Example, illustrative calorimetric

This example illustrates how thermodynamic quantities, the determination of which we might expect would require calorimetric measurements, can often be much more easily obtained from calculations based on equilibrium conditions. 

To our knowledge, the question of the standard state corrections in DSC experiments has never been addressed. These corrections may in general be negligible, because most studies only involve condensed phases and are performed at pressures not too far from atmospheric. This may not be the case if, for example, a decomposition reaction of a solid compound that generates a gas is studied in a hermetically closed crucible, or high pressures are applied to the sample and reference cells. The strategies for the calculation of standard state corrections in calorimetric experiments have been illustrated in chapter 7 for combustion calorimetry. 

In Section 14.3 we showed how to evaluate K from calorimetric data on the pnre reactants and products. Occasionally, these thermodynamic data may not be available for a specific reaction, or a quick estimate of the value of K may suffice. In these cases we can evaluate the equilibrium constant from measurements made directly on the reaction mixture. If we can measure the equilibrium partial pressures of all the reactants and products, we can calculate the equilibrium constant by writing the eqnilibrinm expression and substituting the experimental values (in atmospheres) into it. In many cases it is not practical to measnre directly the equilibrium partial pressure of each separate reactant and prodnct. Nonetheless, the equilibrium constant can usually be derived from other available data, although the determination is less direct. We illustrate the method in the following two examples. 

Another example of physical interest arises in flash desorption. There the population and desorption energy of molecules held in different states of binding can be determined in detail. To compare these measurements with the results of calorimetric and isotherm studies, the desorption energy for each state must first be properly weighted by its population. This is illustrated for the adsorption of CO on tungsten in Fig. 31. There a diminution of the differential heat of adsorption... 

Specific techniques require the recording of other parameters, for example the load on the sample in thermomechanical analysis. Calorimetric methods, too, require attention to the exact details of each experiment. In the following chapters the principles and practice of thermal analysis and of calorimetry will be described and illustrated with some of the many examples of its use in industry, academic research and testing. 

The reversibility and efficiency of this heat pump can be calorimetrically simulated, when using the absorption vapour device which is described in the "calorimeter description" chapter. Its use is illustrated by the following example ... 

In the illustrative example of Section 8.5.2.1, implementation of a closed-loop strategy requires that the instantaneous copolymer composition be evaluated with the help of some of the techniques described in Section 8.3. For instance, combination of calorimetric and spectroscopic techniques can allow for monitoring of monomer concentrations and reaction rates in real time. If copolymer compositions can be inferred in-line, then these values can be compared to the desired setpoint values for formulation of a closed-loop strategy. 

Equation 8.37a can be inverted to provide the corrected trajectory u . This can be performed with the help of standard Newton-Raphson routines or of RSA techniques. In the illustrative example, assuming that the initial states are known (evaluated through combination of spectroscopic and calorimetric techniques, for instance), then one may compute the feed flow rate value that allows for attainment of the desired composition after some time, with the help of the process model. In order to do that, as an explicit solution is not available, it would be necessary to calculate the model responses for different flow rate values and select the best result. 

Another important point, and one of fundamental significance, is that above the isoelectric point, although no precipitation is observed with added SDS, definite indications of interaction can still be obtained see, for example, the surface tension data for gelatin/ SDS presented below, calorimetric data for BSA/SDS (128), and other information to be given later. This means that proteins, like many HM-polyions, are able to interact with ionic surfactants against an unfavorable (overall) electrical gradient. For this reason many studies involving anionic surfactants have been executed above the i.e.p. of the protein, as illustrated below. 

The universal character of calorimetric measurements also pays in the elucidation of the reversible transformations undergone by bilayer-forming phospholipids. The transitions of phosphatidylcholine and similar congeners between their vesicular and micellar states depending on their concentrations, the presence of simple detergents, and the temperature are quite sharp and accompanied by sensible heat effects that allow for their thermodynamic characterization. In a particularly illustrative example, the dissolution and reconstitution of lipid vesicles from Escherichia coli native polar lipid fraction by octyl-jS-o-glucoside as analyzed by ITC was reported (Figure 15). ... 

The values of standard enthalpies of formation listed in Table 6.2 and in other tables are determined by direct measurement in some cases and by applying Hess s law in others. Oxides, such as water, can often be determined by direct calorimetric measurement of the combustion reaction. If you look back at Example 6.7, you will see an illustration of how Hess s law can be used to obtain the enthalpy of formation of tungsten carbide, WC. 

Equation (1.20) can be used as a consistency test of excess molar Gibbs energies obtained from phase equilibria measured over an extended temperature range, by comparing with calorimetric measurements of molar excess enthalpies. This is illustrated for example by the work of Ott et al. (810TT1) on hexane + dodecane (File Number LB 1119, p. 2-3 ). 

Example 7.1 illustrates how the BET equation is used. Example 7.2 shows how calorimetric data can be used in adsorption studies. 

A few examples of adsorption processes accompanied by an endothermic step due to the deformation/reconstruction of the surface in interaction with molecules were illustrated. In the reported cases, the heat measured within the calorimetric cell was the combination of an exothermic (adsorption) and an endothermic (surface reconstruction) effect, which caused the calorimetrically measured heat to be lower than what expected on the basis of a plain adsorption. An extra-care in interpreting (at molecular level) the experimental calorimetric results should be addressed in several cases, and in this respect it is quite fhiitful to complement the molar volumetric-calorimetric data with results from other approaches, typically the various spectroscopic methods and/or the ab initio molecular modeling. 

The book was written first and foremost to stimulate students interest of chemical engineering and chemistry in the kinetic analysis of liquid-phase reactions on the basis of a calorimetric investigation. Therefore, the illustrations accompanying the chapters are essential, detailed, and coherent. The precise depictions of apparatus and the advantages of their use, as demonstrated by a variety of examples, might encourage scientists and engineers to incorporate one of the apparams in their professional practice. 

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