Enthalpies sesquioxides

Vanadium forms numerous oxides, the most important of which are vanadium monoxide, vanadium sesquioxide, vanadium dioxide and vanadium pentoxide. In the earlier examples (e.g., oxides of chromium and of niobium) the enthalpy values for the aluminothermic reduction of each of the oxides was given for the purpose of illustration. Normally, the consideration can be restricted to only those oxides which are readily obtained and which can be handled freely without any special or cumbersome precautions. In the case of vanadium for example, it is sufficient to consider the reduction of the sesquioxide (V203) and the pentoxide (V2Os). The pertinent reactions are ... 

The relative stabilities of the dioxides, sesquioxides and monoxides for first period transition metals are given in Figure 7.11(c). The stability of the higher oxidation state oxides decreases across the period. As we will discuss later, higher oxidation states can be stabilized in a ternary oxide if the second metal is a basic oxide like an alkaline earth metal. The lines in Figure 7.11(c) can in such cases be used to estimate enthalpies of formation for unstable oxidation states in order to determine the enthalpy stabilization in the acid-base reactions see below. Finally, it should be noted that the relative stability of the oxides in the higher oxidation states increases from the 3d via 4d to the 5d elements, as illustrated for the Cr, Mo and W oxides in Figure 7.11(d). 

The second scheme involves the enthalpy of solution of the lanthanide sesquioxide and the ... 

Semiempirical calculations of free energies and enthalpies of hydration derived from an electrostatic model of ions with a noble gas structure have been applied to the ter-valent actinide ions. A primary hydration number for the actinides was determined by correlating the experimental enthalpy data for plutonium(iii) with the model. The thermodynamic data for actinide metals and their oxides from thorium to curium has been assessed. The thermodynamic data for the substoicheiometric dioxides at high temperatures has been used to consider the relative stabilities of valence states lower than four and subsequently examine the stability requirements for the sesquioxides and monoxides. Sequential thermodynamic trends in the gaseous metals, monoxides, and dioxides were examined and compared with those of the lanthanides. A study of the rates of actinide oxidation-reduction reactions showed that, contrary to previous reports, the Marcus equation ... 

The seminal rare-earth scientist F. H. Spedding carried out many calorimetry experiments to determine enthalpies of solution of rare earth elements and chlorides (e.g., [14]), which are indispensable for the determination of the enthalpies of formation of the oxides. In addition he and his team used oxygen combustion calorimetry to determine AfH° of Nd, Sm, Gd, and Er sesquioxides [15]. 

Soviet researchers (Gvelesiani and coworkers) made systematic smdies using solution and enthalpy drop calorimetry on many of the rare-earth sesquioxides in the 1960s and early 1970s. 

Walsh and White and coworkers [17-20] studied the vaporisation of the rare-earth sesquioxides systematically, carrying out mass-spectrometric studies on most of the rare-earth in the gas-phase to derive enthalpies of formation of the monoxide molecules, using vaporisation and isomolecular exchange reactions, and explained the trend observed in the LnO dissociation energies. 

The principal drawback of combustion calorimetry occurs when the product cannot be well characterized. This especially applies to the oxides of Pr and Tb. When Pr metal is burned in oxygen, PreOn is obtained, and so its sesquioxide, dioxide and all intermediate oxides cannot be studied with this technique. When Tb metal is burned in oxygen, the oxide is nonstoichiometric and heterogeneous. Therefore, solution calorimetry is the method of choice for determination of enthalpies of formation of the sesquioxides of Pr and Tb and, in feet, for their dioxides and nonstoichiometric oxides. 

The high temperature heat capacity of the rare-earth sesquioxides is derived from measurements of the enthalpy increment H (T) H (298.15 K) using so-called... 

Table 7-1 shows the recommended values for the enthalpies of formation of all rare earth sesquioxides. The enthalpy of formation of yttrium sesquioxide was re-... 

When the enthalpies of formation of rare earth sesquioxides are combined with enthalpies of formation of rare earth aqueous ions R (aq) to calculate enthalpies of solution. 

Figure 7-1. Enthalpies of solution of the lanthanide sesquioxides as a lunction of Z note that for Sm and Eu data for two crystal modifications are known.

Gschneidner [28,29] showed that the enthalpies of formation of several classes of lanthanide compounds can be correlated systematically as a function of atomic number. He pointed out [30] that the correlations for europium and ytterbium are anomalous because they are divalent in their metallic state but trivalent in the compounds. As shown in Figure 1, the enthalpies of formation of the lanthanide sesquioxides (or of any other class of compounds of R ) do not change in a smooth fashion as a function of Z or of the ionic radius of R. These enthalpies of formation correspond to the reactions that appear to be similar throughout the rare earths,... 

The heat capacity of the sesquioxides above room temperature is principally derived from enthalpy increment measurements. The vast amount of data is however not always concordant. The results from the most reliable studies have been critically reviewed and fitted to polynomial equations that were constrained to the... 

