Thermochemical cycles ionization energies

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).

The most widely studied reference acid is the proton. Proton affinity, PA(B), is defined for a base B as the heterolytic bond dissociation energy for removing a proton from the conjugated acid BH+ (equation 20). The homolytic bond dissociation energy D(B+—H) defined by equation 21 is related to PA(B) and the adiabatic ionization potentials IP(H) and IP(B) (equation 22) are derived from the thermochemical cycle shown in Scheme 6. 

Determined by thermochemical cycle calculations using ionization energies from reference [5[. 

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. 

It is often necessary to incorporate ionization energies into thermochemical calculations (e.g. Bom-Haber or Hess cycles) and it is convenient to define an associated enthalpy... 

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... 

It is often necessary to incorporate ionization energies into thermochemical calculations (e.g. Bom Haber or Hess cycles) and it is convenient to define an associated enthalpy change, A/7(298 K). Since the difference between A/7(298 K) and A17(0K) is very small (see Box 1.7), values of IE can be used in thermochemical cycles so long as extremely accurate answers are not required. 

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 ... 

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) ... 

The bond dissociation energies D(F2N-F), D(FN-F), and D(N-F) have been obtained from appearance potentials (AP) of fragment ions in mass spectra combined with ionization potentials (IP) of the neutral precursors, thermochemical values for atomization enthalpies (AHgt), and standard enthalpies of formation (AH°) of NF3 and NFg [1 to 3]. They have also been obtained from thermochemical cycles alone [4,5]. D(F2N-F) was also directly determined from the equilibrium constant of the gas-phase reaction NF3 Np2+ F [6]. The values are compiled in Table 4. 

Write a Born-Haber cycle for the formation of CaH2 and use it to calculate a value for the lattice energy of this compound. (The standard heat of formation of CaH2 is 186 kJ/mol the heat of sublimation and the first and second ionization energies of calcium are 178.2,589.8, and 1145 kJ/mol, respectively other thermochemical quantities can be found in Table 10.3.)... 

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... 

It is predicted that there should be a linear relationship between the proton affinities of homologous molecules and their ionization energies. A simple thermochemical cycle gives... 

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],... 

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]. 

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... 

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