Cycle of Born-Haber

The cycle of Born-Haber , or cycle of Born-Fajans-Haber , is a technique making it possible to calculate the reticular energy (enthalpy of crystallization) of a ionic Cristal.

The stability of a Cristal is characterized by its reticular energy $E_r$ . The latter represents the quantity of energy necessary to break up a mole of a solid crystallized into its components in gas phase. The more important l' $E_r$ is, the more the solid is stable.

Example of calculation

The traditional example is that of the network of Sodium chloride NaCl. Reticular energy corresponds to the energy released during the formation of the NaCl network starting from the ions $Na^+$ and $Cl^-$ in a gas state. Here various stages necessary to transform metal sodium $Na$ and gas dichlore ( $Cl_2$ ) into a sodium chloride crystal:

solid metal sodium is transformed into gas sodium, energy necessary for this transformation corresponds to the energy of sublimation : $\ Delta H_ {subl}$
atomic gas sodium is ionized in ion $Na^+$ , energy necessary is the energy of Ionization : $\ Delta H_I$
the gas dichlore is dissociated Homolytique lies in two chlorine gas atoms, energy necessary is the energy of Dissociation : $\ Delta H_D$
the atomic chlorine gas receives 1 electron and becomes $Cl^-$ , energy necessary is the energy of electro-affinity : $\ Delta {AE}$
We still have the energy of formation , which represents the energy received or absorptive during the formation of sodium chloride starting from the elements in a native state (either metal sodium, and the gas dichlore): $\ Delta H_f$

We can finally write the assessment as follows:

$E_r = \ Delta E_ {subl} + \ Delta E_I + \ frac {1} {2} \ Delta H_D + \ Delta H_ {AE} - \ H_f$ Delta

Diagrammatic representation of the cycle

Category: Thermochemistry

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