Calorimetric

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. 

The error attributed to the determination of the NHV (calorimetric measurement, determination of hydrogen content, and final calculation) is satisfactory with a repeatability of 0.3% and a reproducibility of 0.4%. 

The heat of immersion is measured calorimetrically with finely divided powders as described by several authors [9,11-14] and also in Section XVI-4. Some hi data are given in Table X-1. Polar solids show large heats of immersion in polar liquids and smaller ones in nonpolar liquids. Zetdemoyer [15] noted that for a given solid, hi was essentially a linear function of the dipole moment of the wetting liquid. 

Fig. X-11. Heats of wetting from 0 ( ) and calorimetric heats of immersion (O) of PTFE in n-alkanes. (From Ref. 67.)...

Since both sides of Eq. X-39 can be determined experimentally, from heat of immersion measurements on the one hand and contact angle data, on the other hand, a test of the thermodynamic status of Young s equation is possible. A comparison of calorimetric data for n-alkanes [18] with contact angle data [95] is shown in Fig. X-11. The agreement is certainly encouraging. 

There are numerous references in the literature to irreversible adsorption from solution. Irreversible adsorption is defined as the lack of desotption from an adsoibed layer equilibrated with pure solvent. Often there is no evidence of strong surface-adsorbate bond formation, either in terms of the chemistry of the system or from direct calorimetric measurements of the heat of adsorption. It is also typical that if a better solvent is used, or a strongly competitive adsorbate, then desorption is rapid and complete. Adsorption irreversibility occurs quite frequently in polymers [4] and proteins [121-123] but has also been observed in small molecules and surfactants [124-128]. Each of these cases has a different explanation and discussion. 

Stem layer adsorption was involved in the discussion of the effect of ions on f potentials (Section V-6), electrocapillary behavior (Section V-7), and electrode potentials (Section V-8) and enters into the effect of electrolytes on charged monolayers (Section XV-6). More speciflcally, this type of behavior occurs in the adsorption of electrolytes by ionic crystals. A large amount of wotk of this type has been done, partly because of the importance of such effects on the purity of precipitates of analytical interest and partly because of the role of such adsorption in coagulation and other colloid chemical processes. Early studies include those by Weiser [157], by Paneth, Hahn, and Fajans [158], and by Kolthoff and co-workers [159], A recent calorimetric study of proton adsorption by Lyklema and co-workers [160] supports a new thermodynamic analysis of double-layer formation. A recent example of this is found in a study... 

A tremendous variety of structures is known, and some of the three-dimensional network ones are porous enough to show the same type of swelling phenomena as the layer structures—and also ion exchange behavior. The zeolites fall in this last category and have been studied extensively, both as ion exchangers and as gas adsorbents (e.g.. Refs. 185 and 186). As an example, Goulding and Talibudeen have reported on isotherms and calorimetric heats of Ca -K exchange for several aluminosilicates [187]. 

Other properties of association colloids that have been studied include calorimetric measurements of the heat of micelle formation (about 6 kcal/mol for a nonionic species, see Ref. 188) and the effect of high pressure (which decreases the aggregation number [189], but may raise the CMC [190]). Fast relaxation methods (rapid flow mixing, pressure-jump, temperature-jump) tend to reveal two relaxation times t and f2, the interpretation of which has been subject to much disagreement—see Ref. 191. A fast process of fi - 1 msec may represent the rate of addition to or dissociation from a micelle of individual monomer units, and a slow process of ti < 100 msec may represent the rate of total dissociation of a micelle (192 see also Refs. 193-195). 

To summarize, the four common heat quantities are 1. Integral calorimetric heat... 

The integral heat of adsorption Qi may be measured calorimetrically by determining directly the heat evolution when the desired amount of adsorbate is admitted to the clean solid surface. Alternatively, it may be more convenient to measure the heat of immersion of the solid in pure liquid adsorbate. Immersion of clean solid gives the integral heat of adsorption at P = Pq, that is, Qi(Po) or qi(Po), whereas immersion of solid previously equilibrated with adsorbate at pressure P gives the difference [qi(Po) differential heat of adsorption q may be obtained from the slope of the Qi-n plot, or by measuring the heat evolved as small increments of adsorbate are added [123]. 

The partial molar entropy of adsorption AI2 may be determined from q j or qsi through Eq. XVII-118, and hence is obtainable either from calorimetric heats plus an adsorption isotherm or from adsorption isotherms at more than one temperature. The integral entropy of adsorption can be obtained from isotherm data at more than one temperature, through Eqs. XVII-110 and XVII-119, in which case complete isotherms are needed. Alternatively, AS2 can be obtained from the calorimetric plus a single complete adsorption isotherm, using Eq. XVII-115. This last approach has been recommended by Jura and Hill [121] as giving more accurate integral entropy values (see also Ref. 124). 

Fig. XVn-21. (a) Differential heat of adsorption of N2 on Graphon, except for Oand , which were determined calorimetrically. (From Ref. 89.) (b) Differential heat of adsorption of N2 on carbon black (Spheron 6) at 78.5 K (From Ref. 124).

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-... 

Most microporous adsorbents have a range of micropore size, as evidenced, for example, by a variation in or in calorimetric heats of adsorption with amount adsorbed [227]. As may be expected, a considerable amount of effort has been spent in seeing how to extract a size distribution from adsorption data. 

It is not surprising, in view of the material of the preceding section, that the heat of chemisorption often varies from the degree of surface coverage. It is convenient to consider two types of explanation (actual systems involving some combination of the two). First, the surface may be heterogeneous, so that a site energy distribution is involved (Section XVII-14). As an example, the variation of the calorimetric differential heat of adsorption of H2 on ZnO is shown in Fig. 

Fig. XVIII-11. Calorimetric differential heat of adsorption of H2 on ZnO. Dashed line differential heat of desorption. (From Ref. 104.)...

The validity of equation (A2.1.70) has sometimes been questioned when enthalpies of reaction detennined from calorimetric experiments fail to agree with those detennined from the temperature dependence of the equilibrium constant. The thennodynamic equation is rigorously correct, so doubters should instead examine the experunental uncertainties and whether the two methods actually relate to exactly the same reaction. 

As seen in previous sections, the standard entropy AS of a chemical reaction can be detemiined from the equilibrium constant K and its temperature derivative, or equivalently from the temperature derivative of the standard emf of a reversible electrochemical cell. As in the previous case, calorimetric measurements on the separate reactants and products, plus the usual extrapolation, will... 

A liquid serves as the calorimetric medium in which the reaction vessel is placed and facilitates the transfer of energy from the reaction. The liquid is part of the calorimeter (vessel) proper. The vessel may be isolated from the jacket (isoperibole or adiabatic), or may be in good themial contact (lieat-flow type) depending upon the principle of operation used in the calorimeter design. 

The reaction vessel is situated inside a metal of high themial conductivity having a cylindrical, spherical, or other shape which serves as the calorimetric medium. Silver is the most suitable material because of its high themial conductivity, but copper is most frequently used. 

Randzio S L 1994 Calorimetric determination of pressure effects Solution Calorimetry, Experimental Thermodynamics vol IV, ed K N Marsh and PAG O Hare (Oxford Blackwell)... 

Hansen L D, Eatough D J, Lewis E A and Bergstrom R G 1990 Calorimetric measurements on materials undergoing autocatalytic decomposition Can. J. Chem. 68 2111-14... 

Partyka S, Linsheimer M and Faucompre B 1993 Aggregate formation at the solid-liquid interface the calorimetric evidence Colloids Surf. A 76 267-81... 

---