The Adsorption Entropy

FIGURE 3.1 Equilibrium concentration of ammonia plotted as a function of temperature and pressure assuming a ratio of 1 3. Low temperatures and high pressures favor 

In order to determine the change in free energy, AG, of an adsorption process, we need to know both the adsorption energy and the adsorption entropy. The previous chapter dealt with the adsorption energy. We now turn to the gas-phase and 

The standard entropy of small gas-phase molecules, such as or CO, is of the order of 2meV/K. Their entropic contribution to the Gibbs free energy at room tan-perature (and at Ibar) is therefore approximately -0.6eV/molecule and increases with temperature to about -1 eV at 500 K. Most smaller molecules involved in heterogeneous catalysis have entropies of this order of magnimde one important exception is having a standard entropy of only 1.35 meV/K. Note that, for example, 

When a molecule adsorbs on the surface, it will lose a major part of its gas-phase entropy, as it loses the translational freedom from the gas phase. The translational and rotational degrees of freedom typically become constrained and turn into vibrational modes (at least at low temperatures—at higher temperatures, they might become frustrated translational or frustrated rotational). The total contribution of a vibrational mode with frequency, i/., to the standard Gibbs free energy is (except for the zero-point energy (ZPE) contributions that are discussed in Chapter 2 and 4) 

The full entropic term is actually more complex than this there is an additional term, but this other term exactly cancels the temperature dependence (the vibrational term) of the enthalpy. As can be seen from Equation (3.23), 5° depends on the 

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Let us consider that Ed corresponding to a peak on the desorption curve is coverage dependent, while kd (and thus the adsorption entropy) remains constant. (For the variability of kd see Section II.A.) When seeking the required function Ed (6) we refer to Eq. (8) in which the term exp (— Edf RT) exhibits the greatest variability. A set of experimental curves of the desorption rate with different initial populations n,B must be available. When plotting ln(— dn,/dt) — x ln(n ) vs 1/T, we obtain the function Ed(ne) from the slope, for the selected n, as has been dealt with in Section V. In the first approximation which is reasonable for a number of actual cases, let us take a simple linear variation of Ed with n ... 

The free translation has a very high entropy, while the entropy of a vibration is moderate. For this reason the adsorption entropy is usually negative. At a given pressure the equilibrium between gas and adsorbate will shift towards desorption when the temperature is increased. 

Whilst hydrogen enters into a chemisorptive bond with charcoal at very low temperatures, oxygen remains physically adsorbed unless relatively high temperatures are reached. At liquid-air temperatures the adsorption entropy of oxygens shows that the adsorbed molecules are completely free to move and rotate over the surface 168). 

The entropy of a mobile adsorption process can be determined from the model given in [4], It is based on the assumption that during the adsorption process a species in the gas phase, where it has three degrees of freedom (translation), is transferred into the adsorbed state with two translational degrees of freedom parallel to the surface and one vibration degree of freedom vertical to the surface. From statistical thermodynamics the following equation for the calculation of the adsorption entropy is derived ... 

Yet, the Information that can be obtained from an entropy calculation is at least as interesting as a knowledge of the heat of adsorption. It is possible in principle to decide whether the adsorbed layer is mobile or localized, hi favorable cases the adsorption entropy will also reveal whether a molecule is rotating freely or not in the adsorbed state. 

The numerous values obtained in [6,9-11] would deserve more analysis, discussion and comparison with later data. There are some unexpected trends and deviations in the Aads H values possibly, they originate from ambiguous chemical states of the particular elements. The experimental data on Aac S.S are also of fundamental interest. As will be seen later in this chapter, evaluation of the experiments with TAEs is based on calculation of the adsorption entropy from the first principles. The studies [6,9-11] reported observation of a correlation between the experimental... 

The above equations, especially Eq. 5.54 (and so the mobile adsorption model) obtained wide use in radiochemistry of TAEs. The adsorption entropy was calculated from Eq. 5.33 accepting A/V = 1. Several authors proposed approximate... 

The determination of the adsorption entropy from the isotherms 38) has unexpectedly established that benzene adsorption on porous glass is of a mobile type, with the properties of a two-dimensional ideal gas. Only at low coverages (less than 1 X 10 mole-gm ) the freedom of motion is decreased, and the molecules may be held on definite sites, which is also reflected by an increase in the adsorption energy. 

