Equilibrium adsorption desorption

Adsorption (or desorption) is the process by which a net accumulation (or loss) of a substance occurs at an interface between two phases. In a typical experiment, two phases are mixed intimately to provoke a chemical reaction leading to adsorption or desorption, and then a physical separation is made, with one of the separates being a single phase and the other, a mixture of the two reacted phases. For example, a solid-phase adsorbent and an aqueous solution could be mixed, and then separated by centrifugation into an aqueous phase (supernatant solution) and a slurry that contains both the solid adsorbent and some aqueous solution. If is the moles of substance i in the reacted mixture and m is the molality of substance i in the separated aqueous phase, then the relative surface excess, np, of substance i, as compared to another substance j, is defined by1 

The conceptual meaning of Eq. 4.1 is that nP is the excess moles of substance i in the reacted mixture, relative to the content of a reference substance j in the mixture and to the composition of the separated aqueous solution, indicated by the molalities nij and mj. In the example of the slurry and supernatant solution, np is the excess moles of i in the slurry, as compared to the content of the reference substance j and to an aqueous solution that has the mixed composition indicated by mj and mj. The right side of Eq. 4.1 can be positive (adsorption), zero (no surface excess), or negative (desorption), depending entirely on the relative behavior of the substances i and j when two phases containing them react. In applications of Eq. 4.1 to the reactions of soils with aqueous solutions, the reference substance j is invariably chosen to be liquid water (j = w)  

An overall reaction describing the adsorption or desorption of aqueous solution species by a solid adsorbent can be written as follows  

Some special cases of the reaction in Eq. 4.3 are listed in Table 4.1. In each case, S represents the adsorbent structure not involved directly in an adsorption-desorption reaction. (It is equivalent to the symbol = M0X in Eq. 3.46 or =C in Eq. 3.61, for example.) Other special cases are given in Eqs. 3.53, 3.56, 3.62, 3.63, and 3.66. Equation 4.3 can be generalized readily to permit more lhan I mol of llie species SR/-sh(s) to react, or to replace Mm by a 

The relationship between mole fraction and activity, and therefore between and Kadsc, is made through rational activity coefficients (cf. Eq. 1.25) 4 

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Surfactant Transport in Porous Media Dynamic Adsorption/Desorption Equilibria... 

Adhesive force, non-Brownian particles, 549 Admicelle formation, 277 Adsorption flow rate, 514 mechanism, 646-647 on reservoir rocks, 224 patterns, on kaolinite, 231 process, kinetics, 487 reactions, nonporous surfaces, 646 surface area of sand, 251 surfactant on porous media, 510 Adsorption-desorption equilibria, dynamic, 279-239 Adsorption plateau, calcium concentration, 229... 

In connection with practical situations where CO oxidation is important, we must also consider the perennial question of how to connect the low pressure results onto those at high pressure. Qualitatively this has been done for the CO oxidation reaction but it would still be worthwhile to attempt a numerical prediction of high pressure results based on low-pressure rate parameters. A very nice paper modeling steady-state CO oxidation data over a supported Pt catalyst at CO and O2 pressures of several torr has very recently appeared (.25). Extension of this work to other systems in warranted and, even though unresolved questions continue to exist, every indication is that the high and low pressure data can be reliably modeled with the same rate parameters if no adsorption - desorption equilibria are assumed. 

Irrespective of the sources of phenolic compounds in soil, adsorption and desorption from soil colloids will determine their solution-phase concentration. Both processes are described by the same mathematical models, but they are not necessarily completely reversible. Complete reversibility refers to singular adsorption-desorption, an equilibrium in which the adsorbate is fully desorbed, with release as easy as retention. In non-singular adsorption-desorption equilibria, the release of the adsorbate may involve a different mechanism requiring a higher activation energy, resulting in different reaction kinetics and desorption coefficients. This phenomenon is commonly observed with pesticides (41, 42). An acute need exists for experimental data on the adsorption, desorption, and equilibria for phenolic compounds to properly assess their environmental chemistry in soil. 

It is rare that a catalyst can be chosen for a reaction such that it is entirely specific or unique in its behaviour. More often than not products additional to the main desired product are generated concomitantly. The ratio of the specific chemical rate constant of a desired reaction to that for an undesired reaction is termed the kinetic selectivity factor (which we shall designate by 5) and is of central importance in catalysis. Its magnitude is determined by the relative rates at which adsorption, surface reaction and desorption occur in the overall process and, for consecutive reactions, whether or not the intermediate product forms a localised or mobile adsorbed complex with the surface. In the case of two parallel competing catalytic reactions a second factor, the thermodynamic factor, is also of importance. This latter factor depends exponentially on the difference in free energy changes associated with the adsorption-desorption equilibria of the two competing reactants. The thermodynamic factor also influences the course of a consecutive reaction where it is enhanced by the ability of the intermediate product to desorb rapidly and also the reluctance of the catalyst to re-adsorb the intermediate product after it has vacated the surface. 

Savage, K.E., Wauchope, R.D. (1974) Flumeturon adsorption-desorption equilibria in soil. Weed Sci. 22, 106-110. 

One may assume that slow conformational transformations in the surfactant macromolecules may affect considerably the adsorption-desorption equilibria at the surface of the semiconductor particles under consideration and thus affect the course of redox processes generated by these particles under the action of light. We present below an attempt in a semiquantitative description of the observed processes. 

Owing to fast competitive adsorption/desorption equilibria, the oxidation products intervene with oxidative surface reactions and thus are further oxidized, ultimately leading to complete mineralization. The Langmuir-Hinshelwood kinetic... 

