Lattice enthalpy table

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. 

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. 

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 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. 

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.

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. 

The qualitative trend predicted by this equation is that, when the heat of solution is negative (the dissolution is exothermic, i.e., heat is evolved, the enthalpy of solvation is more negative than the lattice enthalpy is positive), the solubility diminishes with increasing temperatures. The opposite trend is observed for endothermic dissolution. An analogue of Eq. (2.58), with H replacing G, and the same tables [12] can be used to obtain the required standard enthalpies of solution of ionic solutes. No general analogues to Eqs. (2.53)-(2.55) are known as yet. 

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. 

AH , AS at, AG°at Lattice enthalpy, entropy, and Gibbs energy of the crystalline electrolyte AH v, AS V, AG°V Enthalpy, entropy, and Gibbs energy of solvation of the electrolyte AG° Gibbs energy of solution of the crystalline electrolyte. Taken from Table 1 in Ref. [3], Chapter 1. 

The procedure is illustrated in the following example. Lattice enthalpies of other compounds obtained in this way are listed in Table 6.5. 

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... 

Estimate the enthalpy of solution of SrCl2 from the data for the ion enthalpies of hydration and the lattice enthalpy in Tables 6.3 and 8.8. 

The valence electron configuration of the atoms of the Group 2 elements is ms2, where n is the period number. The second ionization energy is low enough to be recovered from the increased lattice enthalpy (Fig. 14.22). Hence, the Group 2 elements occur with an oxidation number of +2, as the cation M2+, in all their compounds (Table 14.7). Apart from a tendency toward nonmetallic character in beryllium, the elements have all the chemical characteristics of metals, such as having basic oxides and hydroxides. 

The lattice enthalpy U at 298.20 K is obtainable by use of the Born—Haber cycle or from theoretical calculations, and q is generally known from experiment. Data used for the derivation of the heat of hydration of pairs of alkali and halide ions using the Born—Haber procedure to obtain lattice enthalpies are shown in Table 3. The various thermochemical values at 298.2° K [standard heat of formation of the crystalline alkali halides AHf°, heat of atomization of halogens D, heat of atomization of alkali metals L, enthalpies of solution (infinite dilution) of the crystalline alkali halides q] were taken from the compilations of Rossini et al. (28) and of Pitzer and Brewer (29), with the exception of values of AHf° for LiF and NaF and q for LiF (31, 32, 33). The ionization potentials of the alkali metal atoms I were taken from Moore (34) and the electron affinities of the halogen atoms E are the results of Berry and Reimann (35)4. 

There are uncertainties concerning the correctness of some of the data quoted in Table 3. However, the lattice enthalpies are in fair agreement with values from lattice energies computed by the Huggins—Mayer type of treatment (36, 26) — Table 4. Moreover, the results for (PTm+H-W x-) correspond well to the additivity criterion. 

Table 4. Lattice enthalpies of the alkali halides at 298.2° K and 1 aim. from lattice energies computed by the Huggins-Mayer-type treatment (kcal mole-1)...

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. 

Fluoride Ion Affinities of GeF4 and BF3 Table vn. Lattice Enthalpies and Basic Radii ... 

Table VII shows the calculated lattice enthalpies for SFj BF4 , NO UFr, (SF3+)2GeF42-, C102+BF4, and K -BF4-, and the derived basic radii for S -, Cl NO ", and K ". In these calculations a value of p = 0.333 A was chosen, since this is the preferred value for the alkali fluorides. Variation of p between 0.333 and 0.360 produced a variation of 1.5 kcal moi in the lattice enthalpy calculated for SF3 BF4". Likewise, a variation of by 25% ( 9.5 kcal moF )...

For simple compounds, p = 30 pm works well when tq is also in pm. Lattice enthalpies are twice as large when charges of 2 and 1 are present, and four times as large when both ions are doubly charged. Madelung constants for some crystal structures are given in Table 7-2. 

The enthalpy change for the sublimation step is designated the lattice enthalpy, A//l(see Table 6.6 in the text). 

Table 9.4 shows typical values of bond dissociation enthalpies of some hydrogen bonds. The data in the table have been obtained from calculations on isolated species. These enthalpy values are therefore only approximate when applied to hydrogen bonds between molecules in a solid state lattice enthalpy values for these interactions cannot be measured directly. An example of how the strengths of hydrogen bonds can be obtained experimentally comes from the dissociation of a carboxylic acid dimer in the vapour state (equation 9.25). 

The total changes in entropy and enthalpy (Table I) can be considered to be composed of 2 terms, one accounting for the changes in the energy of interaction with the lattice, the other for the changes in the hydration of the ions. This was discussed earlier by Sherry et al. (10) and by Barrer et al. (2). This gives us the following equations where the index 1 indicates the interaction terms with the lattice, and the index h the hydration terms. 

The difference between the two sets of data is due primarily to differences in iv values and we attribute this to different lattice enthalpies used by Rodewald (cf. ref. (d) in Table I of their paper). 

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