Calorimetric reversibility

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... 

Moreover, in many cases, a shift of Tg to lower values of temperature has been detected, but in these cases the quality of adhesion between phases may be the main reason for the reversing of this attitude 11,14). If calorimetric measurements are executed in the neighbourhood of the glass transition zone, it is easy to show that jumps of energies appear in this neighbourhood. These jumps are very sensitive to the amount of filler added to the matrix polymer and they were used for the evaluation of the boundary layers developed around fillers. 

Figure 10 Oscillating differential scanning calorimetric (ODSC) curves showing the separation of the glass transition (reversible, i.e., thermodynamic component) and enthal-pic relaxation (irreversible, i.e., kinetic component) which overlap in the full DSC scan. (Reprinted with permission from Ref. 38.)... 

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. 

The calorimetric method which has been outlined in this section is not applicable to the study of surface interactions or of reaction mechanisms which occur between reversibly adsorbed species. But, even in these unfavorable cases, heat-flow microcalorimetry may still yield useful information concerning either the nature of the adsorbed species, the distribution of sites, or the irreversible modifications which occur frequently on the catalyst surface during the course of the reaction. 

Hysteresis is observed not only in the sorption isotherms but also in calorimetric measurements of heat of wetting at different moisture contents, and it is thus a combined entropy and enthalpy phenomenon. A reliable explanation for this effect is not currently available, but there is speculation that it is due to the stresses which are induced as the cellulose swells. Since the swelling of cellulose is not completely reversible, mechanical recovery is incomplete and hysteresis will therefore be present both in the internal stress-strain curve of the sample, and also in the water adsorption isotherm. 

We can calculate AH from thermal data alone, that is, from calorimetric measurements of enthalpies of reaction and heat capacities. It would be advantageous if we could also compute AS from thermal data alone, for then we could calculate AG or Ay without using equilibrium data. The requirement of measurements for an equilibrium state or the need for a reversible reaction thus could be avoided. The thermal-data method would be of particular advantage for reactions for which AG or AT is very large (either positive or negative) because equilibrium measurements are most difficult in these cases. 

Calorimetric Deconvolution Models and the Reversibility or Irreversibility of Overall Denaturation Processes. The deconvolution procedures used to analyze the thermograms presented in this study are based on equilibrium models, even though the overall denaturation process seen over a cycle of heating to a temperature above T and then cooling to below is, depending on the pH, either completely or partially irreversible. There is ample precedent in the literature for the application of equilibrium models in such cases, however. Convincing evidence has been presented... 

Measurement of the thermokinetic parameter can be used to provide a more detailed characterization of the acid properties of solid acid catalysts, for example, differentiate reversible and irreversible adsorption processes. For example, Auroux et al. [162] used volumetric, calorimetric, and thermokinetic data of ammonia adsorption to obtain a better definition of the acidity of decationated and boron-modified ZSM5 zeolites (Figure 13.7). 

The relationship between the statistical expression (equation (5.6)) and the classical expression (equation (5.8)) for determination of the entropy can be explained by the statement that, due to the additional heat taken up, the system acquires more available microstates (Edsall and Gutfreund, 1983). Equation (5.8) introduces a procedure for the direct calorimetric measurement of the entropy change for a specific process such as the reversible formation of a new set of biopolymer interactions. 

There are a few polymers where reversible transitions have been discovered in the solid state. Furukawa, McCoskey and King (1952) and Marx and Dole (1955) studied calorimetrically the room temperature order-disorder transitions in polytetra-... 

Hen egg-white lysozyme, lyophilized from aqueous solutions of different pH from pH 2.5 to 10.0 and then dissolved in water and in anhydrous glycerol, exhibits a cooperative conformational transition in both solvents occurring between 10 and 100°C (Burova, 2000). The thermal transition in glycerol is reversible and equilibrium follows the classical two-state mechanism. The transition enthalpies AHm in glycerol are substantially lower than in water, while transition temperatures Tm are similar to values in water, but follow similar pH dependences. The transition heat capacity increment ACp in glycerol does not depend on the pH and is 1.25 0.31 kj (mol K) 1 compared to 6.72 0.23 kj (mol K)-1 in water. Thermodynamic analysis of the calorimetric data reveals that the stability of the folded conformation of lysozyme in glycerol is similar to that in water at 20-80°C but exceeds it at lower and higher temperatures. 

Zhan, S., Lin, J., Qin, Z. and Deng, Y. (1996) Studies of thermokinetics in an adiabatic calorimeter. 11 Calorimetric curve analysis methods for ireversible and reversible reactions. Journal of Thermal Analysis, 46,1391—401. 

If we reverse the carbonyl and either the ether or amine groups above, we convert the putatively antiaromatic eight-7t phthalic anhydride and phthalimide into the putatively aromatic ten-7t phenylene carbonate (X = Z = O, Y = CO) (XX) and 2-benzimidazolinone (X = Z = NH, Y = CO) (XXI), and interpolating these last species 2-benzoxazolinone (X = O, Y = CO, Z = NH) (XXII). Calorimetric data are absent for phenylene carbonate (benzo-l,3-dioxole-2-one). 

When a chemical reaction is proceeding, it is, by definition, not at equilibrium and thus not reversible. Thus, entropy changes in chemical reactions cannot be obtained from heat effects in calorimetric experiments. Entropy changes can be obtained by studying chemical equilibrium (Chapter 7) or by opposing the tendency of the reaction to proceed with an applied electric potential (Chapter 10). 

This reaction is reversible.16 The temperature at which decomposition occurs depends therefore on the gas phase for example, under vacuum, decomposition becomes noticeable at as low as 500°C. The lack of S° values for this salt prevents any equilibrium calculations for the above reaction, as well as the gef calculation for the paraperiodate. The enthalpy and entropy increments are based on the calorimetric enthalpy increments of David, Mathurin, and Thevenot.12 Thermodynamic data for these salts are given in Tables 9.2 and 9.3. 

---