Rates of adsorption and desorption

In this section equations are presented for the rates of adsorption, surface reaction, and desorption. In Sec. 9-4 these equations will be combined to give expressions for the rate in terms of fluid concentrations that is, concentrations on the surface (denoted by C) will be eliminated. 

Adsorption The net rate of adsorption of a component A is given by the difference between Eqs. (8-4) and (8-5), written as  

In this equation is the concentration of A in the gas phase at the catalyst surface. If the resistance to adsorption is negligible with respect to other steps in the overall conversion process, the concentration of A on the catalyst surface is in equilibrium with the concentration of A in the gas phase. The net rate of adsorption, from Eq. (9-14), approaches zero, and the equihbrium concentration of A is given by the expression 

Note that this result would reduce to the Langmuir isotherm, Eq. (8-6), if only A were adsorbed. Equations (9-14) and (9-15) are applicable when A occupies one site. Often in chemisorption a diatomic molecule, such as oxygen, will dissociate upon adsorption with each atom occupying one site. Formally, dissociative adsorption may be written 

Surface Reaction The mechanism assumed for the surface process will depend on the nature of the reaction. Suppose that the overall reaction is of the type 

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If we assume that the rates of adsorption and desorption are both large compared with the surface migration rate, the surface and bulk concentrations of each species will be almost in equlibriura, and hence will be... 

Reaction kinetics at phase houndaiies. Rates of adsorption and desorption in porous adsorbents are generally controlled by mass transfer within the pore network rather than by the kinetics of sorption at the surface. Exceptions are the cases of chemisorption and affinity-adsorption systems used for biological separations, where the kinetics of bond formation can be exceedingly slow. 

To solve for ka and kd explicitly, we need one more equation. We can get this from the consideration of an equilibrium condition. When the concentration on the surface of the adsorbent is no longer changing, then rates of adsorption and desorption are equal. From thiswefind ... 

The terms proportional to and describe adsorption on, and desorption from, the reconstructed and unreconstructed surfaces, respectively, without a simultaneous change in the surface structure. The term with accounts for the spontaneous reconstruction and the spontaneous lifting of the reconstruction in the absence of an adsorbate. The expressions with w r and Wsu give the rates of adsorption and desorption with concurrent reconstruction or lifting of the reconstruction. Finally, the terms proportional to... 

Seemingly other problems arise in the treatment of the rate of adsorption, viz. the probability that a gas particle will reach on impact a free adsorption site on a partially covered surface, and the probability that it will remain attached there. Since, however, the rates of adsorption and desorption are connected by the equilibrium requirements, essentially the same problems have to be solved in a theoretical evaluation of both the rates. In practice,... 

Dynamic equilibrium between adsorbate and adsorptive the rate of adsorption and desorption in any layer are equal. 

In genercil, cill structural changes vhich occur during a surface reaction (reconstruction, or removal of reconstruction) can have a marked effect on both the rate of adsorption and desorption. Possible candidates for these phenomena bo occur are all metal surfaces vhich can undergo reconstruction upon interaction with a chemicedly active ad-soj ate. Interesting systems here are (besides the cilready known Pt (100) orNi(IIO) faces) Ir(100)/0,00 or W(100)Al and Mo(100)/H. 

In the steady state, the rates of adsorption and desorption are equal to each other and to the overall rate of this reaction v, = For the steady-state value of... 

There are three approaches that may be used in deriving mathematical expressions for an adsorption isotherm. The first utilizes kinetic expressions for the rates of adsorption and desorption. At equilibrium these two rates must be equal. A second approach involves the use of statistical thermodynamics to obtain a pseudo equilibrium constant for the process in terms of the partition functions of vacant sites, adsorbed molecules, and gas phase molecules. A third approach using classical thermodynamics is also possible. Because it provides a useful physical picture of the molecular processes involved, we will adopt the kinetic approach in our derivations. 

The rates of adsorption and desorption of each species must be equal at equilibrium. Thus ... 

