Born Haber Energy Cycle

 There is no denying the fact that an electron can be transferred from one neutral (uncharged) atom to another. When this happens, the atom from which the electron is transferred becomes a positive ion or cation and the atom to which the electron is transferred becomes a negative ion or anion. The transfer of an electron to or from an atom involves energy. The energy required to remove one electron from an atom is characteristic of the atom and is its ionization energy. The energy released when an electron is acquired by an atom is its electron affinity. The electron transfer can take place with a release of energy only when the electron affinity of the receiving species is greater than the ionization energy of the donating species, which is rarely the case, or, most often, when the resulting ions associate themselves into a new configuration of lower energy. Most electron transfer reactions occur when the ions once formed associate themselves into structured lattices called ionic crystals.

Energy Considerations in Ionic Structures

The energy required to produce any cation from an atom, the ionization energy of the atom, is always larger, and usually much larger, than the energy which is released when an electron is added to any atom, the electron affinity. This is true even if an electron is being removed from an atom which loses it relatively easily, like sodium, and is being added to an atom which readily acquires it, such as chlorine. The ionization energy of sodium is +496 kJ/mole while the electron affinity of chlorine is only -349 kJ/mole. The reaction Na(g) + Cl(g)  Na⁺(g) + Cl^-(g) would require +147 kJ/mole to proceed while the reaction Na(s) + 1/2 Cl₂(g)  Na⁺(g) + Cl^-(g)  requires +377 kJ/mole. Electron affinity alone cannot provide sufficient energy to form ions or ionic structures; the energy must come from the assembly of isolated ions into stable multi-ion structures.

Ions with the same type of charge repel each other, but ions of opposite charge attract each other. The simplest possible ionic structure which might be stable is the gas-phase ion pair, which consists of one cation and one anion held together by electrostatic attraction. It is relatively simple to calculate how much energy would be gained by this association using the Coulomb law of electrostatic attraction. The energy of the attraction is given by

E = (2.31 x 10^-16 J-pm) Z⁺Z^-/d

where Z is the charge on the cation and anion and d is the distance between the ions, in pm.  The energy of the two associated ions will be less than the energy of the two isolated ions by this amount if the ions are of opposite charge. For sodium ion the ionic radius is 97 pm and for chloride ion it is 181 pm so the distance of separation of the centers of the two ions is 278 pm. The energy for one ion pair, multiplied by the Avogadro number N_A, gives the molar energy of [Na⁺Cl^-](g) relative to the molar energy of the isolated ions as:

E = -8.31 x 10^-19 J/molecule x 6.022...x 10²³ molecules/mole

This is -500 kJ/mole, so the standard molar enthalpy of formation of the ion pair estimated using the Coulomb law is -123 kJ/mole (-500 kJ/mole + 377 kJ/mole). Even for a single sodium ion and chloride ion in the gas phase, it is the lower energy available through association of ions of opposite charge that drives the formation of ionic compounds.

The ionic radii used in the calculation above were the radii of sodium and chloride ions found in ionic crystals. They are, however, very similar to the radii of these ions under other conditions. The actual distance between the ions in Na⁺Cl^-(g) has been measured and found to be 236.1 pm.

Association of ions of opposite charge is not normally into ion pairs. It is far more common to find ions in the form of the solid ionic crystals, which are large ordered three-dimensional arrays of ions.

The diagram below is the Born-Haber cycle for the formation of an ionic compound from the reaction of an alkali metal (Li, Na, K, Rb, Cs) with a gaseous halogen (F₂, Cl₂). The Born-Haber thermochemical cycle is named after the two German physical chemists, Max Born and Fritz Haber, who first used it in 1919.

The enthalpy change in the formation of an ionic lattice from the gaseous isolated sodium and chloride ions is -788 kJ/mole. That enthalpy change, which corresponds to the reaction Na⁺(g) + Cl^-(g)  NaCl(s), is called the lattice energy of the ionic crystal. Although the lattice energy is not directly measurable, there are various ways to estimate it from theoretical considerations and some experimental values. For all known ionic crystals, the lattice energy has a large negative value. It is ultimately the lattice energy of an ionic crystal which is responsible for the formation and stability of ionic crystal structures.

In view of the above, for real energy calculation, setting up intermediaries are important where the energy trend are considered according to energy scales.