Lattice Energy Formula per mole is symbolized as
NA = Avogadro’s constant (6.022 × 1022)
α = Madelung constant
e = Electron charge (1.6022 × 10-19C)
Z+ and Z– = Cation and anion charge
= Permittivity of free space
= Closest ion distance
UL = equilibrium value of the lattice energy
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.
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–.
Using the Born-Lande equation.
Substitute all the values in the equation
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.
If the only variance between AgBr and AgI were in the size of the anion, one would expect the lattice energies to be relational to the inverse ratio of rc + ra.
Henceforth we expect the Lattice energy of AgI to be