Adsorption integral entropy

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. 

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). 

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... 

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... 

The adsorption isotherms for many of the samples in Table I have been measured (II), allowing the integral entropies of adsorption to be evaluated according to the prescription of Jura and Hill (16). It was found (II) that the entropy of the adsorbed species relative to that of liquid water decreases regularly with decreasing specific surface area. This would be expected for a gradual decrease in periodicity in the underlying structure and thus in the adsorbed H20. 

Entropy Change. The entropy change in the adsorption of water on barium sulfate is shown in Figure 8. The integral entropy, AS, calculated from AG and A ffl decreases monotonically with increasing amount adsorbed. AS can also be calculated from the temperature coefficient of v by... 

Differential or integral entropies of adsorption can be obtained from calorimetry and together with an adsorption isotherm, or from isotherms at different temperatures (sec. 1.3d). 

In the previous section it was shown that the term heat of adsorption may represent different functions, depending on the experimental conditions under which it is determined. The situation is analogous with the entropy of adsorption which can also be defined in several ways (/1). It is always necessary to specify whether the function considered is a true differential, a derivative, or an integral entropy, and also whether it refers to an equilibrium state (defined by p and T) or to a standard state (defined by p° and T). Moreover, various entropies of adsorption may be defined by choosing different standard states for the adsorptive (this state may be gaseous, but also liquid or solid). In this section, all the thermodynamic quantities of the adsorbate will be defined relative to a Gibbs surface for simplicity, but defining them in terms of an interfacial layer yields the same results. 

Rouquerol et al. (11, 12) have recently described the experimental determination of entropies of adsorption by applying thermodynamic principles to reversible gas-solid interactions. Theoretically, the entropy change associated with the adsorption process can only be measured in the case of reversible heat exchange. The authors showed how isothermal adsorption microcalorimetry can be used to obtain directly and continuously the integral entropy of adsorption by a slow and constant introduction of adsorbate under quasi-equilibrium conditions (11) or by discontinuous introduction of the adsorbate in an open system (12). 

S, and H, are the total or integral entropy and heat content of the one-component system of adsorbed molecules. An isosteric calculation [Eqs. (52) and (53)] from neighboring adsorption isotherms gives the differential entropy and heat content, (dS,/dnf)a.r and (dHJdnfja,t-The integral entropy is the quantity of direct statistical mechanical significance, being related to the number of possible quantum states of We adopt the H, and 3C notation of Everett (86), for clarity. 

It was decided to measure the integral heats of adsorption micro-calorimetrically, free energies of adsorption by a Gibbs integration of the adsorption isotherms, and integral entropies by numerical difference. Though the results of this survey may be incomplete, they have provided some insight into the specificity of physical adsorption processes. 

Adsorption isotherms were obtained for most of the samples shown in Figure 1 and the integral free energies of adsorption were calculated. The entropies of adsorption were obtained by difference. All these thermodynamic parameters are tabulated in Table I. If the amorphous character of the surface has a direct correlation with the particle size, the entropies of adsorption of the adsorbate molecules would be expected to bear some relation to the underlying periodic structure of the adsorbent. In particular, large entropies of adsorption would be expected for crystalline samples and relatively small entropies of adsorption for the supposedly amorphous substrates. That this relationship is observed is clear from the integral entropies of adsorption listed in Table I. 

The integral entropies of adsorption for H2O on many of the AI2O3 and Ti02 samples were also obtained (Table I). The entropies show... 

The lack of variation of immersional heat with outgassing temperature indicates that the hexane molecules are rather insensitive to the chemical nature of the surface and are held primarily by van derWaals forces. The integral entropies of adsorption for a number of adsorbents with hexane are listed in Table III. 

On the other hand, in order to calculate the integral entropy of adsorption, first one has to evaluate the total entropy of the whole lattice,. This can be done from " ... 

The differential molar entropies can be plotted as a function of the coverage. Adsorption is always exothermic and takes place with a decrease in both free energy (AG < 0) and entropy (AS < 0). With respect to the adsorbate, the gas-solid interaction results in a decrease in entropy of the system. The cooperative orientation of surface-adsorbate bonds provides a further entropy decrease. The integral molar entropy of adsorption 5 and the differential molar entropy are related by the formula = d(n S )ldn for the particular adsorbed amount n. The quantity can be calculated from... 

Molar entropy of an adsorbed layer perturbed by the solid surface Total enthalpy change for the immersion of an evacuated solid in a solution at a concentration at which monolayer adsorption occurs Heat of dilution of a solute from a solution Enthalpy change for the formation of an interface between an adsorbed mono-layer and solution Integral heat of adsorption of a monolayer of adsorbate vapor onto the solid surface... 

An analytical method for applying Polanyi s theory at temperatures near the critical temperature of the adsorbate is described. The procedure involves the Cohen-Kisarov equation for the characteristic curve as well as extrapolated values from the physical properties of the liquid. This method was adequate for adsorption on various molecular sieves. The range of temperature, where this method is valid, is discussed. The Dubinin-Rad/ush-kevich equation was a limiting case of the Cohen-Kisarov s equation. From the value of the integral molar entropy of adsorption, the adsorbed phase appears to have less freedom than the compressed phase of same density. 

The integral molar entropy of adsorption is obtained from a well-known thermodynamic relation for a reversible, isothermal process the heat is equal to the change in entropy multiplied by the temperature. This directly leads to... 

It is assumed that the binding energy of an adsorbed single molecule to the surface approximately equals its partial molar adsorption enthalpy at zero surface coverage. In the adsorbed state at zero surface coverage the individual variations of the entropy are partly but not completely suppressed. Hence, it is expected that this adsorption enthalpy is proportional to the standard sublimation enthalpy, which characterizes the volatility properties of pure solid phases as an integral value, ... 

The integral heats and entropies of adsorption for water on fused quartz powder have been obtained as a function of particle size. In the light of previous studies, this is indicative of identical surface structure for all samples studied. The results further indicate that many crystalline quartz powders are amorphous in their surface layers. 

The present study was initiated to eliminate the difficulties inherent in the previous experiments. It consists of measurements of the integral enthalpies (via immersional heat measurements) and entropies (via adsorption isotherms) for ground and fractionated powders of fused quartz with a wide spectrum of specific surface areas. 

Heat and Entropy Functions. Both differential and integral heats and entropies of adsorption were evaluated from the data for argon adsorption on muscovite (3). The variations in these functions with coverage for the potassium and barium muscovite were discussed in terms of localized adsorption on the various kinds of geometrical sites on the mica surface. On the cesium mica, however, the heat of adsorption of argon was higher and more uniform than on the potassium and barium micas, and the entropy functions showed a monotonic decrease with coverage. 

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