Lanthanum atomization enthalpy

The atomization enthalpies AhI,) and the enthalpies of formation AH ) of lanthanum carbide molecules (kJ/mol). 

Question 2.3 Assuming lattice energies for CeFs and Cep4 of —4915 and —8391 kJ/mol respectively, and using the same enthalpy of atomization and electron affinity for fluorine as in the lanthanum examples (Section 2.9.1.), calculate A7/f for Cep3 and Cep4. Take an enthalpy of atomization of 398 kJ/mol for cerium (Table 2.6). Use ionization energies from Table 2.2. 

Lanthanum and the lanthanoids, except Eu, crystallize in one or both of the close-packed structures. Eu has a bcc structure and the value of given in Table 25.1 can be adjusted to 205 pm for 12-coordination (see Section 6.5). It is important to notice in Table 25.1 that Eu and Yb have much larger metallic radii than the other lanthanoids, implying that Eu and Yb (which have well-defined lower oxidation states) contribute fewer electrons to M—M bonding. This is consistent with the lower values of A H° Eu and Yb, 177 and 152kJmor respectively, compared with the other lanthanoids (Table 25.4). The metal with the next lowest enthalpy of atomization after Eu and Yb is Sm. 

The reliability of measurements of the partial pressures of R2CI6 can in principle be verified by a standard procedure based on changes in the thermod)mamic characteristics of these molecules along the lanthanide series. However, the enthalpy of atomization AatH°(298) is not the most convenient parameter for such a check since it does not vary monotoni-cally with the number of the lanthanides in the series. The plot of this dependence is a broken line with maxima at lanthanum, gadolinium, and lutetium compounds and minima at europium and ytterbium compounds. In addition, the enthalpy of atomization usually increases in going from dysprosium to erbium dimers. 

Usually, trends in AatH°(298) variations depending on the atomic numbers of lanthanides are considered. This dependence, however, has the form of a broken line with maxima at lanthanum, gadolinium, and lutetium and minima at europium and ytterbium. In addition, an increase in AatH°(298) is usually observed when going from dysprosium to erbium compoimds. A smoother dependence on the atomic number of lanthanides was obtained for the enthalpies of sublimation of lanthanide trifluorides and trichlorides. We believe that the use of this feature allows Asubhf°(298) values to be predicted more accurately for separate lanthanide dichlorides. Accordingly, the reliability of all the thermodynamic data can then be estimated. 

TABLE 65 Equilibrium constants (log Kp = A + B/T), enthalpies (kj/mol) of gas-phase reactions involving lanthanum fluorides, and enthalpies of atomization of LaF and Lap2 calculated using data from Hildenbrand and Lau (1995)°... 

The second group includes reactions (1) and (2) (Table 65), involving lanthanum fluorides (Hildenbrand and Lau, 1995). Since there are two such reactions and, correspondingly, two sought enthalpies of atomization (for LaF and Lap2) and since the AatH°(BaF, 0) value is known, the wanted quantities can be determined from the enthalpies of reactions (1) and (2), ArH°(l, 0) and ArH (2, 0), respectively. We can then calculate the enthalpy of atomization of Lap2 by the equation... 

Inasmuch as the values of the enthalpy of atomization of lanthanum monofluoride measured by other experimental methods are not available, the values obtained in this work can only be compared to the results of theoretical calculations. In particular, Chen and Shang (2003a) calculated AatH°(LaF, 0) by various methods and obtained 649.0 (B3LYP), 642.5 (CCSD(T)), and 680.9 (MP2) kj/mol. According to these authors, the first two values are more accruate than the last one. In addition, Cao and Dolg (2005) determined AatH°(LaF,0) = 649.4 kj/mol by the relativistic effective core potential (RECP) method. 

Despite the fact that the calculations of both enthalpies of atomization by the second law led to lower consistency than the above calculations, it should be considered that the thermod mamic functions used in their determination adequately describe high-temperature equilibria involving LaF and Lap2. The use of the thermod mamic functions foimd with the inclusion of the electronic excitation energy of the free La ion leads to an error of about 10-15 kj/mol for lanthanum monofluoride while this error is larger for lanthanum difluoride. 

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