Equilibrium heat of adsorption

The quantity 2 has been called (by Hill) the equilibrium heat of adsorption. It follows from the foregoing definitions that... 

Keywords Adsorption, absorption, thermal energy storage, adsorption equilibrium, heat of adsorption... 

The quantity A Ji was called the equilibrium heat of adsorption by Hill (1949) and Everett (1950), but this is no longer appropriate. 

Thus, on a nonuniform surface on which the activation energies for the rate of adsorption varies with coverage, it is expected that there will also be some corresponding variation in the heat of adsorption. However, one energy is associated with an activation barrier E, and the other with an equilibrium heat of adsorption —A.H there is therefore no a priori reason for a specific functional relationship to exist between... 

As also noted in the preceding chapter, it is customary to divide adsorption into two broad classes, namely, physical adsorption and chemisorption. Physical adsorption equilibrium is very rapid in attainment (except when limited by mass transport rates in the gas phase or within a porous adsorbent) and is reversible, the adsorbate being removable without change by lowering the pressure (there may be hysteresis in the case of a porous solid). It is supposed that this type of adsorption occurs as a result of the same type of relatively nonspecific intermolecular forces that are responsible for the condensation of a vapor to a liquid, and in physical adsorption the heat of adsorption should be in the range of heats of condensation. Physical adsorption is usually important only for gases below their critical temperature, that is, for vapors. 

The basic assumption is that the Langmuir equation applies to each layer, with the added postulate that for the first layer the heat of adsorption Q may have some special value, whereas for all succeeding layers, it is equal to Qu, the heat of condensation of the liquid adsorbate. A furfter assumption is that evaporation and condensation can occur only from or on exposed surfaces. As illustrated in Fig. XVII-9, the picture is one of portions of uncovered surface 5o, of surface covered by a single layer 5, by a double-layer 52. and so on.f The condition for equilibrium is taken to be that the amount of each type of surface reaches a steady-state value with respect to the next-deeper one. Thus for 5o... 

The term heat of adsorption has been defined in a number of different ways. Unfortunately, the initial and final states of the adsorption system and the conditions under which the exchange of heat takes place have not always been adequately defined. As in all applications of thermodynamics, it is essential that the experimental data refer to a system which has reached equilibrium. 

H2O/100 kg of adsorbent. At equilibrium and at a given adsorbed water content, the dew point that can be obtained in the treated fluid is a function only of the adsorbent temperature. The slopes of the isosteres indicate that the capacity of molecular sieves is less temperature sensitive than that of siUca gel or activated alumina. In another type of isostere plot, the natural logarithm of the vapor pressure of water in equiUbrium with the desiccant is plotted against the reciprocal of absolute temperature. The slopes of these isosteres are proportional to the isosteric heats of adsorption of water on the desiccant (see... 

In a recent paper [11] this approach has been generalized to deal with reactions at surfaces, notably dissociation of molecules. A lattice gas model is employed for homonuclear molecules with both atoms and molecules present on the surface, also accounting for lateral interactions between all species. In a series of model calculations equilibrium properties, such as heats of adsorption, are discussed, and the role of dissociation disequilibrium on the time evolution of an adsorbate during temperature-programmed desorption is examined. This approach is adaptable to more complicated systems, provided the individual species remain in local equilibrium, allowing of course for dissociation and reaction disequilibria. 

The heat of adsorption can be evaluated from adsorption equilibrium data and Eq. (3). If b values are known for different temperatures, the biosorption heats can be calculated from the plot of In b versus 1/T [Ozer, 2003]. 

In model equations, Uf denotes the linear velocity in the positive direction of z, z is the distance in flow direction with total length zr, C is concentration of fuel, s represents the void volume per unit volume of canister, and t is time. In addition to that, A, is the overall mass transfer coefficient, a, denotes the interfacial area for mass transfer ifom the fluid to the solid phase, ah denotes the interfacial area for heat transfer, p is density of each phase, Cp is heat capacity for a unit mass, hs is heat transfer coefficient, T is temperature, P is pressure, and AHi represents heat of adsorption. The subscript d refers bulk phase, s is solid phase of adsorbent, i is the component index. The superscript represents the equilibrium concentration. 

Here we illustrate how to use kinetic data to establish a power rate law, and how to derive rate constants, equilibrium constants of adsorption and even heats of adsorption when a kinetic model is available. We use the catalytic hydrodesulfurization of thiophene over a sulfidic nickel-promoted M0S2 catalyst as an example ... 

CO oxidation is often quoted as a structure-insensitive reaction, implying that the turnover frequency on a certain metal is the same for every type of site, or for every crystallographic surface plane. Figure 10.7 shows that the rates on Rh(lll) and Rh(llO) are indeed similar on the low-temperature side of the maximum, but that they differ at higher temperatures. This is because on the low-temperature side the surface is mainly covered by CO. Hence the rate at which the reaction produces CO2 becomes determined by the probability that CO desorbs to release sites for the oxygen. As the heats of adsorption of CO on the two surfaces are very similar, the resulting rates for CO oxidation are very similar for the two surfaces. However, at temperatures where the CO adsorption-desorption equilibrium lies more towards the gas phase, the surface reaction between O and CO determines the rate, and here the two rhodium surfaces show a difference (Fig. 10.7). The apparent structure insensitivity of the CO oxidation appears to be a coincidence that is not necessarily caused by equality of sites or ensembles thereof on the different surfaces. 

To run adsorption storage systems efficiently the appropriate adsorbent has to be used. The right choice is possible on the basis of the measured adsorption equilibrium. The adsorption equilibrium of water vapor and different adsorbents (zeolites and silica gels) was experimentally found [3,4], The differential heat of adsorption (AHd) was calculated from the equilibrium data. 

The thermodynamic heats of adsorption (AH) were calculated using equation 3, which is derived as follows from the relationship between free energy and the equilibrium constant ... 

The variation of activation energy as a function of alloy composition is shown in Fig. 23. There is a fairly sharp rise in activation energy from about 0.4 kcal/mole at 50% Ag to 5.9 kcal/mole on pure Ag, but the increase observed with Pd-Au wires 127) was more abrupt. Pd-Ag alloy wires 148) showed a gradual increase from about 2 kcal/mole for pure Pd to 4 kcal/mole at 60% Ag, followed by a more rapid, smooth increase from 4.9 kcal/mole at 80% Ag to 11.5 kcal/mole on pure Ag. The results on films were also used to derive heats of adsorption at equilibrium coverage. Values increased from 1.29 kcal/mole on the 68% Ag alloy to 2.89 kcal/mole on pure Ag. 

True differential heats of adsorption may be determined from equilibrium data when adsorption is thermodynamically reversible. However, when this process is not reversible, a calorimeter must be employed, and the so-called differential heats, which are then measured, refer actually to the average heats evolved during the adsorption of small doses of gas ... 

The final rate expressions, which were used in the present work, were given by Hou and Hughes (2001). In these rate expressions all reaction rate and equilibrium constants were defined to be temperature-dependent through the Arrhenius and van t Hoff equations. The particular values for the activation energies, heats of adsorption, and pre-exponential constants are available in the original reference and were used in our work without alteration. 

A common feature of both NaGeX and SnSbO catalysts is the higher cis/trans equilibrium constants obtained in the adsorbed state in comparison with that of the gas phase value. This difference reflects the greater tendency for adsorption of the cis 2-butene with respect to the trans isomer (4,5,39). On most catalysts the difference in the apparent heats of adsorption is roughly 0.5 kcal mol (40). 

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