Desorption equilibrium curve

Determination of the number of theoretical stages for desorption using countercurrent solvent flow stripping, by means of a stripping gas is analogous. In this case, the fact that Xg is the entry concentration and Xg the exit concentration of the solvent to the stripper must be considered. According to the operating conditions, the course of the desorption equilibrium curve is different from that for the absorption equilibrium curve. The balance line is now below the equilibrium curve and so the reciprocal value of the absorption coefficient is required. 

FIGURE 11.11. Adiabatic desorption equilibrium curves for (a) 4A sieve and (6) silica gel. Curves arc calculated for a uniformly saturated bed at 25 C at the indicated humidity, assuming bone-dry purge gas at the specified temperature. The 25 isotherm is shown as---------, representa-... 

This behavior can be explained if we resort to the imaginary desorption PCT curve at 275°C in Fig. 1.33. The equilibrium plateau pressure at 275°C is higher than 0.1 MPa at which desorption is carried out and at this temperature MgH2 can desorb at atmospheric pressure. However, the kinetics of desorption will depend on the driving force (as shown in Fig. 1.26). Since a larger mass of hydride will produce... 

Fig. 1. (a) A chemical structure of a 2.5th generation carboxylic acid-terminated poly(amido amine) (PAMAM) dendrimer. (b) Transmission surface enhanced infrared absorption spectra (SEIRAS) of dendrimer adlayers prepared at 30 min adsorption from aqueous solutions (0.01 wt.%) of a dendrimer at different pHs. Numerical values are pHs of the solutions, (c) Adsorption-desorption profiles as a function of time at different pHs and adlayer thicknesses at adsorption and desorption equilibrium as a function of pH for aqueous solutions (0.1 wt.%) of the dendrimer. The symbols, j and J, in the top figure denote start of adsorption and desorption, respectively. In the bottom figure, filled circle and opened square denote adlayer thicknesses at adsorption and desorption equilibrium, respectively. The dark tie denotes the calculated dendrimer size width. A solid curve is drawn to be visual, (d) Schematic illustration of dendrimers adsorbed at different pHs. Reprinted with permission from Ref. [69], 2006, American Scientific Publishers. 

A representation of the various concentrations and driving forces in a y—x diagram is shown in Figure 4. The point representing the interfacial concentrations 0, x must he on the equilibrium curve since these concentrations are at equilibrium. The point representing the bulk concentrations (yA,. A) may be anywhere above the equQibrium line for absorption or below it for desorption. The slope of the tie line connecting the two points is given by equations 4 and 5 ... 

Fig. 5. II — A curve of bovine serum albumin on distilled water at 20°C. Curve on left is equilibrium curve, assuming no desorption. Curve on right is dynamic curve, which would be obtained if no expulsion of segments from interface occurred. From MacRitchie (1977a), reproduced with permission.

The reverse of gas absorption is called desorption or stripping, an operation cafried out to recover valuable solute from the absorbing solution and regenerate the solution. The operating line must then lie below the equilibrium line, as in Fig. 17.5c. Usually the temperature or pressure is changed to make the equilibrium curve much steeper than for the absorption process. 

Special care is exercised in the determination of adsorption-desorption hysteresis curves since significant differences in structure are thus established. Time intervals varying from ten minutes to two hours are required for equilibrium, depending on the portion of the isotherm concerned and the amount adsorbed. After apparent equilibrium is reached the system is allowed to stand for an appropriate period to confirm the... 

The conducted experiments showed that isotherms of adsorption and desorption do not always coincide. The difference between adsorption and desorption isotherm curves is called adsorption-desorption hysteresis. It turned out that the desorption rates, as a rule, are lower than adsorption rates. Moreover, it was established that the adsorption and desorption processes often have the rates too low for equilibrium to be reached during experiment. 

Similar to adsorption a hysteresis of the equilibrium curve may also occur in drying. In drying processes, the desorptive equilibrium is relevant. 

Figure 2b. Sorption equilibrium diagram showing desorption scanning curves.

Thus, the only change that has occurred in passing from adsorption to desorption is the replacement of the slope of the operating line AX/AY by the slope of the equilibrium curve at the origin, i.e., the Henry constant. Let us now apply these two expressions to an environmental problem of inferest. 

We start by noting that in the general case of a nonlinear equilibrium relation, the adsorption and desorption periods will always differ because of the different vines of Aq/AY and H (Eigure 7.22). Because the latter quantity is invariably the greater of the two, we conclude that for nonlinear isotherms the adsorption step will proceed at a faster pace than the corresponding desorption step. This difference becomes more pronounced, the steeper the equilibrium curve at the origin. 

The use of Eq. (11.4) assumes that the amount of liquid mechanically retained with the solid (but not adsorbed) after filtration or settling is negligible. This is quite satisfactory for most adsorption, since the quantity of solid employed is ordinarily very small with respect to that of the liquid treated. If the operation under consideration is desorption and if again the quantity of liquid retained mechanically by the solid is negligible, Eq. (11.4) applies, but the operating line lies below the equilibrium curve on Fig. 11.16. In this case, however, it is much more likely that the quantity of liquid retained mechanically with the solid will be an appreciable portion of the total liquid used, and the methods of calculation described in Chap. 13 for leaching should be used. 

The first desorption and second absorption curves are reported as equilibrium curves, meaning that one could go up and down on them, finding the same values. The offset of the second adsorption curve from the first is explained by the authors as an irreversible type of hysteresis possibly due to imperfect rigidity in the gel strucmre. ... 

A somewhat subtle point of difficulty is the following. Adsorption isotherms are quite often entirely reversible in that adsorption and desorption curves are identical. On the other hand, the solid will not generally be an equilibrium crystal and, in fact, will often have quite a heterogeneous surface. The quantities ys and ysv are therefore not very well defined as separate quantities. It seems preferable to regard t, which is well defined in the case of reversible adsorption, as simply the change in interfacial free energy and to leave its further identification to treatments accepted as modelistic. 

Irreversible adsorption discussed in Section XI-3 poses a paradox. Consider, for example, curve 1 of Fig. XI-8, and for a particular system let the equilibrium concentration be 0.025 g/lOO cm, corresponding to a coverage, 6 of about 0.5. If the adsorption is irreversible, no desorption would occur on a small dilution on the other hand, more adsorption would occur if the concentration were increased. If adsorption is possible but not desorption, why does the adsorption stop at 6 = 0.5 instead of continuing up to 0 = 1 Comment on this paradox and on possible explanations. 

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

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