Ionic lattice energy

Referred to the averaged eight-coordination of a B2 lattice, the equivalent separation, d8 =fd6 — (v/3/2)a. The ionic lattice energies of Table 5.3 are... 

Calculated ionic lattice energy, MO (kcal mole-1) -842 -866 - 24... 

At the right-hand side of Fig. 5, a comparison is made between two A-metal ions, Sr2+ and Caa+ (radii 1.13 and 0.99 A). Here the difference in radii is much greater than in any of the A/B pairs with which we have been concerned. However, the differences between one anion and another are now a good deal smaller moreover, these differences agree very well with values calculated on the basis of the differences in ionic size alone. The theoretical predictions given by ionic lattice-energy calculations are shown as circles to the left of the Sr/Ca points. 

Ionic lattice energies are measured experimentally by means of a thermodynamic cycle developed by Max Born and Fritz Haber. The Born-Haber cycle is an application of Hess s law (the first law of thermodynamics). It is illustrated by a determination of the lattice energy of sodium chloride, which is A for the reaction... 

Jenkins HBD, Marcus Y (1995) Ionic B-coefficients in solution. Chem Rev 95 2695-2726 Jenkins HDB, Roobottom HK, Passmore J, Glasser L (1999) Relationships among ionic lattice energies, molecular (formula unit) volumes, and thermochemical radii. Inorg Chem 38 3609-3620... 

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... 

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) ... 

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. 

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. 

M +(g)-(-e" this is 7297kJ mol for Li but drops to 2255kJmol for Cs. The largest possible lattice energy to compensate for this would be obtained with the smallest halogen F and (making plausible assumptions on lattice structure and ionic radius) calculations indicate that CsF2 could indeed be formed exothermically from its elements ... 

Similar observations hold for solubility. Predominandy ionic halides tend to dissolve in polar, coordinating solvents of high dielectric constant, the precise solubility being dictated by the balance between lattice energies and solvation energies of the ions, on the one hand, and on entropy changes involved in dissolution of the crystal lattice, solvation of the ions and modification of the solvent structure, on the other [AG(cryst->-saturated soln) = 0 = A/7 -TA5]. For a given cation (e.g. K, Ca +) solubility in water typically follows the sequence... 

The overall lattice energies of ionic solids, as treated by the Born-Eande or Kaputin-sldi equations, thus depends on (i) the product of the net ion charges, (ii) ion-ion separation, and (iii) pacldng efficiency of the ions (reflected in the Madelung constant, M, in the Coulombic energy term). Thus, low-melting salts should be most... 

We shall, however, wish to make use of the lattice energies which are tabulated for ionic crystals at the absolute zero of temperature. Now... 

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