The BET approach is essentially an extension of the Langmuir approach. Van der Waals forces are regarded as the dominant forces, and the adsorption of all layers is regarded as physical, not chemical. One sets the rates of adsorption and desorption equal to one another, as in the Langmuir case in addition, one requires that the rates of adsorption and desorption be identical for each and every molecular layer. That is, the rate of condensation on the bare surface is equal to the rate of evaporation of molecules in the first layer. The rate of evaporation from the second layer is equal to the rate of condensation on top of the first layer, etc. One then sums over the layers to determine the total amount of adsorbed material. The derivation also assumes that the heat of adsorption of each layer other than the first is equal to the heat of condensation of the bulk adsorbate material (i.e., van der Waals forces of the adsorbent are transmitted only to the first layer). If it is assumed that a very large or effectively infinite number of layers can be adsorbed, the following result is arrived at after a number of relatively elementary mathematical operations... 

Since the rate limiting step in the overall process is the rate of adsorption of species A, the net rate of reaction is equal to the difference between the rates of adsorption and desorption. 

Reaction kinetics at phase boundaries. Rates of adsorption and desorption in porous adsorbents are generally controlled by mass... 

There is a wealth of information available on CO chemisorption over single-crystal and polycrystalline platinum surfaces under ultrahigh-vacuum conditions research efforts in this area have gained a significant momentum with the advent of various surface analysis techniques (e.g., 2-8). In contrast, CO chemisorption on supported platinum catalysts (e.g., 9, 10, 11) is less well understood, due primarily to the inapplicability of most surface-sensitive techniques and to the difficulties involved in characterizing supported metal surfaces. In particular, the effects of transport resistances on the rates of adsorption and desorption over supported catalysts have rarely been studied. 

A difference in the rate of adsorption and desorption of Cr(VI) by alluvium was also observed in a batch experiment (Fig. 8.44b). On the basis of these two experiments, Stollenwerk and Grove (1985) concluded that the quantity of Cr(VI) adsorbed by alluvium is a function of its concentration as well as of the type and concentration of other anions in solution. The Cr(VI) adsorbed through nonspecific processes is desorbed readily by a Cr-free solution. Stronger bonds that are formed between Cr(VI) and alluvium during specific adsorption result in very slow release of this fraction. The Cr(Vl) desorption from the alluvium material illustrates the hysteresis process that results from chemical transformation of a portion of contaminant retained in the subsurface. 

Thirdly, the rates of adsorption and desorption could be calculated by means of the transition state method and be equalized. But, bo... 

Barron,V Rendon, J.L. Torrent, J. Serna, C.J, (1984) Relation of infrared, crystallochemical, and morphological properties of Al-substi-tuted hematites. Clays Clay Min. 32 475-479 Barrow, J.J. Cox,V.C. (1992) The effects of pH and chloride concentration on mercury sorption. I. Goethite. J. Soil Sci. 43 437-450 Barrow, N. Madrid, L. Posner, A.M. (1981) A partial model for the rate of adsorption and desorption of phosphate by goethite. J. Soil Sci. 32 399-407... 

If the reaction step is slower than the rates of adsorption and desorption of A and B, then we can assume thermodynamic equihhrium in adsorption and desorption of A and B. This gives... 

At high temperatures, in the region of equilibrium adsorption, the rate of adsorption and desorption is high. As the temperature is lowered, the amount adsorbed in equilibrium becomes greater, so that E2 increases. From Equation (6), as Ei/T increases, the rate of adsorption decreases rapidly. There may be some temperature at which equilibrium adsorption... 

Important properties of zeolite adsorbents for a fixed-bed application are adsorptive capacity and selectivity, adsorption-desorption rate, physical strength and attrition resistance, low catalytic activity, thermal-hydrothermal stability, chemical stability, and particle size and shape. Apparent bulk density of zeolite adsorbents is important because it is related to the adsorptive capacity per unit volume and also somewhat to rate of adsorption and desorption. However, more important properties related to the rates and therefore to the actual useful capacity would be the zeolite crystal size and the macropore size distribution. Although the ultimate basis in selecting a zeolite adsorbent for a specific application would be the performance, the price, and the projected service life of a product, these factors depend largely upon the above properties. 

To derive equations of the rates of adsorption and desorption we shall assume that the rate of migration of adsorbed molecules along the surface... 

Indeed, the constant k in (296) and (297) characterizes only the rates of adsorption and desorption of nitrogen and is thus one and the same for both reactions. The difference in the rates of these reactions results only from the nonidentity of the fugacities of adsorbed nitrogen pNl and pf,2, the last being determined for reaction (314), instead of (298) by the equation... 

At equilibrium, the above rates of adsorption and desorption are equated, and an expression is obtained for the fraction of sites occupied /, which appears identical to Equation 5.22a for simple hydrates of one component ... 

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