)... 

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. 

Akhrimenko has studied the kinetics of adsorption of iodine from aqueous 0.1 m-KI solutions on single carbon grains, and found that the adsorption rate was greatly affected by the pore dimensions of the charcoal. Kinetic adsorption isosteres and isosteric enthalpies of adsorption were determined. 

Both methods provide very reliable and comparable results, which can be fitted by a Langmuir adsorption isostere [19]. The CO2 method has the advantage that no reference CV needs to be recorded. Nevertheless, in practice not every laboratory is equipped with the required CO2 detector and the method using the reference CV may be more generally applicable. 

The relation between concentration and temperature yielding a given amount adsorbed, q, is called the adsorption isostere (Fig. 3 2),... 

The basics of adsorption phenomena require definitions. In experimental adsorption systems, the gas or vapor of a gas phase, or the solute in a solution, is called the adsorptive (when not in the adsorbed state). It is called the adsorbate when existing as an adsorbed phase within a solid, and the solid is referred to as the adsorbent. Note The terms absorb and absorption refer to such processes as the absorption of light or of X-ray radiation internally by the entire material, where internal surfaces may not exist.) The variations of extents of adsorption n in mmol g ) with relative pressure iplp ) of the adsorptive at constant temperature, when plotted, make up the adsorption isotherm (Figure 4.1(a)). The variation of extents of adsorption (n in mmol g ) with temperature of adsorption Tin K), at constant relative pressure, is the adsorption isobar (Figure 4.1(b)). The variation of the relative pressure of the adsorptive (p/p ), with adsorption temperature (T in K), to maintain a constant amount of adsorbate adsorbed on the adsorbent (n in mmolg ) is the adsorption isostere (Figure 4.1(c)). 

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