Disproportionation standard enthalpy

The p0 dependence of oxygen nonstoichiometry (8) was determined by using coulometric titration. The data were analyzed using a simple point defect model and thermodynamic quantities were calculated. From this model, the standard enthalpy for oxidation (AH0f) and disproportionation (A77D) were determined to be -140.7 and 228.7 kJ/mol, respectively. The mobilities of the electron holes, electrons, and oxygen ions were calculated from the conductivity data using the defect concentrations determined from the stoichiometry and point defect model. 

Thus the standard enthalpy change for the disproportionation can be written as ... 

The three saturated long-chain tert-butyl peresters are members of a homologons series, and as such, the weighted least-squares regression analysis of the enthalpies of formation V5. number of carbons yields a methylene increment of —26.7 kJmol , a typical valne for liquids. The methylene increment for the terf-butyl esters of the Cg, Cjo, Cn and C14 acids is —28.0 kJmol. The closeness of these two values ensures that the enthalpies of formal reaction 16 will be nearly constant. For the three pairs from Table 3, the value is —70.3 8.1 kJmol. The standard deviation from the mean is quite large because the arithmetic difference for the C12 ester and perester, —79.5 kJmol, is quite a bit more negative than the differences for the Cio and C14 pairs, —64.4 and —66.9 kJmol, respectively. Unfortunately, the acids and esters are in different phases and so we are reluctant to attempt any comparison between them, such as a formal hydrolysis reaction or disproportionation with hydrogen peroxide. 

In the case of Hg, the transition 2HgX HgzXa must be considered and in the case of indium and gallium the disproportionation to the trihalide will be considered. It is interesting to note in passing that the value A/7/ InCl = 41 kcal/mole is quite close to the thermochemical value quoted in the U. S. Bureau of Standards, circular 500. The enthalpies of disproportionation are given in Table XXXVIII. The conclusions that... 

Fig. 3. Standard disproportionation enthalpies AH >p of the rare earth difluorides (Greis, 1976).

Thus, one finds that the sesquioxides of Th, Pa, U and Np are thermodynamically unstable with regard to disproportionation to the metals and dioxide (Morss 1986). An overview of the enthalpies of formation and standard entropies for some binary actinide oxides are listed in table 26 (from Katz et al. 1986a). Morss (1986, see also ch. 122 in this volume) has described the cycle employed in obtaining the enthalpies of solution and formation for these oxides. The enthalpies of solution of the actinide oxides is expected to change slowly and smoothly as a function of ionic size of the metal ion. The enthalpies of formation of Am sesquioxide (Morss and Sonnenberger 1985), of Cm sesquioxides (Morss 1983), and of Cf sesquioxide (Morss et al. 1987, Haire and Gibson 1992) have been measured directly. 

Although this seems to be rather confusing, there are, of course, reasons. The relative stabilities of the di-and bivalent states of the respective lanthanides throughout the series follow, more or less, the third ionization potentials of the elements, AH°(3) (Figure 1). With a standard electrode potential of °(Eu +/Eu +) = —0.35 V (which can be measured in aqueous solution), the ionization potentials or disproportionation enthalpies can be used to calculate standard electrode potentials °(R +/R +) for the whole series. This work has essentially been put forward by Johnson and These results may be summarized graphically... 

Unlike the 4f elements, for which sesquioxides are ubiquitous, only the sesquioxides of Ac and Pu through Es have been prepared. Sesquioxides of Th through Np are clearly thermodynamically unstable with respect to disproportionation to the metals and the much more stable dioxides. (Those of heavier actinides would be obtainable if their half-lives were much longer and nuclear yields more favorable.) An overview of known actinide oxides, and their enthalpies of formation and standard entropies, was given earlier in Table 14.9 although most of the actinide sesquioxides have been known since before 1970 (Am203 since before 1950), only in the past decade have thermophysical [98] and thermochemical [99] properties been determined. Since the optimum solvent for solution calorimetry of these sesquioxides is moderately concentrated hydrochloric acid, a systematic approach to the prediction of the enthalpies of formation of other sesquioxides is to devise a cycle yielding the enthalpy of solution in infinitely dilute add ... 

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