Sodium lattice energy

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. 

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) ... 

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... 

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. 

Using the appropriate data for the formation of sodium chloride, U (kj mol-1) = 109 + 121 + 496 — 349 — ( — 411) = 786 kj mol-1. Although this is a useful approach for determining the lattice energy of a crystal, the electron affinity of the atom gaining the electron is difficult to measure experimentally. 

Sodium fluoride, NaF, is a favorable choice for X-ray analysis of the lattice energy of an ionic crystal. Both Na and F are relatively light atoms, and the Na 3s-radial distribution, though diffuse, is not quite as spread out as the Li 2s shell (single-C values are 0.8358 and 0.6396 au-1, respectively see appendix F), and therefore contributes to a larger number of reflections. 

Heats of solution, hydration energies and lattice energies are discussed in reference (77). For oxygen and nitrogen donor atoms, only a few compounds of potassium, rubidium, and caesium are known, but several have been characterised for the smaller cations, sodium and lithium. 

Figure 1.15 Energy band diagram for a sodium lattice. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc. After J. C. Slater, Phys. Rev., 45, 794 (1934).

The electrostatic contribution to the lattice energy, L, for the sodium fluoride arrangement (the energy required to form gas phase ions from the solid crystalline lattice) is the value of the change in internal energy (i.e. A U) for the reaction ... 

Estimate the lattice energy of sodium chloride, using the appropriate data from Appendix F and assuming that the Born exponent is 9. Compare your result with the value given in Eq. 4.8. 

Properties of the alkali fluorides.—The anhydrous alkali fluorides crystallize in the cubic system.8 Lithium fluoride forms regular optohedrons and nacreous plates sodium fluoride crystallizes in cubes, but in presence of sodium carbonate, the crystals are octohedrons. The cubic crystals are frequently en tremies. H. Schwendenwein has discussed the space lattice of the alkali fluorides, and K. Fajans and H. Grimm estimated the distance of the atoms apart in sodium and potassium fluorides to be respectively 2 34 X 10 8 and 2 67 X10-8 cm. and the respective lattice energies to be 210-4 and 192 2 Cals, per mol. The taste of potassium fluoride is acrid and salty. 

The use of Eq. 4.13 to predict the lattice energy of an ionic compound may be illustrated as follows. For sodium chloride the various factors are... 

Sodium fluoride and sodium chloride both crystallize into the same type of structure. Which do you predict to have the higher lattice energy, NaF or NaCl ... 

---