Born-Haber cycle stability

The ligand field stabilization is expressed in the lattice energies of the halides MX2. The values obtained by the Born-Haber cycle from experimental data are plotted v.v. the d electron configuration in Fig. 9.5. The ligand field stabilization energy contribution is no more than 200 kJ mol-1, which is less than 8% of the total lattice energy. The ionic radii also show a similar dependence (Fig. 9.6 Table 6.4, p. 50). 

The initiation of the cationic polymerisation of alkenes is examined in detail by means of simple thermodynamic concepts. From a consideration of the kinetic requirements it is shown that the ideal initiator will yield a stable, singly charged anion and a cation with a high reactivity towards the monomer by simple, well defined reactions. It must also be adequately soluble in the solvent of choice and for the experimental method to be used. The calculations are applied to carbocation salts as initiators and a method of predicting their relative solubilities is described. From established and predicted data for a variety of carbocation salts the position of their ion molecule equilibria and their reactivity towards alkenes are examined by means of Born-Haber cycles. This treatment established the relative stabilities of a number of anions and the reason for dityl, but not trityl salts initiating the polymerisation of isobutene. 

The knowledge of the relative stability of oxidation states, i.e., redox potentials, is very important for a chemical application. Trends in the stability of various oxidation states of the very heavy elements were predicted earlier on the basis of atomic relativistic DF and DS calculations in combination with some models based on a Born-Haber cycle (see [12]). The conclusions were, however, not always unanimous and varied depending on the model. Later, this topic received a more detailed consideration... 

The rel-HFS and rel-HF computer programs allow calculations of electronic energy levels, ionization potentials, and radii of atoms and ions from hydrogen into the superheavy region. In order to arrive at the oxidation states most hkely to be exhibited by each superheavy element and also the relative stabilities of these various oxidation states, we need to be able to relate these properties to calculable electronic properties. The relationship between reduction potentials and the Born-Haber cycle has offered an effective approach to this problem (69, 70). 

For metals exhibiting variable oxidation states, the relative thermodynamic stabilities of two ionic halides that contain a common halide ion but differ in the oxidation state of the metal (e.g. AgF and AgF2) can be assessed using Born-Haber cycles. In such a reaction as 16.16, if the... 

The Born-Haber cycle is also valuable as a means of analyzing and correlating the variations in stability of various ionic compounds. As an example, it enables us to explain why MgO is a stable ionic compound despite the fact that the Mg2+ and O2- ions are both formed endothermally, not to mention the considerable energies required to vaporize Mg(s) and to dissociate 02(g). A Hf is highly negative despite these opposing tendencies because the lattice energy of MgO more than balances them out. 

Many elements exhibit several different oxidation states, and the relative stabilities of MX and MX are often more difficult to assess. Assuming the lattice energy to be Inversely proportional to the shortest M-X distance In the structure, then, since halide Ion radii Increase from to M (Table 1), fiuorldes generally have the largest values and Iodides the smallest values for lattice energies. However, one has to consider the stabilities of fluorides or Iodides with respect to each other, for example, a solid salt MX +i decomposing Into another, MX , and I/2X2. From the Born-Haber cycle (with some approximations) one obtains for such a reaction... 

Born-Haber cycles have been used by Passmore et al. to rationalize the thermodynamic stability of a large number of AsF6 salts of cluster cations. The calculations correctly predict the stability of most characterized compounds and also give indications that some compounds, which never have been synthesized in spite of great efforts eg. AsFe salts of monoatomic halogen cations), are unstable. This success confirms the argument that the formation of sub-valent cations is mainly enthalpy driven and that a Coulombic treatment of their solid compounds often is a reasonable approximation. 

Using the data given below (all values are in kJ/mol) and Born-Haber cycles for the formation of both the hydride and the chloride of sodium, calculate the standard heats of formation in each case. Which type of compound is more stable Briefly discuss the principal reasons for the differences in stabilities as measured by the standard heat of formation. Would you expect differences in entropy of formation to change your conclusions ... 

Only AuF of the gold(I) halides is unknown in the solid state its stability can be examined by means of a Born-Haber cycle, assuming that it would have an ionic lattice like AgF. (AuF has been generated in the gas phase from Au" " and CH3COF [22].)... 

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