Differential adsorption energies

Here A and AZPE are the differential adsorption energy for H and the difference in zero point energy for Reaction (3.4) as given by DFT. A5 is the difference in entropy. At a pH different from zero, the entropy for the H ion wUl change. We can correct expression (3.5) for this effect by adding AG(pH) =... 

Fig.8. The differential adsorption energy of SO2 on ACF samples. The SO2 heat of condensation equals to 24.9 kJ mof. Reprinted with permission from Ref. [35]. Copyright (1998) American Chemical Society...

In order to measure the stability of the newly adsorbed H atom, we have calculated the differential adsorption energy according to equation... 

Thus by measuring the small amount of heat 5Q which is evolved when the adsorption increases by the small amount 6n mole at constant temperature, the differential molar energy of adsorption can be evaluated calorimetri-... 

We have introduced integral molar quantities, which indicates that there are corresponding differential quantities. Integral refers to the fact that the total amount of adsorbed gas is involved. In contrast, the differential molar energy of adsorption is determined only by the last infinitesimal amount adsorbed. It is defined as... 

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. 

Figure 3.16. Pseudo-differential (left) and differential (right) energies of adsorption, as obtained with a discontinuous or continuous procedure, respectively.

Figure 11.4. Differential molar energy of adsorption of Ar and N2 on samples of kaolinite as a function of surface coverage, (a) On sample GB3 (b) On sample FU7 (reproduced courtesy of Cases et al., 1986).

Figure 2 (c) shows and 9b(8a) for the same cases depicted in Fig. 2 (a)-(b). The influence of Wab on the differential heats of adsorption can be easily understood by following the same reasoning like for the corresponding adsorption isotherms. For O<0a even for Wab O, because A and B particles are adsorbed avoiding A-B repulsions. In this regime, 9a measures the adsorption energy of deep sites. For O.2S<0aordered structures in the adsorbate. In O.5<0aO.75, both of them remain constant. 

The differential molar energy of adsorption can be measured by means of a closed isothermal calorimeter. This system consists of two compartments contained in a closed isothermal calorimeter. Initially one compartment is evacuated and contains a given amount of adsorbent but no adsorbate, and the other compartment contains n moles of gas at pressure p. The two compartments are then connected physically until the pressure equilibrates. 

The differential heat of adsorption is related to the integral heat and to the differential molar energy of adsorption according to... 

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