Effectiveness factors adsorption equilibrium constants

The simplest mode of IGC is the infinite dilution mode , effected when the adsorbing species is present at very low concentration in a non-adsorbing carrier gas. Under such conditions, the adsorption may be assumed to be sub-monolayer, and if one assumes in addition that the surface is energetically homogeneous with respect to the adsorption (often an acceptable assumption for dispersion-force-only adsorbates), the isotherm will be linear (Henry s Law), i.e. the amount adsorbed will be linearly dependent on the partial saturation of the gas. The proportionality factor is the adsorption equilibrium constant, which is the ratio of the volume of gas adsorbed per unit area of solid to its relative saturation in the carrier. The quantity measured experimentally is the relative retention volume, Vn, for a gas sample injected into the column. It is the volume of carrier gas required to completely elute the sample, relative to the amount required to elute a non-adsorbing probe, i.e. 

Note Since the model is linear for the special case considered, the same equation is also satisfied by the other three variables.) The following observations may be made from Eq. (98) that expresses the dimensionless dispersion coefficient A (i) The first term describes dispersion effects due to velocity gradients when adsorption equilibrium exists at the interface. We note that this expression was first derived by Golay (1958) for capillary chromatography with a retentive layer, (ii) The second term corresponds to dispersion effects due to finite rate of adsorption (since this term vanishes if we assume that adsorption and desorption are very fast so that equilibrium exists at the interface), (iii) The effective dispersion coefficient reduces to the Taylor limit when the adsorption rate constant or the adsorption capacity is zero, (iv) As is well known (Rhee et al., 1986), the effective solute velocity is reduced by a factor (1 + y). (v) For the case of irreversible adsorption (y — oo and Da —> oo), the dispersion coefficient is equal to 11 times the Taylor value. It is also equal to the reciprocal of the asymptotic Sherwood number for mass transfer in a circular... 

An important result is that the effective desorption energy for the heterogeneous surfaces depends on temperature Nevertheless, let us for a while abandon it and suppose that jjet does not depend on temperature. Another assumption will be that the entropy change is the same for all partial isotherms, independent of EA. Then we take into account Eq. 5.3 for the experimental constant of adsorption and move to the characteristics of desorption from heterogeneous surfaces. It follows that the measurements yield an equilibrium constant, which is to be interpreted as the entropy factor multiplied by the expectation value of the desorption energy factor ... 

For example, the concept of Kj, (Eq. (4.9)) corresponds to Henry adsorption isotherm (adsorption is proportional to the equilibrium concentration/pressure of the adsorbate), which can be derived from the adsorption reaction 4.1, whose equilibrium constant defined by Eq. (4.2) depends only on the nature of the adsorbent and the adsorbate, but it is independent of the experimental conditions (over certain limited range). It is well known that in principle Kjy is variable, e.g. the effect of the pH on is demonstrated in Figs. 4.28-4.63. These figures show that the pH is an important but not unique factor affecting the distribution of the adsorbate, e.g. the usually decreases when the concentration of the adsorbate increases at constant pH. However, a few cases of constant over a broad range of concentrations of the adsorbate are also reported in Tables 4.1 and 4.2. 

E vs. Aa seems to be most sensitive to product concentrations near the external surface of the catalyst and adsorption/desorption equilibrium constants. I c.surf. I d, surf, and 6>, directly affect the vacant-site fraction on the interior catalytic surface and the rate of reactant consumption. In the previous simulations, product molar densities near the external surface of the catalyst were varied by a factor of 50 (i.e., from 0.1 to 5), and 0, was varied by a factor of 20 (i.e., from 0.05 to 1). The effectiveness factor increases significantly when either 4 c,surf, I d. surf or 6i is larger. E vs. Aa is marginally sensitive to a stoichiometric imbalance between reactants A2 and B, but I B.sur ce was only varied by a factor of 4 (i.e., from 0.5 to 2). A four-fold decrease in the molecular weight of reactant B, which produces two-fold changes in 30b, effective and 5b, does not affect E. 

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