Thermodynamics, adsorbate

The bulk properties of celluloses are generally influenced by adsorbed moisture. The effect of the change in bulk solid properties for microcrystalline cellulose has been demonstrated by a tableting operation in a very simplistic manner. Dry microcrystalline cellulose (%MC = 0.07) was compared with material with a moisture content above that associated with completion of the monolayer (%MC = 5.1). A thermodynamic picture of the character of water in these samples can be based on the adsorbate thermodynamic properties A// > 3.5kcal/mole (14.65 kJ/mole),... 

Figure 8.2 summarizes the methods discussed here. The organization of this chapter is as follows. First, methods for calculating the rate constant of an elementary step are described. Then DFT is briefly introduced for estimation of adsorption properties and barriers, followed by an outline of selected statistical Ihermodynantics. Examples of the thermochemistry on Ni(l 11) and Pt(lll) are presented to address thermodynamic consistency of the DFT-predicted adsorption properties. S iempirical methods for predicting adsorbate thermodynamic properties and kinetic parameters are also presented. With this input, microkinetic models can be solved. Finally, analytical tools are described to develop and analyze a nticrokinetic model, with the water-gas shift (WGS) reaction on Pt-based catalysts taken as an example. 

Adsorbate-adsorbent thermodynamic equilibrium relationships (as described in Chapters), including appropriate interaction data for multicomponent systems-, it is necessary initially to identify an adsorbent which is... 

The treatments that are concerned in more detail with the nature of the adsorbed layer make use of the general thermodynamic framework of the derivation of the Gibbs equation (Section III-5B) but differ in the handling of the electrochemical potential and the surface excess of the ionic species [114-117]. The derivation given here is after that of Grahame and Whitney [117]. Equation III-76 gives the combined first- and second-law statements for the surface excess quantities... 

Equations X-12 and X-13 thus provide a thermodynamic evaluation of the change in interfacial free energy accompanying adsorption. As discussed further in Section X-5C, typical values of v for adsorbed films on solids range up to 100 ergs/cm. ... 

Statistical Thermodynamics of Adsorbates. First, from a thermodynamic or statistical mechanical point of view, the internal energy and entropy of a molecule should be different in the adsorbed state from that in the gaseous state. This is quite apart from the energy of the adsorption bond itself or the entropy associated with confining a molecule to the interfacial region. It is clear, for example, that the adsorbed molecule may lose part or all of its freedom to rotate. 

However, a body of thermodynamic treatment has been developed on the basis that the adsorbent is inert and with attention focused entirely on the adsorbate. The abbreviated presentation given here is based on that of Hill (see Refs. 65 and 113) and of Everett [114]. First, we have the defining relationships ... 

Thus the new thermodynamic heats and entropies of adsorption differ from the preceding ones by the heats and entropies of vaporization of liquid adsorbate. 

There are alternative ways of defining the various thermodynamic quantities. One may, for example, treat the adsorbed film as a phase having volume, so that P, V terms enter into the definitions. A systematic treatment of this type has been given by Honig [116], who also points out some additional types of heat of adsorption. 

It is generally assumed that isosteric thermodynamic heats obtained for a heterogeneous surface retain their simple relationship to calorimetric heats (Eq. XVII-124), although it may be necessary in a thermodynamic proof of this to assume that the chemical potential of the adsorbate does not show discontinu-... 

In Section XVII-16C there is mention of S-shaped isotherms being obtained. That is, as pressure increased, the amount adsorbed increased, then decreased, then increased again. If this is equilibrium behavior, explain whether a violation of the second law of thermodynamics is implied. A sketch of such an isotherm is shown for nitrogen adsorbed on a microporous carbon (see Ref. 226). 

Ideal Adsorbed Solution Theory. Perhaps the most successful approach to the prediction of multicomponent equiUbria from single-component isotherm data is ideal adsorbed solution theory (14). In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equiUbrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equihbrium pressure for the pure component at the same spreadingpressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption (7) as well as in the original paper (14). Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, ate not consistent with an ideal adsorbed... 

