Lattice Energy
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
ϵo = Permittivity of free space
n = Born Exponent
r0 = Closest ion distance
UL = 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–.
Answer:
Using the Born-Lande equation.
Substitute all the values in the equation
UL= – 755 KJmol-1
Example 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 321 pm for AgBr and 342 pm 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
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