Adsorption thermodynamic quantities

The determination of adsorption thermodynamic quantities such as adsorption heats can now be performed through direct or indirect methods with a great degree of accuracy. The foundations of gas—solid interface calorimetry have been well established by combining adsorption microcalorimetry with adsorption in quasi-equilibrium. The experimental results reported so far, obtained from different calorimetries, concur with the values calculated from adsorption isotherms. 

Systems involving an interface are often metastable, that is, essentially in equilibrium in some aspects although in principle evolving slowly to a final state of global equilibrium. The solid-vapor interface is a good example of this. We can have adsorption equilibrium and calculate various thermodynamic quantities for the adsorption process yet the particles of a solid are unstable toward a drift to the final equilibrium condition of a single, perfect crystal. Much of Chapters IX and XVII are thus thermodynamic in content. 

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. 

A MC study of adsorption of living polymers [28] at hard walls has been carried out in a grand canonical ensemble for semiflexible o- 0 polymer chains and adsorbing interaction e < 0 at the walls of a box of size C. A number of thermodynamic quantities, such as internal energy (per lattice site) U, bulk density (f), surface coverage (the fraction of the wall that is directly covered with segments) 9, specific heat C = C /[k T ]) U ) — U) ), bulk isothermal compressibility... 

Once the kinetic parameters of elementary steps, as well as thermodynamic quantities such as heats of adsorption (Chapter 6), are available one can construct a micro-kinetic model to describe the overall reaction. Otherwise, one has to rely on fitting a rate expression that is based on an assumed reaction mechanism. Examples of both cases are discussed this chapter. 

Cassel and Neugebauer (18) investigated the adsorption of some of the rare gases on mercury over a range of temperatures by surface tension measurements. They found that the curves for surface pressure against gas pressure were almost linear and it is possible to interpolate their results to the standard state ir = 0.0608 dynes/cm., obtaining the pressure p0 in equilibrium with a film at this surface pressure. The thermodynamic quantities for the adsorption of xenon are given in Table IV ... 

Taylor and Sickman (31) measured the adsorption of water on ZnO in the neighborhood of 634°K. Data were not available at that time to indicate the extent of the surface available, so as standard state we adopt a system containing 1.03 cc. (measured at N.T.P.) per g. of adsorbent. As far as may be ascertained from isotherms, this represents the surface about half covered. The thermodynamic quantities for this adsorption are given in Table XI. 

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. 

It is important to recognize that Kp is unitless, and is related to thermodynamic quantities by Eq. 9.93, for example. However, Eq. 11.17 has exactly the same form as the classic Langmuir adsorption isotherem, Eq. 11.11, if we take K = Kp/p°. Thus the two approaches are entirely equivalent. In addition the discussion above shows how the more restrictive form that is usually written for the Langmuir adsorption isotherm can be converted to the extensible mass-action kinetics form to be used, for example, within a more extensive surface reaction mechanism. 

In this section we consider the thermodynamics of heterogeneous processes, particularly, adsoption processes. Entropy losses upon converting a gas-phase species to a surface-adsorbed species are very important in such cases. The heat of adsorption must counterbalance the entropy decrease for the process to occur spontaneously. These thermodynamic quantities are considered in Sections 11.5.1 and 11.5.2... 

Empirical models are frequently applied in chemistry to relate experimental observations to physicochemical or thermodynamical quantities. This has extensively been used over several decades for the interpretation of experimental results obtained from gas phase adsorption processes and is still used to interpret the gas chromatographic results discussed in Chapter 7. These empirical procedures and correlations are outlined in Chapter 6 for a deeper understanding of one of the possible ways to interpret experimental findings from gas phase chemistry. 

Partial molar thermodynamic quantities close to bulk water values. Region of rapid rise in adsorption isotherm. Transition region in heat capacity... 

The aim of this chapter is simply to introduce a selection of the most appropriate thermodynamic quantities for the processing and interpretation of adsorption isotherm and calorimetric data, which are obtained by the methods described in Chapter 3. We do not consider here the thermodynamic implications of capillary condensation, since these are dealt with in Chapter 7. Special attention is given to the terminology and the definition of certain key thermodynamic quantities, for example, the difference between corresponding molar integral quantities and differential quantities. 