Kinetics of heterogeneous catalysis has received much attention. Its mathematical theory is well advanced, largely thanks to extensive work of Boudart, Temkin, and others. On the other hand, heterogeneous catalysis has to deal not only with the same kind of difficulties homogeneous catalysis faces, but with the added complications of surface properties, adsorption/desorption equilibria and rates, and mass transfer to and from catalytic sites, phenomena whose effects often are more important than those of actual kinetics of the reaction on the surface. 

Adsorption and desorption of molecules in the gas (or liquid) phase (steps 7 and 7 ) lead to adsorption/desorption equilibria. 

Consider monomeric metal alkyl A and monomer M to be competitors for the adsorption sites S on the catalyst surface. Only a portion of the surface may be covered with either metal alkyl or monomer and adsorption-desorption equilibria exist ... 

Even from the very beginning it became clear that kinetic methods generally accepted in heterogeneous catalysis, which are based on the analysis of adsorption-desorption equilibria and surface reactions in the steady-state approximation, cannot be applied to the studies of heterogeneous-homogeneous processes. However, on the eve of 1980s no developed methodology applicable... 

For the investigation of adsorption/desorption kinetics and surface diffusion rates, SECM is employed to locally perturb adsorption/desorption equilibria and measure the resulting flux of adsorbate from a surface. In this application, the technique is termed scanning electrochemical induced desorption (SECMID) (1), but historically this represents the first use of SECM in an equilibrium perturbation mode of operation. Later developments of this mode are highlighted towards the end of Sec. II.C. The principles of SECMID are illustrated schematically in Figure 2, with specific reference to proton adsorption/desorption at a metal oxide/aqueous interface, although the technique should be applicable to any solid/liquid interface, provided that the adsorbate of interest can be detected amperometrically. 

The preferred way of studying adsorption/desorption equilibria and kinetics is therefore a one- or two-run procedure, as follows. 

In the absence of chemical reaction between adsorbed species, it is instructive to analyze adsorption/desorption equilibria via steps 3 and 6. The overall objective here is to develop expressions between the partial pressnie / a of gas A above a solid surface and the fraction of active sites a on the catalyst that are occnpied by this gas when it adsorbs. The phenomenon of chemisorption and the relation between pa and a apply to a unimolecular layer of adsorbed molecnles on the catalytic surface. This is typically referred to as a monolayer, where the intermolecular forces of attraction between adsorbed molecules and active snrface sites are characteristic of chemical bonds. When complete monolayer coverage of the surface exists, subsequent adsorption on this saturated surface corresponds to physisorption, which is analogous to condensation of a gas on a cold snbstrate. The enthalpy change for chemisorption is exothermic with valnes between 10 and 100 kcal/mol. The Langmuir adsorption isotherm, first proposed in 1918 (see Langmuir, 1918), is based on the following reversible elementary step that simulates single site adsorption on a catalytic surface when there is only one adsorbate (i.e., gas A) present ... 

The previous discussion of adsorption/desorption equilibria in this chapter allows one to calculate fractional surface coverage by gases A and D as follows ... 

This mechanism, which was developed in 1940, employs Langmuir isotherms to describe adsorption/desorption equilibria of all reactants and products. Chemical reaction on the catalytic surface is the rate-limiting step, which governs the overall rate of reaction. Each component adsorbs without preference on one active site. The five-step sequence of elementary steps is... 

This example illustrates the difficulty encountered when multisite adsorption occurs without dissociation. If molecular A requires n adjacent surface sites for adsorption, then the elementary steps that describe adsorption/desorption equilibria are... 

The PAD obtained experimentally from potentiometric titration of alumina shows four peaks from pH 3-11. They correspond to the following proton adsorption/desorption equilibria which take place specifically on four of the five types of surface hydroxyls predicted by the structural models ... 

Perform equilibrium calculations for systems involving adsorption-desorption equilibria. 

These processes are interfacial protolytic equihbria existing between the large number of active sites on the surface and H+/OH ions in the aqueous medium, which are the product of a water autoprotolysis reaction (H2O H -I- OH ). The question of our approach or the choice of model by which the surface-charging mechanism can be described is whether to consider them a surface association-dissociation or an interfacial adsorption-desorption equilibria. Charging of an amphoteric oxide surface can be modeled with a simple one-step protonation reaction [14] ... 

When conventional surfactants are used in dispersion polymerization, difficulties are encountered which are inherent in their use. Conventional surfactants are held on the particle surface by physical forces thus, adsorption/desorption equilibria always exist, which may not be desirable. They can interfere with adhesion to a substrate and may be leached out upon contact with solvent. Surfactant migration affects fQm formation and their lateral motion during particle - particle interactions can cause destabilization of the colloidal dispersion. On the contrary, reactive surfactants contain a polymerizable group thus, they can overcome some of the difficulties encountered with conventioncd surfactants and can also be incorporated into the surface layer of the polymer particles by copolymerization with other unsaturated comonomers. In this manner, these reactive surfactants are bound to the particle surface and therefore they are prevented from subsequent migration. 

Equilibria (7.46) and (7.47) account for tlie fact that complexation is related to acid-base reactions, and that it is involved in the mechanism of charge generation, with proton adsorption/desorption equilibria. The charge o-q. obtained by proton titration, reprc.sents the number of protons released or consumed in all reactions within the Stern layer, and not only the protons involved in the formation of the MO and MOH 2. species. Hence, all ions participating in the creation of charges op and <7h are called potential-determining ions (PDls), although this name is very often reserved for H and HO . 

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