Thermodynamically Consistent Isotherm Models. These models include both the statistical thermodynamic models and the models that can be derived from an assumed equation of state for the adsorbed phase plus the thermodynamics of the adsorbed phase, ie, the Gibbs adsorption isotherm,... 

Statistical Thermodynamic Isotherm Models. These approaches were pioneered by Fowler and Guggenheim (21) and Hill (22). Examples of the appHcation of this approach to modeling of adsorption in microporous adsorbents are given in references 3, 23—27. Excellent reviews have been written (4,28). 

Isotherm Models for Adsorption of Mixtures. Of the following models, all but the ideal adsorbed solution theory (lAST) and the related heterogeneous ideal adsorbed solution theory (HIAST) have been shown to contain some thermodynamic inconsistencies. References to the limited available Hterature data on the adsorption of gas mixtures on activated carbons and 2eohtes have been compiled, along with a brief summary of approximate percentage differences between data and theory for the various theoretical models (16). In the following the subscripts i and j refer to different adsorbates. 

Physica.1 Properties. Carbonyl sulfide [463-58-1] (carbon oxysulfide), COS, is a colorless gas that is odorless when pure however, it has been described as having a foul odor. Physical constants and thermodynamic properties are Hsted ia Table 1 (17,18). The vapor pressure has been fitted to an equation, and a detailed study has been made of the phase equiUbria of the carbonyl sulfide—propane system, which is important ia the purification of propane fuel (19,20). Carbonyl sulfide can be adsorbed on molecular sieves (qv) as a means for removal from propane (21). This approach has been compared to the use of various solvents and reagents (22). 

This reaction is catalyzed by iron, and extensive research, including surface science experiments, has led to an understanding of many of the details (72). The adsorption of H2 on iron is fast, and the adsorption of N2 is slow and characterized by a substantial activation energy. N2 and H2 are both dis so datively adsorbed. Adsorption of N2 leads to reconstmction of the iron surface and formation of stmctures called iron nitrides that have depths of several atomic layers with compositions of approximately Fe N. There is a bulk compound Fe N, but it is thermodynamically unstable when the surface stmcture is stable. Adsorbed species such as the intermediates NH and NH2 have been identified spectroscopically. 

Because some substances may preferentially adsorb onto the surface of the electrode, the composition near the iaterface differs from that ia the bulk solution. If the cell current is 2ero, there is no potential drop from ohmic resistance ia the electrolyte or the electrodes. Yet from the thermodynamic analysis it is seen that there is a measurable cell potential. The question from where this potential arises can be answered by considering the iaterface. 

When more than one adsorbed species or more than two ion-exchanged species interact in some manner, equilibrium becomes more complicated. Usually, thermodynamics provides a sound basis for prediction. 

Thermodynamic paths are necessary to evaluate the enthalpy (or internal energy) of the fluid phase and the internal energy of the stationary phase. For gas-phase processes at low and modest pressures, the enthalpy departure function for pressure changes can be ignored and a reference state for each pure component chosen to be ideal gas at temperature and a reference state for the stationarv phase (adsorbent plus adsorbate) chosen to be adsorbate-free solid at. Thus, for the gas phase we have... 

This expression can be used to describe both pore and solid diffusion so long as the driving force is expressed in terms of the appropriate concentrations. Although the driving force should be more correctly expressed in terms of chemical potentials, Eq. (16-63) provides a qualitatively and quantitatively correct representation of adsorption systems so long as the diffusivity is allowed to be a function of the adsorbate concentration. The diffusivity will be constant only for a thermodynamically ideal system, which is only an adequate approximation for a limited number of adsorption systems. 

Zeohte ciyst lite diffusivities for sorbed gases range from 10" to lO" " cmVs. These diffusivities generally show a strong increase with the adsorbate concentration that is accounted for by the Darken thermodynamic correction factor... 

The effect of increasing pressure is to move the average hydrocarbon content towards the heavier species, but increasing temperature seems to favour the production of lighter species. The final proportions are also determined by the state of the catalyst, and the physical anangement of tire reactor. The formation of the oxygenated compounds could also involve reactions between the H2O content of tire gas in the form of adsorbed OH radicals and hydrocarbon radicals since the production of these molecules is also well beyond the thermodynamic expectation. 

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