Adsorption average heat

Brunauer (see Refs. 136-138) defended these defects as deliberate approximations needed to obtain a practical two-constant equation. The assumption of a constant heat of adsorption in the first layer represents a balance between the effects of surface heterogeneity and of lateral interaction, and the assumption of a constant instead of a decreasing heat of adsorption for the succeeding layers balances the overestimate of the entropy of adsorption. These comments do help to explain why the model works as well as it does. However, since these approximations are inherent in the treatment, one can see why the BET model does not lend itself readily to any detailed insight into the real physical nature of multilayers. In summary, the BET equation will undoubtedly maintain its usefulness in surface area determinations, and it does provide some physical information about the nature of the adsorbed film, but only at the level of approximation inherent in the model. Mainly, the c value provides an estimate of the first layer heat of adsorption, averaged over the region of fit. 

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 ... 

In part (a) of Table II is is seen that the first third of a monolayer to adsorb tends to occupy the more strongly acid sites, for each successive increment is less strongly adsorbed. In part (b) the decrease in average heats of adsorption with increasing coverage is quite consistent with the above. 

The ability to obtain isotherms on individual groups also enable the calculation of the isosteric heat of adsorbtion on that site (as distinct from the heats of adsorption averaged over the whole surface which are normally obtained from adsorption isotherms). Relationships between the OH frequency shifts and heats of adsorbtion have been obtained this way (18). A relationship between the frequency shift and the ionisation potential of the adsorbing molecules has been demonstrated by several authors (20-22) and a theoretical explanation based on the Mullikan-Puranik approach to H-bonding has been given by Low and Cusamano (23). 

A change in partial molal free energy of the adsorbent calculated from adsorption isotherms is an average for the exterior and interior adsorbent because we have taken the total number of moles of adsorbent as rq. This average, multiplied by the total number of moles of adsorbent, is an extensive free energy function. Its temperature variation yields a heat of adsorption which is also extensive. This heat divided by the number of moles of adsorbent is the average heat of adsorption per mole. Fortunately, it is this quantity which is most directly determined in a calorimeter. 

Here, Ey is defined as a positive quantity and interpreted by Brunauer (Brunauer, 1945, p.158) as the average heat of adsorption on the less active part of the adsorbing surface . 

Microcalorimetry provides a direct and accurate method for the determination of the site strength. Furthermore, if the temperature is sufficiently high that the adsorption is specific, that is, at low temperatures one will only get average heats of adsorption, then this technique will also provide the site strength distribution without any other assumptions about kinetic effects or... 

The initial heat of adsorption of oxygen on lithiated oxides and the total amount of adsorbed gas increase when the lithium content increases (Table XI). Moreover, the average heat of adsorption on lithium-doped samples is larger than on pure NiO(250°) since differential heats decrease more progressively with increasing coverage on doped samples (Fig. 27) than on pure NiO(250°) (Fig. 9). These results indicate that incorporation of lithium ions in vacuo enhances the surface affinity toward oxygen and confirm, therefore, the mechanism of incorporation... 

All portions of an adsorbed gas do not liberate equal amounts of heat, therefore the integral heat is the average heat for the total gas adsorbed in the experiment. In order to know the amount of heat corresponding to each portion of adsorbed gas, it is necessary to determine the differential heat of adsorption. This can be approximated by introducing the gas in very small increments into a calorimeter containing the carbon and measuring the heat evolved by each increment of gas adsorbed. Differential heats are reported as calories per mole of adsorbed gas. 

Higher coverages of CO lead to repulsive interactions between the coadsorbed molecules. These higher coverages (a) lower the average heat of adsorption (as shown in Figure 3.20) and (b) push the CO molecules into new adsorption sites (as shown in Figure 2.31) to maximize the distance between them. When CO is coadsorbed... 

Excellent correlation coefficients (>0.98) were obtained for the 12 sorbates on Tenax and the average differential heat of adsorption for these compounds was -1.45 kcal/mole at 250 atmospheres and -0.87 kcal/mole at 350 atmospheres. The magnitude of the heats of adsorption indicate very weak enthalpic interactions between the adsorbate vapors and the adsorbent and the recorded values are significantly less than the corresponding heats of liquefaction of the adsorbates. The almost 0.6 kcal/mole difference in the average heat of adsorption recorded at 250 versus 350 atmospheres of pressure indicates weaker interaction between the sorbates and the adsorbent at the higher pressure. 

For each of the studied solids, the differential heat of adsorption of the probe molecule has been plotted as a function of the coverage. Scales of acidic and basic strength have been established (Figures 9 and 10), based on the average heat at the plateau of the differential heat curve, or at half coverage when no plateau is observed, as was found for most of the oxide samples [129,130]. The scales are based on average heats of adsorption rather than on initial heats, because the latter determination is not always reliable. Indeed, initial heats of... 

The average concentration (or temperature) and the half-time solutions are particularly useful in adsorption and heat transfer studies, as a means to extract parameters from experimental measurements. 

Figure 5.21 shows a typical DSC curve obtained an initial endothermic blip occurs when the gas is introduced, followed by a large exothermic peak due to the chemisorption reaction. The PdO/carbon catalyst shown in Figure 5.21 was measured six times and the average heat of reaction was 81.6 +1.05 J g (1.25% rel.). A shoulder peak is observed on the exothermic peak at around 5 min, which is attributed to physical adsorption on the carbon. However, it was difficult to separate the heat of chemisorption and physical adsorption on the carbon from Figure 5.21. 

Refs. Si/Al % Exchange Activation Adsorption Initial heat Average heat... 

In Eq. (354), k and k are kinetic constants of the rate of adsorption and desorption, respectively, is the average heat of adsorption taking place on the first (already adsorbed) layer, is the total (monolayer plus multilayer) adsorbed amount, and n is the amount of gas adsorbed onto the first layer only. From the definitions of n, rf and n it follows that... 

Where 4//average is the average heat of adsorption over the temperature range (assumed to be a constant in the integration leading to Eq. 5.10.)... 

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