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Born Haber Cycle and Lattice Enthalpy

LATTICE ENTHALPY

The Lattice enthalpy of ionic compound is the enthalpy change which occurs when one mole of ionic compound in solid state dissociates into its gaseous ions.

Na+ Cl (s)  à  Na+(g) + Cl-(G) ; ΔL H = + 788 KJ mol-1

Lattice enthalpy may also be defined as energy released when one mole of ionic crystal is formed by close packing of constituent ions in gaseous state.

Na+ Cl (s)  à  Na+(g) + Cl-(G) ; ΔL H = + 788 KJ mol-1

The magnitude of lattice enthalpy gives the idea of the stability of the ionic crystal. It is not possible to determine lattice enthalpies of ionic compounds directly by experimental techniques. However, we can use indirect method by constructing an enthalpy diagram called Born Haber Cycle. Born Haber cycle is a simplified method which was developed in 1919 by Max Born and Fritz Haber to correlate lattice energies of ionic crystals to other thermodynamic data. The development of Born Haber cycle was primarily based on Hess’s law. Let us consider the energy changes during the formation of sodium chloride crystal from the metallic sodium and chlorine gas to calculate lattice enthalpy of NaCl(s). The net enthalpy of formation of NaCl Δ f H = – 411.2 KJ mol-1

Na(s) + 1/2 Cl2(g)  à  NaCl (s) ; Δ f H = – 411.2 KJ mol-1

The overall process can be imagined to occur in following steps:

(i) Sublimation of metallic sodium

(ii) Ionization of sodium atoms

Δ ie H is ionization enthalpy of sodium.

 

(iii) Atomisation of Cl2. This step involves dissociation of Cl2(g) into Cl(g) atoms. The reaction enthalpy is half of the bond dissociation enthalpy of chlorine.

(iv) Conversion of Cl( g) to Cl-( g).

Δ ea H is electron gain affinity of chlorine.

(v) Combination of Na+(g) and CI-(g) ions to form 1 mole of NaCl(s). The energy released here is called lattice enthalpy (ΔLH). The sequence of steps (i)-(v) is shown in Fig. 17.12 and is known as Born Haber cycle. The sum of the enthalpy changes round a cycle is zero.

The various changes in the Born Haber Cycle for sodium chloride are shown in Fig 17.13.

Applying Hess’s law we get

Let us now proceed to solve some numerical problems based upon thermochemical calculations