Entropy change in adsorption

Evaluation of the entropy change in adsorption by the statistical mechanics approach can be found in numerous sources. Making use of Refs. [22,23], we will outline what is required for the present purpose. The partition function for a gaseous molecule qm is the product of the translational component qlr and the internal components rotational rot vibrational qviu and electronic qt. ... 

If one observes the above limitations for the standard values, a working formula which explicitly shows some dependencies of the entropy change in adsorption looks like... 

It can be expected that the electronic structure changes would be reflected by the heats of adsorption of suitable chosen molecules. Indeed, Shek et al (17) report that one maximum in the thermal desorption profile of CO shifts to lower temperatures when the Cu content of alloys increases. If the variations in the entropy changes upon adsorption can be neglected (probably - they can) this would indicate a lower heat of adsorption of CO on alloys than on Pt from abt. 33 Kcal/mol on pure Pt,to 26 Kcal/mol for an alloy with abt. 20% Cu. 

Most widely used is the two-dimensional combination of SEC and HPLC for copolymer characterization. The typical HPLC instrument is very similar to an SEC apparatus. While the ideal SEC separation is exclusively determined by entropy changes, in HPLC or adsorption chromatography it is assumed that no... 

The entropy factor should also be considered since cyclization results in a more ordered structure. The C5 cyclization of n-hexane involves an entropy decrease of about 15-17 entropy units (e.u.). The corresponding values for cyclohexane and benzene formation are about 25 and 38-45 e.u., respectively. These values are comparable with calculated values of adsorption entropy (29). Thus, adsorption of a molecule to be cyclized may supply a considerable part of the entropy change in other words, adsorption should take place in a geometry favorable for cyclization. This is one of the main roles of the catalyst. 

The very low water adsorption by Graphon precludes reliable calculations of thermodynamic quantities from isotherms at two temperatures. By combining one adsorption isotherm with measurements of the heats of immersion, however, it is possible to calculate both the isosteric heat and entropy change on adsorption with Equations (9) and (10). If the surface is assumed to be unperturbed by the adsorption, the absolute entropy of the water in the adsorbed state can be calculated. The isosteric heat values are much less than the heat of liquefaction with a minimum of 6 kcal./mole near the B.E.T. the entropy values are much greater than for liquid water. The formation of a two-dimensional gaseous film could account for the high entropy and low heat values, but the total evidence 22) indicates that water molecules adsorb on isolated sites (1 in 1,500), so that patch-wise adsorption takes place. 

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. 

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... 

The entropy of TMA+ adsorption is another important factor controlling lysis.25 The relevant quantity now is not ASads rMA+-ASadsNa+, but rather, ASadsXMA+. This is because regardless of the entropy change in replacing Na+ by TMA+, an unfavorable... 

When evaluating the entropy change in the mobile adsorption it is assumed that the rotational, vibrational and electronic degrees of freedom of the molecules are preserved. It allows considering only the translational entropy of the surface gas and the entropy of vibrations of its molecules perpendicular to the surface. These oscillations are induced by the characteristic vibration frequency of the adsorbent... 

The entropy change in localized adsorption is interpreted as the loss of three translational degrees of freedom and the gain of three vibrational degrees of freedom. Strictly speaking, the vibration frequencies vx, vy, vq are not exactly equal to... 

It is evident that the positive entropy change upon adsorption is by far the major contributor to the negative values of the free energy change and thus the main driving force for adsorption at the interface in these compounds. The —AG°d per —CH2— group at 25°C is 3.0-3.5 kJ increase in the length of the alkyl chain therefore increases the tendency of the compound to adsorb. 

Cyclic polymers are unable to form tails and hence the conformational energy change on adsorption is less for the cyclic polymer at low relative molecular masses when the surface concentration is small. As the relative molecular mass increases, cyclics form larger loops that reduce the entropy change on adsorption whereas in the linear polymer the contribution of the tails to the entropy change becomes diluted at higher relative molecular masses. Figure 5.17 shows the volume fraction profiles calculated from self-consistent field theory, with the separate contributions from loops and tails. 

Almost all adsorptive separation processes depend on physical adsorption rather than chemisorption and this is therefore the focus of the present review. The heat of adsorption provides a direct measure of the strength of the bonding between sorbate and surface. Physical adsorption from the gas phase is invariably exothermic, as may be shown by a simple thermodynamic argument. Since the adsorbed molecule has at most two degrees of translational freedom on the surface and since the rotational freedom of the adsorbed species must always be less than that of the gas phase molecule, the entropy change on adsorption (A5 = is necessarily negative. In... 

Source or sink term or consumption rate of gas species Specific entropy or entropy per unit mass or adsorption cross section of the adsorbing species Molar specific entropy Absolute entropy Change of entropy Change in absolute entropy Temperature High temperature Low temperature Dew point temperature Temperature of product of combustion Saturation temperature Critical temperature Reduced temperature Temperature at inlet of gas channel... 

In order to illustrate the role played by entropy S in adsorption processes, the entropy change AaS accompanying the adsorption in a very simple case was computed, by using the standard statistical mechanics rigid rotor/harmonic oscillator formula[94]. In Fig. 1.18 the adsorption of an Ar atom at the surface of an apolar solid is schematically illustrated. The Ar atom approaches the solid surface from the gas phase the translation entropy of the solid, which is fixed in the space, is taken as zero, whereas the free Ar atoms, before interacting with the solid surface, possess a translational entropy St which amounts to 150 and 170 J moP at T = 100 and 298K, respectively, at pAr = 100 Torr. 

Vibrational energy states are too well separated to contribute much to the entropy or the energy of small molecules at ordinary temperatures, but for higher temperatures this may not be so, and both internal entropy and energy changes may occur due to changes in vibrational levels on adsoiption. From a somewhat different point of view, it is clear that even in physical adsorption, adsorbate molecules should be polarized on the surface (see Section VI-8), and in chemisorption more drastic perturbations should occur. Thus internal bond energies of adsorbed molecules may be affected. 

Thus the entropy of localized adsorption can range widely, depending on whether the site is viewed as equivalent to a strong adsorption bond of negligible entropy or as a potential box plus a weak bond (see Ref. 12). In addition, estimates of AS ds should include possible surface vibrational contributions in the case of mobile adsorption, and all calculations are faced with possible contributions from a loss in rotational entropy on adsorption as well as from change in the adsorbent structure following adsorption (see Section XVI-4B). These uncertainties make it virtually impossible to affirm what the state of an adsorbed film is from entropy measurements alone for this, additional independent information about surface mobility and vibrational surface states is needed. (However, see Ref. 15 for a somewhat more optimistic conclusion.)... 

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