Equilibrium Adsorption of Gases on Solids

The process by which certain porous solids bind large numbers of molecules to their surfaces is known as adsorption. Not only does it serve as a separation process, but it is also a vital part of catalytic-reactionprocesses. As a separation process, adsorptionis used most oftenfor removal of lo w-concentrationimpurities and pollutantsfrom fluid streams. It is also the basis for cliromatography. In surface-catalyzedreactions, the initial step is adsorptionof reactant species the final step is the reverse process, desorption of product species. Since most industrially important reactions are catalytic, adsorption plays a fundamental role in reaction engineering. 

In the adsorptionof gases, the number of molecules attracted to a solid surface depends on conditions in the gas phase. For very low pressures, relatively few molecules are adsorbed, and only a fraction of the solid surface is covered. As the gas pressure increases at a given temperature, surface coverage increases. When all sites become occupied, the adsorbed molecules are said to form a monolayer. Further increase in pressure promotes multilayer adsorption. It is also possible for multilayer adsorption to occur on one part of a porous surface when vacant sites still remain on another part. 

The complexities of solid surfaces and onr inability to characterize exactly their interactions with adsorbed molecules hmits our understanding of the adsorption process. It does not, however, prevent development of an exact thennodynamic description of adsorption equilibrium, applicable alike to physical adsorption and chemisorption and equally to monolayer and multilayer adsorption. The thermodynamic frame work is independent of any particular theoretical or empirical description of material behavior. However, in application such a description is essential, and meaningful results require appropriate models of behavior. 

This problem is circumvented by a construct devised by J. W. Gibbs. Imagine that the gas-phase properties extend unchanged up to the solid surface. Differences between the actual and the unchangedproperties can then be attributed to a mathematical surface, treated as a two-dimensional phase with its own thenuodynamic properties. This provides not only a precisely defined surface phase to accountfor the singularitiesof the interfacial region, but it also extracts them from the three-dimensional gas phase so that it too may be treated precisely. The solid, despite the influence of its force field, is presumed inert and not otherwise to participate in the gas/adsorbate equilibrium. Thus for purposes of thenuodynamic analysis the adsorbate is treated as a two-dimensionalphase, inherently an open system because it is in equilibrium with the gas phase. 

An analogous equation may be written for a two-dimensionalphase. The only difference is that pressure and molar volume are not in this case appropriate variables. Pressure is replaced by the spreading pressure FI, and the molar volume by the molar area a  

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The adsorption of gases on solid surfaces proceeds to such an extent that approximately 10 7 gr. is present per cm.2 in the equilibrium state. This is of the same order of magnitude as the strength of the limiting capillary layer of a liquid ( 184), hence it is not improbable, as suggested by Faraday (9) (1884), that the adsorbed gas is sometimes present in the liquid state. The adsorbed amount increases with the pressure and diminishes with rise of temperature. The first effect does not follow a law of simple proportionality, as in the case of the absorption of gases by liquids, rather the adsorbed amount does not increase so rapidly, and the equation ... 

The Langmuir equation (Eq. 5.1), derived originally to describe the adsorption of gases on solids, assumes that the adsorbed entity is attached to the surface at specific, homogeneous, localized sites, forming a monolayer. It is also assumed that the heat of adsorption is constant over the entire monolayer, that there is no lateral interaction between adsorbed species, that equilibrium is reached, and that the energy of adsorption is independent of temperature ... 

Adsorption isotherms represent a relationship between the adsorbed amount at an interface and the equilibrium activity of an adsorbed particle (also the concentration of a dissolved substance or partial gas pressure) at a constant temperature. The analysis of adsorption isotherms can yield thermodynamic data for the given adsorption system. Theoretical adsorption isotherms derived from statistical and kinetic data, and using the described assumptions (see 3.1), are known only for the gas-solid interface or for dilute solutions of surfactants (Gibbs). Those for the system gas-solid are of a few basic types that can be thermodynamically predicted81. From temperature relations it is possible to calculate adsorption and activation energies or rate constants for individual isotherms. Since there are no theoretically founded equations of adsorption isotherms for dissolved surfactants on solids, the adsorption of gases on solides can be used as a starting point for an interpretation. 

The determination of the adsorption of gases on solids can be a time consuming matter. Already in 1969 Jantti suggested to measure three points of the initial course of the kinetic adsorption curve and to extrapolate the equilibrium value (3PM). When the specific molecular model of the adsorption of a gas on a solid surface is known and when it can be expected that only one kind of adsorption is at stake, this method delivers good results and allows a very fast stepwise measurement of adsorption isotherms-. ... 

Adsorption from solution is discussed by Adamson, but with emphasis on the equilibrium aspects, rather than the kinetics. The subject can conveniently be divided into adsorption of non-electrolytes and adsorption of electrolytes. The former can be treated for dilute solutions, in a similar manner to adsorption of gases on solid surfaces. Multilayer adsorption has been observed however, so that... 

The study of adsorption from solution is experimentally straightforward. A known mass of the adsorbent material is shaken with a solution of known concentration at a fixed temperature. The concentration of the supernatant solution is determined by either physical or chemical means and the experiment continued until no further change in the concentration of the supernatant is observed, that is, until equilibrium conditions have been established. Equations originally derived for the adsorption of gases on solids are generally used in the interpretation of the data, the Langmuir and Freundlich equations being the most commonly used. 