Equation (2.182) is commonly used to calculate the standard enthalpy of adsorption [83, 160, 171, 186, 187]. The constant K usually exhibits a weak dependence on temperature. The value of AH° calculated from Eq. (2.182) was found to be in the range of +10 to -20 kJ/mol for various surfactants. As mentioned above AG lies in the range -20 to -60 kJ/mol, hence the standard free energy of adsorption is mainly controlled by the adsorption entropy, see Eq. (2.180), and the value of TAS can amount to 10 to 50kJ/mol. The most significant contribution of entropy was found for the water/oil interface [160]. The increase of AS due to adsorption can be ascribed mainly to the disorder of water structure in the solution bulk [83, 160]. In solution the hydrocarbon chains of the surfactant molecules are surrounded by a structured water shell, while during the adsorption these shells are destructed. This leads to an increase in entropy of the system. The entropy also increases due to the transfer of hydrocarbon chains from the water phase to the gas phase and, especially, to the oil phase where they become more flexible. 

Theoretically calculated values of the heat of adsorption for n-hexane and 2-methylpentane are 70 kj mol and 65 kj mol, respectively [46,47], which is in agreement with the average values determined by Zhu et al. [48]. As the heats of adsorption of these alkanes are very close, the difference in adsorption is caused by an entropic effect. Indeed, the conformations of the bulkier branched alkanes are much more restricted in the narrow pores of the medium-pore MEI zeoUte. Eor the branched isomer in siUcaUte-1 there is a large difference in the adsorption entropy between the molecular locations in the intersections and in the channels as shown by Zhu et al. [48]. Therefore, the adsorption of 2-methylpentane from the gas phase leads to a higher reduction in entropy compared to adsorption of n-hexane. This makes it en-tropically less favorable to adsorb the branched isomer [44]. 

These theoretical considerations of the thermochromatographic process presume that the adsorption entropy and enthalpy do not depend on the temperature. It was also postulated that the adsorbent was homogeneous, its surface was not saturated with the adsorbate (monolayer or less), and the carrier (reagent) gas was unsorbable. Diffusion in the solid phase (adsorbent) and surface diffusion were ignored. Furthermore, in the theoretical considerations the effect of the carrier (reagent) gas pressure on the substance transport was not taken into account, which, however, should be considered in the case of TC at reduced reactant gas pressures and vacuum TC or with densely filled columns. 

The adsorption entropy and enthalpy of naphthalene (80 J/molK and 13 kJ/mol, respectively) were higher than the entropy and enthalpy of tetralin (60 J/molK and 5 kJ/mol) or hydrogen (64 J/molK and 5 kJ/mol). The higher enthalpy of naphthalene is indicative of the stronger adsorption of naphthalene, which was also qualitatively observed (see 3.3 Naphthalene and Tetralin Conversion). However, these adsorption parameters indicate that the adsorbed compounds, which are active for the hydrogenation, are fairly mobile on the surface and their adsorption is energetically weak. 

The work of adsorption is determined from Eq. (1) by using the Hnear section of the surface pressure curve as a function of the bulk concentration of the surfactant (the surface pressure does not exceed 3mN/M). The values obtained for the work of adsorption are usually compared with the values obtained for certain fractional surface coverages. Thus, it becomes possible to estimate the change in the free energy as a function of the molecular interaction in the monolayer. (The relation between the values of the work of adsorption determined from different isotherms is discussed in Refs. [37-39]). The adsorption entropy and enthalpy are determined from the temperature dependence of the work of adsorption [36-39]. 

As a rule, the following limits for the adsorption entropy are observed ... 

The adsorption entropy, AS, reported in Table 2 is calculated fiom the Langmuir adsorption equilibrium coefficient, CKpressed in atm, according to the follovring expression... 

In the following, the evaluation of the adsorption entropy change for the slightly more complex case of CO a-coordinated (at T = 303 K) on a variety of 1102 — anatase specimens (pre-outgassed at T = 673 K) will be illustrated. At the 1102 dehydrated surface, CO was adsorbed giving rise to two adspecies, as witnessed by two distinct IR bands located at uco = 2188 and 2206 cm , as reported in Ref. [18] As illustrated schematically in Fig. 1.19 the two adspecies were formed on two different Lewis acidic sites made up of stmcturally different cus Ti" " " cations. They were named species A and B, and their spectroscopic and energetic features are summarized in the figure. 

In agreement with the linearity in the -AG /T versus 1/r, the adsorption entropies are independent of the temperature. 

In addition to the contribution to the adsorption entropy from the vibrational (lirus-trated translational and rotational) degrees of freedom, there is an entropy contribution from the different configurations the adsorbate can have on the surface. Consider the adsorption of a gas-phase molecule onto a surface ... 

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