Sodium chloride lattice energy

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) ... 

We have already mentioned that for sodium chloride approximately 1.78 times as much energy is released when the crystal lattice forms as when ion pairs form. This value, the Madelung constant (A) for the sodium chloride lattice, could be incorporated to predict the total energy released when 1 mole of NaCl crystal is formed from the gaseous Na+ and Cl- ions. The result would be... 

Now in the crystal lattice there will be more interactions than the simple one in an ion pair. In the sodium chloride lattice, for example, there are attractions to the six nearest neighbors of opposite charge, repulsions by the twelve next nearest neighbors of like charge, etc. The summation of all of these geometrical interactions is known as the Modelling constant, A. The energy of a pair of ions in the crystal is then ... 

Figure 19.1 A model of the sodium chloride lattice. The energy released when gaseous ions combine to form a lattice is called the 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. 

Because the enthalpy of solution is positive, there is a net inflow of energy as heat when the solid dissolves (recall Fig. 8.23b). Sodium chloride therefore dissolves endothermically, but only to the extent of 3 kj-mol-1. As this example shows, the overall change in enthalpy depends on a very delicate balance between the lattice enthalpy and the enthalpy of hydration. 

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. 

For sodium chloride, since there are eight molecules per unit cell, and the cell volume is ao where a0 is the lattice parameter, the energy per unit volume becomes ... 

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. 

The formation energy of Schottky defects in NiO has been estimated at 198 kJ mol-1. The lattice parameter of the sodium chloride structure unit cell is 0.417 nm. (a) Calculate the number of Schottky defects per cubic meter in NiO at 1000°C. (b) How many vacancies are there at this temperature (c) Estimate the density of NiO and hence the number of Schottky defects per gram of NiO. 

As a relevant example, Figure 6.4 shows the room temperature absorption spectrum of Eu + in sodium chloride (NaCl). In this crystal, europium is incorporated in the divalent state, replacing Na+ lattice ions. The spectrum of Eu + ion in NaCl consists of two broad bands, centered at about 240 nm and 340 nm, which correspond to transitions from the ground state ( 87/2) of the 4f electronic configuration to states of the 4f 5d excited electronic configuration. In fact, the energy separation between... 

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. 

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 ... 

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