In the following, we consider the equilibrium and kinetics of adsorption of surfactants at the air-water interface on the basis of Langmuir s theory of adsorption of gases on solids. According to Langmuir s theory, it is assumed that the adsorption surface consists of sites, which can be occupied by adsorbed molecules. These sites correspond to the minimum of surface free energy. At achieving the balance between the adsorbed molecules and molecules of gas, only some parts of the potentially available adsorption sites are occupied by gas molecules. This part is equal to 0, and the total number of molecules Na adsorbed on the surface obeys the ratio... 

The relation between the amount of substance adsorbed by an adsorbent and the equilibrium partial pressure or concentration at constant temperature is called an adsorption isotherm. The adsorption isotherm is the most important and by far the most often used of the various equilibria data that can be measured. Five general types of isotherms have been observed in the adsorption of gases on solids. These are shown in Figure 17.2. In cases of chemisorption, only isotherms of type I are encountered, while in physical adsorption, all five types occur. Also note that the development to follow will primarily be concerned with gas-solid adsorption. 

Type 1 isotherms exhibit prominent adsorption at low relative pressures p/po (the relative pressure p/po is defined as the equilibrium v or pressure divided by the saturation vapor pressure) and then level off. Type 1 isotherm is usually considered to be indicative of adsorption in micropores (e.g., adsorption of benzene on microporous active carbon) or monolayer adsorption due to the stror adsorbent-adsorbate interactions (which may be the case for chemisorption, which involves chemical bonding between adsorbate and the adsorbent surface, e.g., adsorption of hydrogen on iron). In the case of nonpolar gases commonly used for charactmzation of porous solids (nitrogen, argon) [10, 12, 13, 17, 56], chemisorption is unlikely and therefore e I reflects usually adsorption on microporous solids. However, type I isotherms may also be observed for mesoporous materials with pore size close to the micropore range. In particular, in the case of adsorption of N2 at 77 K or Ar at both 77 K and 87 K in cylindrical pores, a type I isotherm would have to level off below the relative pressure of about 0.1 for the material to be exclusively microporous, as inferred fi-om tile results of recent studies of siliceous and carbonaceous ordered mesoporous materials (OMM) [57-59]. Consequently, when a type 1 isotherm does not level off below the relative... 

Separation of gases is a very important process in several industries (e.g., chemical, petrochemical, and related industries). Although cryogenics and absorption remain the most widely used processes, the last two decades have seen a tremendous growth in research activities and commercial applications of adsorption-based gas separation. Separation by adsorption is based on the selective accumnlation of one or more components of a gas mixture on the surface of a microporous solid. The separation is achieved by one of three mechanisms steric, kinetic, or equilibrium. Most processes operate by virtue of equilibrium (or competitive) adsorption of gases from binary or multicomponent mixtures [143]. 

Experimental study of adsorption of fission product gases. Evaluation of various ad. orbcr materials based on experimental measurements of the equilibrium adsorption of krypton or xenon under static conditions is in progress [7]. Results in the form of adsorption isotherms of various solid adsorber materials are presented in Fig. 6-8. 

In the early fifties, there has been considerable discussion in the literature regarding the thermodynamical treatment of the physical adsorption of vapors and gases on solid surfaces. This subject is reviewed in books by Adamson [1960], and by Young and Crowell [1962]. In principle, solution thermodynamics may be applied to the system of moles of adsorbent and moles of adsorbed gas in equilibrium with vapor. However, in adsorption, the roles of adsorbent and adsorbate are not symmetrical if the adsorbent may be considered to be inert. In that case, the system can be treated as a one-component system, and thermodynamic functions associated with the formation of the surface layer of adsorbed molecules may be defined. This approach is treated by Hill [1949,1950], Hill et al [1951], and also by Everett [1950]. 

Measurement of heat of adsorption by means of microcalorimetry has been used extensively in heterogeneous catalysis to gain more insight into the strength of gas-surface interactions and the catalytic properties of solid surfaces [61-65]. Microcalorimetry coupled with volumetry is undoubtedly the most reliable method, for two main reasons (i) the expected physical quantities (the heat evolved and the amount of adsorbed substance) are directly measured (ii) no hypotheses on the actual equilibrium of the system are needed. Moreover, besides the provided heat effects, adsorption microcalorimetry can contribute in the study of all phenomena, which can be involved in one catalyzed process (activation/deactivation of the catalyst, coke production, pore blocking, sintering, and adsorption of poisons in the feed gases) [66]. 

Fundamental studies on the adsorption of supercritical fluids at the gas-solid interface are rarely cited in the supercritical fluid extraction literature. This is most unfortunate since equilibrium shifts induced by gas phase non-ideality in multiphase systems can rarely be totally attributed to solute solubility in the supercritical fluid phase. The partitioning of an adsorbed specie between the interface and gaseous phase can be governed by a complex array of molecular interactions which depend on the relative intensity of the adsorbate-adsorbent interactions, adsorbate-adsorbate association, the sorption of the supercritical fluid at the solid interface, and the solubility of the sorbate in the critical fluid. As we shall demonstrate, competitive adsorption between the sorbate and the supercritical fluid at the gas-solid interface is a significant mechanism which should be considered in the proper design of adsorption/desorption methods which incorporate dense gases as one of the active phases. 

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