Adsorption constants, intrinsic

Cations that form strong inner-sphere aqueous complexes are often strongly and specifically adsorbed when the same ligand is involved in solution and at the sorbent surface. Conversely, species forming weak aquocomplexes or ion pairs tend to be weakly adsorbed. These observations have formed the basis for most estimates of intrinsic adsorption constants (cf. Dzombak and Morel 1990 Smith and Jenne 1991). The extensive literature of solution complexation constants (cf. Smith and Martell 1976 Baes and Mesmer 1976, 1981) has facilitated such estimation methods. As an example, log K - values for cation adsorption by specific metal oxyhydroxides plotted against the first hydrolysis constants of the same cations are often strongly correlated. Such plots, called linear free... 

Figure 10.28 Correlations between (a) cation hydrolysis constants and TL intrinsic adsorption constants for cations adsorbed by HFO (goethite and amorphous...

Hachiya et al. [60,61] found a linear relationship between the logarithms of intrinsic adsorption constants and the hydrolysis constant of the metal ions for Cu, Pb, Zn, Co. and Mn. They described pressure jump experiments [61] with y AI2O3, showing a fast and a slow process — attributed to two surfaces sites — with Cu ", Zn, Co, and The relaxation times decreased with metal ion... 

In contrast, physical adsorption is a very rapid process, so the rate is always controlled by mass transfer resistance rather than by the intrinsic adsorption kinetics. However, under certain conditions the combination of a diffiision-controUed process with an adsorption equiUbrium constant that varies according to equation 1 can give the appearance of activated adsorption. 

The material balance was calculated for EtPy, ethyl lactates (EtLa) and CD by solving the set of differential equation derived form the reaction scheme Adam s method was used for the solution of the set of differential equations. The rate constants for the hydrogenation reactions are of pseudo first order. Their value depends on the intrinsic rate constant of the catalytic reaction, the hydrogen pressure, and the adsorption equilibrium constants of all components involved in the hydrogenation. It was assumed that the hydrogen pressure is constant during... 

Formation of products in paraffin cracking reactions over acidic zeolites can proceed via both unimolecular and bimolecular pathways [4], Based on the analysis of the kinetic rate equations it was suggested that the intrinsic acidity shows better correlation with the intrinsic rate constant (kinl) of the unimolecular hexane cracking than with the apparent rate constant (kapp= k K, where K is the constant of adsorption equilibrium). In... 

The dashed line in the complex in (4.21) and (4.22) indicates an outer-sphere (o.s.) surface complex, Kos stands for the outer-sphere complex formation constant and kads [M 1 s 1] refers to the intrinsic adsorption rate constant at zero surface charge (Wehrli et al., 1990). Kos can be calculated with the help of a relation from Gouy Chapman theory (Appendix Chapter 3). 

The term F2/CsRT is obtained from the constant capacitance model (Chapter 3.7). Fig. 4.6 gives a plot of the linear free energy relation between the rate constants for water exchange and the intrinsic adsorption rate constant, kads. 

It is assumed i) that the concentration c remains constant and ii) that transport by diffusion is rate controlling, i.e., the adsorbate arriving at the interface is adsorbed fast (intrinsic adsorption). This intrinsic adsorption, i.e., the transfer from the solution to the adsorption layer is not rate determining or in other words, the concentration of the adsorbate at the interface is zero iii) furthermore, the radius of the adsorbing particle is relatively large (no spherical diffusion). 

If this is not the case, the adsorption behavior can be described by competitive adsorption. The extent of adsorption depends not only on the individual adsorption constants but also on the intrinsic kinetics of adsorption of the individual adsorbates and thus, the adsorption layer formed is influenced by the qualitative and quantitative composition of the complex mixture of adsorbable solutes full equilibrium is often not attained (Cosovic, 1990). 

Hiemstra, T W. H. van Riemsdijk, and H. G. Bolt (1989), "Muitisite Proton Adsorption Modeling at the Solid/Solution Interface of (Hydr)Oxides, I. Model Description and Intrinsic Reaction Constants", J. Colloid Interf. Sci. 133, 91-104. 

Gouy-Chapman, Stern, and triple layer). Methods which have been used for determining thermodynamic constants from experimental data for surface hydrolysis reactions are examined critically. One method of linear extrapolation of the logarithm of the activity quotient to zero surface charge is shown to bias the values which are obtained for the intrinsic acidity constants of the diprotic surface groups. The advantages of a simple model based on monoprotic surface groups and a Stern model of the electric double layer are discussed. The model is physically plausible, and mathematically consistent with adsorption and surface potential data. 

What remains is to relate the surface potential to activation potentials for the adsorption/desorption reaction steps. Defining the activation potentials as iji, ijjf for the activation required to overcome the EDL potential for the adsorption, desorption steps, respectively, allows the intrinsic rate constants to be directly related to the rate constants k, k (4), i.e.,... 

In the results presented in Table 13.5, the addition of tin affects the kinetic selectivity r differently, depending on the catalyst preparation method. When compared to the monometallic PdO catalyst, r slightly decreases for the coimpregnated PdSn catalyst, but it sharply increases for the PdOSn catalyst prepared via the colloidal oxide synthesis. As the intrinsic kinetic constant rates k do not show significant discrepancies between the different catalysts, the main contribution of the variation of the kinetic selectivity is ascribed to the adsorption constant ratio fBo/ Butenes- In the case of the PdOSn catalyst, formation of but-l-ene is favored compared to its consumption because the X Bo/ Butenes ratio increases, indicating that olefin adsorption is much more destabilized than diene adsorption. Thus, the olefin easily desorbs before being hydrogenated into butane. 

T. Hiemstra, W. H. van Riemsdijk, and G. H. Bolt, Multisite proton adsorption modeling at the solidZsolution interface of (hydr)oxides A new approach 1. Model description and evaluation of intrinsic reaction constants, J. Colloid Interface Sci. 133(1), 99-104 (1989). 

Here kgr is the surface reaction rate constant, Rr is the adsorption equilibrium constant for product R, Pr is the partial pressure of R and Kp is the reaction equilibrium constant. At low loading the reaction rate simply becomes proportional to the product of the intrinsic rate constant and the Henry coefficient. 

The above surface complexation models enable adsorption to be related to such parameters as the number of reactive sites available on the oxide surface, the intrinsic, ionization constants for each type of surface site (see Chap. 10), the capacitance and the binding constants for the adsorbed species. They, therefore, produce adsorption isotherms with a sounder physical basis than do empirical equations such as the Freundlich equation. However, owing to differences in the choice of adjustable... 

Prediction of the breakthrough performance of molecular sieve adsorption columns requires solution of the appropriate mass-transfer rate equation with boundary conditions imposed by the differential fluid phase mass balance. For systems which obey a Langmuir isotherm and for which the controlling resistance to mass transfer is macropore or zeolitic diffusion, the set of nonlinear equations must be solved numerically. Solutions have been obtained for saturation and regeneration of molecular sieve adsorption columns. Predicted breakthrough curves are compared with experimental data for sorption of ethane and ethylene on type A zeolite, and the model satisfactorily describes column performance. Under comparable conditions, column regeneration is slower than saturation. This is a consequence of non-linearities of the system and does not imply any difference in intrinsic rate constants. 

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