Lattice enthalpy change

A H(X, g) = Enthalpy change associated with the attaehment of an electron Ajif°(MX, s) = Standard enthalpy of formation Lattice enthalpy change (see text)... 

Prediction of solubility for simple ionic compounds is difficult since we need to know not only values of hydration and lattice enthalpies but also entropy changes on solution before any informed prediction can be given. Even then kinetic factors must be considered. 

FIGURE 6.32 In a Born-Haber cycle, we select a sequence of steps that starts and ends at the same point (the elements, for instance). The lattice enthalpy is the enthalpy change accompanying the reverse of the step in which the solid is formed from a gas of ions. The sum of enthalpy changes around the complete cycle is 0 because enthalpy is a state function. 

The lattice enthalpy of a solid cannot be measured directly. However, we can obtain it indirectly by combining other measurements in an application of Hess s law. This approach takes advantage of the first law of thermodynamics and, in particular, the fact that enthalpy is a state function. The procedure uses a Born-Haber cycle, a closed path of steps, one of which is the formation of a solid lattice from the gaseous ions. The enthalpy change for this step is the negative of the lattice enthalpy. Table 6.6 lists some lattice enthalpies found in this way. 

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. 

FIGURE 6.33 The Born FHabcr cycle used to determine the lattice enthalpy of potassium chloride (see Example 6.13). The enthalpy changes are in kilojoules per mole. 

A/ /so, is the sum of the enthalpy change required to separate the molecules or ions of the solute, the lattice enthalpy,... 

In the second hypothetical step, we imagine the gaseous ions plunging into water and forming the final solution. The molar enthalpy of this step is called the enthalpy of hydration, AHhvd, of the compound (Table 8.7). Enthalpies of hydration are negative and comparable in value to the lattice enthalpies of the compounds. For sodium chloride, for instance, the enthalpy of hydration, the molar enthalpy change for the process... 

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. 

Table 1.3 Esti mated values of the four components of the contribution made by ligand field stabilization energy to the lattice enthalpy of KsCuFe, to the hydration enthalpy of Ni (aq), AH (Ni, g), and to the standard enthalpy change of reaction 13.

The lattice enthalpy, Aiatt//m, is the molar enthalpy change accompanying the formation of a gas of ions from the solid. Since the reaction involves lattice disruption the lattice enthalpy is always large and positive. Aatom//m and Adiss//m are the enthalpies of atomization (or sublimation) of the solid, M(s), and the enthalpy of dissociation (or atomization) of the gaseous element, X2(g). The enthalpy of ionization is termed electron gain enthalpy, Aeg//m, for the anion and ionization enthalpy, Ajon//m, for the cation. 

The lattice enthalpy is defined as the standard change in enthalpy when a solid substance is converted from solid to form gaseous constituent ions. Accordingly, values of AH(iattice) are always positive. 

N is here the number of lattice defects (vacancies or interstitials) which are responsible for non-stoichiometry. AHfon is the variation of lattice enthalpy when one noninteracting lattice defect is introduced in the perfect lattice. Since two types of point-defects are always present (lattice defect and altervalent cations (electronic disorder)), the AHform takes into account not only the enthalpy change due to the process of introduction of the lattice defect in the lattice, but also that occurring in the Redox reaction creating the electronic disorder. 

The lattice energy, L, of a crystal is the standard enthalpy change when one mole of the... 

The enthalpy change of the reaction in Equation (1.18) is minus the proton affinity of ammonia, -P(NH3,g). This could be calculated from the thermochemical cycle shown in Figure 1.58, provided the lattice energy of ammonium chloride is known. 

The negative values of the lattice enthalpies are plotted against the cation radii in Figure 3.3. The negative values represent the enthalpy changes accompanying the conversion of the solid compounds to their gaseous constituent ions (the opposite of lattice formation). 

The trends in Figure 3.3 are best interpreted by using the using the theoretical Born-Lande equation for the enthalpy change for lattice formation from the constituent gaseous ions ... 

Step 4 Let the gas of ions form the solid compound. This step is the reverse of the formation of the ions from the solid, so its enthalpy change is the negative of the lattice enthalpy, —AHL. Denote it by an arrow pointing downward, because the formation of the solid is exothermic. 

FIGURE 8.23 The enthalpy of solution, AHSC, is the sum of the enthalpy change required to separate the molecules or ions of the solute (the lattice enthalpy, AH,) and the enthalpy change accompanying their hydration, AHhvd. The outcome is finely balanced (a) in some cases, it is exothermic (b) in others, it is endothermic. The figures in (b) refer to sodium chloride, in kilojoules per mole (not to scale). For gaseous solutes, the lattice enthalpy is 0 because the molecules are already widely separated. 

To understand the values in Table 8.6, we can think of dissolving as a two-step process (Fig. 8.23). In the first hypothetical step, we imagine the ions separating from the solid to form a gas of ions. The change in enthalpy accompanying this highly endothermic step is the lattice enthalpy, AHL, of the solid, which was introduced in Section 6.20 (see Table 6.3 for values). The lattice enthalpy of sodium chloride (787 kj-mol-1), for instance, is the molar enthalpy change for the process... 

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