Molar Energy of Adsorption

If Ua and fxg represent the molar internal energies of the adsorbed phase and of the adsorbate, respectively, then change in internal energy as a result of adsorption can be represented as 

When an infinitesimally small amount, dn moles, of the adsorbate is transferred to the surface of the solid from the gas phase at constant volume, then the change in the internal energy of the system is given by the relationship 

---

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 first introduce the integral molar energy of adsorption ... 

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... 

The integral molar energy of adsorption is therefore obtained by integrating the differential energy of adsorption between the limits 0 and n°. It equals the mean of the differential energy of adsorption over the range of surface excess concentration from 0 to r. 

Originally Ex - EL was known as the net heat of adsorption (Lamb and Coolidge, 1920). It is now recommended that the more general term net molar energy of adsorption should be adopted (cf. Chapter 2). 

Finally, when integral molar energies of adsorption are directly measured by gas adsorption calorimetry, it is possible to obtain the corresponding integral molar entropies of adsorption from Equations (2.65) and (2.66). 

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).

Evaluation of integral molar quantities of adsorption 42 Integral molar energy of adsorption 42... 

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... 

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... 

---