Lattice Energy; Calculation of lattice energy

Table of Contents

The lattice energy (U) of a crystal is the energy evolved when one gram of the crystal is formed from gaseous ions. For sodium chloride, the lattice energy, U, is equal to the enthalpy change for the reaction.

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Schematic representation of lattice energy at inter-ionic distance ro

Lattice energy

Lattice energy is defined as the energy released in the process when the constituents ions are placed in their respective position in the crystal lattice or, amount of energy required to separate the solid ionic crystal into its constituent ions.

Calculation of Lattice Energy

Lattice energies cannot be measured directly, but experimental values are obtained from thermodynamics data using the Born Haber cycle.

;lattice energy 
Born haber cycle
calculation of lattice energy
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Theoretical evaluation of lattice energy

Theoretical values for lattice energy may be calculated. The ions are treated as point charges, and the electrostatic energy E between two ions of opposite charge is calculated.

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A portion of three-dimensional cubic lattice and its unit cell
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Where Z+ and Z are the charges on the positive and negative ions,
e is the charge on an electron
r is the interionic distance.

Attractive energy for a simple lattice of the crystal

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M = Madelung constant, which is related to geometry of the crystal

Repulsive force

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where, B = constant,
n = Born-exponent

Total energy = Attractive energy + Repulsive energy

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For one mole of the ionic crystal U = Etotal NA

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This is Born Lande equation.

Where NA is the Avogadro constant the number of molecules in a mole has the value 6.023×1023 mol-1; A is the Madelung constant, which depends on the geometry of the crystal.

The lattice energy of the ionic crystal is inversely proportional to the Inter-ionic distance and directly proportional to the product of charges of the ions, Madelung constant, and Born exponent.

Madelung Constant (A)

The value of the Madelung constant has been calculated for all common crystal structures by summing the contributions of all the ions in the crystal lattice.

Madelung constant value of some structure

Types of structure Madelung constant (A)
zinc blende1.63806
wurtzite ZnS1.64132
sodium chloride NaCl 1.74756
Caesium chloride CsCl1.76267
rutile TiO22.408
fluorite CaF22.51939
Corundum Al2O34.17186


What is lattice energy?

The lattice energy (U) of a crystal is the energy evolved when one gram of the crystal is formed from gaseous ions.

How lattice energy can be calculated?

Lattice energy can be calculated by using the Born Haber cycle.

Lattice energy

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