Calorimetric Data

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. 

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. 

Furfural is very thermally stable in the absence of oxygen. At temperatures as high as 230°C, exposure for many hours is required to produce detectable changes in the physical properties of furfural, with the exception of color (17). However, accelerating rate calorimetric data shows that a temperature above 250°C, in a closed system, furfural will spontaneously and exothermically decompose to furan and carbon monoxide with a substantial increase in pressure. The pressure may increase to 5000 psi or more, sufficient to shatter the container (18). 

Conventional Partial Molal Entropy of (H30)+ and (OH)-. Let us now consider the partial molal entropy for the (1I30)+ ion and the (OH)- ion. If we wish to add an (HsO)+ ion to water, this may be done in two steps we first add an H2O molecule to the liquid, and then add a proton to this molecule. The entropy of liquid water at 25°C is 16.75 cal/deg/mole. This value may be obtained (1) from the low temperature calorimetric data of Giauque and Stout,1 combined with the zero point entropy predicted by Pauling, or (2) from the spectroscopic entropy of steam loss the entropy of vaporization. 2 Values obtained by the two methods agree within 0.01 cal/deg. 

Polymerization thermodynamics has been reviewed by Allen and Patrick,323 lvin,JM [vin and Busfield,325 Sawada326 and Busfield/27 In most radical polymerizations, the propagation steps are facile (kp typically > 102 M 1 s l -Section 4.5.2) and highly exothermic. Heats of polymerization (A//,) for addition polymerizations may be measured by analyzing the equilibrium between monomer and polymer or from calorimetric data using standard thermochemical techniques. Data for polymerization of some common monomers are collected in Table 4.10. Entropy of polymerization ( SP) data are more scarce. The scatter in experimental numbers for AHp obtained by different methods appears quite large and direct comparisons are often complicated by effects of the physical state of the monomei-and polymers (i.e whether for solid, liquid or solution, degree of crystallinity of the polymer). 

The nucleation parameters have to be determined with the help of the chain length dependence of Tm, since no calorimetric data are available. Using Eqs. (2, 7, 8) we obtain... 

We can conclude that plots of AS versus AG (62, 74-77) and of AH versus AS (63-66) are both fallacious. The former gives a wrong picture about the accuracy, usually overestimating the fit the latter yields, in addition, a wrong value of the slope. The method of choice for calorimetric data is regression in the coordinates AH versus AG according to eq. (13) or (13a). 

The main calorimetric studies on adsorption of water and ammonia on TS-1 and silicalite-1 have been reported by Bobs et al. [64,83,84,86], while other contributions came from the Auroux group [92] and Janchen et al. [93]. Cor-ma s group has investigated the interaction of water on zeolite [39]. The most important conclusion from the available literature is that calorimetric data require a very careful analysis, as probe molecules interact both with the silanols of the internal hydroxyl nests (see Sect. 3.8) and with Ti(lV) species. 

The lack of calorimetric data is particularly evident in the case of the adsorption of gases on oxides or on oxide-supported metals, i.e., on solids similar to most industrial catalysts. Moreover, adsorption calorimeters are generally used at temperatures that are much lower than those usually found in industry, and it would be difficult indeed to adapt most usual adsorption calorimeters for the measurement of heats of adsorption of gases on industrial catalysts at elevated temperatures. The present success of gas chromatographic techniques for determining heats of reversible adsorption may be explained by the gap between the possibilities of the usual adsorption calorimeters and the requirements of industrial catalysis research. 

Although most heat-flow calorimeters are multipurpose instruments, it is clear that for each particular type of experiment, the inner calorimeter cell must be especially designed and carefully tested. The reliability of the calorimetric data and, thence, the precision of the results depend, to a large extent, upon the arrangement of the inner cell. Typical arrangements for adsorption studies are described in the next section (Section VI.A). 

