Entropy of adsorbates

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.)...

The average entropy decrease on adsorption of approximately 0.75 erg per sq. cm. when converted to a molar basis from the volume adsorbed at saturation vapor pressure is 1.8 0.4 e.u. less than liquid water at 25° C. or about that of liquid water at 0° C. The large uncertainty is due to difficulty in extrapolating to P/P° = 1. Since the entropy of adsorbed water molecules in the outermost layer must approximate that of liquid water at 25° C., then the inner layers, to maintain the average of 1.8 e.u., must be icelike with loss of translational modes. 

If 0 = I is adopted as the standard state for the adsorbed phase, s" = s") ), the last term in Eq. (54) (configurational contribution to entropy of adsorbed phase) disappears. As a result, the standard entropy of adsorption is shown to be... 

Hence, for example, Dollimore etal have considered thermodynamic aspects of the adsorption of organic vapours on graphites and carbon blacks. Heats of adsorption and entropies of adsorbed vapours were determined, and the authors came to the conclusion that mobile adsorption appeared to be very important in the systems. In some ways the observation that C2-C4 hydrocarbons were adsorbed flat on a graphite surface tends to support this conclusion, although Hoory and Praunitz prefer to explain their results in terms of double bond interaction with the graphite.Jonas et al. find... 

Integral entropy of rii moles of adsorbate on surface S./m, integral entropy per mole of adsorbate on surface Differential entropy of adsorbate on surface. 

In the following, the application of this method of analysis will be illustrated for the case of Pt(l 11) in 0.1 M HCIO4 solutiom First, the evaluation of the entropies of formation of the interphase, double-layer and the interfacial water network will be described in Sections IV. 1, IV.2 and IV.3, respectively. Then, these results will be employed to evaluate the absolute molar entropy of adsorbed hydrogen and OH on Pt(lll), in Section IV.4. Finally, these results will be critically compared with those obtained with a generalized isotherm in Section IV.5. 

Nevertheless, it should be kept in mind that the evaluation of ASai involves a number of uncertainties. For this reason, it is convenient to evaluate the effect of ASdi data on the results of the molar entropies of adsorbed hydrogen and OH species. For this purpose, it is convenient to define effective absolute molar entropies of adsorbed hydrogen and OH species, and, which will contain contributions from the entropy change of double-layer phenomena coupled to the adsorption process under study. These quantities are obtained by assuming A5 [Pg.44]

It should be noted that these methods of evaluation of the entropy of adsorbed hydrogen and OH species provide integral molar entropies, which are defined as the entropy of the adlayer divided by the number of moles of adsorbed species. Conversely, differential molar entropies are defined as the derivative of the entropy of the adlayer with the number of moles of adsotbed species. Clearly, with the available experimental data, the evaluation of integral molar entropies involves a smaller uncertainty, in comparison to differential molar entropies. 

Figure 11. Absolute molar entropies of adsorbed hydrogen and OH species on Pt(l 11), as evaluated by different approximations (solid...

However, the derivation in Appendix 3 shows that the integral absolute molar entropy of adsorbed species at a given coverage, 9, is given by ... 

On other hand, in relation to OH adsorption, the results of values agree well with at > 0.75 V, but exhibit clear deviations at lower potentials. This deviation is, as in the case of hydrogen adsorption, originated by the different double-layer correction employed in both mathematical treatments. If one calculates the entropy of adsorbed OH by using Gibbs thermodynamics, but assuming a constant double-layer capacity, then the resulting... 

Entropy of adsorbed ions. Since (1 -a )A counterions are adsorbed to each chain on an average and there are A /[((l -a)A ) ][(aA ) ] ways of formation of ion pairs, the free energy associated with the entropy of adsorbed counterions, with the Stirling approximation, is... 

Differential Adsorption Entropy and Molar Entropy of Adsorbate... 

NH3 NH3+ (see also Fig. 2.6). Data was obtained from CatApp and corrected forZPE and entropy contribntions. The entropy of adsorbed species was assumed to be zero. A pressure of 1 bar was assumed for aU species involved. 

FIGURE 3.9 Gibbs free energy diagram for ammonia synthesis on the stepped Ru(OOOl) surface at 1,10, and 100 har. The numbers correspond to the six different reaction steps (see also Figs. 2.6 and 3.9) as defined in the preceding text. Data was obtained from the CatApp and corrected for ZPE and entropy contrihutions. The entropy of adsorbed species was assumed to be zero. Reaction conditions are as follows T = 700 K, = 1 3, conversion to ammonia = 10%. 

The standard entropy of adsorbed hydrogen may be estimated from the formula (3.25) for the entropy of an oscillator. (The frequency of the M-H stretching vibration can be found by using the value of the energy of the M-H bond[130], with the help of an empirical relation[31]. It was found to be equal to 850 cm . The frequency of the doubly degenerate bending vibrations is approximately equal to half this value.) Calculation yields a value Sg =1.93 entropy units[261]. The entropy of adsorption of water can%e found from the temperature dependence of the difference in the surface tension at... 

This gives the entropy of adsorbed chlorine, S l 5.1 entropy... 

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