Lattice Energy Formula

The total potential energy of the ionic compounds which is also referred to the 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 symbolized as

Born-Lande equation - Lattice Energy Formula

NA = Avogadro’s constant (6.022 × 1022)

α = Madelung constant

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

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  Born-Lande equation.

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

Answer:

Using the Born-Lande equation.

Born-Lande equation - Lattice Energy Formula

Substitute all the values in the equation

Lattice Energy Related Problems

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.
Answer:

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

Lattice Energy Related Problems

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