Lattice energy and born haber's cycle

Lattice energy and born haber's cycle :–

Electron affinity values can be determined directly using spectroscopic methods and indirectly by the application of bone haber's cycle. this cycle allows us to understand and determine the lattice energies of ionic solids. it relates the lattice energy of crystal to other thermochemical data. Born haber's cycle is based on Hess's law which States that "Overall change in energy of a process can be determined by breaking the process into steps, then adding the changes in energy of each step"

 Considered the formation of a crystal lattice of sodium chloride(NaCl) following steps are involved

step1. the elements in their standard states are first converted to gaseous States

Na (s) + sublimation energy (∆H) → Na(g)

step2. gaseous Cl2(g) is dissociated into Cl atom by supplying dissociation energy(∆H )

1/2cl2 + 1/2 (D) → Cl(g)

step 3. Na(g) is converted into Na+ by providing ionization energy(IE)

Na(g) +IE → Na+(g)

step4. Cl(g) is converted into Cl– by releasing electron affinity 

Cl(g) → Cl–(g) + EA

step 5. The gaseous ions formed are brought closer to give solid NaCl(crystal) releasing energy called lattice energy.

Na+(g) + Cl–(g) → NaCl(s) + U 

 according to Hess's law of heat summation (for NaCl)

∆Hf = S + 1/2(D) + IE – EA – U

Or

U = S + 1/2(D) + IE – EA –∆Hf

 in this expression, the values of different energies are put without sign (+ or –)

Lattice energy: Amount of energy required at O°K to convert one mole of the salt into gaseous ions infinitely removed from one another.

U = NAZ Z_ e²/ r (1– 1/n)

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