Adsorption, coefficient entropy

The proposed mechanism of the effect of water can be supported by two other findings (i) the calculations of Maatman et al. [410] revealed that the active sites could be identified with surface silanol groups [Sect. 4.1.2.(a)] and(ii) independent studies of other authors [424—426] showed that silica gel could actually adsorb two layers of water the first layer is strongly chemisorbed whereas the second is less strongly adsorbed and retains much of the character of free water. The standard enthalpy and entropy changes on adsorption determined from kinetic adsorption coefficients, Kr and Kr, for the first and second layer, respectively [411], are consistent with this observation. 

Relative Adsorption Coefficients (zr), Free Energies (A F°), Enthalpies (—AH °), and Entropies (AS°) of Adsorptive Exchange Rate Constants (K), Activation Energies (e), and the h Parameters in Catalytic Dehydrogenation. AF°, AH°, and t cal./mole AS° e.u. Ai Rate of Reactant Supply, andmo Reaction Rate ml. Substance Vapor/min., K-ml./(ml. min.). All Valuesfor N.T.P. Original Data Are Reduced to the Same Units. 

Surface tension is ususally measured in the presence of air (component 2), and the effects of concentration of another component, temperature, and pressure on the surface tension are examined to determine respectively the relative adsorption, the entropy change, and the volume change upon adsorption. For this examination, the two coefficients to be eliminated are those of the solvent (component 1), and air ... 

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

The Hg/dimethyl formamide (DMF) interface has been studied by capacitance measurements10,120,294,301,310 in the presence of various tetraalkylammonium and alkali metal perchlorates in the range of temperatures -15 to 40°C. The specific adsorption of (C2H5)4NC104 was found to be negligible.108,109 The properties of the inner layer were analyzed on the basis of a three-state model. The temperature coefficient of the inner-layer potential drop has been found to be negative at Easo, with a minimum at -5.5 fiC cm-2. Thus the entropy of formation of the interface has a maximum at this charge. These data cannot be described... 

The orders of the reaction appear as coefficients of activation energies and adsorption energies and their corresponding entropies. Eor more detailed discussions... 

Hence, according to the transition state theory, adsorption becomes more likely if the molecule in the mobile physisorbed precursor state retains its freedom to rotate and vibrate as it did in the gas phase. Of course, this situation corresponds to minimal entropy loss in the adsorption process. In general, the transition from the gas phase into confinement in two dimensions will always be associated with a loss in entropy and the sticking coefficient is normally smaller than unity. 

Clearly, the sticking coefficient for the direct adsorption process is small since a considerable amount of entropy is lost when the molecule is frozen in on an adsorption site. In fact, adsorption of most molecules occurs via a mobile precursor state. Nevertheless, direct adsorption does occur, but it is usually coupled with the activated dissociation of a highly stable molecule. An example is the dissociative adsorption of CH4, with sticking coefScients of the order 10 -10 . In this case the sticking coefficient not only contains the partition functions but also an exponential... 

If a model is inadequate and/or experimental data are insufficiently accurate, the minimization methods might show up a tendency to simultaneously decrease or increase both coefficients outside the range of physical meaning. In this case fixation of AS, is can be a sufficient remedy. For evaluation of the entropy change due to adsorption, books and papers of Adamson (1982), Barrow (1973), Cerny (1983), Waugh (1994), and Zhdanov et al. (1988) are recommended. 

In this combined approach, water does not have any contribution to the entropy of mixing. In addition, this model considers only one interaction coefficient p, which presents an average value for all the interactions in the adsorption and Stern layers, p is determined by the molecular interactions... 

As appears from the examination of the equations (giving the best fit to the rate data) in Table 21, no relation between the form of the kinetic equation and the type of catalyst can be found. It seems likely that the equations are really semi-empirical expressions and it is risky to draw any conclusion about the actual reaction mechanism from the kinetic model. In spite of the formalism of the reported studies, two observations should be mentioned. Maatman et al. [410] calculated from the rate coefficients for the esterification of acetic acid with 1-propanol on silica gel, the site density of the catalyst using a method reported previously [418]. They found a relatively high site density, which justifies the identification of active sites of silica gel with the surface silanol groups made by Fricke and Alpeter [411]. The same authors [411] also estimated the values of the standard enthalpy and entropy changes on adsorption of propanol from kinetic data from the relatively low values they presume that propanol is weakly adsorbed on the surface, retaining much of the character of the liquid alcohol. 

Specific rate coefficients (related to unit amount of acid centres) were approximately the same for solid catalysts as well as for HC1 [474]. However, when a montmorillonite clay activated by adsorption of protons on its surface was used as the catalyst in ethyl acetate hydrolysis [475], a higher specific rate coefficient (about 1.8 times at 25°C) was found for the reaction catalysed by adsorbed protons than by dissolved acid, this result being explained by the authors by an increase of activation entropy in the former case. 

