Enthalpy isothermal

As noted above, normalization of the carboxylate ionization is likely the source of the reaction heat observed in region IV of the heat capacity isotherm. The carboxylate ionization process must contribute to the enthalpy isotherm in the low-hydration region. 

Flfure 2.28. Adsorption of long-chain alkanes from n-heptane on various grades of graphite, (a, left). Enthalpy isotherms for n-docosane (n-CjjH g) (a, right), correlation with the enthalpy of adsorption for a reference sample (b) adsorption Isotherms for four alkanes on Vulcan 3G. (Redrawn from H.E. Kem, G.H. Findenegg, J. Colloid Interface Set 75 (1980) 346.)... 

The integral exchange enthalpy isotherm calculated from the flow microcalorimetric measurements is shown in Fig. 12. The course of the isotherm - in case of a U-shaped adsorption excess isotherm - is determined by the composition of the interfacial phase ( ) according to the following equation[45-47] ... 

If the immersion experiment is repeated at different solution concentrations, the enthalpy isotherm of immersion, A Hvs. Ci, is obtained. For immersion calorimetry, the presentation of the results is often more appropriate in terms of the relative enthalpy of immersion, AnH, which, for dilute solutions, is equal to the integral enthalpy of displacement A2 Hi, more generally obtained Ifom batch or flow sorption microcalorimetric measurements. The relative enthalpy of immersion is defined as the enthalpy of immersion in the solution minus the enthalpy of immersion in pure solvent 2 ... 

If the step-by-step displacement enthalpies and the amounts adsorbed are collected after k=. , K steps and the cumulative data are gathered, the integral enthalpy isotherm of displacement, Zk Aas/Zk = vs. Ci and the adsorption isotherm Zk AT k = Tj vs. Ci are obtained. Alternatively, the measured heat can be divided by the amount adsorbed for each step ... 

FIG. 8 Cumulative enthalpy isotherms of displacement of water by V,V-dimethyldecyl-amine-V-oxide onto CPG silica glass (O) and Vulcan 3G graphitized carbon black ( ) at 298.15 K. 

C. Combination of Adsorption Excess Isotherms and Enthalpy Isotherms New Way to Determine Adsorption Capacity... 

D. Adsorption Excess and Enthalpy Isotherms on Solids in Binary Liquids... 

In this chapter we give a parallel analysis of the liquid sorption excess isotherms and adsorption exchange enthalpy isotherms of benzene-n-heptane and methanol-benzene mixtures on adsorbents with polar and apolar surfaces. Systems with U- or S-shaped excess isotherms were selected. Our aim is to examine the presence and character of a connection between adsorption excess and enthalpy isotherms for the various isotherm types [36],... 

In the case of adsorption of ideal or quasi-ideal mixtures on adsorbents with polar or apolar surfaces, usually U-shaped excess isotherms are obtained (type I according to the Schay-Nagy classification [46-49]. On adsorbents with polar surfaces, in the case of liquid pairs made up of components with a large difference in polarity (e.g., alcohol-benzene), the polar component is preferentially adsorbed on the surface (type II) and again U-shaped excess isotherms are obtained. Thus, in these systems the composition of the interfacial layer (< )f > or x]) increases monotonously as a function of equilibrium composition consequently, according to Eq. (8b), the enthalpy isotherm A // wiU also be a monotonously increasing function (Fig. 11a). 

For S-shaped excess isotherms (Schay-Nagy types IV and V [46-49]), < )i is nearly constant in a relatively wide concentration range, and at o(n) = Q (j)S = ( ja j adsorption azeotropic composition, appears. In this case the value of A ,// changes very little in the middle section of the enthalpy isotherm, where ( )5 is constant then at the azeotropic composition a maximum... 

FIG. 11 Classification of immersional wetting enthalpy isotherms (a) U-shaped excess isotherm, with corresponding enthalpy of irmnersion isotherm, (b) S-shaped excess isotherm, with corresponding enthalpy of immersion isotherm. 

Division of the enthalpy isotherms into two sections can be considered justified only if the adsorption layer is ideal in the vicinity of azeotropic composition, i.e., A21// = 0. Displacement enthalpy isotherms calculated according to Eqs. (18) and (19) change parallel with the isotherms [Pg.377]

FIG. 15 Immersional wetting enthalpy isotherms on Na-illite and on HDP-illite derivatives in methanol (l)-benzene (2) mixtures. Na sodium illite 1,2,3, hexadecylpyridinium illites. 

