Born-Haber thermochemical cycle

When the multiplicity of a complex is the same for ionic or ion-dipole bonds and for covalent bonds, the decision as to which extreme bond type is the more closely approached in any actual case must be made with the aid of less straightforward arguments. Sometimes theoretical energy diagrams can be constructed with sufficient accuracy to decide the question. A discussion of crystals based on the Born-Haber thermochemical cycle has been given by Rabinowitsch and Thilo3), and more accurate but less extensive studies have been made by Sherman and Mayer4). 

Calculate the values for the proton affinities of the halide anions shown in Table 9.5 from a Born-Haber thermochemical cycle and values for ionization energies, electron affinities, and bond energies. 

Direct measurements of the hydration values AG, AH and AS are not feasible and they are usually calculated indirectly using semi-empirical methods (Born-Haber thermochemical cycles). These cycles lead to the general equations (Rosseinsky 1965, Morss 1976, Bratsch and Lagowski 1985b)... 

Fig. 6.24 A Born-Haber thermochemical cycle for the formation of a salt MX . This gives an enthalpy change associated with the formation of the ionic lattice MX .

The enthalpy of formation of a compound is a so-called thermodynamic state function, which means that the value depends only on the initial and final states of the system. When the formation of crystalline NaCl from the elements is considered, it is possible to consider the process as if it occurred in a series of steps that can be summarized in a thermochemical cycle known as a Born-Haber cycle. In this cycle, the overall heat change is the same regardless of the pathway that is followed between the initial and final states. Although the rate of a reaction depends on the pathway, the enthalpy change is a function of initial and final states only, not the pathway between them. The Born-Haber cycle for the formation of sodium chloride is shown as follows ... 

From the standpoint of energy, the processes of separating the crystal lattice and solvating the ions can be related by means of a thermochemical cycle of the Born-Haber type. For an ionic compound MX, the cycle can be shown as follows ... 

The relationships between the two different states and between the enthalpy of formation from the elements at standard state (H°) and the lattice energy (U) are easily understood by referring to the Born-Haber-Fayans thermochemical cycle. In this cycle, the formation of a crystalline compound from isolated atoms in the gaseous state is visualized as a stepwise process connecting the various transformations. Let us follow the condensation process of a crystal MX formed from a metal M and a gaseous molecule X2 ... 

We have also seen (in chapter 1) that enthalpy and lattice energy are related through the Born-Haber-Fayans thermochemical cycle, on the basis of the energy additivity principle of Hess. The enthalpy or heat content of a phase H) is composed of the internal energy U at the T of interest and the PV product ... 

Table 5.37 Lattice energy terms for C2/c pyroxenes. Values in kJ/mole. bhf = energy of Born-Haber-Fayans thermochemical cycle U- = lattice energy Ec = coulombic energy = repulsive energy Edd = dipole-dipole interactions E q = dipole quadrupole interactions =...

The Born-Haber Thermoche mi cal Cycle. -The following cycle was devised by Born and Haber to relate the crystal energy to other thermochemical quantities ... 

In cases where the lattice energy is known from the Born-Haber cycle, the Kapustinskii equation can be used to derive the ionic radii of complex anions such as S042- and P043-. The values determined in this way are known as thermochemical radii some values are shown in Table 4.2.6. 

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. 

Sherman (114) and other workers have compared crystal energies obtained by the Born-Haber cycle from experimental thermochemical data with theoretical values calculated assuming strict ionic character. The differences obtained have been used to indicate deviations from strict heteropolarity. Sherman 114) in his review gives results for 50 crystals, the computations being made with the Born-Lande equation. 

Born-Haber cycle A series of thermochemical reactions or cycles used for calculating the lattice energies of ionic crystalline solids. 

Lattice energies can be related to the heats of formation AHf of ionic solids through the Born-Haber cycle, which is the counterpart of the thermochemical cycle for covalent compounds given in Section 2.7. 

By considering the definition of lattice energy, it is easy to see why these quantities are not measured directly. However, an associated lattice enthalpy of a salt can be related to several other quantities by a thermochemical cycle called the Born-Haber cycle. If the anion in the salt is a haUde, then all the other quantities in the cycle have been determined independently the reason for this statement will become clearer when we look at applications of lattice energies in Section 5.16. 

The heats of formation of various ionic compounds show tremendous variations. In a general way, we know that many factors contribute to the over-all heat of formation, namely, the ionization potentials, electron affinities, heats of vaporization and dissociation of the elements, and the lattice energy of the compound. The Born-Haber cycle is a thermodynamic cycle that shows the interrelation of these quantities and enables us to see how variations in heats of formation can be attributed to the variations in these individual quantities. In order to construct the Born-Haber cycle we consider the following thermochemical equations, using NaCl as an example... 

The standard reduction potentials (see Redox Potential) of the elements and their compounds have many important applied implications for chemists, not the least of which is being aware when a compound or mixture of compounds they are handling has the potential for exploding. This should be considered as a possibility when the appropriate potentials differ by more than about one volt and appropriate kinetics considerations apply. A simply predictable case is the sometimes-violent reaction of metals with acids, as illustrated in a recently produced discovery video. Redox activities of elements are most commonly (and most precisely) analyzed via thermochemical cycles such as the familiar Born-Haber cycle for the production of NaCl from Na and CI2. A similar analysis of the activities of different metals in their reactions with acids shows that the standard reduction potential for the metal (the quantitative measure of the activity of the metal) can be expressed in terms of the appropriate ionization energies of the metal, the atomization energies of the metal see Atomization Enthalpy of Metals), and the hydration energies... 

The Born-Haber cycle relates several thermochemical quantities needed later in the manner shown in Figure 6. For simplicity a monovalent azide compound... 

In theory, the standard reduction potential for a metal ion can be calculated using a Born-Haber-type thermochemical cycle. The reduction half-reaction is the sum of the negative of the atomization energy, the negative of the ionization energy, and the negative of the hydration enthalpy, as shown in Equations (14.26)-( 14.28) ... 

B0 Write a Born-Haber cycle for the formation of potassium hydride, KH, and use it to calculate a value for the lattice energy of this compound. (The standard heat of formation of KH is —57.8 1 /mol other thermochemical quantities can be found... 

A number of efforts have been made to calculate ionization-potential sums from thermochemical data and appropriate Born-Haber cycles. When an isostructural set of compounds is used, and covalence/repulsion corrections are made from a systematic lanthanide-actinide comparison, such sums can be quite reliable, as has been repeatedly demonstrated for the trivalent lanthanides [88]. For example, Morss [89] was able to estimate the sum of the first three ionization energies (/i +I2 + I3) for Pu as... 

The lattice energy may be determined experimentally from thermochemical data by considering a suitable cycle of changes (Born and Haber, 1919). The cycle for formation of sodium chloride is ... 

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