Liquid adsorption equilibrium

As also noted in the preceding chapter, it is customary to divide adsorption into two broad classes, namely, physical adsorption and chemisorption. Physical adsorption equilibrium is very rapid in attainment (except when limited by mass transport rates in the gas phase or within a porous adsorbent) and is reversible, the adsorbate being removable without change by lowering the pressure (there may be hysteresis in the case of a porous solid). It is supposed that this type of adsorption occurs as a result of the same type of relatively nonspecific intermolecular forces that are responsible for the condensation of a vapor to a liquid, and in physical adsorption the heat of adsorption should be in the range of heats of condensation. Physical adsorption is usually important only for gases below their critical temperature, that is, for vapors. 

As stated earlier, the retardation term owing to the product adsorption or the constant K in the Langmuir-type equation, v = k/(l + /<[P]) (Equation 13.4), where P is the condensable product), is related to its adsorption equilibrium driven by the concentration term in solutions. Under boiling conditions, the reaction products are desorbed not only to the solution bulk but also into the bubble formed at the catalyst surface. Because the molecular translational entropy is far larger in the gas phase than in the liquid phase, the... 

At the beginning stage of dehydrogenation, the substrate organic hydride is adsorbed onto the catalyst surface from the liquid phase directly and easily. Catalytic reaction processes will succeed it, until the surface sites are filled with the adsorbed reactant and products. Once product desorption starts to form and grow a bubble, product readsorption becomes unfavorable due to the increment of translational entropy of the product molecule in the bubble, if compared with that in the solution, shifting the adsorption equilibrium for the product and suppressing its effect of rate retardation. 

Adsorption Equilibrium Numerous purification and recovery processes for gases and liquids Activated carbon-based applications Desiccation using silica gels, aluminas, and zeolites Oxygen from air by PSA using LiX and 5A zeolites... 

The assessment of reaction kinetics by means of batch tests may be strongly affected by dye adsorption on the biophase and supports. The relevance of the adsorption phenomena of dyes on biophase has been addressed in studies regarding free cells [41], granular support biofilm [24], entrapped cells [11, 18], anaerobic sludge [10,24,31,34] and biological activated carbon (BAC) [42,45,47,48]. They have pointed out that the kinetics may be overestimated if the assessment of the adsorption contribution to the dye removal is not taken into account. Under batch conditions, the dye is fastly split between the liquid phase and the biophase, resulting in a sharp reduction of the dye concentration in the liquid phase until adsorption equilibrium is approached. The rate of dye adsorption must be estimated and ruled out in the kinetic assessment. 

The equilibrium adsorption characteristics of gas or vapor on a solid resemble in many ways the equilibrium solubility of a gas in a liquid. Adsorption equilibrium data are usually portrayed by isotherms lines of constant temperature on a plot of adsorbate equilibrium partial pressure versus adsorbent loading in mass of adsorbate per mass of adsorbent. Isotherms take many shapes, including concave upward and downward, and S-curves. Equilibrium data for a given adsorbate-adsorbent system cannot generally be extrapolated to other systems with any degree of accuracy. 

Adsorption from liquids is less well understood than adsorption from gases. In principle the equations derived for gases ought to be applicable to liquid systems, except when capillary condensation is occurring. In practice, some offer an empirical fit of the equilibrium data. One of the most popular adsorption isotherm equations used for liquids was proposed by Freundlich 21-1 in 1926. Arising from a study of the adsorption of organic compounds from aqueous solutions on to charcoal, it was shown that the data could be correlated by an equation of the form ... 

The relevance of LSC data to reverse osmosis stems from the physicochemical basis (adsorption equilibrium considerations) of liquid-solid chromatography (52), and the principle that the solute-solvent-membrane material (column material) Interactions governing the relative retention times of solutes in LSC are analogous to the interactions prevailing at the membrane-solution Interface under reverse osmosis conditions. The work already reported in several papers on the subject (53-58) indicate that the foregoing principle is valid, and hence LSC data offer an appropriate means of characterizing interfacial properties of membrane materials, and understanding solute separations in reverse osmosis. 

