# Lattice Energy Formula

## Lattice Energy Formula

The overall potential energy of an ionic compound, which is frequently referred to as the lattice energy, UL per mole might be represented as the total of the electrostatic and repulsive energy terms. The Born-Lande equation provides lattice energy.

Lattice Energy Formula per mole is symbolized as

$U_{L}=(\frac{N_{A}\alpha&space;Z^{2}e^{2}}{4\pi&space;\varepsilon&space;_{o}r^{2}o})(1-\frac{1}{n})$

Where

• the equilibrium value of the inter ionic separation is ro
• the equilibrium value of the lattice energy is UL and

Lattice Energy Solved Examples

Solved questions based on lattice energy are provided below.

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

Using the Born-Lande equation.

$U_{L}=(\frac{N_{A}\alpha&space;Z^{2}e^{2}}{4\pi&space;\varepsilon&space;_{o}r^{2}o})(1-\frac{1}{n})$

Substitute all the values in the equation

$=\frac{1.74756\times6.022\times10^{23}\times1\times-1\times(1.60210\times10^{-19})^{2}}{4\times3.14159\times8.78541\times10^{-12}\times2.81\times10^{-10}}\times(1-\frac{1}{8})$

UL= – 755 KJmol-1

Problem  2: The lattice energy of AgBr is 895 KJ mol-1. Predict the Lattice energy of the isomorphous AgI using Born-Lande equation. The numerics of rc + ra is 321pm for AgBr and 342pm for AgI.
$=(895)(\frac{321}{342})=840KJmole^{-1}$