The development of the theory of heat-flow calorimetry (Section VI) has demonstrated that the response of a calorimeter of this type is, because of the thermal inertia of the instrument, a distorted representation of the time-dependence of the evolution of heat produced, in the calorimeter cell, by the phenomenon under investigation. This is evidently the basic feature of heat-flow calorimetry. It is therefore particularly important to profit from this characteristic and to correct the calorimetric data in order to gain information on the thermokinetics of the process taking place in a heat-flow calorimeter. 

However, for a quantitative kinetic analysis of the calorimetric data, corrections must be applied, because the thermal inertia of the calorimeter, which cannot be completely removed, causes in many cases the blurring of the thermogenesis. Several methods have been proposed, with different levels of sophistication. 

The manual method of data correction, which has been described, though efficient and theoretically sound, is however very tedious and requires skilled experimenters. For this reason, various other methods have been proposed to correct automatically the calorimetric data. In some methods ( on-line correction), raw data may be processed immediately, i.e., during the course of the experiment itself. In other methods ( off-line correction),... 

The large amount of calorimetric data, which can be conveniently stored in a digital form, may, of course, be used in a computer to solve the general equation for the heat transfer in a heat-flow calorimeter (Section IV.B) ... 

All heat evolutions which occur simultaneously, in a similar manner, in both twin calorimetric elements connected differentially, are evidently not recorded. This particularity of twin or differential systems is particularly useful to eliminate, at least partially, from the thermograms, secondary thermal phenomena which would otherwise complicate the analysis of the calorimetric data. The introduction of a dose of gas into a single adsorption cell, containing no adsorbent, appears, for instance, on the calorimetric record as a sharp peak because it is not possible to preheat the gas at the exact temperature of the calorimeter. However, when the dose of gas is introduced simultaneously in both adsorption cells, containing no adsorbent, the corresponding calorimetric curve is considerably reduced. Its area (0.5-3 mm2, at 200°C) is then much smaller than the area of most thermograms of adsorption ( 300 mm2), and no correction for the gas-temperature effect is usually needed (65). 

It appears, therefore, that although it is often difficult to determine the nature of the adsorbed species, or even to distinguish between the different kinds of adsorbed species from the calorimetric data, the change of the... 

The stoichiometry of an interaction between gas molecules and preadsorbed species may thus be deduced from the modifications of the Q-6 curves for a given reactant which are produced by the presence of preadsorbed species on the solid. The results are, of course, particularly conclusive when the differential heats of adsorption of small doses of reactant are measured in a sensitive calorimeter. But, such a qualitative analysis of the calorimetric data, though very useful, does not allow definite conclusions. In the preceding example, for instance, a fraction of carbon dioxide may remain adsorbed on the solid ... 

The calorimetric data indicate the number, the strength and the distribution of the acid sites, and give some indications about their nature. Infrared spectroscopy of pyridine... 

Thermochemical investigations of molybdate solutions have been carried out and reaction heats were measured (108,109). As the interpretation of calorimetric data depends heavily on the correct reaction model, progress in determining reliable enthalpy and entropy changes for condensation reactions have been hampered. However, since there is little doubt that [M07O24]6 is the first polyanion which forms on acidification, the enthalpy and entropy changes obtained for its formation should be meaningful. The values for Eq. (30) are AH° =... 

These data obtained from TG and DTA are in good agreement with the literature values based on calorimetric data. 

The obtained A 7 a() value and the energy equivalent of the calorimeter, e, are then used to calculate the energy change associated with the isothermal bomb process, AE/mp. Conversion of AE/ibp to the standard state, and subtraction from A f/jgp of the thermal corrections due to secondary reactions, finally yield Ac f/°(298.15 K). The energy equivalent of the calorimeter, e, is obtained by electrical calibration or, most commonly, by combustion of benzoic acid in oxygen [110,111,113]. The reduction of fluorine bomb calorimetric data to the standard state was discussed by Hubbard and co-workers [110,111]. 

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