Gibbs representation

Figure 2.1. The Gibbs representation of the surface excess amount c, local concentration dn/dV of adsorbable gas z, distance from the surface.

The Gibbs representation provides a simple, clear-cut mode of accounting for the transfer of adsorptive associated with the adsorption phenomenon. The same representation is used to define surface excess quantities assumed to be associated with the GDS for any other thermodynamic quantity related with adsorption. In this way, surface excess energy (U°), entropy (Sa) and Helmholtz energy (Fa) are easily defined (Everett, 1972) as ... 

For the sake of completeness, Ua and Ha are separately defined above. Actually, when the enthalpy is defined in the standard way (H-U + pV), the Gibbs representation results in a useful simplification since the surface excess volume Va<=0 and we can write Ha = Ua (as in Sections 2.4.2 and 2.5.1). 

Thermodynamic Quantities Related to the Adsorbed States in the Gibbs Representation... 

Both have the advantage of giving a sample volume (and therefore a location of the dividing surface) which is, by definition, perfectly reproducible from one adsorption bulb to another and from one laboratory to another. Even if not always realistic, it is a sound convention, if the aim is to obtain reproducible measurements and calculations and is consistent with the spirit of the Gibbs representation. It is, for these reasons, certainly well suited for the study of reference materials. Of course, this approach would replace Step 3 in the procedure described above, whereas Steps 1 and 2 would remain necessary. 

Figure 3.22. Buoyancy in relation to the Gibbs representation the surface excess mass ma and the corresponding buoyancy effect is indicated (top left).

A pertinent question is as the volume of the adsorbed phase increases, do we have to take into account the corresponding increase of buoyancy (e.g. the buoyancy doubles after saturation of an adsorbent with 50% porosity). The answer is no, provided we want to assess the surface excess mass m°. As illustrated in Figure 3.22, because of the buoyancy effect, we do not measure the total mass of the adsorbed layer (shaded+hatched areas) but simply a surface excess mass (hatched area only). Thus, adsorption gravimetry and the Gibbs representation are highly compatible (Findenegg, 1997). 

The above equations are all based on the internal energy. Similar equations can be written with the enthalpy since the surface excess enthalpy and energy are identical in the Gibbs representation when 1 =0 (Harkins and Boyd, 1942). Therefore the various energies of immersion defined by Equations (5.6)—(5.8) are all virtually equal to the corresponding enthalpies of immersion, i.e. (A inmH°, AimmHr and Ah 1), thus ... 

Thermodynamic quantities related to the adsorbed states in the Gibbs representation 36... 

Fig. 7.2 Concentration of the gas c as a function of the distance z from the solid surface. Graphic representation of adsorbed amount and Gibbs surface excess amount, a Layer model b Gibbs representation...

Guffey and Wehe (1972) used excess Gibbs energy equations proposed by Renon (1968a, 1968b) and Blac)c (1959) to calculate multicomponent LLE. They concluded that prediction of ternary data from binary data is not reliable, but that quarternary LLE can be predicted from accurate ternary representations. Here, we carry these results a step further we outline a systematic procedure for determining binary parameters which are suitable for multicomponent LLE. 

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. ... 

Figure A2.5.2. Schematic representation of the behaviour of several thennodynamic fiinctions as a fiinction of temperature T at constant pressure for the one-component substance shown in figure A2.5.1. (The constant-pressure path is shown as a dotted line in figure A2.5.1.) (a) The molar Gibbs free energy Ci, (b) the molar enthalpy n, and (c) the molar heat capacity at constant pressure The fimctions shown are dimensionless...

Figure 4.12 (a) Gibbs energy representation of the phases in the system Zr02-Ca0 at 1900 K. McaO - MzrO = TSZ n°t deluded for clarity, (b) Calculated phase diagram of the system Zr02 Ca0. Thermodynamic data are taken from reference [9]. 

Figure 2.24 The Gibbs triangle for the representation of the composition in a ternary system.

The Gibbs free energy of formation for small values of r using classical nucleation theory (- - -)> classical nucleation theory with Tolman s representation of the... 

This chapter will begin, very briefly, with the thermodynamic representation of Gibbs energy for stoichiometric compounds before concentrating on the situation when mixing occurs in a phase. 

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