Electron affinity Born-Haber cycle

Electron affinities may be estimated using a Born-Haber cycle. 

In more detail, the interaction energy between donor and acceptor is determined by the ionisation potential of the donor and the electron affinity of the acceptor. The interaction energy increases with lowering of the former and raising of the latter. In the Mulliken picture (Scheme 2) it refers to a raising of the HOMO (highest occupied molecular orbital) and lowering of the LUMO (lowest unoccupied molecular orbital). Alternatively to this picture donor-acceptor formation can be viewed in a Born-Haber cycle, within two different steps (Scheme 3). 

In fact, it may be impossible to measure the heat associated with an atom gaining two electrons, so the only way to obtain a value for the second electron affinity is to calculate it. As a result, the Born-Haber cycle is often used in this way, and this application of a Born-Haber cycle will be illustrated later in this chapter. In fact, electron affinities for some atoms are available only as values calculated by this procedure, and they have not been determined experimentally. 

The consideration of a Born-Haber cycle shows that the energy-supplying terms for the ionization are apart from the electron affinity of X the solvation... 

Fig. 7. Born-Haber cycle for the formation of ions by heterolytie fission of a covalent bond. I ionization potential of M, E electron affinity of X...

FIGURE 1.65 Born-Haber cycle for the calculation of the electron affinity of sulfur. 

E. A. Hylleraas, Z. Physik 63, 771 (1930). The calculated value of the crystal energy is 219 kcal/mole, and the Born-Haber cycle value is 218 kcal/mole, using for the electron affinity of hydrogen the reliable quantum-mechanical value 16.480 kcal/mole (see Introduction to Quantum Mechanics, Sec. 29c). The calculated value for the lattice constant, 4.42 A, is less reliable than the value... 

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. 

The electron affinities of elements (Chap, 7) that form negative ions may be calculated by considering the formations of compounds containing such negative ions. The formation of such a compound from the elements (the heat of such a reaction being directly measurable) may be broken down into a series of simpler steps. The treatment is again called a Born-Haber cycle and is analogous to the treatment of the conversion of an alkali metal to its hydrated ion (discussed in Chap. 6). Consider the formation of sodium chloride from the elements ... 

D is the dissociation enthalpy of Cl2,1 is the ionization potential of Na, E is the electron addition enthalpy of Cl (which is the negative of the electron affinity), and U is the lattice energy. The Born-Haber cycle shows that the lattice energy corresponds to the energy required to separate a mole of crystal into the gaseous ions, and forming the crystal from the ions represents -U. 

The oxides of the alkaline earth metals crystallize in a sodium chloride lattice although in SrO and BaO the radius ratio is greater than 0 732. It has been proposed that the crystals are constructed from the ions M + and the electron affinity of the oxygen atom calculated on this assumption by the Born-Haber cycle for the different oxides give rather... 

In the sulphides, selenides, tellurides and arsenides, all types of bond, ionic, covalent and metallic occur. The compounds of the alkali metals with sulphur, selenium and tellurium form an ionic lattice with an anti-fluorite structure and the sulphides of the alkaline earth metals form ionic lattices with a sodium chloride structure. If in MgS, GaS, SrS and BaS, the bond is assumed to be entirely ionic, the lattice energies may be calculated from equation 13.18 and from these values the affinity of sulphur for two electrons obtained by the Born-Haber cycle. The values obtained vary from —- 71 to — 80 kcals and if van der Waal s forces are considered, from 83 to -- 102 kcals. 

The electron affinity of ClOt has been estimated from a Born—Haber cycle, employing a lattice energy calculation, to be 134 kcal mof (V. I. Medeoeyev, L. V. Gurvich, V. N. Kondrat yev, V. A. Medvedev, and Ye, L Frankevich, "Bond Energies, Ionization Potentials and Electron Affinities," St. Martin s Press, New York, N. Y., 1966), whereas the electron affinity of the P atom has been determined spectroscopically to be 79.5 d 0.1 kcal mol (R. S. Berry and C. W. Reimann, J. Ckem. Pkys., 18, 1540 (1963)). 

In this experiment ionisation potentials ,(n) and dissociation energies for positively charged clusters EM) have been measured. Fig. 10 shows the Born-Haber cycle relating these quantities with the electron affinities [ e.(n)] and dissociation energies for neutral clusters [ d(n)]. Energy conservation... 

