Lattice enthalpies ionic solids

In a Born-Haber cycle, we imagine that we break apart the bulk elements into atoms, ionize the atoms, combine the gaseous ions to form the ionic solid, then form the elements again from the ionic solid (Fig. 6.32). Only the lattice enthalpy, the enthalpy of the step in which the ionic solid is formed from the gaseous ions, is unknown. The sum of the enthalpy changes for a complete Born-Haber cycle is zero, because the enthalpy of the system must be the same at the start and finish. 

Born-Habcr cycle A closed series of reactions used to express the enthalpy of formation of an ionic solid in terms of contributions that include the lattice enthalpy. 

Lattice enthalpies of ionic solids can be predicted from several equations, which account for the coulombic interactions [45-47,49]. The estimates can then be used to derive the standard enthalpies of formation, by equation 2.47. However,... 

Figure 2.5 shows yet another way of destroying the lattice The ionic solid can be dissolved in water and the ions become hydrated. This solution enthalpy, As n//°(I.i()( T I3, cr), which is related to the lattice enthalpy by... 

To understand the dissolution of ionic solids in water, lattice energies must be considered. The lattice enthalpy, A Hh of a crystalline ionic solid is defined as the energy released when one mole of solid is formed from its constituent ions in the gas phase. The hydration enthalpy, A Hh, of an ion is the energy released when one mole of the gas phase ion is dissolved in water. Comparison of the two values allows one to determine the enthalpy of solution, AHs, and whether an ionic solid will dissolve endothermically or exothermically. Figure 1.4 shows a comparison of AH and A//h, demonstrating that AgF dissolves exothermically. 

This calculation is still hypothetical, in that the actual substance formed when sodium metal reacts with difluorine is solid sodium fluoride, and the standard enthalpy of its formation is -569 kJ mol-1. The actual substance is 311 kJ mol-1 more stable than the hypothetical substance consisting of ion pairs, Na+F (g), described above. The added stability of the observed solid compound arises from the long-range interactions of all the positive Na+ ions and negative F ions in the solid lattice which forms the structure of crystalline sodium fluoride. The ionic arrangement is shown in Figure 7.5. Each Na+ ion is octahedrally surrounded (i.e. coordinated) by six fluoride ions, and the fluoride ions are similarly coordinated by six sodium ions. The coordination numbers of both kinds of ion are six. 

Given the enthalpy of formation of an ionic solid, an experimental lattice energy can be obtained by thermochemical analysis. For example, the formation of crystalline sodium chloride is broken down as follows ... 

We first look at the fluorides of barium. Only BaF2 is known, a typically ionic solid having the fluorite (8 4) structure. From Table 5.2, we see that the calculated lattice energy is very close to the experimental value in other words, we can calculate the enthalpy of formation of BaF2(s) almost within the limits of experimental uncertainty. Why have BaF3 and BaF not been prepared Presumably they are thermodynamically unstable with respect to other species. In order to verify this supposition, let us estimate the enthalpies of formation AHf of BaF(s) and BaF3(s), assuming these to be ionic. 

This, of course, is always negative, and plays the same role in aqueous thermochemistry as the lattice energy does in the energetics of ionic solids. The hydration enthalpy cannot be measured directly, and many thermodynamicists frown upon this or any other single-ion quantity. For example, the enthalpy of solution of sodium chloride can be measured and subjected to the following analysis ... 

In the case of ionic solids of the type AB, AB2 or A2B, the lattice energy (Af/L) and lattice enthalpy (AHL) can be calculated by using the Jenkin s method proposed [26-29]. Only the molecular volumes of the ions are required. These can be most easily obtained from single crystal X-ray diffraction data ... 

Table 4.12 presents the calculated energies of formation for the solid neutral species and salts based on the CBS-4M method (see Ch. 4.2.1). Furthermore we see from table 4.12 that for the nitronium ([N02]+) species the covalently bound form is favored over the ionic salt by 26.9 kcal mol 1 while for the nitrosonium species ([NO]+) the salt is favored over the covalent isomer by 10.5 kcal mol-1. This change from the preferred covalent form of —N02 compound (actually a nitrato ester) to the ionic nitronium salt can be attributed almost exclusively to the increased lattice enthalpy of the (smaller ) N0+ species (AffL(N0+ - N02 salt) = 31.4 kcal mol-1) (N.B. The difference in the ionization potentials of NO (215 kcal mol-1) and N02 (221 kcal mol-1) is only marginal). 

Lattice enthalpies are important thermodynamic parameters and depend upon the solid state structures of the compound and hence the ionic radius of the metal ion. 

E20.21(b) The lattice enthalpy is the difference in enthalpy between an ionic solid and the corresponding isolated ions. In this exercise, it is the enthalpy corresponding to the process... 

The negative of this value, 1050 kJ, is the lattice energy of LiF. The lattice energy ( attice) is the enthalpy change that occurs when 1 mol of ionic solid separates into gaseous ions. It indicates the strength of ionic interactions and influences melting point, hardness, solubility, and other properties. 

The solubility of the ions in water, on the other hand, is a tradeoff between the hydration enthalpy and the lattice energy. The solubility product, K p, for an ionic compound dissolving in water can be calculated from the sum of the hydration enthalpies for the ions and the reverse of the lattice energy for the ionic solid, as shown in Equations (5.2)-(5.5) ... 

The lattice enthalpy (Table 6.3) of an ionic solid is a measure of the strength of the bonds in that compound. The decrease of the lattice energy from LiE to LiBr or from NaE to NaBr depends mainly on the inaeased bond distance. The large values for MgO to SrO depend on the higher charge of the ions. 

Lattice energy, U is defined as the enthalpy of formation of a mole of an ionic solid from free gaseous ions brought from infinity to their respective equilibrium sites in their crystalline lattice under standard conditions. It may also be defined as the change in energy that occurs when an ionic solid is separated into isolated ions in the gas phase. 

Lattice energy is the enthalpy of formation of a mole of ionic solid from free gaseous ions brought from infinity to their respective equilibrium sites in their crystalline lattice under standard conditions. 

The lattice energy of an ionic solid such as NaCl is the enthalpy change A/7° for the process in which the solid changes to ions. For example. 

Note that the sign of the lattice enthalpy must always be included in the thermochemical equation the reverse of lattice enthalpy is the heat energy released (at constant pressure) when one mole of ionic solid is formed from gaseous ions (Figure 15.5). 

---