Ionization energy Born-Haber cycle

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... 

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. 

Although the differences between the first and second ionization enthalpies, especially for beryllium, might suggest the possibility of a stable +1 state, there is no evidence to support this. Calculations using Born-Haber cycles show that owing to the much greater lattice energies of MX2 compounds, MX compounds would be unstable and disproportionate ... 

The rel-HFS and rel-HF computer programs allow calculations of electronic energy levels, ionization potentials, and radii of atoms and ions from hydrogen into the superheavy region. In order to arrive at the oxidation states most hkely to be exhibited by each superheavy element and also the relative stabilities of these various oxidation states, we need to be able to relate these properties to calculable electronic properties. The relationship between reduction potentials and the Born-Haber cycle has offered an effective approach to this problem (69, 70). 

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)). 

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 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. 

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. 

Energy terms such as ionization energies and lattice energies (defined at 0 K) can be used in Born-Haber cycles to estimate unknown quantities under standard conditions. 

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 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 Born-Haber cycle also enables us to understand why most metals fail to form stable ionic compounds in low valence states (e.g., compounds such as CaCl, AlO and ScCl2). Let us consider a metal with 1st and 2nd ionization energies of 600 and 1200 kJ mol-1, which are fairly typical values (of Ca, for example). Let us suppose that this metal forms a +2 ion with a radius of 1.00 A and that its dichloride would have the fluorite structure (as does CaCl2). The M+ ion would have to be appreciably larger than the M2+ ion and a radius of 1.20 A is a fair estimate. With a radius ratio of 1.5, MCI may be expected to have the NaCl structure. For the two compounds, MCI and MC12 then, the Born-Haber cycles are as shown in Table 2-6. 

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... 

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.

Following a similar approach, a Born-Haber cycle can be used to approximate the ability of other transition metal surfaces to activate water in the aqueous phase from the energetics of water activation in the vapor phase. This is quite useful since the vapor phase calculations are much less computationally intensive. The Born-Haber cycle for such a reaction scheme is given in Figure 19.3. The heterolytic activation of water over a metal surface is directly tied to the homolytic dissociation of water (Eq. 19.1) on that surface and the ease with which it can form protons from adsorbed hydrogen (Eq. 19.3). The specific steps in the Born cycle presented in Figure 19.3 include (1) the dissociation of H2O in the vapor phase to form OH(avapor phase)], (2) the desorption of H(ad) into the gas phase as H- [AE = Eb(n gas phase)], 0) the ionization of H to form H+ + e [A = E(h. ionization)], (4) the solvation of H [AE = E (h+solvation)], and (5) the capture of the electron by the metal surface [AE = — ]. The overall reaction energy for heterolytic aqueous-phase water activation, A , . , (aqueous phase), is ... 

Construct a Born-Haber cycle for the formation of the hypothetical compound NaCl2, where the sodium ion has a 24-charge (the second ionization energy for sodium is given in Table 7.2). (a) How large would the lattice energy need to be... 

Born-Haber cycle. The cycle that relates lattice energies of ionic compounds to ionization energies, electron affinities, heats of sublimation and formation, and bond enthalpies. (9.3)... 

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... 

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