Entropy desorption

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 solid product, BaO, was apparently amorphous and porous. Decomposition rate measurements were made between the phase transformation at 1422 K and 1550 K (the salt melts at 1620 K). The enthalpy and entropy of activation at 1500 K (575 13 kJ mole-1 and 200 8 J K"1 mole-1) are very similar to the standard enthalpy and entropy of decomposition at the same temperature (588 7 kJ and 257 5 J K-1, respectively, referred to 1 mole of BaS04). The simplest mechanistic explanation of the observations is that all steps in the reaction are in equilibrium except for desorption of the gaseous products, S02 and 02. Desorption occurs over an area equivalent to about 1.4% of the total exposed crystal surface. Other possible models are discussed. 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

A reaction with a high activation energy tends to have a weaker interaction with the surface and hence will have enhanced mobihty that is reflected in a larger activation entropy. For this reason, the pre-exponents of surface desorption rate constants are lO — lO larger than the pre-exponents of surface reaction rates. 

It can be expected that the electronic structure changes would be reflected by the heats of adsorption of suitable chosen molecules. Indeed, Shek et al (17) report that one maximum in the thermal desorption profile of CO shifts to lower temperatures when the Cu content of alloys increases. If the variations in the entropy changes upon adsorption can be neglected (probably - they can) this would indicate a lower heat of adsorption of CO on alloys than on Pt from abt. 33 Kcal/mol on pure Pt,to 26 Kcal/mol for an alloy with abt. 20% Cu. 

The Xj is a relative population of adsorption site of type i in the sample and cmax is the Cu+ ions concentration in the sample of the catalyst related to its volume V. F is the rate of flow of the carrier gas, e is a porosity of the layer of the catalyst bed. p is the rate of temperature change. The populations of the Cu+ site types and both desorption energies and desorption entropies for all Cu+ site types were optimized to obtain the best fit with the experimental data. All three experimental Cu-K-FER TPD curves were fitted at once together with all Cu-Na-FER previously measured TPD curves constraining the parameters AHads i and ASads,i to be the same for all samples. 

Due to the presence of low-temperature desorption peak a new desorption site was included to phenomenological model of TPD experiments previously used for the description of the Cu-Na-FER samples [5], The fit of experimental TPD curves was performed in order to obtain adsorption energies and populations for individual site types sites denoted A (A1 pair), B (sites in P channel (A1 at T1 or T2)), C (sites in the M channel and intersection (A1 at T3 or T4)) [3] and D (newly introduced site). The new four-site model was able to reproduce experimental TPD curves (Figure 1). The desorption energy of site D is cu. 82 kJ.mol"1. This value is rather close to desorption energy of 84 kJ.mol"1 found for the site B , however, the desorption entropy obtained for sites B and D are rather different -70 J.K. mol 1 and -130 J.K. mol"1 for sites B and D , respectively. We propose that the desorption site D can be attributed to so-called heterogeneous dual-cation site, where the CO molecule is bonded between monovalent copper ion and potassium cation. The sum of the calculated populations of sites B and D (Figure 2) fits well previously published population of B site for the Cu-Na-FER zeolite [3], Because the population of C type sites was... 

At the beginning stage of dehydrogenation, the substrate organic hydride is adsorbed onto the catalyst surface from the liquid phase directly and easily. Catalytic reaction processes will succeed it, until the surface sites are filled with the adsorbed reactant and products. Once product desorption starts to form and grow a bubble, product readsorption becomes unfavorable due to the increment of translational entropy of the product molecule in the bubble, if compared with that in the solution, shifting the adsorption equilibrium for the product and suppressing its effect of rate retardation. 

Expression (2-16) is approximately correct for first-order desorption and for values of vt[ between 108 and 1013 K l. It is very often applied to determine from a single TDS spectrum. The critical point however is that one must choose a value for v, the general choice being 1013 s, independent of coverage. As we explain below, this choice is only valid when there is little difference between the entropy of the molecule in the ground state and that in its transition state 125, 27], The Redhead formula should only be used if a reliable value for the prefactor is available ... 

Is it possible that low site densities are obtained in some desorption reactions because an incorrect assumption is made about the entropy of activation For Step 5 we have assumed that AS = 0. Were we to modify this step to obtain a larger log L, we would have to postulate that the adsorbed molecule loses more entropy as the activated complex forms (4.6 e.u. per unit change in log L) than it does in Step 5 as we have described it. Such a sequence of events is not impossible for a surface reaction. But if the adsorbed molecule is immobile, it is difficult to imagine such a species losing... 

