Desorption calculation

Detailed Modeling Results. The results of a series of detailed calculations for an ideal isothermal plug-flow Langmuir system are summarized in Figure 15. The soHd lines show the form of the theoretical breakthrough curves for adsorption and desorption, calculated from the following set of model equations and expressed in terms of the dimensionless variables T, and P ... 

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. 

Figure 25. Illustration of the kinetics of adsorption and desorption, calculated assuming first-order kinetics and rate constants obtained from coreflood experiments. (Reproduced with permission from reference 128. Copyright 1991 Royal Society of Chemistry.)...

Fig. 8 shows a plot of the Br2(2co) data according to eq. (9). The slope yields 2= 131 kJ mole for the activation energy to associative desorption of Br as Br2. The intercept yields a value of 6.3 X 10 s for the quantity /<2 o-Knowing /o and X (see above) gives us 2 3.6X 10 ° m s for the pre-exponential factor to second-order desorption. Calculation of kjMo these data shows that the condition <0 2/10 indeed apply. 

Davies [114] found that the rates of desorption of sodium laurate and of lauric acid films were in the ratio 6.70 1 at 21.5°C at molecular areas of 90 and 60 per molecule, respectively. Calculate o. the potential at the plane CD in Fig. XV-12. 

A more elaborate theoretical approach develops the concept of surface molecular orbitals and proceeds to evaluate various overlap integrals [119]. Calculations for hydrogen on Pt( 111) planes were consistent with flash desorption and LEED data. In general, the greatly increased availability of LEED structures for chemisorbed films has allowed correspondingly detailed theoretical interpretations, as, for example, of the commonly observed (C2 x 2) structure [120] (note also Ref. 121). 

Fig. XVIII-13. Activation energies of adsorption and desorption and heat of chemisorption for nitrogen on a single promoted, intensively reduced iron catalyst Q is calculated from Q = Edes - ads- (From Ref. 130.)...

If the desorption rate is second-order, as is often the case for hydrogen on a metal surface, so that appears in Eq. XVIII-1, an equation analogous to Eq. XVIII-3 can be derived by the Redhead procedure. Derive this equation. In a particular case, H2 on Cu3Pt(III) surface, A was taken to be 1 x 10 cm /atom, the maximum desorption rate was at 225 K, 6 at the maximum was 0.5. Monolayer coverage was 4.2 x 10 atoms/cm, and = 5.5 K/sec. Calculate the desorption enthalpy (from Ref. 110). 

Another view of the Si(lOO) etching mechanism has been proposed recently [28], Calculations have revealed that the most important step may actually be the escape of the bystander silicon atom, rather than SiBr2 desorption. In this way, the SiBr2 becomes trapped in a state that otherwise has a very short lifetime, pennitting many more desorption attempts. Prelimmary results suggest that indeed this vacancy-assisted desorption is the key step to etching Si(lOO) with Br2. 

Fig. 3.2 Adsorption isotherms for argon and nitrogen at 78 K and for n-butane at 273 K on porous glass No. 3. Open symbols, adsorption solid symbols, desorption (courtesy Emmett and Cines). The uptake at saturation (calculate as volume of liquid) was as follows argon at 78 K, 00452 nitrogen at 78 K, 00455 butane at 273 K, 00434cm g .

Thus, as pointed out by Cohan who first suggested this model, condensation and evaporation occur at difi erent relative pressures and there is hysteresis. The value of r calculated by the standard Kelvin equation (3.20) for a given uptake, will be equal to the core radius r,. if the desorption branch of the hysteresis loop is used, but equal to twice the core radius if the adsorption branch is used. The two values of should, of course, be the same in practice this is rarely found to be so. 

