Entropy of sorption

In principle, the Henry constant may be predicted theoretically by evaluation of the configuration integral for an occluded molecule. Such calculations are subject to the considerable uncertainties implicit in theoretical potential calculations (17), and the utility of this approach is now limited to simple spherical molecules such as the inert gases (18, 19). A fair estimate of the standard entropy of sorption or of the value of K0 may, however, be obtained from a simple idealized model. 

Standard Entropies of Sorption. The standard entropies of sorption are almost independent of temperature over the temperature intervals involved (excluding fluctuations from experimental uncertainties) but vary considerably in magnitude among the different crystals. The larger the value of — AE9, the larger tends to be that of — ASe, although this overall relation between AE6 and AS6 is also subject to specific fluctuation. ASf... 

Both models give substantially similar integral molar entropies of sorption. 

As the two sorbates methane and krypton on 5A appeared to have different mechanistic behaviour, further theoretical study appeared warranted. Two hypothetical gases P and Q whose properties are tabulated in Table 1 were used for comparison with the behaviour of methane and krypton. Hypothetical gas P was designed to have a Henry constant equal to methane, but to be a localized sorbate having entropy of sorption values decreasing incrementally as for krypton. Conversely, hypothetical gas Q had a Henry constant equal to that of krypton, but entropy of sorption values non-localized and decreasing incrementally as for methane. 

The total partial molar entropy of sorption (AS°t =AS°s) is then calculated using... 

The energetics of the sorption process are in satisfactory agreement with the views developed here. The first amounts of water bound by dry cellulose give rise to a considerable evolution of heat, the differential heat of sorption of the dry material being about 4300 cal/mol HgO. Stamm and Loughborough have shown the differential heat and the entropy of sorption to be independent upon temperature up to a moisture content of 6% for native cotton fibres, and, moreover, the entropy to be negative. 

Additional information concerning the nature of an adsorbed species may sometimes be obtained from a detailed analysis of the entropy of sorption. The absolute molar entropy of a gaseous molecule may be calculated from the Sackur-Tetrode equation, or its extension for a polyatomic species. Equa-... 

The thermodynamic analysis of these systems played an important role in the interpretation of these data and of the high selectivity. It was found that selective sorption of complex organic ions is accompanied by an increase in the entropy of the system (Table 6). 

A comparison of the effects of increasing selectivity of sorption of organic counterions and the entropy control of the replacement of small ions by large organic ions in CP is a rational explanation of these phenomena. 

Apart from the above mentioned redox type reactions, we like to consider (in connection with work to be published by us elsewhere) another type of relaxations, due to the possible reorganisations of sorption intermediates on the catalyst surface, as suggested by some investigations in our laboratory. This structuring on the catalyst surface is equivalent to a change in the entropy of the system catalyst surface / adsorbed intermediates and seems to be responsible e.g. for the selectivity change under transient conditions in the oxidation of hydrocarbons. Actually this structural organization of the surface intermediates is also a rate process which can be observed under transient conditions. 

The standard heat of sorption, Afl°, can then be interpreted in terms of appropriate energy contributions and the corresponding entropy, AS°, in terms of various degrees of freedom of the guest molecules relative to the host lattice (Table II) (10). An example of the use of the above method is given elsewhere in this volume (11). In comparing observed standard entropies with those based on the models of Table II, only empirical methods (12) are available for a priori estimates of the frequencies v. Nevertheless, comparisons have been of considerable interest (10). 

The virial isotherm equation, which can represent experimental isotherm contours well, gives Henry s law at low pressures and provides a basis for obtaining the fundamental constants of sorption equilibria. A further step is to employ statistical and quantum mechanical procedures to calculate equilibrium constants and standard energies and entropies for comparison with those measured. In this direction moderate success has already been achieved in other systems, such as the gas hydrates 25, 26) and several gas-zeolite systems 14, 17, 18, 27). In the present work AS6 for krypton has been interpreted in terms of statistical thermodynamic models. 

Figure 2. Variation of the integral net heat of sorption (—Qs), change of free energy (—AG), and change of the integral entropy (TaS) with surface coverage (6) of beechwood (39)...

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" . ... 

Figure 4. Standard sorption entropies of N2O 2nd CO2 on CaLSX and NaLSX... 

Lyklema (1985) provides the following semiquantitative thermodynamic argument. Suppose that a given polymer molecule loses a conformational entropy of 100 (where is Boltzmann s constant) upon sorption in a certain... 

When wood below the fiber-saturation point interacts with water, heat is evolved, and there are changes in the free energy and entropy of the sorbed water. Furthermore, the wood exerts swelling forces that can be measured. These effects can be treated by classical thermodynamic methods although moisture sorption by wood is not a perfectly reversible process because sorption hysteresis is involved, as was pointed out in the section on Moisture Sorption Isotherms (p. 136). 

Free Energy and Entropy Changes. The heat of sorption Qi consists of two parts, the free energy change AG and the entropy change AS. The loss in free energy AG (cal/g of water) can be calculated at any moisture content by... 

Inverse gas chromatography, IGC, has been used to study water sorption of two poly (vinylidene chloride-vinyl chloride) and poly (vinylidene chloride-acrylonitrile) copolymers, at temperatures between 20 and 50°C and low water uptakes. It was found that the specific retention volume of water increases with decreasing amount of water injected, increases dramatically with decreasing temperature and strongly depends on the type of copolymer. Thermodynamic parameters of sorption namely free energy, entropy, enthalpy of sorption and activity coefficient were calculated. 

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