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 ... 

If the adsorption isotherm is entirely reversible (i.e. the adsorption and desorption paths coincide), we can assume that thermodynamic equilibrium has been established and maintained over the complete range of pip0. It is then possible to obtain useful thermodynamic quantities from the adsorption isotherm, by applying Equation (2.20), since each point on the isotherm represents a particular adsorbed state defined by one value of r (or n) and one value of the equilibrium pressure p (at temperature T). 

The difference between a molar surface excess thermodynamic quantity xar r and the corresponding molar quantity x p for the gaseous adsorptive at the same equilibrium T and p is usually called the integral molar quantity of adsorption, and is denoted Aads r,r ... 

When the main purpose of the gas adsorption measurements is to characterize the adsorbent surface or its pore structure, the preferred approach must be to follow the change in the thermodynamic quantity (e.g. the adsorption energy) with the highest available resolution. This immediately leads to a preference for the differential option, simply because the integral molar quantity is equivalent to the mean value of the corresponding differential quantity taken up to a recorded amount adsorbed. Their relationship is indicated by the mathematical form of Equation (2.64), which is explained in the following section. 

In Chapter 2 we have introduced a number of thermodynamic surface excess quantities (Equations (2.11)—(2.14)) in the case of a simple gas adsorption system involving a single adsorptive. These quantities were expressed as a function of the surface excess amount, na. In the case of the process of immersion of a solid in a pure liquid, the same surface excess quantities can still be defined and it is useful to express them as a function of the surface area. Thus ... 

Since l is a thermodynamic quantity, the most reliable procedures for its determination are based on a thermodynamic analysis of adsorption data, possibly at low coverages. Adsorption data to be analyzed by the Gibbs adsorption equation can be obtained by measuring the interfacial tension y, the charge density crM or the differential capacity C. Direct y measurements are equilibrium measurements that can only be carried out on mercury. Direct charge measurements are conveniently carried out by the potential-step chronocoulometric technique, which can be... 

The definition of the various heats of adsorption/desorption and their relationship with thermodynamic quantities directly obtainable by calorimetry are given in Table 9.2 [2]. 

Several heats, energies and other thermodynamic quantities for adsorption can, and have been, defined, depending on the conditions under which the experiments have been performed. The most rational approach is to consider the way In which the adsorption calorimetry is carried out. We shall do so after defining some relevant parameters... 

Isosterlc thermodynamic quantities are in practice not directly measured but follow from the shift of the adsorption equilibrium, caused by changes in temperature and pressure. To formulate this shift, we equate the shifts of the chemical potentials of gas and adsorbate ... 

G. Schay, A Comprehensixje Presentation of the Thermodynamics of Adsorptive Excess Quantities, Pure Appl Chem. 48 (1976) 393. 

The description of real adsorption requires to take into account two main effects on the calculation of the thermodynamic quantities lateral ad-ad interactions, and characteristics of the energy surface. In addition, in the case of multicomponent adsorption, different species could "see" different disordered topographies. 

Other thermodynamic quantities that can be evaluated equally well by Monte Carlo and by MD simulations include the molar energy of adsorption, which is just the total potential energy of the adsorbed particles divided by their number, for a classical system [7] the surface tension of the adsorbed fUm [3] and the pressure normal to the surface. In principle, the dependence of the normal component of the pressure tensor upon amount adsorbed could be used to construct an adsorption isotherm since this pressure must be independent of distance from the surface in order to maintain mechanical equilibrium [3,7]. Thus, fer from the surface it must be equal to the bulk gas pressure. However, in practice the normal pressure is hard to evaluate with sufficient accuracy to be useful in an isotherm calculation, especially at the temperatures at or below the normal boiling point of the bulk... 

In general, any extensive thermodynamic quantity X may be written as the sum of the contributions from the adsorbent, the adsorbate, and the adsorptive ... 

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