Adsorption differential heats

Equilibrium vapor pressure of bulk liquid Relative pressure, p/p 0 Statistical mechanical partition function Density in molecules/cubic centimeter Gas constant per mole Number of moles of adsorbed gas Number of moles of adsorbent Isosteric heat of adsorption Differential heat of adsorption Isothermal heat of adsorption Adiabatic heat of adsorption... 

The heat evolved will now be a differential heat of adsorption, equal at constant volume to Qd or per mole, to qd - AI2, where Ae2 is the change in partial molar energy. It follows that... 

The integral heat of adsorption Qi may be measured calorimetrically by determining directly the heat evolution when the desired amount of adsorbate is admitted to the clean solid surface. Alternatively, it may be more convenient to measure the heat of immersion of the solid in pure liquid adsorbate. Immersion of clean solid gives the integral heat of adsorption at P = Pq, that is, Qi(Po) or qi(Po), whereas immersion of solid previously equilibrated with adsorbate at pressure P gives the difference [qi(Po) differential heat of adsorption q may be obtained from the slope of the Qi-n plot, or by measuring the heat evolved as small increments of adsorbate are added [123]. 

Fig. XVn-21. (a) Differential heat of adsorption of N2 on Graphon, except for Oand , which were determined calorimetrically. (From Ref. 89.) (b) Differential heat of adsorption of N2 on carbon black (Spheron 6) at 78.5 K (From Ref. 124).

Differential heats of adsorption generally decrease steadily with increasing amount adsorbed and, in the case of physical adsorption tend to approach the heat of liquefaction of the adsorbate as P approaches P. Some illustrative data... 

It is not surprising, in view of the material of the preceding section, that the heat of chemisorption often varies from the degree of surface coverage. It is convenient to consider two types of explanation (actual systems involving some combination of the two). First, the surface may be heterogeneous, so that a site energy distribution is involved (Section XVII-14). As an example, the variation of the calorimetric differential heat of adsorption of H2 on ZnO is shown in Fig. 

Fig. XVIII-11. Calorimetric differential heat of adsorption of H2 on ZnO. Dashed line differential heat of desorption. (From Ref. 104.)...

Fig. 2.25 The differential heat of adsorption of argon on carbon blacks at 78 K, before and after graphitizalion.. Spheron O, Graphon. , and El denote molar heat of sublimation and of evaporation respectively.

Fig. 4.6 Plat of the net differential heat of adsorption q — qj against the relative adsorption n/no.j, where H(,.2 is the adsorption at p/p° = 0-2. (A) active carbon (B) carbon black. (After Dubinin.)...

Differential heats of adsorption for several gases on a sample of a polar adsorbent (natural 2eohte chaba2ite) are shown as a function of the quantities adsorbed in Figure 5 (4). Consideration of the electrical properties of the adsorbates, included in Table 2, allows the correct prediction of the relative order of adsorption selectivity ... 

At low adsorbate loadings, the differential heat of adsorption decreases with increasing adsorbate loadings. This is direct evidence that the adsorbent surface is energetically heterogeneous, ie, some adsorption sites interact more strongly with the adsorbate molecules. These sites are filled first so that adsorption of additional molecules involves progressively lower heats of adsorption. 

At low relative humidities, adsorption is due to interaction of water with accessible hydroxyl groups. These are present on the lignin and on the carbohydrates ia the noncrystalline or poorly crystalline regions. The high differential heat of adsorption by dry wood, - 1.09 kJ/g (469 Btu/lb) water. 

At high relative humidities, adsorption is befleved to occur in response to a tendency for cellulose chains and lignin to disperse (solution tendency). Complete dispersion (dissolution) is prevented because of the strong interchain or interpolymer bonding at certain sites or regions. The differential heats of adsorption are much smaller than at low relative humidities. 

Differential Heats of Adsorption—corresponding with heats of evaporation ( 178), and evolved or absorbed when one equili-... 

Figure 7.5. Sticking coefficients along with differential heats of adsorption as measured by microcalorimetry for ethylene and acetylene on Rh(lOO). [Adapted from R. Kose, W.A. Brown and D.A. King, Chem. Rhys. Lett. 311 (1999) 109.]...

