Lattice energy trends

T1C1). These differences are related to lattice energy trends (see Topics D6 and E4). 

However, solubility, depending as it does on the rather small difference between solvation energy and lattice energy (both large quantities which themselves increase as cation size decreases) and on entropy effects, cannot be simply related to cation radius. No consistent trends are apparent in aqueous, or for that matter nonaqueous, solutions but an empirical distinction can often be made between the lighter cerium lanthanides and the heavier yttrium lanthanides. Thus oxalates, double sulfates and double nitrates of the former are rather less soluble and basic nitrates more soluble than those of the latter. The differences are by no means sharp, but classical separation procedures depended on them. 

In Fig. 8-13 are plotted lattice energies for MCI2 species. The metal ions are high-spin and lie in octahedral sites in the lattice. The double-hump form of the curve is obviously similar to that for the hydration energies we have just discussed. The reasons for the observed trend in lattice energy are virtually identical to those described for hydration energies. In one system, a metal(ii) ion is octahedrally coordinated by six water molecules within a liquid medium in the other, a metal(ii) ion is octahedrally coordinated by six chlorine atoms within a solid lattice. 

The lattice energy is the sum of all Ion interactions, each of which is described by Equation. Looking at this equation, we can predict that lattice energy will increase as ionic charge increases and that it will decrease as ionic size Increases. A third trend occurs in the summing of all the ion contributions Lattice energy increases with the number of ions in the chemical formula of the salt. 

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. 

The trinitrotoluene isomers follow the same trends, invoking dinitro steric interactions and favorable solid lattice energies, as the dinitrotoluenes. 

Trends in Lattice Energy. We have seen that the lattice energy of ionic crystals is affected to some extent by the coordination numbers of the ions (Table 3.4) and by repulsion between ions in contact with each other (Eq. 3.14). These factors are, however, of minor importance when compared to the effect of ionic charge and ionic size. 

One of the most successful applications of crystal field theory to transition metal chemistry, and the one that heralded the re-discovery of the theory by Orgel in 1952, has been the rationalization of observed thermodynamic properties of transition metal ions. Examples include explanations of trends in heats of hydration and lattice energies of transition metal compounds. These and other thermodynamic properties which are influenced by crystal field stabilization energies, including ideal solid-solution behaviour and distribution coefficients of transition metals between coexisting phases, are described in this chapter. 

There are several other types of thermodynamic data that reflect the ligand field stabilization caused by splitting the d orbitals. For example, the lattice energies of the MC12 (where M is a +2 transition metal ion) compounds also show a double humped shape when plotted as shown in Figure 19.8. However, these types of data will not be discussed because the trends follow naturally from the principles that have already been presented. 

Trends in enthalpies of formation (Table 4) are not as regular as those of lattice energy. For fluorides, lattice energies dominate A//f therefore the smallest cation gives the most stable fluoride. For the other hahdes, the ease of production... 

Thinking Critically Using the concepts of ionic radii and lattice energy, account for the trend in melting points shown in the following table. 

The values of A//l are proportional to the product of the charges on ions divided by the sum of their ionic radii. So the 3+/3- system will get a x9 multiplier, whereas the 2+/2- will have a x4 on the 1+Zl- system. Within compounds that have the same charges, tbe bigger ions lead to larger sums on the radii and smaller lattice energies. Considering both of these factors, one can substantiate the trend shown above for increasing lattice enthalpies. 

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