can lattice energy be estimated by born-haber cycle? what about hydration energy and electron gain enthalpy?

Dear student,

The answer is yes.

Lattice energy of ionic solids

Born Haber Cycle helps us to calculate the lattice energy of ionic solid, provided other thermodynamic data is known. For example, the lattice energy of magnesium fluoride (MgF₂) can be calculated when the sublimation energy (S) of Mg = 146.4 kJ mol^-1; IE₁ and IE₂ values of Mg=737 and 1449 kJ mol ^-1 respectively; Dissociation energy (D) of fluorine = 158.8 kJ mol ^-1; EA of fluorine = - 328 kJ mol ^-1 and DH_f of MgF₂ =- 1096.5 kJ mol ¹. Born Haber Cycle for MgF₂ is as shown:

Born Haber Cycle for MgF₂

DH_f = DH_s + DH_d + (IE₁ + IE₂) + 2 EA₁+ U

U = DH_f - DH_s - DH_d - (IE₁ + IE₂) - 2 EA₁

= -1096.5 - 146.4 - 158.8 - (737 + 1449) - 2(-328)

= -2931.7 kJmol^-1

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All the best.

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