Thermochemical cycles electron affinities

In Chapter 1 we discussed the electron affinities of atoms and how they vary with position in the periodic table. It was also mentioned that no atom accepts two electrons with a release of energy. As a result, the only value available for the energy associated with adding a second electron to O- is one calculated by some means. One way in which the energy for this process can be estimated is by making use of a thermochemical cycle such as the one that follows, showing the steps that could lead to the formation of MgO. 

Figure 4.5 Thermochemical cycle (T = 298.15 K), showing how the proton affinities of A and A- are related. Fj(AH) is the adiabatic ionization energy of AH, and fea(A) is the adiabatic electron affinity of A. A, A, and X are thermal corrections (see text).

In the gas phase, homolytic bond dissociation enthalpies (D//) relate the thermochemical properties of molecules to those of radicals while ionization potentials (IP) and electron affinities (EA) tie the thermochemistry of neutral species to those of their corresponding ions. For example, Scheme 2.1 represents the relationships between RsSiH and its related radicals, ions, and radical ions. This representation does not define thermodynamic cycles (the H fragment is not explicitly considered) but it is rather a thermochemical mnemonic that affords a simple way of establishing the experimental data required to obtain a chosen thermochemical property. 

Thermochemical information about neutral species can also be obtained from measurements of ions. Indeed, accurate bond dissociation energies for neutral molecules have been obtained from gas-phase ion chemistry techniques. In this section, we will summarize both the negative-ion and hydride-affinity cycles involving silicon hydrides (RsSiH) which are connected to electron affinity (EA) and ionization potential (IP) of silyl radicals, respectively [22-24]. 

It is not yet possible to measure lattice energy directly, which is why the best experimental values for the alkali halides, as listed in Table 1.16, are derived from a thermochemical cycle. This in itself is not always easy for compounds other than the alkali halides because, as we noted before, not all of the data is necessarily available. Electron affinity values are known from experimental measurements for... 

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. 

Experimentally, the electron affinity is difficult to measure, and most of the tabulated values are obtained from thermochemical cycles where the other quantities are known (see Chapter 4). Electron affinities are often given in units other than those needed for a particular use. Therefore, it is useful to know that 1 eV molecule-1 = 23.06 kcal mole-1 and 1 kcal = 4.184 kJ. Electron affinities for many nonmetallic atoms are shown in Table 2.3. 

The H-H bond energy is 431 kJ mol-1, the heat of formation of LiH is -90.4 kJ mol-1, and the lattice energy of LiH is 916 kJ mol-1. Use these data and those shown in Table 3.1 to construct a thermochemical cycle and determine the electron affinity of the hydrogen atom. 

It should be noted that thermochemical cycles are often calculated at 298 K, whereas the energy terms such as electron affinity or ionization energy are defined at 0 K. Therefore, the values calculated by thermochemical cycles have an error of approximately 2-5 kJ mol. ... 

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. 

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... 

NaCl ) = 2.497 A, and 5g = 0.195 cm Finally, the position of the origin peak gives the electron binding energy (the electron affinity of NaCl, 0.727 eV) and a thermochemical cycle allows one to calculate the bond... 

The methyl radical has a small electron affinity (1.8 0.7kcalmol and this has been combined with the bond dissociation energy (BDE) of methane and the ionization potential of H atoms to give the enthalpy for the deprotonation of methane using the thermochemical cycle (equation 24). For most alkyl radicals the electron affinities are... 

AHacid values can also be calculated from thermochemical cycles involving measurements of bond dissociation energies, ionization potentials, and electron affinities. Consider the reactions in equations 7.20 through 7.22 ... 

Similar experiments, involving electron transfer between an anion and a neutral molecule, yield relative or absolute EAs. The method has been used to determine relative free energies for electron attachment for a variety of metallocenes and /3-diketonate molecules. Electron photodetachment spectroscopy of negatively charged ions is another source for obtaining electron affinities of molecules. These data provide an important component of thermochemical cycles involving oxidation/reduction of metal complexes, and serve as a basis for obtaining other thermochemical values. 

The electron affinity of NFJ was estimated as <10 eV (NF4 unstable with respect to NF4) on the basis of a comparison of thermochemical cycles leading to O2BF4 or NF4BF4 [17]. 

Before the advent of mass spectrometric methods, thermochemical data on isolated (gas-phase) ions were obtained from thermodynamic cycles involving lattice energies (or enthalpies), enthalpies of formation, ionization energies and/or electron affinities [2],... 

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