Alkali halides lattice energy, 40 Table

These trends are apparent In the values of lattice energy that appear in Table Notice, for example, that the lattice energies of the alkali metal chlorides decrease as the size of the cation increases, and the lattice energies of the sodium halides decrease as the size of the anion increases. Notice also that the lattice energy of MgO is almost four times the lattice energy of LiF. Finally, notice that the lattice energy of Fc2 O3, which contains five ions in its chemical formula, is four times as large as that of FeO, which contains only two ions in its chemical formula. 

As was indicated in Sec. 1.2, the conclusion that the deformation phenomena play the smallest role in NaF was based first on the statement that its heat of sublimation (S) constitutes among the alkali halides the largest fraction of the lattice energy (17). The corresponding data in Table 5 show that the gradation of this fraction, SjU, is in fact closely parallel to that of the degree of polarity p both properties show a... 

TABLE 1.16 Lattice energies of some alkali and alkaline earth metal halides at 0 K... 

It is not yet possible to measure lattice energy directly, which is why the best experimental values for the alkali halides, as listed in Table 1.16, are derived from a thermochemical cycle. This in itself is not always easy for compounds other than the alkali halides because, as we noted before, not all of the data is necessarily available. Electron affinity values are known from experimental measurements for... 

TABLE 3.7. Heats of Formation and Lattice Energies of Alkali Metal Halides ... 

Table 4.2.4. Lattice energies (in kJ mol 1) of some alkali metal halides and divalent transition metal chalcogenides...

Table 4. Lattice enthalpies of the alkali halides at 298.2° K and 1 aim. from lattice energies computed by the Huggins-Mayer-type treatment (kcal mole-1)...

For the constitution of the ionic lattices also, the Van der Waals attraction has been found to be a very decisive factor. We know the forces at present much better for these ions than for the neutral molecules. Using an interaction of the form (21), Born and Mayer have calculated the lattice energy of all alkali halides for the NaCl-type and simultaneously for the CsCl-type and comparing the stability of the two types they could show quantitatively that the relatively great Van der Waals attraction between the heavy ions Cs, I , Br, Cl cf. Table II.) accounts for the fact that CsCl, CsBr, Csl, and these only, prefer a lattice structure in which the ions of the same kind have smaller distances from each other than in the NaCl-type. The contribution of the Van der Waals forces to the total lattice energy of an ionic lattice is of course a relatively small one, it varies from I per cent, to 5 per cent., but just this little amount is quite sufficient to explain the transition from the NaCl-type to the CsCl-type. 

Fajans (1962) was the first scientist to put these thoughts into practice. One finds that the determined heats of solvation are relatively small and endothermic (+) for some salts but exothermic (-) for others. However, lattice energies are known to be in the region of several hundreds of kilojoules mol , so that, in rough terms [Eq. (2.3)], heats of solvation should not be more than a dozen kilojoules moF (numerically) different from lattice energies. In Table 2.4 a compilation is given of the quantities mentioned earlier in the case of the alkali halides. Now, the method described here gives the sum of the heat of hydration of the ions of a salt. The question of how to divide this sum up into individual contributions from each of the ions of a salt requires more than the thermodynamic approach that has been used so far. The way this is done is described in later sections (e.g., in Section 2.6.2 or 2.15.9). 

The Born-Mayer equation is an alternative (and possibly more accurate) form based on the assumption of an exponential form for the repulsive energy. Both equations predict lattice energies for compounds such as alkali halides that are in reasonably close agreement with the experimental values from the Born-Haber cycle. Some examples are shown in Table 1. A strict comparison requires some corrections. Born-Haber values are generally enthalpies, not total energies, and are estimated from data normally measured at 298 K not absolute zero further corrections can be made, for example, including van der Waals forces between ions. 

TABLE 9.1 Lattice Energies and Melting Points of Some Alkali Metal and Alkaline Earth Metal Halides and Oxides... 

The radius ratio r+jr for each of the alkali halides is shown in table 3.03. Consideration of these values reveals that CsCl, CsBr and Csl would, indeed, be expected to have the caesium chloride structure, and that the majority of the remaining halides would be expected to show the sodium chloride arrangement. There are, to be sure, a number of halides with r+jr > 0 7 which, nevertheless, have the sodium chloride rather than the caesium chloride structure. Fig. 3.08, however, emphasizes that energetically there is little difference between these two structures when the radius ratio is large, and there are in any case other factors contributing to the lattice energy which we have so far ignored in our discussion. 

Lattice energies of the alkali halides computed from equation (3.04) are given in column (3) of table 3.04. 

Column (4) of table 3.04 shows the total lattice energies of the alkali halides as computed by more recent and refined methods. These values include the effect of the van der Waals forces and also include a contribution representing the zero-point energy. It will be seen that they do not differ greatly from the values in column (3) derived on the elementary theory. 

Table 10.2 Standard enthalpies of formation and lattice energies of alkali metal halides, MX.

Table 4.1. Specific surface energies E , specific surface energies of the rigid lattice (0) and relaxation energies AE computed for several rare gas, alkali halide and metaj surfaces.(After ref. (2]).

TABLE 4.5 Lattice Energies of Some Alkali and Alkaline Earth Metal Halides at OK (kJ/mol) ... 

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