Enthalpy of displacement isotherms were determined by the flow technique. The heat effects recorded on dodecylammonium and dodecyldiammonium ver-miculites are found to be endothermic in both cases, i.e., the measured heat exchange process results in heat extraction. Since the adsorption isotherms unambiguously indicate positive adsorption of n-butanol, the question arises as to why an exothermic exchange enthalpy is not recorded. In our opinion, the reason for this is the endothermic enthalpy of dilution [59-61,69], which overcompensates for the interlamellar adsorption of butanol. When, knowing the adsorption excesses, the enthalpy isotherm A21// = f Xy,) characteristic of the solid/Uquid interfacial adsorption layer can be calculated, it is indeed the exothermic adsorption enthalpy isotherm specific for the surfacial interaction that is obtained (Fig. 30). This measurement suggests that the interlamellar adsorption of n-butanol is thermodynamically preferred and is accompanied by the liberation of a very large amount of heat (A21// = 16.0-16.5 J/g). 

The dispersed systems are mostly silicates. The author discusses interparticle interactions as a tool for evaluating the stability of dispersions. Parameters such as heat of immersion at solid-liquid interfaces and adsorption capacity are determined, and the mathematical treatment for determining the enthalpy isotherms is described. The heat of wetting in amorphous silica dispersion and on zeolites is discussed. 

FIG. 30 Adsorption isotherm and integral enthalpy isotherm of displacement for the of w-octyl-3-D-monoglucoside (1) - water (2)/graphitized carbon black V3G at 298.15 K [88],... 

The integral enthalpy isotherms of displacement for the alsorption of DDA on Silicagel R and precipitated silica adsorbents (Fig. 4) indicate that the mechanisms of... 

This increase is due to the partial degradationof the chain structure during displacement of the lattice metal ions (mainly and Fe ) by in the process of acid treatment. From the adsorption isotherm and the integral molar enthalpy isotherm of HDP, it can be seen that hydrated individual molecules and, at higher concentrations, hydrated micelles are adsorbed on the surface of the protonated sepiolite particles. Further evidence of such a mechanism is that the maximum amount of HDP adsorbed is much smaller (2.19 nmVmolecule) than required for close-packed monolayer coverage. 

Elg. 10 Integral enthalpy isotherms of adsorption ( ) and desorption ( ) of HDP+ on sepiolite ( ) and 36-h acid-treated sepiolite... 

In some applications, because of the weak dependence of the b parameter on temperature at low vapor pressures (Panagiotopoulos Kumar 1985), it is held constant also, some investigations (Trebble Bishnoi 1986 Hngdkovsk Cibulka 1990) have shown that varying the b parameter with temperature may lead to thermodynamic inconsistencies in the compressed liquid region at elevated pressures and above the critical temperature, which result in the prediction of negative heat capacities and crossovers in enthalpy isotherms. In these cases equations (8.14) are solved for the unknowns a, V and Fg by fitting to vapor pressure data alone. 

IV. COMBINATION OF ADSORPTION EXCESS ISOTHERMS AND ENTHALPY ISOTHERMS NEW WAY FOR DETERMINATION OF ADSORPTION CAPACITY... 

V. ADSORPTION EXCESS AND ENTHALPY ISOTHERMS ON SOLIDS IN BINARY LIQUIDS... 

An excess isotherm determined in a methanol-benzene mixture on silica gel is U-shaped. If, however, the silica surface is modified by octadecyldimethylchlorosilane (Silicagel-Cig) in methanol-benzene mixtures, an S-shaped excess isotherm is obtained, the azeotropic point of which is Xj =0.615 (Fig. 10a). When the displacement process is started from benzene, it can be seen that up to a molar fraction of Xj = 0.6, the incorporation of methanol into the adsorption layer results in a change in enthalpy of 7.35 J/g. However, the displacement of benzene is not yet complete Up to the azeotropic point, the adsorption layer will also contain benzene. A common characteristic of the two isotherms presented in Fig. 8 is that the isotherm =/( i) is linear in a very wide range of compositions (xj = 0.1,..., 0.7), whereas the enthalpy isotherm 2 H =/(xi) is approximately constant. In other words, within this range of composition, a very small exchange heat effect is produced consequently, the composition of the layer is not constant. The maximum value of the enthalpy isotherm is at the azeotropic composition further... 

When alcohol-benzene mixtures are adsorbed on adsorbents with low surface energies, S-shaped excess isotherms are measured [17-19,32,33]. When changes in enthalpy accompanying the adsorption displacement process are examined in these systems, the integral exchange enthalpy isotherms usually do not increase monotonously but possess a backward section. After... 

---