Use the Born-Haber cycle to calculate the enthalpy of formation of MgO, which crystallizes in the mtile lattice. Use these data in the calculation O2 bond energy = 247 kJ/mol AHj ji,(Mg) = 37 kJ/mol. Second ionization energy of Mg = 1451 kJ/mol second electron affinity of O = —744 kJ/inol. 

The energy drop when an extra electron is taken up by an atom is its electron affinity. This is generally estimated indirectly by applying the Born-Haber cycle to ionic compounds (p. 92). 

Note that the proton affinity (PA) has the opposite sign from the enthalpy of reaction of Eq. 9.47 Proton affinities are always listed as positive numbers despite referring to exothermic reactions (recall the same convention with electron affinities. Chapter 2). Proton affinities may be obtained in a number of ways. The simplest, and most fundamental for defining an absolute scale of proton affinities, is to use a Born-Haber cycle of the sort ... 

The electron affinities Ea of the main group atoms are the most precisely measured values. Recall that the Ea is the difference in energy between the most stable state of the neutral and a specific state of a negative ion. It was once believed that only one bound anion state of atoms and molecules could exist. However, multiple bound states for atomic and molecular anions have been observed. This makes it necessary to assign the experimental values to the proper state. The random uncertainties of some atomic Ea determined from photodetachment thresholds occur in parts per million. These are confirmed by photoelectron spectroscopy, surface ionization, ion pair formation, and the Born Haber cycle. Atomic electron affinities illustrate the procedure for evaluating experimental Ea. 

As new values were obtained, atomic electron affinities were reviewed periodically beginning in 1953 [1-13]. All the available experimental, extrapolated, and theoretical values were tabulated in 1984 [7]. Presently, experimental values are available at the NIST website [12]. Prior to 1970 the majority of the values for the main group elements were determined by the Born Haber cycle, electron impact, or relative and absolute equilibrium surface ionization techniques. However, values for C, O, and S had been measured by photodetachment [1-3]. By the mid-1970s virtually all the Ea of the main group elements in the first three rows had been measured by photon methods [4-7]. By the early 1980s values were obtained for the transition elements by photon techniques [7, 8]. In the 1990s the values of Ca, Sr, and Ba were measured [9-13]. Recently, experimental values have been reported for Ce, Pr, Tm, and Lu [14-17],... 

In addition to the lattice energy, electron affinity and ionization energy which have already been defined in this chapter, Born-Haber cycles also contain other quantities which allow for the fact, for example, that metals are not in the gaseous state at 298 K and that the halogens do not exist as mononuclear species. 

Oxide Lattice energy calculated by equation 13.18 Affinity of oxygen atom for two electrons Oxide Lattice energy calculated by equation 13.18 Lattice energy calculated by Born-Haber cycle Oxide Lattice energy calculated by equation 13.18 Lattice energy calculated by Born-Haber cycle... 

We can also determine lattice energy indirectly, by assuming that the formation of an ionic compound takes place in a series of steps. This procedure, known as the Born-Haber cycle, relates lattice energies of ionic compounds to ionization energies, electron affinities, and other atomic and molecular properties. It is based on Hess s law (see Section 6.5). Developed by Max Bom and Fritz Haber, the Bom-Haber cycle defines the various steps that precede the formation of an ionic solid. We will illustrate its use to find the lattice energy of lithium fluoride. 

The availability of laser photodetachment techniques has permitted more accurate experimental determinations of electron affinities. Even so, tables of electron affinities list some calculated values, in particular for the formation of multiply charged ions. One method of estimation uses the Born-Haber cycle, with a value for the lattice energy derived using an electrostatic model. Compounds for which this is valid are limited (see Section 5.15). 

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... 

LJ Can use a Born-Haber cycle to calculate lattice energy or electron affinity. 

Fig. 1.4 Schematic Born-Haber cycle for the formation of solid NaCI the energetic data (kJ/mol) are Na sublimation enthalpy AHsubi = 100.5 x CI2 dissociation enthalpy H iss = 121.4 Na ionization energy I = 495.7 Cl electron affinity A = -360.5 experimental reaction enthalpy AHr = -411.1.

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