Saturday, May 14, 2011

BORN-HABER Cycle

It has been observed that lattice energy of a very few compounds has been determined directly. However, a cyclic process called Born Haber Cycle has been devised by M. Born and F. Haber in the year 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 X2(g) combine directly in one step reaction and energy is released which is equal to the heat of formation of MX.
     M(s) + X2(g) MX (solid) + ∆Hform.
2.     ALTERNATIVE PROCESS
(a).     Sublimation of M(s) to M(g).
        Here one mole of solid 'M' absorbs energy equal to its sublimation energy, ∆Hsub and is converted to gaseous M(g).
M(s) + ∆Hsub M(g)
        Where ∆Hsub
represents difference in enthalpy (heat content) between, initial state M(s) and final state M(g).
(b).    Dissociation.
        In this step, mole of X2 absorbs energy equal to half the dissociation energy of X2(g),
i.e. ∆Hdiss. of X2(g) and is converted to X(g).
X2(g) + ∆Hdiss 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 Hess's Law, heat of formation of 'MX' in direct process is equal to the sum of energies of all steps in alternate process.
Therefore,
     ∆Hform = ∆Hsub + ½∆Hdiss + I.E + E.A

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