Lanthanides atomization enthalpies

Figure 7.10 Thermodynamic data (b)-(d) needed in analysis of the enthalpy of formation of the binary lanthanide metal compounds given in (a), (b) Sum of first, second and third ionization enthalpies of lanthanide metals (c) atomization enthalpy of lanthanide metals (d) derived lattice enthalpy of lanthanide trichlorides.

A plot of atomization enthalpy against atomic number for the lanthanides is shown in Figure 3.4. Refer to Figure 2.5 and account for the appearance of the maxima in this plot. (A consideration of the solution to Worked Problem 2.4 may help in finding an answer). 

Figure 3.4 The variation in atomization enthalpy with atomic number for the lanthanides...

An electrostatic hydration model, previously developed for ions of the noble gas structure, has been applied to the tervalent lanthanide and actinide ions. For lanthanides the application of a single primary hydration number resulted in a satisfactory fit of the model to the experimentally determined free energy and enthalpy data. The atomization enthalpies of lanthanide trihalide molecules have been calculated in terms of a covalent model of a polarized ion. Comparison with values obtained from a hard sphere modeP showed that a satisfactory description of the bonding in these molecules must ultimately be formulated from the covalent perspective. 

TABLE 18 Recommended enthalpies of sublimation, enthalpies of formation and enthalpies of atomization for lanthanide trifluorides (kJ/mol)... 

The primary analysis of the data from Tables 73 and 74 allows us to suggest a scheme for calculating the enthalpies of atomization of lanthanide mono- and difluorides. 

As is known, the development of the LFT (Field, 1982) made it possible to refine the enthalpies of atomization of lanthanide monoxides and to elucidate their behavior for RO (Dulick et al., 1986). However, when comparing the performance of different methods, including DFT, for describing the chemical bond in RX, some authors (Heiberg et al., 2003 Wang and Li, 2002) arrived at the conclusion that it is currently impossible to adequately describe the role of the 4f shell in chemical bonding. All corollaries from such a description are qualitative. Among RX molecules, accurate calculations of electronic excitation have only been performed for LaX (Fahs et al., 2002, 2004 see Section 10 for details). 

Figure 30.3 Variation with atomic number of some properties of La and the lanthanides A, the third ionization energy (fa) B, the sum of the first three ionization energies ( /) C, the enthalpy of hydration of the gaseous trivalent ions (—A/Zhyd)- The irregular variations in I3 and /, which refer to redox processes, should be contrasted with the smooth variation in A/Zhyd, for which the 4f configuration of Ln is unaltered.

Figure 7.17 Enthalpy of formation of selected perovskite-type oxides as a function of the tolerance factor. Main figure show data for perovskites where the A atom is a Group 2 element and B is a d or/element that readily takes a tetravalent state [19,20]. The insert shows enthalpies of formation of perovskite-type oxides where the A atom is a trivalent lanthanide metal [21] or a divalent alkaline earth metal [22] whereas the B atom is a late transition metal atom or Ga/Al.

From Fig. 8, one notices that the localized enthalpy is lower by about 0.9 eV than the itinerant one, thus classifying americimn metal among the lanthanide-like, heavier actinides. The picture is consistent with the results of magnetic measurements, which explain magnetism in americium metal as derived from a 5f, J s 0 atomic ground state. 

Values in boldface type are from Durwent and represent his estimates of ihc "best value" and uncertainties for the energies required to break the bonds at 0 K. Where values are not available from Darwent. they arc taken from Brewer and coworkers for metal halides and dihaiidcs (boldface italics) or from Feber for transition metal, lanthanide, and actinide halides (italics). These values represent enthalpies of atomization at 298 K. The remaining values are from Cottrell (Arabic numerals) and other sources (Arabic numerals with superscripts keyed to references at end of table). 

The atomisation enthalpies of the lanthanides as metallic elemental substances exhibit very different trends. From La to Eu, we see a steady decrease, followed by an abrupt increase at Gd. The atomisation enthalpies then decrease (not quite monotonically) to Yb, then increase at Lu. These trends may be rationalised as follows. According to magnetic studies, the lanthanide atoms in the elemental substances have the electronic configurations 6s25d14f" Eu and Yb are exceptions, discussed further below. The band structure is evidently complex and will not be described in detail. The atomisation enthalpy can be broken down for thermochemical purposes into two steps ... 

Fig. 21. The enthalpy of formation of the lanthanide trilluorides as a function of the atomic number, o and indicate the experimental results from fluorine combustion studies at ANL and Kyoto University, respectively the broken curve shows the estimated values using the Bom-Lande equation (Kim and lohnson, 1981) the solid curve shows...

Fig. 24. The enthalpy of formation of the lanthanide trichlorides, tribromides and triiodides as a function of the atomic number. Estimated values are indicated by closed symbols.

The stabilities of the Eu2+, Yb2+, and Sm2+ ions correlate with the third ionization enthalpies of the atoms and the sublimation enthalpies of the metals. The Eu2+(aq) ion is readily obtained by reducing Eu3+(aq) with Zn or Mg, while preparation of the others requires use of Na/Hg or electrolysis. The aqueous Eu2+ solutions are easily handled, but those of Sm2+ and Yb2+ are rapidly oxidized by air and by water itself. The Ln2+ ions show many resemblences to Ba2+, giving insoluble sulfates, for example, but soluble hydroxides. Europium can be easily separated from other lanthanides by Zn reduction followed by precipitation of the other Ln3+ hydroxides. 

Q The first two ionization enthalpies of the lanthanide elements increase only slightly with increasing atomic number, but the third increases strongly from La to Eu, then drops back at Gd, only to increase again to Yb and drop back at Lu (see Figure 2.5). Explain these observations. 

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