Adsorbate entropy

A comparison of expression (54) with the statistical interpretation of the adsorbate entropy provides additional insight to the significance of the different terms in this equation. The total partition function adsorbed molecules where M > N is (5, 8)... 

Adsorption entropy and molar adsorbate entropy are related by the relation ... 

Fig. 7.10 Change of the molar adsorbate entropy as a function of the adsorbed amount for localized and mobile adsorption process. S° is the standard molar entropy of the adsorptive in the gas, liquid or solid state...

Returning to more surface chemical considerations, most literature discussions that relate adhesion to work of adhesion or to contact angle deal with surface free energy quantities. It has been pointed out that structural distortions are generally present in adsorbed layers and must be present if bulk liquid adsorbate forms a finite contact angle with the substrate (see Ref. 115). Thus both the entropy and the energy of adsorption are important (relative to bulk liquid). The... 

Statistical Thermodynamics of Adsorbates. First, from a thermodynamic or statistical mechanical point of view, the internal energy and entropy of a molecule should be different in the adsorbed state from that in the gaseous state. This is quite apart from the energy of the adsorption bond itself or the entropy associated with confining a molecule to the interfacial region. It is clear, for example, that the adsorbed molecule may lose part or all of its freedom to rotate. 

Vibrational energy states are too well separated to contribute much to the entropy or the energy of small molecules at ordinary temperatures, but for higher temperatures this may not be so, and both internal entropy and energy changes may occur due to changes in vibrational levels on adsoiption. From a somewhat different point of view, it is clear that even in physical adsorption, adsorbate molecules should be polarized on the surface (see Section VI-8), and in chemisorption more drastic perturbations should occur. Thus internal bond energies of adsorbed molecules may be affected. 

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

Calculate the rotational contribution to the entropy of adsorption of benzene on carbon at 35°C, assuming that the adsorbed benzene has one degree of rotational freedom. 

Calculate the rotational contribution to the entropy of adsorption of ammonia on silica at -30°C, assuming (n) that the adsorbed ammonia retains one degree of rotational freedom and (b) that it retains none. In case (n) assume that the nitrogen is bonded to the surface. 

The following several sections deal with various theories or models for adsorption. It turns out that not only is the adsorption isotherm the most convenient form in which to obtain and plot experimental data, but it is also the form in which theoretical treatments are most easily developed. One of the first demands of a theory for adsorption then, is that it give an experimentally correct adsorption isotherm. Later, it is shown that this test is insufficient and that a more sensitive test of the various models requires a consideration of how the energy and entropy of adsorption vary with the amount adsorbed. Nowadays, a further expectation is that the model not violate the molecular picture revealed by surface diffraction, microscopy, and spectroscopy data, see Chapter VIII and Section XVIII-2 Steele [8] discusses this picture with particular reference to physical adsorption. 

Thus the entropy of localized adsorption can range widely, depending on whether the site is viewed as equivalent to a strong adsorption bond of negligible entropy or as a potential box plus a weak bond (see Ref. 12). In addition, estimates of AS ds should include possible surface vibrational contributions in the case of mobile adsorption, and all calculations are faced with possible contributions from a loss in rotational entropy on adsorption as well as from change in the adsorbent structure following adsorption (see Section XVI-4B). These uncertainties make it virtually impossible to affirm what the state of an adsorbed film is from entropy measurements alone for this, additional independent information about surface mobility and vibrational surface states is needed. (However, see Ref. 15 for a somewhat more optimistic conclusion.)... 

I. Adsorption Heats and Entropies. It is not necessary, phenomenologically, to state whether the process is adsorption, absorption, or solution, and for the adsorbent-adsorbate complex formal equations can be written, such as... 

Thus the new thermodynamic heats and entropies of adsorption differ from the preceding ones by the heats and entropies of vaporization of liquid adsorbate. 

As with enthalpies of adsorption, the entropies tend to approach the entropy of condensation as P approaches in further support of the conclusion that the nature of the adsorbate is approaching that of the liquid state. 

The accepted explanation for the minimum is that it represents the point of complete coverage of the surface by a monolayer according to Eq. XVII-37, Sconfig should go to minus infinity at this point, but in real systems an onset of multilayer adsorption occurs, and this provides a countering positive contribution. Some further discussion of the behavior of adsorption entropies in the case of heterogeneous adsorbents is given in Section XVII-14. 

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. 

The standard entropy of adsorption AS2 of benzene on a certain surface was found to be -25.2 EU at 323.1 K the standard states being the vapor at 1 atm and the film at an area of 22.5 x T per molecule. Discuss, with appropriate calculations, what the state of the adsorbed film might be, particularly as to whether it is mobile or localized. Take the molecular area of benzene to be 22 A. ... 

A(liquid adsorbate at 7 ) = (adsorbed, in equilibrium with pressure P, at T) for 6 values of 0.1 and 1.5. Calculate also the entropies of adsorption for the same... 

Ref. 205). The two mechanisms may sometimes be distinguished on the basis of the expected rate law (see Section XVni-8) one or the other may be ruled out if unreasonable adsorption entropies are implied (see Ref. 206). Molecular beam studies, which can determine the residence time of an adsorbed species, have permitted an experimental decision as to which type of mechanism applies (Langmuir-Hinshelwood in the case of CO + O2 on Pt(lll)—note Problem XVIII-26) [207,208]. 

We assume for simplicity that the adsorbed phase has the same entropy as the solid so that only an energy change is associated with the transfer of material from the bnlk to the adsorbed phase, then ... 

To characterize the state of the adsorbed phase, it is useful to evaluate its molar entropy, s , defined as the mean molar value for all the molecules adsorbed over the complete range of surface coverage up to the given amount adsorbed. The molar integral entropy of adsorption. As, is then defined as... 

Fig. 2.16 The molar entropy for nitrogen adsorbed ongraphitizedcarbon (Graphon) at — 189-3°C, as a function of the amount adsorbed s, = molar entropy of adsorbed nitrogen s, = molar entropy of liquid nitrogen. (Courtesy Hill, Emmett and Joyner.)...

When the film thickens beyond two or three molecular layers, the effect of surface structure is largely smoothed out. It should therefore be possible, as Hill and Halsey have argued, to analyse the isotherm in the multilayer region by reference to surface forces (Chapter 1), the partial molar entropy of the adsorbed film being taken as equal to that of the liquid adsorptive. By application of the 6-12 relation of Chapter 1 (with omission of the r" term as being negligible except at short distances) Hill was able to arrive at the isotherm equation... 

When a gas comes in contact with a solid surface, under suitable conditions of temperature and pressure, the concentration of the gas (the adsorbate) is always found to be greater near the surface (the adsorbent) than in the bulk of the gas phase. This process is known as adsorption. In all solids, the surface atoms are influenced by unbalanced attractive forces normal to the surface plane adsorption of gas molecules at the interface partially restores the balance of forces. Adsorption is spontaneous and is accompanied by a decrease in the free energy of the system. In the gas phase the adsorbate has three degrees of freedom in the adsorbed phase it has only two. This decrease in entropy means that the adsorption process is always exothermic. Adsorption may be either physical or chemical in nature. In the former, the process is dominated by molecular interaction forces, e.g., van der Waals and dispersion forces. The formation of the physically adsorbed layer is analogous to the condensation of a vapor into a liquid in fret, the heat of adsorption for this process is similar to that of liquefoction. 

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