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Born-Haber cycle


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Fritz Haber (1868—1934)

 

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A cycle of reactions used for calculating the lattice energies of ionic crystalline solids. For a compound MX, the lattice energy is the enthalpy of the reaction

M+(g) + X(g) → M+X(s) ΔHL

The standard enthalpy of formation of the ionic solid is the enthalpy of the reaction

M(s) + ½X2(g) → M+X(s) ΔHf

The cycle involves equating this enthalpy (which can be measured) to the sum of the enthalpies of a number of steps proceeding from the elements to the ionic solid. The steps are:(1) Atomization of the metal:M(s) → M(g) ΔH1(2) Atomization of the nonmetal:½X2(g) → X(g) ΔH2(3) Ionization of the metal:M(g) → M+(g) + e ΔH3This is obtained from the ionization potential.(4) Ionization of the nonmetal:X(g) + e → X(g) ΔH4This is the electron affinity.(5) Formation of the ionic solids:M+(g) + X(g) → M+X(s) ΔHL Equating the enthalpies gives:

(1) Atomization of the metal:M(s) → M(g) ΔH1

(2) Atomization of the nonmetal:½X2(g) → X(g) ΔH2

(3) Ionization of the metal:M(g) → M+(g) + e ΔH3This is obtained from the ionization potential.

(4) Ionization of the nonmetal:X(g) + e → X(g) ΔH4This is the electron affinity.

(5) Formation of the ionic solids:M+(g) + X(g) → M+X(s) ΔHL

ΔHf = ΔH1 + ΔH2 + ΔH3 + ΔH4 + ΔHL

from which ΔHL can be found. It is named after Max Born and the German chemist Fritz Haber (1868–1934).

Subjects: Chemistry — Physics.


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