Equation 1.34 is plotted for a number of hydrides in Fig. 1.25. As can be seen all the data points fit very well in a simple straight line whose slope is equal to AS -130 J mol" K [162]. This clearly shows that the entropy term is, indeed, a nearly constant value for all the solid state hydrogen systems. Figure 1.25 also shows that a low desorption temperature at 1 atm of pressure (more or less an operating pressure of a PEMFC) can only be achieved with hydrides having the forma-tion/decomposition enthalpies not larger than 50 kJ moF. For example, hydrides that desorb at room temperature such as LaNi and TiFe have AH 30 and 33.3 kJ mol", respectively [163]. However, too small an enthalpy term would require at 1 atm to be much below 0°C. From this point of view the enthalpy term is one of the most important factors characterizing any hydride. 

Fig. 2.11 (a) PCX desorption curves at various temperatures for the activated commercial MgH Tego Magnan powder numbers indicate the average mid-plateau pressure, (b) The Van t Hoff plot for finding the enthalpy and entropy of decomposition, which is equal to -71 kJ/mol and-134 J/ mol K, respectively. Note excellent coefficient of fit = 0.991 (p - pressure)... 

As shown in Fig. 2.43b, the enthalpy of absorption and desorption calculated from the Van t Hoff plots using the mid-plateau pressures of PCT curves in Fig. 2.43a, which are listed in Table 2.18, is equal to -72 and 83 kJ/mol, respectively. The value of entropy is 138 and 151 J/mol K for absorption and desorption, respectively. The enthalpy value for absorption is very close to the values found in the literature for MgHj as discussed in Sect. 2.1.2 and 2.1.3. Surprisingly, however, the enthalpy of desorption at 83 kJ/mol is much greater than the former and also greater than the enthalpy of desorption of the as-received and activated MgH as shown in Fig. 2.11. The coefficients of fit are excellent and give good credibility to the obtained values. 

From the Van t Hoff plot the decomposition enthalpy change AH) and entropy change (AS) for the first and second step were calculated to be AH j = 93.9 kJ/mol-Hj and AS, = 116.2 J/mol-H K, and AH = 102.2 kJ/mol-H and = 125.9 1/ mol-HjK. Taking into account the very high desorption temperature of this compound, much higher than that of a catalyzed MgH, and the fact that MgH is used in its synthesis by ball milling, the compound is not at all competitive to MgH. ... 

From the Van t Hoff plot they calculated the enthalpy and entropy change of absorption as AH = -69.5 kJ/molH and AS = -129.6 J/moIH K, respectively. Correspondingly, for desorption they calculated AH = -83.2 kJ/molH and AS = -146.7 J/molH K. It is interesting that the enthalpy of desorption of ball-milled, nanocrystalline Mg CoH is higher than that for absorption. This is a very similar behavior to the one observed for the ball-milled, nanocrystalline MgH as discussed in Sect. 2.1.4 (Fig. 2.43). 

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. 

The activation free energy of desorption may be computed from the rate of desorption as determined experimentally from the change in the surface potential with time. The theory of absolute rates has been applied to desorption by Eley (120) and Higuchi et cd. (107) to obtain energies and entropies of activation as a function of coverage. The rate of desorption is given by,... 

In these relations, Ki denotes the equilibrium constant of reaction step i. For the numerical evaluation of the model, it is assumed that the backward reaction of step lb has the same transition state as the transition state for the re-desorption of A2 in Model 1, and that the entropy of the molecular precursor on the surface is negligible. The results are shown in Figure 4.37. It is observed that the model predicts that catalysts of much larger reactivity (more negative AEt) will be optimal for reactions where the diatomic molecule is strongly bound to the surface before the dissociation. 

Finally, nothing has been said as yet about the effect of entropy and ordering factors on the geometry of the surface. The discussion looks at OH adsorption and desorption as though it were happening in isolation. What of the buildup of OH on... 

Now, neglecting entropy changes due to the adsorption and desorption of physically adsorbed particles, and assuming that the empty adsorption traps are physically adsorbed particles present in surface concentration No (which is assumed independent of E2), the number of these will be, by the Boltzmann distribution... 

Since T ASr is generally quite negative, the entropy term favors the reverse process, such as desorption from the surface into the gas. 

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