Isosterism

The general type of approach, that is, the comparison of an experimental heat of immersion with the expected value per square centimeter, has been discussed and implemented by numerous authors [21,22]. It is possible, for example, to estimate sv - sl from adsorption data or from the so-called isosteric heat of adsorption (see Section XVII-12B). In many cases where approximate relative areas only are desired, as with coals or other natural products, the heat of immersion method has much to recommend it. In the case of microporous adsorbents surface areas from heats of immersion can be larger than those from adsorption studies [23], but the former are the more correct [24]. 

Alternatively, data may be plotted as n versus T at constant pressure or as P versus T at constant n. One thus has adsorption isobars and isosteres (note Problem XVII-2). 

The constants in Eqs. XVII-88-XVI1-90 may be calculated fiom theory to give the Henry s law constant K from Eq. XVII-87, the experimental n /P dien gives the surface area. Alternatively, the constants may be arrived at from an experimental K (assuming that A is known) and either the isosteric heat of adsorption... 

Fig. XVII-20. Isosteric heat of adsorption of Xe on a stepped Pd surface [8(100) x (110)]. (From Ref. 111.)...

Fig. XVII-21. Continued) (c) Isosteric heats of adsorption of n-hexane on ice powder Vm = 0.073 cm STP. (From Ref. 125). (d) Isosteric heats of adsorption of Ar on graphitized carbon black having the indicated number of preadsorbed layers of ethylene. (From Ref. 126.)...

Fig. XVII-22. Isosteric heats of adsorption for Kr on graphitized carbon black. Solid line calculated from isotherms at 110.14, 114.14, and 117.14 K dashed line calculated from isotherms at 122.02, 125.05, and 129.00 K. Point A reflects the transition from a fluid to an in-registry solid phase points B and C relate to the transition from the in-registry to and out-of-registry solid phase. The normal monolayer point is about 124 mol/g. [Reprinted with permission from T. P. Vo and T. Fort, Jr., J. Phys. Chem., 91, 6638 (1987) (Ref. 131). Copyright 1987, American Chemical Society.]...

It is generally assumed that isosteric thermodynamic heats obtained for a heterogeneous surface retain their simple relationship to calorimetric heats (Eq. XVII-124), although it may be necessary in a thermodynamic proof of this to assume that the chemical potential of the adsorbate does not show discontinu-... 

Read off points from Fig. XVII-1 and plot a set of corresponding isosteres and isobars. 

The nitrogen adsorption isotherm is determined for a finely divided, nonporous solid. It is found that at = 0.5, P/P is 0.05 at 77 K, gnd P/F is 0.2 at 90 K. Calculate the isosteric heat of adsorption, and AS and AC for adsorption at 77 K. Write the statement of the process to which your calculated quantities correspond. Explain whether the state of the adsorbed N2 appears to be more nearly gaslike or liquidlike. The normal boiling point of N2 is 77 K, and its heat of vaporization is 1.35 kcal/mol. 

C W 1979. Isosterism and Molecular Modification in Drug Design. Chemical Society Reviews 53-580. 

Erlenmeyer and Schmid (459), in the course of a fundamental comparison between pyridine and its isosteric thiazole structures, prepared the... 

Isosteric heat of adsorption (at half coverage) q of nitrogen and argont... 

Now A. the diflerential molar enthalpy of adsorption, is often termed the isosteric enthalpy of adsorption (or alternatively the isosteric heat of adsorption) and is given the opposite sign. Thus... 

This equation, which represents an adsorption isostere—the relation between p and T for a given amount adsorbed—can be plotted from the isotherms for a series of temperatures. The value of tf is then immediately calculable from the slope of the isosteric plot. 

