Na(s) + 1/2 Cl(g) → NaCl(s) ∆_fH

BORN-HABER CYCLE is an enthalpy diagram which is an indirect method of calculating lattice enthalpy.

One mole of NaCl(s) is prepared by the following steps:

FIRST STEP: Sublimation of Na (sodium) (∆_subH)

• Na(s) → Na(g)

SECOND STEP: Ionization of sodium (∆_iH)

• Na(g) → Na⁺ + 1e^-

THIRD STEP: Dissociation of chlorine molecule to a chlorine atom (∆_aH)

• 1/2 Cl₂(g) → Cl(g)

FOURTH STEP: Chlorine atom gains 1e^- (∆_egH)

• Cl(g) + 1e^-→ Cl^-

Na⁺(g) + Cl^- (s) → NaCl(s) ∆_latticeH

The sequence of the steps is known as BORN-HABER CYCLE. The importance of this cycle is, the sum of enthalpy changes round a cycle is zero.

Applying Hess’sLaw

Hess’s law state that if the reaction takes place in many steps, then the standard enthalpy of the reaction is the sum of the standard enthalpies of intermediate reaction, into which overall is divided at the same temperature.

∆_fH = ∆_subH + ∆_iH + ∆_aH + ∆_egH + ∆_latticeH

∆_latticeH = ∆_subH + ∆_iH + ∆_aH + ∆_egH - ∆_fH