Lattice enthalpies

The lattice enthalpy of an ionic crystal is the enthalpy lowering when 1 mol of crystal is formed from its ions. It consists particularly of the attraction between ions of different signs of charge, according to Equation 6.1. The standard formation enthalpy of crystal is the energy lowering from the pure phases, usually the metal phase for the metal ion and the halogen gas phase at standard conditions. 

If a very electronegative atom is bonded with a very electropositive one, in a condensed medium, one electron will be transferred to the electronegative one, which forms a negative ion. One example is LiF formed from the ions Li and F . Each 

Li+ ion is coordinated to six F ions, and every F ion coordinated to six Li+ ions. The crystal is an insulator, but there is a strong absorption of infrared radiation. No electronic transitions are expected at a low energy, so the low energy absorption in the infrared must be due to vibrations. 

Step (1) is the vaporization energy of Li. Step (2) is the charge separation step from Li gas to Li+ and free electrons, which may be calculated from ionization energies. Step (3) is the dissociation energy of F2, which may be obtained from vibration spectra or from accurate quantum chemical calculations. Step (4) is the electron affinity of the fluorine atom. 

The experimental lattice enthalpy obtained from the Born-Haber cycle (step 5) may be compared to a theoretical estimation. The major component of the lattice enthalpy is the Coulomb attraction (U) between the ions, given in Equation 6.1. As the ions approach each other, the electronic shells will start to overlap and repulsive forces become important. 

The cohesion of the atoms of a crystal lattice is determined by the energy that holds the atoms together and which is released when the crystal is disassembled into its atomic, molecular, or ionic components. It will be called the lattice energy or lattice enthalpy 

Forces of different origin contribute to the lattice energy and depend on the distances in the lattice. 

The exponent 12 is often used in this equation but smaller values are also found in the literature. The combination of the two equations is called the Lennard-Jones potential. 

When ions form the lattice Coulomb forces as described in Section 2.7. Orbital interaction energies as described in Section 2.9. 

The lattice enthalpy is the sum of all interactions in the lattice. Sometimes it is necessary to separate it into contributions from interactions between two atoms, molecules, or ions, mostly the nearest neighbors. This will be called the bond energy q j between components i and j. 

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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. 

The very low bond dissociation enthalpy of fluorine is an important factor contributing to the greater reactivity of fluorine. (This low energy may be due to repulsion between non-bonding electrons on the two adjacent fluorine atoms.) The higher hydration and lattice enthalpies of the fluoride ion are due to the smaller size of this ion. 

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. 

EXAMPLE 6.13 Using a Bom-Haber cycle to calculate a lattice enthalpy... 

Devise and use a Born-Haber cycle to calculate the lattice enthalpy of potassium chloride. 

Sf.if-Test 6.17A Calculate the lattice enthalpy of calcium chloride, CaCl2, by using the data in Appendices 2A and 2D. 

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. 

Whereas a lattice enthalpy is equal to the heat required (at constant pressure) to break up an ionic substance, a bond enthalpy is the heat required to break a specific type of bond at constant pressure. For example, the bond enthalpy of H2 is derived from the thermochemical equation... 

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. 

J 15 Calculate a lattice enthalpy by using the Born-Haber cycle (Example 6.13). 

By assuming that the lattice enthalpy of NaCl, is the same as that of MgCI2, use enthalpy arguments based on data in Appendix 2A, Appendix 2D, and Fig. 1.54 to explain why NaCl, is an unlikely compound. 

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. 

Enthalpies of solution in dilute solutions can be expressed as the sum of the lattice enthalpy and the enthalpy of hydration of the compound. 

Interpret enthalpies of solution in terms of lattice enthalpies and enthalpies of hydration (Section 8.12). 

The enthalpy of solution of ammonium nitrate in water is positive, (a) Does NH4N05 dissolve endothermically or exothermically (b) Write the chemical equation for the dissolving process, (c) Which is larger for NH4NO , the lattice enthalpy or the enthalpy of hydration ... 

The valence electron configuration of the atoms of the Group 2 elements is ns1. The second ionization energy is low enough to be recovered from the lattice enthalpy (Fig. 14.18). Flence, the Group 2 elements occur with an oxidation number of +2, as the cation M2+, in all their compounds. Apart from a tendency toward nonmetallic character in beryllium, the elements have all the chemical characteristics of metals, such as forming basic oxides and hydroxides. 

Explain the trend of decreasing lattice enthalpies of the chlorides of the Group 2 metals down the group. 

Because the fluoride ion is so small, the lattice enthalpies of its ionic compounds tend to be high (see Table 6.6). As a result, fluorides are less soluble than other halides. This difference in solubility is one of the reasons why the oceans are salty with chlorides rather than fluorides, even though fluorine is more abundant than chlorine in the Earth s crust. Chlorides are more readily dissolved and washed out to sea. There are some exceptions to this trend in solubilities, including AgF, which is soluble the other silver halides are insoluble. The exception arises because the covalent character of the silver halides increases from AgCl to Agl as the anion becomes larger and more polarizable. Silver fluoride, which contains the small and almost unpolarizable fluoride ion, is freely soluble in water because it is predominantly ionic. 

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 solubilities of the ionic halides are determined by a variety of factors, especially the lattice enthalpy and enthalpy of hydration. There is a delicate balance between the two factors, with the lattice enthalpy usually being the determining one. Lattice enthalpies decrease from chloride to iodide, so water molecules can more readily separate the ions in the latter. Less ionic halides, such as the silver halides, generally have a much lower solubility, and the trend in solubility is the reverse of the more ionic halides. For the less ionic halides, the covalent character of the bond allows the ion pairs to persist in water. The ions are not easily hydrated, making them less soluble. The polarizability of the halide ions and the covalency of their bonding increases down the group. 

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.

Theoretical calculations on the dithiazolyl radical 4 (R=CF3) have recently shown that n -n dimerisation was unfavourable but association of two such dimers via electrostatic interactions generated a thermodynamically stable tetramer consistent with single crystal X-ray studies. Thus while the value of [AE-P ] may favour (or disfavour) dimer formation, the van der Waals, dipole contributions and electrostatic interactions to the lattice enthalpy should not be underestimated in assessing the thermodynamic stability or instability of these... 

In some instances, distinct polymorphic forms can be isolated that do not interconvert when suspended in a solvent system, but that also do not exhibit differences in intrinsic dissolution rates. One such example is enalapril maleate, which exists in two bioequivalent polymorphic forms of equal dissolution rate [139], and therefore of equal free energy. When solution calorimetry was used to study the system, it was found that the enthalpy difference between the two forms was very small. The difference in heats of solution of the two polymorphic forms obtained in methanol was found to be 0.51 kcal/mol, while the analogous difference obtained in acetone was 0.69 kcal/mol. These results obtained in two different solvent systems are probably equal to within experimental error. It may be concluded that the small difference in lattice enthalpies (AH) between the two forms is compensated by an almost equal and opposite small difference in the entropy term (-T AS), so that the difference in free energy (AG) is not sufficient to lead to observable differences in either dissolution rate or equilibrium solubility. The bioequivalence of the two polymorphs of enalapril maleate is therefore easily explained thermodynamically. 

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. 

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