If the fraction of sites occupied is 0, and the fraction of bare sites is 0q (so that 00 + 1 = 0 then the rate of condensation on unit area of surface is OikOo where p is the pressure and k is a constant given by the kinetic theory of gases (k = jL/(MRT) ) a, is the condensation coefficient, i.e. the fraction of incident molecules which actually condense on a surface. The evaporation of an adsorbed molecule from the surface is essentially an activated process in which the energy of activation may be equated to the isosteric heat of adsorption 4,. The rate of evaporation from unit area of surface is therefore equal to... 

Fig. 2.14 The isosteric heat of adsorption ( ) of argon, nitrogen and oxygen of rutile at 95 K, plotted as a function of the amount adsorbed (expressed in cm (stp). The uptake of each gas corresponding to the completion of a monolayer is marked. Note the more rapid decrease in as the amount adsorbed approaches monolayer completion. (After Drain.)...

Fig. 2.15 Isosteric heat of adsorption of nitrogen on molecular (low-evergy) solids and on carbons (high-energy solids), plotted as a function of i/n . (A) Diamond (B) gruphitized carbon black. P.33 (D) Benzene (E) Teflon. The curve for amorphous carbon was very close to Curve (A). (Redrawn from a Figure of Adamson . )...

Fig. 4.7 Isosteric heat of adsorption q of nitrogen adsorbed at 77 K on non-porous and porous silica.(I) 4. Fransil", non-porous (2) gel A, mesoporous (. ) A gel B, mesoporous and microporous (4) gel D,...

Even so, it is of interest to calculate the BET monolayer capacity from the composite isotherm of Fig. 5.12(b). Though the isotherm did not conform very closely to the BET equation, the isosteric net heat of adsorption was... 

In Fig. 5.21, from Dawson s paper, the uptake at X for the 250°C-outgassed sample is dose to the calculated value for a monolayer of water with a (H20) = 101 A. Point X has therefore been ascribed to a close-packed monolayer of water on a hydroxylated surface of rutile. The fact that the differential entropy of adsorption relative to the liquid state (calculated from the isosteric heat of adsorption) changes sharply from negative to positive values in this region with A s 0 at X was regarded as supporting evidence. ... 

Fig. 5. Variation of isosteric heat of adsorption with adsorbed phase concentration. Reprinted from ref. 10, courtesy of Marcel Dekker, Inc. To convert kj...

The replacement of the /V-methyl group on the nitrogen atom of the piperidine ring of morphine and analogues by aHyl, isopropyl, or methyl cyclopropyl, an isopropyl isostere, results in compounds which antagonize opioid responses, especially respiratory depression. Naloxone [465-65-6] C22H2 N04 (10... 

The presence of a small substituent capable of forming hydrogen bonds in the 4 -position. Isosteric groups such as NH2 reduce activity, whereas any other group that cannot be converted metabohcaHy to a 4 -OH group results in inactive compounds. 

Adsorption Plots. Isotherm plots are the most common method of presenting adsorption data. An isotherm is a curve of constant temperature the adsorbed water content of the adsorbent is plotted against the water partial pressure in equiHbrium with the adsorbent. An isostere plot shows curves of constant adsorbed water content the vapor pressure in equiHbrium with the adsorbent is plotted against temperature. Figure 13 shows isosteres for the three primary adsorbents described previously. In this case, the dew points for the three adsorbents are plotted at 0.5, 5, and 10 kg... 

H2O/100 kg of adsorbent. At equilibrium and at a given adsorbed water content, the dew point that can be obtained in the treated fluid is a function only of the adsorbent temperature. The slopes of the isosteres indicate that the capacity of molecular sieves is less temperature sensitive than that of siUca gel or activated alumina. In another type of isostere plot, the natural logarithm of the vapor pressure of water in equiUbrium with the desiccant is plotted against the reciprocal of absolute temperature. The slopes of these isosteres are proportional to the isosteric heats of adsorption of water on the desiccant (see... 

Fig. 13. Adsorbent isosteres for activated alumina (AA), siUca gel (SG), and molecular sieves (MS).

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