It has been observed that lattice energy of a very few compounds has been determined directly. However, a cyclic process called

**has been devised by***Born Haber Cycle***and***M. Born***in the year***F. Haber***1919**. It is helpful to calculate lattice energy in terms of thermo-chemical quantities like*ionisation energy*,*electron affinity*, etc. The formation of ionic solid can be described by the two processes.**1.**

**DIRECT PROCESS**

**M(s) and X**

_{2}(g) combine directly in one step reaction and energy is released which is equal to the heat of formation of MX.

M

_{(s)}+ X_{2}(g) MX_{(solid) }+ ∆H_{form.}**2.**

*ALTERNATIVE PROCESS*

*(a). Sublimation of M*

_{(s)}to M_{(g)}.
Here one mole of solid 'M' absorbs energy equal to its sublimation energy, ∆H

_{sub}and is converted to gaseous M(g).
M

_{(s)}+ ∆H_{sub }M_{(g)}
Where

*∆H*

represents difference in enthalpy (heat content) between, initial state M(s) and final state M(g)._{sub}**.**

*(b). Dissociation*
In this step, mole of X

_{2}absorbs energy equal to half the dissociation energy of X_{2(g)},_{ }i.e. ∆H_{diss. }of X_{2(g) }and is converted to X_{(g)}.
X

_{2(g)}+ ∆H_{diss}X_{(g) }**.**

*(c). Ionisation of M*_{(g)}to M^{+}_{(g)}
M

_{(g)}atom absorbs energy, equal to ionisation energy (I.E.) and is converted to M^{+}_{(g)}ion.
M

_{(g) }+ I.E. M^{+}_{(g) }+ e^{–}.**.**

*(d). Conversion of X(g) to X*^{–}(g)
X

_{(g)}atom accepts an electron released by M_{(g)}to form X^{-}_{(g)}. In this step, energy released is equal to its electron affinity, ( E. A.).
X

_{(g)}+ e^{– }X^{–}_{(g) }+ E. A.**.**

*(e). Combination of M*^{+}_{(g)}and X^{–}_{(g)}to form MX
In this step M

^{+}_{(g) }combines with X^{–}_{(g)}to form one mole of MX_{(solid)}. Here, energy equal to the lattice energy (U) of MX,*is released.*

M

^{+}_{(g) }+ X^{–}_{(g) }MX_{(solid) }+ U (lattice energy).
The whole process can be diagrammatically represented below.

Thus, applying

**, heat of formation of '***Hess's Law***MX'**in direct process is equal to the sum of energies of all steps in alternate process.
Therefore,

**∆H**

_{form}= ∆H_{sub }+ ½∆H_{diss}+ I.E + E.A
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