The Enthalpy and Entropy of Adsorption

Thus, we could find the variation of AGads by finding out the corresponding variation in the enthalpy and entropy of adsorption. However, the knowledge of A//ads and ASads leads to some interesting questions related to the adsorption process. The bond strength between the adsorbed ion and the metal is determined by the value of the enthalpy. Is this enthalpy value constant through the whole adsorption process (i.e., from the first adsorbed ions to the last ones), or does A//ads vary as the population of the adsorbed ions increases ... 

The theoretical calculations described have recently been supported by an extraordinary kinetic analysis conducted by Vanrysellberghe and Froment of the HDS of dibenzothiophene (104). That work provides the enthalpies and entropies of adsorption and the equilibrium adsorption constants of H2, H2S, dibenzothiophene, biphenyl, and cyclohexylbenzene under typical HDS conditions for CoMo/A1203 catalysts. This work supports the assumption that there are two different types of catalytic sites, one for direct desulfurization (termed a ) and one for hydrogenation (termed t). Table XIV summarizes the values obtained experimentally for adsorption constants of the various reactants and products, using the Langmuir-Hinshelwood approach. As described in more detail in Section VI, this kinetic model assumes that the reactants compete for adsorption on the active site. This competitive adsorption influences the overall reaction rate in a negative way (inhibition). 

Protein conformational changes contribute positively both to the enthalpy and entropy of adsorption. Such contributions are pH-dependent. 

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). 

Up to this point the essential equations have been presented. Now, it is possible to analyze the work carried out in connection with the classical thermodynamic approach. The first systematic study of a thermodynamic adsorption quantity was perhaps the work done by de Boer and coworkers [10] on the determination, interpretation and significance of the enthalpy and entropy of adsorption. Their papers analyzed almost all aspects of the experimental determination of the entropy and how to interpret the values obtained in terms of two extreme models, i.e., those of mobile and locahzed adsorption, which today have lost much of their usefulness. To catalog the behavior of the adsorbed film as localized or mobile is a very simplistic solution and it has been demonstrated [9] that in most cases the adsorbed film is neither completely localized nor completely mobile. This approach also is somehow outdated because numerical simulations provide a better microscopic interpretation of the system s behavior. 

The enthalpy and entropy of adsorption can be calculated from the surface free energy of adsorption based on the thermodynamic relationship (62)... 

Measurement of the enthalpies and entropies of adsorption and their variation as the pore space is filled is important to establish chemical models of the interactions and to enable chemical engineers to model and optimise catalytic reactors and large-scale separations. For physisorption of gases and vapours, the most widely available approach is to measure the equilibrium uptake as a function of adsorbate pressure and at a series of constant temperatures, giving a series of isotherms. This then permits the dependence of the equilibrium pressure with temperature to be derived for any value of the uptake, or fractional coverage, 0. The differential heat of adsorption (the heat at a particular coverage, 0 ) can then be calculated using the linearised form of the Clausius lapeyron equation ... 

In general, non-linear van t Hoff behavior may be indicative of a change in the mechanism of retention. Basically, any reversible process which alters the enthalpy and entropy of adsorption can, in principle, give rise to non-linear van t Hoff plots. Dissociative processes, such as ionisation, change in conformation, or changes in the extent to which the mobile phase interacts with either the analyte or stationary phase are examples of such reversible processes. In addition, the presence of multiple types of retention mechanisms or multiple types of binding sites may also lead to non-linear van t Hoff plots. 

The capability of this rate expression to describe the data is illustrated in Figures 7.17 and 7.18. The optimized rate parameters at various temperatures are listed in Table 7.13, and Arrhenius plots of these values yield the thermodynamic properties in Table 7.14. The enthalpies and entropies of adsorption are consistent with the rules in Table 6.9, eonsidering the uncertainty of the numbers. Again, this does not prove that the proposed model is correct, but only that it is consistent and should not be rejeeted at this time. This same model was also capable of providing satisfactory fits of the data... 

If the dependence on temperature as well as on composition is known for a solution, enthalpies and entropies of adsorption may be calculated from the appropriate thermodynamic relationships [82]. Neam and Spaull [147] have, for example, calculated the enthalpies of surface adsorption for a series of straight-chain alcohols. They find an increment in enthalpy of about 1.96 kJ/mol per CH2 group. 

The determination of the adsorption parameter (Vg) at three temperatures permits the calculation of the free energy, enthalpy, and entropy of adsorption. A plot of log Vg versus 1/T has a slope of -AHa(js/2.3R. AGacjs is obtained by... 

