Dissociation energy, Born-Haber cycle

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. 

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... 

Most of the enthalpies associated with steps in the cycle can be estimated, to a greater or less accuracy, by experimental methods. The lattice energy, however, is almost always obtained theoretically rather than from experimental measurement. It might be supposed that the enthalpy of dissociation of a lattice could be measured in the same way as the enthalpy of atomization of the metal and nonmctal, that is, by heating the crystal and determining how much energy is necessary to dissociate it into ions. Unfortunately, this is experimentally very difTicull. When a crystal sublimes (AHj), the result is not isolated gaseous ions but ion pairs and other clusters. For this reason it is necessary to use Eq. 4.13 or some more accurate version of it. We can then use the Born-Haber cycle to check the accuracy of our predictions if we can obtain accurate data on every other step in the cycle. Values computed from the Bom-Haber cycle are compared with those predicted by Eq. 4.13 and its modifications in Table 4.3. 

The calculation of lattice energies of ionic compounds is very important since, in general, there is no direct way to measure them experimentally, although they can be obtained from certain experimental data using the Born-Haber cycle which is discussed immediately below. For example, the heat of vaporization of NaCl does not give the lattice energy because up to the highest temperatures at which accurate measurements can be made the gas phase consists of NaCl molecules (or ion pairs), and it has so far proved impossible to get an accurate estimate of the heat of dissociation of NaCl(g) into Na+(g) and Cl (g) since NaCl(g) normally dissociates into atoms. 

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 is also valuable as a means of analyzing and correlating the variations in stability of various ionic compounds. As an example, it enables us to explain why MgO is a stable ionic compound despite the fact that the Mg2+ and O2- ions are both formed endothermally, not to mention the considerable energies required to vaporize Mg(s) and to dissociate 02(g). A Hf is highly negative despite these opposing tendencies because the lattice energy of MgO more than balances them out. 

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 ... 

Sometimes the Born-Haber cycle is used in reverse to predict whether the enthalpy of formation of an unknown ionic compound is favorable or not For example, the theoretical enthalpy of formation of Nap2 can be predicted using the Born-Haber cycle as shown here. The fictional Nap2 molecule would dissociate into three ions one Na + and two F ions. The lattice energy of Nap2 was calculated using the Kapustinskii equation, where r(F ) = 133 pm and assuming that r(Na2+) r(Mg2+) = 72 pm. 

In order for an ionic compound to dissolve, the Madelung energy or electrostatic attraction between the ions in the lattice must be overcome. In a solution in which the ions are separated by molecules of a solvent with a high dielectric constant (e,., o = 8l.7e ) the attractive force will be considerably less. The process of solution of an ionic compound in water may be considered by a Born-Haber type of cycle. The overall enthalpy of the process is the sum of two terms, the enthalpy of dissociating the ions from the lattice (the lattice energy) and the enthalpy of introducing the dissociated ions into the solvent (the solvation energy) ... 

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