Solid lattice enthalpy

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. 

For a given solid, the difference in molar enthalpy between the solid and a gas of widely separated ions is called the lattice enthalpy of the solid, AHl ... 

The lattice enthalpy can be identified with the heat required to vaporize the solid at constant pressure. The greater the lattice enthalpy, the greater is the heat required. Heat equal to the lattice enthalpy is released when the solid forms from gaseous ions. In Section 2.4 we calculated the lattice energy and discussed how it depended on the attractions between the ions. The lattice enthalpy differs from the lattice energy by only a few kilojoules per mole and can be interpreted in a similar way. 

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. 

The strength of interaction between ions in a solid is measured by the lattice enthalpy, which can be determined by using a Bom-Haber cycle. 

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. 

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. 

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. 

Strategy. (1) We start by compiling data from tables. (2) We construct an energy cycle. (3) Conceptually, we equate two energies we say the lattice enthalpy is the same as the sum of a series of enthalpies that describe our converting solid NaCl first to the respective elements and thence the respective gas-phase ions. 

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. 

Table 2.12 gives the absolute enthalpies of hydration for some anions. The values are derived from thermochemical cycle calculations using the enthalpies of solution in water of various salts containing the anions and the lattice enthalpies of the solid salts. 

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 lattice enthalpy can be identified with the heat required to vaporize the solid at constant pressure and the greater the lattice enthalpy, the greater the heat required. Heat equal to the lattice enthalpy is released when the solid forms from 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. 

Calculate the lattice enthalpy of solid potassium bromide, KBr(s) - K+(g) + Br (g), from the following information ... 

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... 

These semiempirical models postulate that local strain associated with different atomic sizes of the elements is the major contribution to the solid-solution enthalpy of mixing. An estimate of lattice strain energy has been compared to fitted values of the enthalpy of mixing for several group III-V systems (156). The results led to a calculated enthalpy of mixing that was a... 

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). 

Solution microcalorimetry is another thermal method for the determination of the difference in lattice energy of polymorphic solids. The difference in heat of solution of two polymorphs is also the difference in lattice energy (more precisely lattice enthalpy), provided of course, that both dissolution experiments are carried out in the same solvent (Guillory andErb 1985 Lindenbaum and McGraw 1985 Giron 1995). The actual value for A Hi is independent of the solvent, as demonstrated in Table 4.1 for the two polymorphs of sodium sulphathiazole. Note also that the calculated heats of transition are virtually identical in spite of the fact that the heat of solution (A//s) is endothermic in acetone and exothermic in dimethylformamide. 

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. 

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