The thermodynamic functions of fc-mers adsorbed in a simple model of quasi-one-dimensional nanotubes s adsorption potential are exactly evaluated. The adsorption sites are assumed to lie in a regular one-dimensional space, and calculations are carried out in the lattice-gas approximation. The coverage and temperature dependance of the free energy, chemical potential and entropy are given. The collective relaxation of density fluctuations is addressed the dependence of chemical diffusion coefficient on coverage and adsorbate size is calculated rigorously and related to features of the configurational entropy. 

Q q R i l, i 2 Rb Rd Rg RP Ro r rc S Electric charge (As), heat (J), quality factor of a resonator Heat per unit area (J m-2), integer coefficient Radius of a (usually) spherical object (m), gas constant Two principal radii of curvature (m) Radius of a spherical bubble (m) Radius of a spherical drop (m) Radius of gyration of a polymer (m) Radius of a spherical particle (m) Size of a polymer chain (m) Radius (m), radial coordinate in cylindrical or spherical coordinates Radius of a capillary (m) Entropy (J K-1), number of adsorption binding sites per unit area (mol m-2), spreading coefficient (Nm-1)... 

Here A//adS is the enthalpy of adsorption, T is the temperature, and AAads is the entropy change associated with the adsorption of the protein onto the surface. Protein adsorption will take place if AGads < 0. Considering a complex system, where proteins are dissolved in an aqueous environment, and are brought into contact with an artificial interface, there are a vast number of parameters that impact AGads due to their small size (i.e., large diffusion coefficient), water molecules are the first to reach the surface when a solid substrate is placed in an aqueous biological environment. Hence, a hydrate layer is formed. With some delay, proteins diffuse to the interface and competition for a suitable spot for adsorption starts. This competition... 

The activation energy for adsorption of hydrogen on copper was set at 30 kJ mol-1, in agreement with the literature (80). A sticking coefficient of unity was assumed for this step. Furthermore, the entropy of the adsorbed surface hydrogen was adjusted in the analysis. 

Entropy Change. The entropy change in the adsorption of water on barium sulfate is shown in Figure 8. The integral entropy, AS, calculated from AG and A ffl decreases monotonically with increasing amount adsorbed. AS can also be calculated from the temperature coefficient of v by... 

Here the pre-exponential factor, K, is equal to the ratio of the adsorption and desorption coefficients, a//. Alternatively, b may be regarded as a function of the enthalpy and entropy of adsorption (Everett, 1950 Barrer, 1978, p. 117). 

Sorption of Cu(tfac)2 on a column depends on the amount of the compound injected, the content of the liquid phase in the bed, the nature of the support and temperature. Substantial sorption of Cu(tfac)2 by glass tubing and glass-wool plugs was observed. It was also shown that sorption of the copper chelate by the bed is partialy reversible . The retention data for Cr(dik)3, Co(dik)3 and Al(dik)3 complexes were measured at various temperatures and various flow rates. The results enable one to select conditions for the GC separation of Cr, Al and Co S-diketonates. Retention of tfac and hfac of various metals on various supports were also studied and were widely used for the determination of the metals. Both adsorption and partition coefficients were found to be functions of the average thickness of the film of the stationary phase . Specific retention volumes, adsorption isotherms, molar heats and entropy of solution were determined from the GC data . The retention of metal chelates on various stationary phases is mainly due to adsorption at the gas-liquid interface. However, the classical equation which describes the retention when mixed mechanisms occur is inappropriate to represent the behavior of such systems. This failure occurs because both adsorption and partition coefficients are functions of the average thickness of the film of the stationary phase. It was pointed out that the main problem is lack of stability under GC conditions. Dissociation of the chelates results in a smaller peak and a build-up of reactive metal ions. An improvement of the method could be achieved by addition of tfaH to the carrier gas of the GC equipped with aTCD" orFID" . ... 

It follows from [4.6.8ff] that the Interfacicd excess entropy cem in principle be obtained from the temperature dependence of the surface tension. Such experiments require some scrutiny both technically (how to prevent evaporation ) and interpretationally (now to account for the temperature coefficients of chemical potentials at fixed concentrations ). Detailed studies are welcome. However, one striking trend may be mentioned ). Adsorption of (at least some) non-ionics is accompanied by an increase of entropy, whereas for the cationic Cj TMA Br" a decrease is observed. Again, more systematic study seems appropriate, before... 

Both the In k values and the sorption enthalpies, AHm s, may be determined experimentally from the temperature dependence of retention. To calculate the sorption entropy, the phase volume ratio must be known. However, the thermodynamic data may be regarded simply as formal quantities, since the capacity factors correlate directly with AGm >s via the distribution coefficient according to Eq. (38), and since sorption exhibits both distributive and adsorptive character. 

Absolute entropy, 51 Absorption edge, 351 Activated carbon, 710-713 adsorption of metal cations on, 712, 713 de-ashed, 713 heteroelenients in, 711 lEP and PZC of, 711, 712 reductive adsorption on, 711 Activation, 710 energy, 532 Activity, 50 coefficient, 588, 589 of surface species, 591 Adhesion method, 84 Adsolubilization, 494 Adsorbates, index of, 356-358, 428 32, 476, 477 Adsorption capacity, 581 competition, 510-530 dynamic studies, 335 edge, 328 envelope, 328 isotherm, 327... 

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