Entropy of adsorption

In order to illustrate the role played by entropy S in adsorption processes, the entropy change AaS accompanying the adsorption in a very simple case was computed, by using the standard statistical mechanics rigid rotor/harmonic oscillator formula[94]. In Fig. 1.18 the adsorption of an Ar atom at the surface of an apolar solid is schematically illustrated. The Ar atom approaches the solid surface from the gas phase the translation entropy of the solid, which is fixed in the space, is taken as zero, whereas the free Ar atoms, before interacting with the solid surface, possess a translational entropy St which amounts to 150 and 170 J moP at T = 100 and 298K, respectively, at pAr = 100 Torr. 

The adsorbed atom, which is not allowed to translate freely anymore, starts vibrating. Taking as reasonable vibrational frequency 100cm , the adsorbed atoms 

This means that in a spontaneous process, which requires a negative free energy change (see Eq. 1.12), the enthalpy of adsorption must be negative in order to compensate the loss of entropy. In other words, the process must be exothermic of an amount of heat evolved at least as high as the decrease of the T AaS term. 

The adsorbate can be held at the surface more or less strongly and so the negative entropy change (with respect to the free molecules in the gas phase) will be more or less pronounced, according to the nature/structure of the adsorbate and to the nature and strength of the surface atoms/molecules bonds. 

From a molar point of view, the term entropy of adsorption covers a great number of different functions and it is required to specify whether the function considered is a derivative or an integral, and if it refers to an equilibrium state ip, T) or to a standard state (p°, T) [95, 96], 

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If the dependence on temperature as well as on composition is known for a solution, enthalpies and entropies of adsorption may be calculated from the appropriate thermodynamic relationships [82]. Neam and Spaull [147] have, for example, calculated the enthalpies of surface adsorption for a series of straight-chain alcohols. They find an increment in enthalpy of about 1.96 kJ/mol per CH2 group. 

There is no reason why the distortion parameter should not contain an entropy as well as an energy component, and one may therefore write 0 = 0q-sT. The entropy of adsorption, relative to bulk liquid, becomes A5fi = sexp(-ca). A critical temperature is now implied, Tc = 0o/s, at which the contact angle goes to zero [151]. For example, Tc was calculated to be 174°C by fitting adsorption and contact angle data for the -octane-PTFE system. 

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 thermodynamic description of the Langmuir model is that the energy of adsorption Q is constant and that the entropy of adsorption varies with 6 according to Eq. XVII-37. 

We can now proceed with various estimates of the entropy of adsorption Two extreme positions are sometimes taken (see Ref. 14). First, one assumes that for localized adsorption the only contribution is the configurational entropy. Thus... 

Thus from an adsorption isotherm and its temperature variation, one can calculate either the differential or the integral entropy of adsorption as a function of surface coverage. The former probably has the greater direct physical meaning, but the latter is the quantity usually first obtained in a statistical thermodynamic adsorption model. 

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

Before taking up the results of measurements of heats and entropies of adsorption, it is perhaps worthwhile to review briefly the various alternative procedures for obtaining these quantities. 

The partial molar entropy of adsorption AI2 may be determined from q j or qsi through Eq. XVII-118, and hence is obtainable either from calorimetric heats plus an adsorption isotherm or from adsorption isotherms at more than one temperature. The integral entropy of adsorption can be obtained from isotherm data at more than one temperature, through Eqs. XVII-110 and XVII-119, in which case complete isotherms are needed. Alternatively, AS2 can be obtained from the calorimetric plus a single complete adsorption isotherm, using Eq. XVII-115. This last approach has been recommended by Jura and Hill [121] as giving more accurate integral entropy values (see also Ref. 124). 

Some representative plots of entropies of adsorption are shown in Fig. XVII-23, in general, T AS2 is comparable to Ah2, so that the entropy contribution to the free energy of adsorption is important. Notice in Figs. XVII-23 i and b how nearly the entropy plot is a mirror image of the enthalpy plot. As a consequence, the maxima and minima in the separate plots tend to cancel to give a smoothly varying free energy plot, that is, adsorption isotherm. 

Fig. XVII-23. (a) Entropy enthalpy, and free energy of adsorption relative to the liquid state of N2 on Graphon at 78.3 K (From Ref. 89.) b) Differential entropies of adsorption of n-hexane on (1) 1700°C heat-treated Spheron 6, (2) 2800°C heat-treated, (3) 3000°C heat-treated, and (4) Sterling MT-1, 3100°C heat-treated. (From Ref 18.)...

The data on heats and entropies of adsorption do allow a more discriminating test of an adsorption model, although even so only some rather qualitative conclusions can be reached. The discussion of these follows. 

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... 

Entropies of adsorption are obtainable in the same manner as discussed in Chapter XVII. 

Calculate the entropy of adsorption A 2 for several values of d for the case of nitrogen on an iron catalyst. Use the data of Scholten and co-workers given in Section XVIII-4B. 

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... 

Also, the differential molar entropy of adsorption, AJ, is defined as... 

J is alternatively called "derivative enthalpy of adsorption", and "derivative entropy of adsorption". ... 

In Fig. 5.21, from Dawson s paper, the uptake at X for the 250°C-outgassed sample is dose to the calculated value for a monolayer of water with a (H20) = 101 A. Point X has therefore been ascribed to a close-packed monolayer of water on a hydroxylated surface of rutile. The fact that the differential entropy of adsorption relative to the liquid state (calculated from the isosteric heat of adsorption) changes sharply from negative to positive values in this region with A s 0 at X was regarded as supporting evidence. ... 

UHV surface analysis, apparatus designs, 36 4-14 see also Ultrahigh vacuum surface analysis mechanisms, 32 313, 319-320 Modified Raney nickel catalyst defined, 32 215-217 hydrogenation, 32 224-229 Modifying technique of catalysts, 32 262-264 Modulated-beam mass spectrometry, in detection of surface-generated gas-phase radicals, 35 148-149 MojFe S CpjfCOlj, 38 352 Molar integral entropy of adsorption, 38 158, 160-161... 

Equation (46) holds, of course, only if the entropies of adsorption are similar. Equation (44) then becomes, when rearranged. 

We assumed earlier that both the concentrations and the entropies of adsorption are similar for the two gases. Then the partition functions are about the same and Eq. (49) can be simplified ... 

Hydrogen Fluoride Catalysis J. H. Simons Entropy of Adsorption Charles Kemball... 

Figure 13.13 Compensation relation between differential heat and differential entropy of adsorption.

For various alkanes over TON, MFI, MOR and FAU framework types the entropy of adsorption was calculated based on the measured values for the adsorption equilibrium constant and for the heat of adsorption. Figure 13.13 indicates that each time a linear relation is found between the entropy and the heat of adsorp-... 

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