What is Born-Haber cycle? How can we obtain lattice enthalpy of a solid with its help?
In 1919, Born and Haber proposed a method in which lattice enthalpy of an ionic crystal is related to certain thermodynamic parameters. The formation of ionic crystal from its elements by applying different thermochemical quantities is called Born-Haber cycle.
Consider the enthalpy change during the formation of ionic solid MX from its elements M and X.
Formation of ionic solid MX may be done by two different methods:
(A) Indirect method
(B) Direct method
(A) Indirect method:
The various terms are
Since energy is required for the process (endothermic), therefore, 
is taken as a positive quantity.
Since the process is endothermic, therefore ionisation enthalpy is taken as a positive quantity.
Since the process is exothermic, therefore electron gain enthalpy is taken as negative quantity.
Energy is released in this process i.e. process is exothermic, therefore 
is always taken as negative quantity.
Direct method: Let 
be the enthalpy of formation of 1 mol of MX(s) from its constituent species.
where 
is the enthalpy change for lattice formation from,
The reverse of the above equation is
Thus by using the Born-Haber cycle, one can determine the lattice enthalpy of an ionic compound.
According to Hess’s law, the enthalpy of formation of one mole of ionic solid MX should be the same irrespective of the fact whether it takes place directly in one step (Direct method) or through a number of steps (Indirect method).
