Lattice energy, definition

Write Born-Haber cycles showing the relationship between the formation reaction and the lattice energy definitions of each of the ionic compounds in exercise 21.49. You may need to review the definition of "formation reaction" from earlier in the text. 

In the case of ionic solid substances, an important quantity is the free lattice energy AGS, i.e., the energy liberated when one type of crystalline substance is formed from its ionic constituents in the gas phase. This definition implies that this magnitude for a simple 1 1 solid electrolyte is a sum of the real potentials of cation and anion ... 

Definition Lattice energy is the energy released when one mole of a crystalline compound is assembled at a temperature of 0 K from its infinitely separated components. 

As Skinner has pointed out [7], there is no evidence for the existence of BFyH20 in the gas phase at ordinary temperatures, and the solid monohydrate of BF3 owes its stability to the lattice energy thus D(BF3 - OH2) must be very small. The calculation of AH2 shows that even if BFyH20 could exist in solution as isolated molecules at low temperatures, reaction (3) would not take place. We conclude therefore that proton transfer to the complex anion cannot occur in this system and that there is probably no true termination except by impurities. The only termination reactions which have been definitely established in cationic polymerisations have been described before [2, 8], and cannot at present be discussed profitably in terms of their energetics. It should be noted, however, that in systems such as styrene-S C/4 the smaller proton affinity of the dead (unsaturated or cyclised) polymer, coupled, with the greater size of the anion and smaller size of the cation may make AHX much less positive so that reaction (2) may then be possible because AG° 0. This would mean that the equilibrium between initiation and termination is in an intermediate position. 

For crystals containing unequal numbers of multiple cations and anions, the definition of a Madelung constant becomes more complicated, but the Madelung (or lattice) energy can always be calculated by simple computerized methods [76]. In principle, a dimensionless interaction curve can be derived for any structure type. 

A similar success rate, four and 44 out of 50 attempts for the anatase and rutile polymorphs, respectively, was more recently found by Reinaudi et al. [68]. Their initial work differs from that of Freeman and coworkers in that the lattice energy (Eq. 2 with identical potential parameters) rather than the r12 cost function was used as the measure of quality during the SA stage. Although a better measure of quality for candidate structures that are similar to the desired structure, this definition of the cost function can be problematic, however, if there are very short interatomic distances. Thus, the benefit of using the r12 cost function, to help prevent creating candidate structures that may contain collapsed regions, is lost. 

There is much confusion about the definition of lattice energy. In some textbooks it is described in terms of the formation of the lattice from the gaseous ions. Throughout this text the lattice energy will be described as a positive endothermic quantity which involves the separation of ions (bond breaking) rather than lattice formation. 

By considering the definition of lattice energy, it is easy to see why these quantities are not measured directly. However, an associated lattice enthalpy of a salt can be related to several other quantities by a thermochemical cycle called the Born-Haber cycle. If the anion in the salt is a haUde, then all the other quantities in the cycle have been determined independently the reason for this statement will become clearer when we look at applications of lattice energies in Section 5.16. 

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