It was suggested by Alstrup et al. (19) that the heat of adsorption varies linearly with coverage according to the Temkin law, but Wise et al. (20) proposed a modified Temkin equation taking into account a linear variation of the enthalpy and entropy of sulfur chemisorption. 

Standard Gibbs energies of adsorption are often encountered. When A j G is accurately known as a function of temperature, standard enthalpies and entropies of adsorption can also be obtained, using the appropriate Gibbs Helmholtz relations (sec. 1.2.15). 

Increase of temperature increased the per cent removal. The change in standard free energy, enthalpy and entropy of adsorption were calculated using the following equations ... 

Thus liquid chromatography makes it possible to determine the equilibrium constant at small coverage (the retention volume or Henry constant) and to characterize the compounds adsorption from multicomponent solutions. From the dependence of retention volumes on temperature the changes of enthalpy and entropy of adsorption can be calculated. 

In a recent paper, Chiang et al. [22] reported values of the free energy, enthalpy, and entropy of adsorption of volatile organic compounds (exemplified by benzene and methylethylketone) on seven samples of activated carbon. The starting point for their development was Eqn (3.11) for the isosteric heat of adsorption. Linders et al. [23] determined adsorption heats from the adsorption equilibrium constant and found that these values agree quite well with those obtained from uptake experiments using the integrated form of Eqn (3.11). They analyzed the experimental data obtained for -butane adsorbed on two commercial activated carbons (Kureha and Sorbonorit B3) and for hexafluoropropylene adsorbed on activated carbon. 

This distribution is useful to calculate enthalpy and entropy of adsorption in the micropores (Jaroniec, 1987) and the heat of immersion (Jaroniec and Madey, 1988). 

Retention volumes are commonly used for the determination of enthalpy and entropy of adsorption, but Kovats retention indices can also be successfully used for such... 

Grajek, H. Rediscovering the problem of interpretation of chromatographicaUy determined enthalpy and entropy of adsorption of different adsorbates on carbon materials. Critical appraisal of literature data. J. Chromatogr. A, 2007,1145, 1-50. 

Developing this assumption, B. Eichler et al. (1992) determined the enthalpy and entropy of the dissociative adsorption for the reactions... 

The major difference between gas phase adsorption and electrosorption is that in the former case adsorption occurs on a bare surface, while in the latter case the metal substrate is solvated, i.e., covered with an adsorbed layer of solvent molecules. Thus it is evident that adsorption on electrodes is a replacement reaction. The observed standard free energy, enthalpy and entropy of adsorption can therefore only be related to the type of interaction between the adsorbate and the electrode if the corresponding thermodynamic quantities for the solvent are known and the number of solvent molecules replaced by each adsorbed organic molecule can be estimated. 

The standard free energy of adsorption is thus the difference between the standard free energies of adsorption for the organic and for n water molecules. The same statement may be applied to the standard enthalpy and entropy of adsorption on electrodes. 

The diffusion and permeabihty are closely interconnected with the solubility of a polymer. The permeation of the permeants through polymeric membrane film occurs in three stages (1) Sorption includes the initial adsorption, absorption, penetration, and dispersal of penetrant into the voids of the polymer membrane surface and cluster formation. The distribution of permeant in the membrane may depend on penetrant size, concentration, temperature, and swelling of the matrix as well as on time. The extent to which permeant molecules are sorbed and their mode of sorption in the polymer depends upon the enthalpy and entropy of permeant-polymer mixing, i.e., upon the activity of the permeant within the polymer at equilibrium. When both polymer-permeant and permeant-permeant interactions are weak relative to polymer-polymer interactions, i.e., dilute solution occurs, Henry s law is obeyed. The solubihty coefficient S is a constant independent of sorbed concentration at a given temperature. (2) Diffusion includes the transfer of the penetrant through the polymer membrane which depends on penetrant concentration that leads to a plasticization effect, penetrant size and shape, polymer Tg, time, and temperature. The diffusion coefficient is determined by Pick s first law of diffusion. (3) Desorption includes release of the penetrant from the opposite side of the membrane face. 

There is an advantage in using the constant surface pressure standard state since it yields molar properties (enthalpies and entropies of adsorption) analogous to those associated with phase changes evaluated from the Clapeyron equation [80]. The use of the standard state with constant surface concentration provides differential quantities for the enthalpy and entropy changes which are not directly comparable with those calculated using the methods of statistical thermodynamics. The values of AS calculated by these two standard states differ only by the gas constant, B, and are readily interconverted. 

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