Adsorption experiments are conducted at constant temperature, and an empirical or theoretical representation of the amount adsorbed as a function of the equilibrium gas pressure is called an adsorption isotherm. Adsorption isotherms are studied for a variety of reasons, some of which focus on the adsorbate while others are more concerned with the solid adsorbent. In Chapter 7 we saw that adsorbed molecules can be described as existing in an assortment of two-dimensional states. Although the discussion in that chapter was concerned with adsorption at liquid surfaces, there is no reason to doubt that similar two-dimensional states describe adsorption at solid surfaces also. Adsorption also provides some information about solid surfaces. The total area accessible to adsorption for a unit mass of solid —the specific area Asp — is the most widely encountered result determined from adsorption studies. The energy of adsorbate-adsorbent interaction is also of considerable interest, as we see below. 

Here the state with [ZA] = [Z] is taken as a standard state of the adsorbed layer thus, in the case when only one gas is adsorbed, the layer is in the standard state at the coverage 1 /2. It can be easily seen that 1 /a is the equilibrium pressure at [ZA] = [Z], i.e., at the standard state of the adsorbed substance. This value may be called desorption pressure we shall denote it as b. It is analogous to vapor pressure or dissociation pressure in monovariant systems (24). Indeed, in the case of equilibrium of liquid with its vapor, the surface from which evaporation occurs is equal to the surface for condensation the same equality is realized at the adsorption equilibrium if the fraction of the occupied surface is equal to that of the free surface. This analogy explains the applicability of the Nernst approximate formula to desorption pressure (24) ... 

Adsorption equilibria for the systems phenol-p-toluene sulfonate, phenol-p-bromophenol and phenol-dodecyl benzene sulfonate are shown in Figures 5, 6 and 7. In these figures, the ratio of the observed equilibrium values and computed values from equation (14) are plotted against the equilibrium liquid phase concentration of the solute in the mixture. It is seen that most of the data points are well within a deviation of 20%. The results for these diverse solute systems indicate that equation (14) is suitable for correlating binary equilibrium data for use in multicomponent rate models. 

This approach is based on the similarity between a TCC and a SMB unit, such that the flow rates in a TCC can be converted easily to the equivalent ones in a SMB unit. In the frame of equilibrium theory - that is, a model assuming one-dimensional flow - adsorption equilibrium between solid and liquid phase and neglecting axial dispersion, the following mass balances are obtained for each component i in every section j of a TCC unit ... 

At this point, it is feasible to correlate the liquid-phase adsorption equilibrium single component data, with the help of isotherm equations developed for gas-phase adsorption, since, in principle, it is feasible to extend these isotherms to liquid-phase adsorption by the simple replacement of adsorbate pressure by concentration [92], These equations are the Langmuir, Freundlich, Sips, Toth, and Dubinin-Radushkevich equations [91-93], Nevertheless, the Langmuir and Freudlich equations are the most extensively applied to correlate liquid-phase adsorption data. [2,87],... 

The Langmuir isotherm equation for the correlation of the liquid-phase adsorption equilibrium of a single component, can, in principle, as was previously stated, be extended to liquid-phase adsorption by the simple replacement of adsorbate pressure by concentration [2,87] ... 

Consider now that some adsorption of liquid vapours on the solid surface occurs (Figure 1,34.b), leading to a reduction of its surface energy by a quantity Aliquid surface). For the sake of clarity, we denote by cr< v and W the solid surface energy and the work of adhesion in the absence of adsorption, while pure solid/pure liquid/vapour system held at constant temperature, the solid surface is in equilibrium with a saturated vapour of the liquid at a partial pressure of Psat, the equilibrium values of [Pg.45]

The individual specific rate and adsorption equilibrium constants are defined in Table 1. In Equations (4) and (5) [Sitesjrefer to the available concentration of sites for adsorption on the Ti02 film, [O2] to the liquid phase oxygen concentration, [M] to the concentration of water, atomic or free radical species, reactor walls or other surfaces trapping atomic chlorine, and Rg to the superficial rate of electrons and holes generation. 

Adsorption equilibrium has an extra degree of freedom compared to conventional vapor-liquid equilibrium. This extra degree of freedom increases the difficulty in experimental measurements. It is difficult to find enough experimental data on binary equilibria in the adsorption literature. On the other hand, pure component isotherm measurement is so common that commercial push-button systems are available in the market for over a decade [1]. 

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