Adsorption condensation coefficient

If the fraction of sites occupied is 0, and the fraction of bare sites is 0q (so that 00 + 1 = 0 then the rate of condensation on unit area of surface is OikOo where p is the pressure and k is a constant given by the kinetic theory of gases (k = jL/(MRT) ) a, is the condensation coefficient, i.e. the fraction of incident molecules which actually condense on a surface. The evaporation of an adsorbed molecule from the surface is essentially an activated process in which the energy of activation may be equated to the isosteric heat of adsorption 4,. The rate of evaporation from unit area of surface is therefore equal to... 

This ideal expression for the rate of adsorption does not usually agree with experimental data. Observed rates decrease so rapidly with increasing coverage 6 that they can be explained only if the activation energy increases with 9. Also, the condensation coefficient may vary with d. These variations may be caused by surface heterogeneity that is, the activity of the sites varies, so that different sites possess different values of a and E. The most active sites would have the lowest activation energy and would be occupied first. Alternately, interaction forces between occupied and unoccupied sites could explain the deviations. In any event, it is necessary to rewrite Eq. (9-3) as... 

In this equation a is the condensation coefficient. It is the probability that a molecule is adsorbed provided it has the necessary activation energy and collides with a vacant surface site. The rate of adsorption is given by,... 

The observations in the field emission microscope establish that under the conditions of the adsorption studies of Section II, C, 1, a, xenon was mobile, and that the binding energy varies with the crystal orientation. The structure of the filament surface is not known in detail however, this is a polycrystalline specimen, the cylindrical surfaces of which are made up of planes with the orientation (hhk). The condensation coefficient must therefore be an average quantity, and energy transfer may thus not be the limiting step. 

In the adsorbed phase, in which the particles are mobile because of surface diffusion, the chemical reaction of the metal-oxide formation takes place via dissociative chemisorption of the oxygen. This means that, since the reaction takes place in the adsorption phase and the various reaction partners can have different condensation coefficients, the ratio of the rates of incidence is a necessary but not adequate criterion. According to Ritter [293, 298], the chemisorption rate of oxygen is the critical step for the completion of the reaction ... 

The quantity c is the condensation coefficient (of the order of unity) which describes the energy accomodation of the adsorbing species. The activation energy of adsorption is illustrated by the onedimensional adsorption potential shown in Fig. 3. 

In this equation, refers to the condensation coefficient (c.f.. Chap. 3) and Ml is Avogadro s number. By definition, the surface coverage with oxygen is equal to do = Wo/Wi, where Wq represents the number of sites occupied by the oxygen atoms, and Wt is the total number of adsorption sites. 

Activated Adsorption. Activated adsorption—that is, adsorption with a measurable rate of adsorption and a measurable temperature coefficient of rate of adsorption—is a type of chemisorption which is, for instance, found in the adsorption of nitrogen on certain metals at elevated temperatures. The difficulties of deciding whether or not true van der Waal s adsorption exists in cases where the heats of adsorption exceed considerably the heats of condensation will become apparent later in the text. 

Since adsorption to a surface is directly proportional to the surface area of the condensed phase, it is most useful to define the equilibrium partition coefficient, Kiasnr[, as the concentration of the compound in the gas phase (i.e., air, subscript a ) divided by the concentration per unit surface area (therefore subscript surf of the condensed phase ... 

The particulate activity trapped on the membrane filters in the sampling packs increased during the first hour (Fig. 3.2). The concentration of condensation nuclei in air in the reactor shell was 1.2 x 1010 m-3. Megaw May showed that an accommodation coefficient of 5 x 10-3 (compare Section 1.12) would explain the observed rate of increase in particulate iodine due to adsorption on the nuclei. The subsequent decline in particulate activity was due to deposition of nuclei on surfaces. Surprisingly, in this and other experiments, release of stable iodine vapour into the containment shell 4 h after the start of the experiment made little difference to the concentration of particulate 132I. Subsequently, Clough et al. (1965) showed that the amount of... 

The fact that the sticking coefficient of TDF on Li (vide supra) at ca. 300 K was found to be negligible points to a high activation energy for gas phase adsorption however, once this barrier is overcome by, for example, forcing molecules on the surface via condensation (as was the case in these experiments), more complex pathways may be favored. Far more revealing information was obtained from the results of TPD experiments described in detail below. 

Material balance calculations on separation processes follow the same procedures used in Chapters 4 and 5. If the product streams leaving a unit include two phases in equilibrium, an equilibrium relationship for each species distributed between the phases should be counted in the degree-of-freedom analysis and included in the calculations. If a species is distributed between gas and liquid phases (as in distillation, absorption, and condensation), use tabulated vapor-liquid equilibrium data, Raoult s law, or Henry s law. If a solid solute is in equilibrium with a liquid solution, use tabulated solubility data. If a solute is distributed between two immiscible liquid phases, use a tabulated distribution coefficient or equilibrium data. If an adsorbate is distributed between a solid surface and a gas phase, use an adsorption isotherm. 

NMR and used it to determine the pore size distribution of mesoporous silicates. They also derived the self-diffusion coefficient of water in MCM-41 and MCM-48 [94,107]. Llewellyn et aL [109] found that MCM-41 exhibits a type V water adsorption isotherm indicating an initial repulsive character followed by capillary condensation at higher pressures. 

The condensation process in physisorption can therefore be regarded as a very efficient process with sticking coefficient close to unity quite irrespective of the considered adsorption site (7 1. The constancy of cr implies the constancy of r so that, quite irrespective of the homogeneous or heterogeneous structure of the surface, no Elovich behaviour is expected for physisorption kinetics. 

The specific properties of hydrated hydrotalcites appear not only in the aldoli-zation of acetone, but in many other aldolization reactions. For example, in the aldol condensation of benzaldehyde with acetone the hydrated form catalyzes the reaction at 273 K, yielding aldol as the main product instead of benzalacetone, obtained on the calcined sample. Competitive adsorption kinetics are still observed, with a much greater adsorption coefficient for benzaldehyde. As suggested earlier from Hammett relationships, this reaction can be generalized with success to many substituted benzaldehydes [32], although the reaction could be performed selectively at 273 K with benzaldehyde only, and substituted benzaldehydes required a reaction temperature of 333 K. Because of this high temperature the reaction usually gives a, unsaturated ketones isolated yields are > 95 %. 

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