Heat of Adsorption, qst

The parameter determined from simulations that can be most readily compared to an experimentally observable quantity is the heat of sorption. The mean total internal energy determined by the simulations, (V), can be equated to the isosteric heat of adsorption, Qst, in the limit of low occupancy, as follows ... 

To get more insight in the description of interaction properties of water with silica surfaces, the isosteric heat of adsorption Qst has been calculated fiom cross-fluctuations in energy U and adsorbed quantity N through equation 1 [27] ... 

Henry constants (b), isosteric heats of adsorption qst and lower limiting temperature for sorption behaviour TiimiHenry for CH4, H2, CO2 and isobutane in microporous silica at P < 125 kPa. After de Lange et al. [59,63]... 

The features of the theoretical BET isotherm are well-known, but the related features of other thermodynamic functions have been rarely discussed, for instance, the corresponding expression for the isosteric heat of adsorption Qst. ... 

This is the case for water adsorbed on the silica (ground quartz). The corresponding experimental heats of immersion curve were reported by Partyka et al. [76,77] and are redrawn here by us in Fig. 7(A). Also in this figure the heat of immersion of kaolinite in water is shown for comparison, redrawn from the work of Fripiat et al. [95]. Figure 7(B) shows the comparison of the isosteric heats of adsorption Qst calculated from these immersion curves according to Eq. (35). Note that also in the case of water adsorption on kaolinite, Qst does not reach the value of the heat of liquefaction, equal to 40.7 kj mol . ... 

Figure 7. (A) The experimental heats of immersion Qim(p/Po) into water for silica at 31°C ( ) and for kaolinite at 30°C (O). The solid lines represent a numerical smoothing of the experimental points. (B) The isosteric heats of adsorption Qst(p/po) of water onto silica ( ) and onto kaolinite (O) calculated from the smoothed heats of immersion.

An illustration of the surface heterogeneity of silica, deduced from isotherm measurements, is shown in Figure 10 which indicates the variation, with the coverage degree (0), of the isosteric heat of adsorption Qst of heptane and toluene, calculated from adsorption isotherms determined at 37° and 47°C, on a talc by Jagiello et al.[19]. 

Figure 10. Variation of the isosteric heat of adsorption Qst of toluene (1) and heptane (2) on a talc, with surface coverage.

Here W is the amount of adsorption at P/Po, Wo the micropore volume, Eq the characteristic energy, and the affinity coefficient., 3Eo can be associated with the isosteric heat of adsorption, qst,. =i/e, at the fractional filling of 1/e using the heat of vapourization, AH , at the boiling point ... 

The isosteric heat of adsorption qst is an important thermodynamic quantity, because it can reflect the interaction strength of the adsorbates and the materials. It is the released heat for each molecule added to the adsorbed phase, given by ... 

For carbon dioxide sorption applications, apart from the amine grafting of POFs, other functional groups with different polarities also contribute to the improvement of the carbon dioxide sorption capacity. Combined with the simulations, the isosteric heats of adsorption (Qst) of modified POFs are in the order of -COOH >-(0H)2 NH2 (0113)2 non-functionalized framework. Selecting the optimal reaction route to graft these specific units on POFs is one of the hot directions of the PSM of POFs. 

An important quantity characterizing the interaction of the molecules with the surface is the isosteric heat of adsorption, qst, defined via... 

Figure 4.2 Heats of adsorption (—Qst) as a function of the number of carbon atoms Nc of the alkanes adsorbed in Silicalite.

In writing this last result, it has been explicitly noted that the number of moles of adsorbed gas ns is constant. If the process under consideration is carried out reversibly, Sg — Ss may be replaced by qsl/T, where qst is known as the isosteric (the same coverage) heat of adsorption ... 

For an arbitrarily chosen extent of adsorption, a horizontal line such as the dashed line in Figure 9.7 may be drawn that cuts the various isotherms at different pressures. The pressure coordinates of these intersections can be read off the plot. According to Equation (90), a graph of In p versus l/T should be linear with a slope of ( — qs,/R). From Figure 9.7, for example, when the adsorption is 0.10 g ethyl chloride (g charcoal)-1 (which corresponds to 8 = 0.2), the equilibrium pressures are 0.20, 0.63, and 2.40 torr at —15.3, 0, and 20°C, respectively. When plotted in the manner just described, these data yield a line of slope — 5330 K. Multiplication by R gives qst = 44.3 kJ mole -1 as the isosteric heat of adsorption for this system at 8 = 0.2. Table 9.3 lists values of qst for different 8 values as calculated from the data in Figure 9.7. 

Use the data from Problem 3 to estimate the isosteric heat of adsorption of pentane on carbon black at 6 - 0.3, 0.6, and 0.9. Under what conditions would greater variation of qs, be expected What prevents these conditions from being examined in this problem How does qs, compare with the energy of adsorption for this system as determined in Problem 4 How does the difference between qst and Eads compare with AHv for pentane ... 

Fuerstenau et al.35) mention an indirect method of determining the adsorption heat. According to this method, the adsorbed amount of a surfactant T is determined as a function of c (at a constant pH) at two or more different temperatures. According to the Clausius-CIapeyron type of Eq. 85 (in 4.2), the AHj is the same as the isosteric heat of adsorption Qa. For surfactants such as amines and sulfonates which do not chemically react with the solid, Qst is the heat of adsorption in the real sense of the word35. In contradiction to this type on interaction they mention a chemical reaction of a surfactant such as e.g. of xanthates or salicylaldehyde156) when metal-surfactant complexes are formed both on the surface and in the bulk phase. In these cases Q t is not the real heat of adsorption but represents an intermediate heat between the reaction heat and the adsorption heat. 

Now, we consider the behaviour of the isosteric heat of adsorption of water, Qst, as predicted by the model of a heterogeneous oxide surface. After certain rearrangements for the heterogeneous surface, Eqn (10) can be written as follows ... 

There has been considerable experimental uncertainty for some time about the connections between calorimetric and isosteric heats. Hill (18) showed that in the reversible isothermal process, Eq. (56) must be replaced by Eq. (57). Kington and Aston (87) derived the analogous Eq. 58 for the reversible adiabatic process and then proceeded to show experimentally that their adiabatic calorimeter actually behaves reversibly. Thus for six values of 6 from 1.16 to 1.33, qa is larger than qBt by successive values of 84, 107, 143, 128, 154, and 111 cal./mole. But qa is larger than the right-hand side of Eq. (58), i.e., qst properly corrected, only by the successive values —48, —25, +10, —9, +14 and —34 cal./mole, which is excellent agreement in view of the estimated maximum error of 15 cal./mole in qa and +15 cal./mole in q,t. Hence the work of Kington and Aston completely clarifies for the first time the relations between isosteric and calorimetric heats of adsorption. 

Heats of adsorption and other thermodynamic parameters can be obtained either by direct calorimetric determination, - AH =/( a)r ( a = adsorbed amount), or by using the Clausius-Clapeyron equation and the data from the isosteric measurements. Isosteric heats of adsorption is calculated from the temperature dependence of the adsorption isotherms, i.e. from the isosteres. Indeed, qst can be computed from the experimental isosteres for each average temperature according to the equation... 

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