The steps may be so chosen as to correspond to consecutive points on the experimental isotherm. In practice it is more convenient to divide the desorption process into a number of standard steps, either of relative pressure, or of pore radius, which is of course a function of relative pressure. The amount given up during each step i must be converted into a liquid volume i , (by use of the normal liquid density) in some procedures the conversion is deferred to a late stage in the calculation, but conceptually it is preferable to undertake the conversion at the outset. As indicated earlier, the task then becomes (i) to calculate the contribution dv due to thinning of the adsorbed film, and thus obtain the core volume associated with the mean core radius r by the subtraction = t ... 

Before proceeding to detail, however, it is necessary to consider the question as to which branch of the hysteresis loop—the adsorption or the desorption branch—should be used. Though the mode of calculation is... 

Fig. 3.18 Pore size distributions of a silica geP GSSO, calculated from the desorption branch of the isotherm at 77 K by dilTerent methods. (A) x,...

In using the table for pore size calculations, it is necessary to read off the values of the uptake from the experimental isotherm for the values of p/p° corresponding to the different r values given in the table. Unfortunately, these values of relative pressure do not correspond to division marks on the scale of abscissae, so that care is needed if inaccuracy is to be avoided. This difficulty can be circumvented by basing the standard table on even intervals of relative pressure rather than of r but this then leads to uneven spacings of r . Table 3.6 illustrates the application of the standard table to a specific example—the desorption branch of the silica isotherm already referred to. The resultant distribution curve appears as Curve C in Fig. 3.18. 

Calculation of pore size distribution (Roberts Method"). Worked example from desorption branch of nitrogen isotherm on... 

Fig. 3.20 Pore size distributions (calculated by the Roberts method) for silica powder compacted at (A) Ibtonin" (B) 64tonin (C) 130 ton in". The distributions in (a) were calculated from the desorption brunch of the isotherms of nitrogen, and in (h) from the adsorption branch.

Fig. 3.28 The Kiselev method for calculation of specific surface from the Type IV isotherm of a compact of alumina powder prepared at 64 ton in". (a) Plot of log, (p7p) against n (showing the upper (n,) and lower (n,) limits of the hysteresis loop) for (i) the desorption branch, and (ii) the adsorption branch of the loop. Values of. 4(des) and /4(ads) are obtained from the area under curves (i) or (ii) respectively, between the limits II, and n,. (6) The relevant part of the isotherm.

Fig. 5.19 Adsorption of water vapour on a silica gel which had been heated at 900°C. (The water content, calculated from the loss in weight at 1000°C, was 0-2%.) First run O, adsorption ( ), desorption. Second run , adsorption desorption.

The computation of mesopore size distribution is valid only if the isotherm is of Type IV. In view of the uncertainties inherent in the application of the Kelvin equation and the complexity of most pore systems, little is to be gained by recourse to an elaborate method of computation, and for most practical purposes the Roberts method (or an analogous procedure) is adequate—particularly in comparative studies. The decision as to which branch of the hysteresis loop to use in the calculation remains largely arbitrary. If the desorption branch is adopted (as appears to be favoured by most workers), it needs to be recognized that neither a Type B nor a Type E hysteresis loop is likely to yield a reliable estimate of pore size distribution, even for comparative purposes. 

The value of equilibrium moisture content, for many materials, depends on the direction in which equilibrium is approached. A different value is reached when a wet material loses moisture by desorption, as in drying, from that obtained when a diy material gains it by adsorption. For diying calculations the desorption values are preferred. In the general case, the equilibrum moisture content reached by losing moisture is higher than tnat reached by adsorbing it. 

In a recent paper [11] this approach has been generalized to deal with reactions at surfaces, notably dissociation of molecules. A lattice gas model is employed for homonuclear molecules with both atoms and molecules present on the surface, also accounting for lateral interactions between all species. In a series of model calculations equilibrium properties, such as heats of adsorption, are discussed, and the role of dissociation disequilibrium on the time evolution of an adsorbate during temperature-programmed desorption is examined. This approach is adaptable to more complicated systems, provided the individual species remain in local equilibrium, allowing of course for dissociation and reaction disequilibria. 

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