Born Haber Cycle

Born Haber Cycle

Energy change associated with the formation of an ionic compound in a regular crystal lattice in a systemic manner constitute a cycle called Born Haber Cycle named after Max Born and Fritz Haber, who used this method for calculating lattice energies of crystals.
The lattice energy of sodium chloride, for example is the change in enthalpy, ∆H, when Na⁺ and Cl^- ions in the gas phase come together to form one mole of NaCl crystal.
Sodium chloride can be obtained in the following steps-
1. Conversion of sodium metal to gaseous atoms (sublimation), energy required for this sublimation process is ∆H = ∆H_S
Na(s) → Na(g), ∆H = ∆H_s
2. Conversion of gaseous sodium to sodium ions by loosing electron. Energy required for ionisation is I.
Na(g) → Na⁺(g) + e^-, ∆H = IP
3. Dissociation of chlorine molecule to chlorine atoms. Energy required for this process is ½D as half molecule is dissociated
½Cl₂(g) → Cl(g) , ∆H = ½∆H_d
4. Chlorine atoms gain electron to form chloride ions. Energy released is the electron affinity E.
Cl(g) + e- → Cl^-(g), ∆H = EA
5. Sodium and chloride ions get together and form the crystal lattice. Energy released in this process is known as lattice energy and is equal to U.
Na⁺(g) + Cl^-(g) → NaCl (s). ∆H = U
The enthalpy change for the direct formation of sodium chloride for sodium metal and chlorine is heat of formation ∆H. This amount of heat is released in this process.
Na(s) + ½Cl₂(g) → NaCl(s), ∆H = ∆H_f
We know that from the Hess' law of constant heat summation that the heat of a reaction is the same whether the reaction occurs in one or more than one stepss. Hence-
∆H_f = ∆H_S + IP + ½∆H_d + EA + U

Born Haber Cycle used six energy terms out of which ∆H_s, IP and ∆H_d are positive because of absorption of heat while EA, ∆H_f and U are negative because of exothermic nature. Therefore, the above equation may be written as-
−∆H_f = ∆H_S + IP + ½∆H_d − EA − U
Any term can easily be calculated by using the above equation.