Nagoe, M. Morimoto, T. (1969). Differential heat of adsorption and entropy of water absorbed on zinc oxide surface. Journal of Physical Chemistry, 73, 3809-14. 

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 adsorption of dnB moles of gas, at a constant temperature, is accompanied usually by the transfer of an amount of heat dQ to the surrounding constant temperature shield. The magnitude of dQ depends, of course, upon the conditions prevailing during the adsorption process, but, in all cases, differential heats of adsorption are defined by... 

The usual, differential heat of adsorption, qisothermal process during which the volumes Fg and Fs of, respectively, the gas and adsorbent phases and the area, A, of the adsorbent remain constant, the adsorbent and chamber being inert (66) ... 

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 ... 

Differential heats of adsorption yield, in many instances, very relevant information concerning not only the type, or types, of bond between the adsorbed particles and the adsorbent but also the heterogeneity of the catalyst surface. Comparison of Eqs. (39) and (40) shows, however, that a closer approximation to true differential heats is obtained when smaller doses of gase are admitted in the adsorption cell. Clearly, a very sensitive calorimeter is required, particularly when adsorption occurs slowly. 

Calvet microcalorimeters are particularly convenient for such studies. Figure 19 show s, for instance, the evolution of the differential heat of adsorption of oxygen, measured at 30°C with a Calvet calorimeter, as a function of the total amount of oxygen adsorbed on the surface of a sample (100 mg) of nickel oxide, NiO(200) (19, 73). The volume of the first... 

Fig. 19. Differential heats of adsorption of oxygen on nickel oxide, NiO (200), at 30°C. Reprinted from (19) with permission. 

It must be acknowledged, however, that the determination of the number of the different surface species which are formed during an adsorption process is often more difficult by means of calorimetry than by spectroscopic techniques. This may be phrased differently by saying that the resolution of spectra is usually better than the resolution of thermograms. Progress in data correction and analysis should probably improve the calorimetric results in that respect. The complex interactions with surface cations, anions, and defects which occur when carbon monoxide contacts nickel oxide at room temperature are thus revealed by the modifications of the infrared spectrum of the sample (75) but not by the differential heats of the CO-adsorption (76). Any modification of the nickel-oxide surface which alters its defect structure produces, however, a change of its energy spectrum with respect to carbon monoxide that is more clearly shown by heat-flow calorimetry (77) than by IR spectroscopy. 

Fig. 22. Differential heats of adsorption of oxygen at 30°C on four different samples of pure and doped nickel oxide, (a) NiO (200), (b) NiO(Li) (250), (c) NiO (250), (d) NiO(Ga) (250). Reprinted from (8) with permission. Copyright 1969 by Academic Press, Inc. New York.

It ought to be verified, however, in all cases, that the experimental Q-9 curve truly represents the distribution of surface sites with respect to a given adsorbate under specified conditions. The definition of differential heats of adsorption [Eq. (39) 3 includes, in particular, the condition that the surface area of the adsorbent A remain unchanged during the experiment. The whole expanse of the catalyst surface must therefore be accessible to the gas molecules during the adsorption of all successive doses. The adsorption of the gas should not be limited by diffusion, either within the adsorbent layer (external diffusion) or in the pores (internal diffusion). Diffusion, in either case, restricts the accessibility to the adsorbent surface. 

The most reliable method for detecting the influence of internal diffusion upon the profile of Q-6 curves would be to determine calorimetrically and to compare the differential heats of adsorption of a given gas on the surface of similar samples with different porosities. But it would be very difficult... 

Fig. 25. Differential heats of adsorption of carbon monoxide at 30°C on fresh (A) or oxygenated (B) samples of a gallium-doped nickel oxide. Reprinted from (63) with permission J. Chim. Phys.

The stoichiometry of an interaction between gas molecules and preadsorbed species may thus be deduced from the modifications of the Q-6 curves for a given reactant which are produced by the presence of preadsorbed species on the solid. The results are, of course, particularly conclusive when the differential heats of adsorption of small doses of reactant are measured in a sensitive calorimeter. But, such a qualitative analysis of the calorimetric data, though very useful, does not allow definite conclusions. In the preceding example, for instance, a fraction of carbon dioxide may remain adsorbed on the solid ... 

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