Isosteric measurements

The average errors in evaluation of the differential heats of adsorption, as estimated by Stach et al. [152], are 1-2% only for the direct measurement and around 5% for the isosteric measurements. 

Sorption isosteres measured for the N20-NaLSX and N20-CaLSX systems over complete of sorption-phase concentrations, n, are presented in Figs. I and 2, respectively. Slopes... 

Values of the enthalpy of adsorption, determined either from the variation of adsorption with temperature (isosteric enthalpy of adsorption) or by direct calorimetric measurements, provide a valuable insight into the mechanism of adsorption. When taken together wifri the data from adsorption isotherms, they provide information which could not be extracted from either set of data alone. Heats of adsorption and other thermodynamic parameters can be obtmned either by direct calorimetric determination, -AH =j n (where ria = adsorbed amount), or by using the Clausius-Clapeyron equation and the data from isosteric measurements. However, the faacX tiiat adsorption is often irreversible in the presence of micropores, fr equently makes estimates of adsorption heats obtained from isosteres very unreliable. 

Sorption isosteres and sorption thermodynamic data for CO2 on specific FAU zeolite modifications, NaLSX and NaX, i.e., FAU-I and FAU-n (data obtained for a DAY zeolite, viz., dealuminated sub-type of the FAU-framework species. Figure 10 shows sorption isosteres measured for a DAY san tle with a framework elemental Si/Al ratio of c. 56, supplied by Germany. 

SIM experiments for binary N2-O2 mixtures on Li,RE-LSX zeolite were performed in conjunction with single-component investigations. Mixture measurements are exemplified by isosteres for a sorption-phase composition of 80 % N2 and 20 % O2 as shown in Figure 24, over the entire concentration ranges for zeoUtic intracrystalline void volume up to filling secondary pore volumes of the beads, as also observed from isosteres. In those representations, each Une of symbols is one isostere measured at the respective sorption-phase concentration. As the latter concentration approaches saturation, the orresponding isostere approaches the sublimation curve of either the single component or the binary mixture. The coincidence between isostere and sublimation curve beyond saturation capacity proves that isosteric measurements were correct and thermodynamically consistent. 

A modem version of the sorption-isosteric method has been shown to be a very useful tool for sorption-thermodynamic studies. Concenhation dependences of thermodynamic functions over entire sorption-phase concentration ranges can be determined. During an isosteric measurement, fluid-component transfer between co-existing phases is kept to aminimum to ensure that isosteric conditions are maintained, and to accelerate equilibration between phases. Isostere linearity is assumed to occur, and its validity is discussed. 

The heats of adsorption provide a direct measure of the strength of the bonding between adsorbate and the active site at the surface of solid substance. Therefore, it is of importance to estimate these values, particularly in the domain of catalysis where the strength of active sites determines the mechanism and the yield of certain process. One possible way to determine the heat of adsorption is to apply calorimetry, experimental technique which provides the heats of adsorption as a function of the adsorbed amount (—AH = f(n ), where Ua is the adsorbed amount and — AH is, in that case, so-called differential heat) [9]. The heats of adsorption can be derived also from the variation of adsorption with temperature. In that case, Clausius-Clapeyron equation and the data from isosteric measurements are used (in that way, so-called isosteric enthalpy of adsorption can be obtained). 

The working capacity of a sorbent depends on fluid concentrations and temperatures. Graphical depiction of soration equilibrium for single component adsorption or binary ion exchange (monovariance) is usually in the form of isotherms [n = /i,(cd or at constant T] or isosteres = pi(T) at constant /ij. Representative forms are shown in Fig. I6-I. An important dimensionless group dependent on adsorption equihbrium is the partition ratio (see Eq. 16-125), which is a measure of the relative affinities of the sorbea and fluid phases for solute. 

The basic measurement of adsorption is the amount adsorbed v, which usually is given in units of cm of gas adsorbed per gram of adsorbent. Usually this quantity is measured at constant temperature as a function of pressure p (in mm Hg), and hence is termed an isotherm. Isobars and isosteres also can be measured, but have little practical utility. It has been found that isotherms of many types exist, but the five basic isotherm shapes are shown in Figure 1, where />ois the vapor pressure. 

Once again, clinical studies reveal a divergence between potency and qualitative effect. No in vitro or animal model studies have yet indicated any major difference between oxygen at the 4-position and its sulfur isostere, although there are changes in their experimentally measured ionization potentials (54). 

Heats of adsorption are usually determined in two ways either by direct calorimetric determination at a chosen temperature, or by calculating the isosteric heats from adsorption isotherms measured at different temperatures and using the Clausius-Clapeyron equation. Thus, isosteric heats of adsorption are calculated from the... 

Heats of adsorption measurements do not lead to very specific interpretation since the isosteric heat of adsorption (AH) arises from both nonspecific interactions, which occur in all cases of adsorption, and from specific interactions with the hydroxy groups nevertheless, valuable conclusions about the binding forces can be deduced. Saturated hydrocarbons, e.g., n-pentane, have a value of — AH of 8.0 kcal/mole, while saturated ethers have values of around 16 kcal/mole.14 Probably dispersion forces only are involved in the former case and additional specific interaction with the silanol-OH occurs in the second case. On graphite, where there is no specific interaction, the heats of adsorption of hydrocarbons and ethers are very similar.17 The heat of adsorption of furan (11 kcal/mole) is 5 kcal/mole less than that of tetrahydrofuran this again indicates the effect that delocalization of electrons by the double bonds has on the binding forces.14... 

In chemisorption where severe surface perturbations can occur, the Clausius-Clapeyron equation cannot be applied, since equilibrium pressures are low and often unobtainable. Nonetheless, a differential heat analogous to the isosteric heat can be obtained from heats of immersion without recourse to pressure data where the amounts adsorbed prior to immersion can be measured gravimetrically (Sec. VII,A). 

The very low water adsorption by Graphon precludes reliable calculations of thermodynamic quantities from isotherms at two temperatures. By combining one adsorption isotherm with measurements of the heats of immersion, however, it is possible to calculate both the isosteric heat and entropy change on adsorption with Equations (9) and (10). If the surface is assumed to be unperturbed by the adsorption, the absolute entropy of the water in the adsorbed state can be calculated. The isosteric heat values are much less than the heat of liquefaction with a minimum of 6 kcal./mole near the B.E.T. the entropy values are much greater than for liquid water. The formation of a two-dimensional gaseous film could account for the high entropy and low heat values, but the total evidence 22) indicates that water molecules adsorb on isolated sites (1 in 1,500), so that patch-wise adsorption takes place. 

Tn presenting the adsorptive properties of molecular sieve zeolites, most authors (1, 2) report isosteric heats. These are obtained from the application of the thermodynamically derived Clausius-Clapeyron type equation to experimentally measured equilibrium data. At a constant... 

These observations suggest that the heterogeneous effect in the S02-modenite system represents an extreme case, so much so that chemisorp-tive bonds may be stipulated (probably between the S02 and the cations). These effects would, of course, involve energy emission and show up in the calorimetric measurements. However, the specificity of the adsorption would tend to show a relatively temperature-insensitive isotherm in the low-pressure region, thus rendering the isosteric techniques of obtaining heats of adsorption/chemisorption ineffective. 

The isosteric heats of sorption reported in Table VI are also in acceptable agreement with values based on sorption measurements made near ambient temperature by other investigators, as the comparisons in Table VIII show. 

To compare the calorimetrically determined heats with the results of the equilibrium measurements, we have to calculate the isosteric heats from the latter. At equilibrium... 

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