Born cycle

As was pointed out by Byakov,195 it is very probable that molecules in a liquid form dimers and clusters, the ionization energy of which can be expressed through their dissociation energy using the Born cycle. In the case of a dimer we have... 

Equation 6.98 is general and it is easily deduced from the Born cycles in Figure 6.21, where hvo oN is the molar Gibbs energy (in V C) gained in the 0-0 electronic... 

FIGURE 6.21 Born cycles for the reduction and oxidation of an excited state. 

Ps02 1959 > 2.3 Positron lifetime spectra in liquid oxygen [62] gas-phase quenching data with a Born cycle interpretation [63]. 

That is, the increased solvation around the newly formed Fe ", arising in part from readjustment of the solvent, which would be required to stabilize this Fe + is quite considerable. From a Born cycle and the relevant thermal data, this heat of hydration is found equal to [A//hyd(H ) — 326 Kcal]. If we accept Latimer s value for AiySydCH" ) = —260 Kcal/mole, this gives the net change in heat of hydration for Fe++-> Fe3+as —596 Kcal/mole. A similar problem is associated with the shift of H2O around the newly formed Ce " ion. 

Solvent effects can be easily included in the thermodynamic model. The reactions formulated so far for the isolated species simply need to be formulated with an environment and can be treated in a Born cycle ... 

The original values given by Weiss (55) in 1935 were all too high this was almost entirely due to the low value used for the heat of hydration of the proton (SH+). The electron affinity of 02 can also be estimated by a Haber-Born cycle on the (ionic) alkali peroxides (M+-Or) as follows ... 

The values given by Miedema are the formation enthalpies of solid solutions of A in B or vice versa. The solved metal is embedded into the matrix of the solvent. Using a Haber-Born cycle as shown in Figure 2.39 the sublimation enthalpy of the solved metal embedded in the matrix of the solvent can be calculated. Results of sublimation enthalpies of the solved metal embedded in the matrix of the solvent are shown in Table 2.4b. 

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 ... 

Born s work on this paper evidently began when he read a pair of articles in which Fajans [8] had attempted to calculate the Born-cycle component of the work or free energy (there is some confusion in the works of the time using the words energy and free energy somewhat indiscriminantly as there is even today on occasion) for... 

A detailed dissection of the amine basicities has been made by Arnett [22] on basis of thermodynamic (Born) cycles as shown below ... 

The volume effect and charge redistribution effect in general cannot be easily separated on basis of gas phase and solution acidities and Born cycles like that used... 

The concept of electronegativity, based on considerations of the Born cycle and Coulomb s law, is now well established and as a result it is possible to estimate the enthalpies of formation of strongly polar, i.e. ionic, compounds with a fair degree of reliability, the accuracy depending on the extent to which covalent bonding occurs. On the other hand, the enthalpies of formation of predominantly metallic compounds in which... 

Figure 11.2 Born cycle for ion solvation in a dielectric medium.

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