Differential standard entropy of adsorption

The differential standard entropy of adsorption A may also be deduced from... 

The most convenient method of study of adsorption at small coverage is gas chromatography. By this method it is possible to determine the constant of adsorption equilibrium (retention volume) and from the retention volumes at different temperatures to calculate the heat of adsorption and changing of differential standard entropy of adsorption. If the support for fullerene crystals is the adsorbent with inert and small specific surface area so the retention of compounds will be determined by intermolecular interaction of compounds with fullerene crystal surface. The deposition of fullerene crystals on support surface is quite difficult owing to small solubility of fullerene in organic solvents [21, 22] as well as small vapour pressure of fullerene [23]. 

From the retention volumes at different temperatures the heats of adsorption at small coverage and changes of differential standard entropy of adsorption were calculated (see Table 1 and 2). The heats of adsorption are less sensitive to the properties of fullerene molecules and to the distinction in geometry of surface of fullerene crystals and surface of Carbopack. 

In the previous section it was shown that the term heat of adsorption may represent different functions, depending on the experimental conditions under which it is determined. The situation is analogous with the entropy of adsorption which can also be defined in several ways (/1). It is always necessary to specify whether the function considered is a true differential, a derivative, or an integral entropy, and also whether it refers to an equilibrium state (defined by p and T) or to a standard state (defined by p° and T). Moreover, various entropies of adsorption may be defined by choosing different standard states for the adsorptive (this state may be gaseous, but also liquid or solid). In this section, all the thermodynamic quantities of the adsorbate will be defined relative to a Gibbs surface for simplicity, but defining them in terms of an interfacial layer yields the same results. 

The thermodynamic characteristic of adsorption from solutions can be determined from the dependence of adsorption on temperature. But the determination of adsorption isotherms from solution at different temperatures is the rather complicate problems. Liquid chromatography may be very useful method for the determination of thermodynamic characteristics of adsorption at small coverage [11] because of the measurement of retention volume (the Henry constant) at different temperatures of the chromatographic columns makes it possible to calculate the heats of adsorption and the differential standard change entropy of adsorption from ... 

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. 

The first attempts to predict macroscopic properties such as Henry constants, initial isosteric heats of adsorption, or changes in the standard differential entropies for noble gases, H2, N2, O2, CO, H2O, NH3, CO2, n-alkanes up to Cg, ethylene, acetylene, and benzene in silicalite were performed by Kiselev and coworkers about 20 years ago.224-227 These workers used potential param-... 

The quantities of interest are (i) n, moles of adsorbate (ii) m, mass of adsorbent (iii) V, volume (iv) p, pressure (v) T, absolute temperature (vi) R, molar ideal gas constant (vii) A, surface area of the adsorbent (viii) Q heat (ix) U, internal energy (x) H, enthalpy (xi) 5, entropy and (xii) G, Gibbs free energy. Superscripts refer to differential quantities (d) experimentally measured quantities (exp) integral quantities (int) gas phase (g), adsorbed phase (s) and solid adsorbent (sol) quantities standard state quantities (°). Subscript (a) refers to adsorption phenomena (e.g. AaH) [13, 91]. 

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