Enthalpies of formation remain to be measured for some of the lanthanide sesquioxides, e.g. La203(bcc), Nd203(monoclinic) and Gd203(monoclinic). The enthalpy of formation of Ce203 remains in doubt because of the discrepancy between solution and combustion calorimetry values (section 4.1). The thermochemical properties of metallic monoxides should be measured, but only when stoichiometric samples that are fi ee of unreacted metal can be synthesized. 

The thermochemical and thermophysical properties of the rare earth sesquioxides were critically evaluated in 1973 (Gschneidner etal. 1973). A systematic comparison of rare-earth and actinide sesquioxides was published in 1983 (Morss 1983). Thermodynamic properties of europium oxides were assessed by Rard (1985). Since then the enthalpies of formation of AmjOj and CfjOj were determined by solution microcalorimetry. The Afif [Am (aq)] has been redetermined even more recently so the Af//°[Y (aq)] has been corrected in table 4. Recently, the enthalpy of formation of YjOj was redetermined by combustion calorimetry (Lavut and Chelovskaya 1990) and independently by solution calorimetry (Morss et al. 1993). The latter determination took advantage of a determination of Afff [Y (aq)] that used very pure Y metal (Wang et al. 1988). Assessed values are listed in table 4. 

Enthalpies of formation and solution (in water) of sesquioxides, trichlorides and hydroxides at 298 K (kJ moP ) (see text for general references estimated values in parentheses). ... 

Fig. 6. Enthalpies of solution of rare-earth (open symbols) and actinide (shaded symbols) sesquioxides, trichlorides and elpasolites CsjNaMCl as a function of molar volume (representing ionic size). The molar volumes were calculated from crystallographic unit cell parameters, normalized to one mole of M Smooth curves have been drawn through each class of compounds to guide the eye. In all cases the enthalpies of solution of actinide (III) compounds are less exothermic than those of structurally similar lanthanide (III) compounds.

Some relevant data are compiled in table 4 and the enthalpies of solution are plotted in fig. 6. We note that, as is the case for sesquioxides, all enthalpies of solution of actinide trihalides are less exothermic than those of structurally similar lanthanide trihalides. See section 4.1.1 for further discussion. 

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. 

The vaporization behavior for Cm sesquioxide has been reported (Smith and Peterson 1970). Mass-spectrometric data were not obtained in this study and the species were assigned based only on the systematics. The researchers believed these data support the congruent vaporization of Cm203 to yield CmO(g) and 0(g). An enthalpy of vaporization of 1795kJmol at OK was derived. Curium oxides with O/M ratios higher than 1.5 are not stable above 900°C (Cm02 decomposes above 400°C), and therefore the vaporization processes of oxides having O/M ratios above 1.5 cannot be measured experimentally. 

A cycle for yielding the enthalpy of solution of the lanthanide and actinide sesquioxides has been used and is described by Morss. A graphical approach (see fig. 24) has been devised using data for the different crystal forms of the lanthanide and actinide sesquioxides, which is useful for predictive purposes. The enthalpies of formation and... 

Fig. 24. The enthalpies of solution of actinide and lanthanide sesquioxides (three different values exist for plutonium sesquioxide).

All of the actinides from Th through Cf form dioxides, whereas only three lanthanides, Ce, Pr and Tb, form dioxides. A correlation similar to that developed for the sesquioxides (using their enthalpy of solution and molar volume) has been devised from data for the dioxides (Morss 1986, Morss and Fuger 1981, Fuger 1982). This relationship provides both correlative and predictive capabilities, similar to that provided in fig. 24. One noted difference is that, for the dioxides, there does not appear to be a shift in the enthalpies for the elements in the two series, as is seen for the sesquioxides. The enthalpies of formation and solution for the dioxides are listed in table 31. 

Another interesting correlation exists between the enthalpy of formation of the sesquioxides and the enthalpy of formation of the trivalent aquo ions, as shown in... 

One of the earliest systematic studies of the lanthanide monoxides was by White et al. (1962). They measured the vaporization rates of the sesquioxides and determined the enthalpies of formation of gaseous monoxides. Later, they extended this study by including a number of isomolecular equilibration studies (Ames et al. 1967) using high temperature mass spectrometry. Ackermann and Rauh (1975, 1974, 1971) have also studied the vaporization of some sesquioxides... 

The standard enthalpies of formation of rare-earth sesquioxides (kJ/inol). 

The dissociation energies, D°(RO, g), and the standard enthalpies of formation, AHf RO, g, 0 K) of the rare-earth monoxides have been recalculated using the recent values of the enthalpies of formation of solid sesquioxides (table 5) and of the gaseous metal atoms AH°(R, g, OK) (table 1). These recalculated values along with a few of the previous data are presented in table 7. In this reevaluation of Z>o(RO), we have made considerable use of the recent review by Pedley and Marshall (1983). 

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