 # Lattice Energy Formula

## Lattice Energy

Lattice energy refers to the energy which is released while two oppositely charged gaseous ions attract to each other and form an ionic solid. The total potential energy of the ionic compounds is also referred as the lattice energy. Lattice energy UL  per mole may be defined as the sum of the electrostatic and repulsive energy. The Born-Lande equation provides lattice energy.

Lattice Energy Formula per mole is symbolised as

NA = Avogadro’s constant (6.022 × 1022)

e = Electron charge (1.6022 × 10-19C)

Z+ and Z– = Cation and anion charge

ϵo = Permittivity of free space

n = Born Exponent

r0 = Closest ion distance

U= equilibrium value of the lattice energy

### Solved Examples

Example 1: Compute the Lattice energy of NaCl by using Born-Lande equation.

Given
α = 1.74756
Z = -1 (the Cl ions charge)
Z+ = +1 (the charge of the Na+ ion)
NA = 6.022 × 1023 ion pairs mol-1

C = 1.60210 × 10-19C (the charge on the electron)
π = 3.14159
εo  = 8.854185 × 10-12 C2 J-1 m-1
ro = 2.81 × 10-10 m, the sum of radii of  Born-Lande equation.

Na+ and Cl
n = 8 the average of the values for Na+ and Cl.