Lattices lattice energy

Ionic substances will be water soluble if the energy required to separate the ions in the lattice (lattice energy) is compensated for by the exothermic nature of hydration. This is the energy released when the very polar water molecules are attracted to the + and - ions. 

S = Heat of sublimation of sodium D = Dissociation energy of chlorine / = Ionization energy of sodium = Electron affinity of chlorine Uq = Lattice energy of sodium chloride AHf = Heat of formation of sodium chloride. 

Born-Haber cycle A thermodynamic cycle derived by application of Hess s law. Commonly used to calculate lattice energies of ionic solids and average bond energies of covalent compounds. E.g. NaCl ... 

Kapustinskii equation For an ionic crystal composed of cations and anions, of respective charge and z, which behave as hard spheres, the lattice energy (U) may be obtained from the expression... 

Lattice energies may be derived from the Born-Haber cycle or calculated using the Kapustinskii equation. ... 

A/ij the lattice energy of sodium chloride this is the heat liberated when one mole of crystalline sodium chloride is formed from one mole of gaseous sodium ions and one mole of chloride ions, the enthalpy of formation of sodium chloride. 

To date there is no evidence that sodium forms any chloride other than NaCl indeed the electronic theory of valency predicts that Na" and CU, with their noble gas configurations, are likely to be the most stable ionic species. However, since some noble gas atoms can lose electrons to form cations (p. 354) we cannot rely fully on this theory. We therefore need to examine the evidence provided by energetic data. Let us consider the formation of a number of possible ionic compounds and first, the formation of sodium dichloride , NaCl2. The energy diagram for the formation of this hypothetical compound follows the pattern of that for NaCl but an additional endothermic step is added for the second ionisation energy of sodium. The lattice energy is calculated on the assumption that the compound is ionic and that Na is comparable in size with Mg ". The data are summarised below (standard enthalpies in kJ) ... 

AI14 electron affinity of chlorine, x 2 (two ions are formed) —728 A/15 calculated lattice energy —2539... 

The enthalpy of solution is quite small for many simple ionic compounds and can be either positive or negative. It is the difference between two large quantities, the sum of the hydration enthalpies and the lattice energy. 

Although the data for the silver halides suggest that silver(I) fluoride is likely to be more soluble than the other silver halides (which is in fact the case), the hydration enthalpies for the sodium halides almost exactly balance the lattice energies. What then is the driving force which makes these salts soluble, and which indeed must be responsible for the solution process where this is endothermic We have seen on p. 66 the relationship AG = — TAS and... 

In this discussion, entropy factors have been ignored and in certain cases where the difference between lattice energy and hydration energy is small it is the entropy changes which determine whether a substance will or will not dissolve. Each case must be considered individually and the relevant data obtained (see Chapter 3), when irregular behaviour will often be found to have a logical explanation. 

From the standpoint of thermodynamics, the dissolving process is the estabHsh-ment of an equilibrium between the phase of the solute and its saturated aqueous solution. Aqueous solubility is almost exclusively dependent on the intermolecular forces that exist between the solute molecules and the water molecules. The solute-solute, solute-water, and water-water adhesive interactions determine the amount of compound dissolving in water. Additional solute-solute interactions are associated with the lattice energy in the crystalline state. 

Watson G W, P Tschaufeser, A Wall, R A Jackson and S C Parker 1997. Lattice Energy and Free Energy Minimisation Techniques. Computer Modelling in Inorganic Crystallography. San Diego, Academic Press, pp. 55-81. 

A linear relationship exists between the cohesive energy density of an abrasive (10) and the WoodeU wear resistance values occurring between comndum H = 9) and diamond H = 42.5). The cohesive energy density is a measure of the lattice energy per unit volume. 

Some properties of selected vanadium compounds are Hsted in Table 1. Detailed solubiUty data are available (3), as are physical constants of other vanadium compounds (4). Included are the lattice energy of several metavanadates and the magnetic susceptibiUty of vanadium bromides, chlorides, fluorides, oxides, and sulfides (5). 

The fluorite stmcture, which has a large crystal lattice energy, is adopted by Ce02 preferentially stahi1i2ing this oxide of the tetravalent cation rather than Ce202. Compounds of cerium(IV) other than the oxide, ceric fluoride [10060-10-3] CeF, and related materials, although less stable can be prepared. For example ceric sulfate [13590-82-4] Ce(S0 2> certain double salts are known. 

When an impacting particle transfers energy to a near sinface carbon atom in an amount sufficient to overcome the lattice bond energy or surface binding energy, some carbon atoms may be displaced and move in a direction defined by the angle... 

There is a lively controversy concerning the interpretation of these and other properties, and cogent arguments have been advanced both for the presence of hydride ions H" and for the presence of protons H+ in the d-block and f-block hydride phases.These difficulties emphasize again the problems attending any classification based on presumed bond type, and a phenomenological approach which describes the observed properties is a sounder initial basis for discussion. Thus the predominantly ionic nature of a phase cannot safely be inferred either from crystal structure or from calculated lattice energies since many metallic alloys adopt the NaCl-type or CsCl-type structures (e.g. LaBi, )S-brass) and enthalpy calculations are notoriously insensitive to bond type. 

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