What is Lattice Energy? | Born-Lande Equation | ScienceMonk

Lattice Energy, for a crystalline solid, is the measure of the energy released when ions are combined to make a compound. We can also describe it as a measure of the cohesive forces that bind ions.



It is relevant to many properties such as solubility, hardness, and volatility. It is usually deduced from the Born-Haber cycle. Often, the energy is exothermic, i.e., the value of ΔHlattice is negative because it corresponds to the coalescing of infinitely separated gaseous ions in vacuum to form the ionic lattice.

The concept of this energy was originally developed for sphalerite and rock salt-structured compounds where the ions occupy high-symmetry crystal lattice sites such as NaCl, ZnS.

For Example, if we consider NaCl,

Na+ (g) + Cl− (g) → NaCl (s)

The energy released by this reaction, which is also can be termed as Lattice energy is -786 KJ/mol. Just like Sodium Chloride, a few compounds energy is listed below:

Compound Experimental Lattice energy Structure type
LiF  −1030 kJ/mol  NaCl
NaCl −786 kJ/mol  NaCl
NaBr  −747 kJ/mol  NaCl
NaI  −704 kJ/mol  NaCl
CsCl  −657 kJ/mol  CsCl
CsBr  −632 kJ/mol  CsCl
CsI  −600 kJ/mol  CsCl
MgO  −3795 kJ/mol  NaCl
CaO  −3414 kJ/mol  NaCl
SrO −3217 kJ/mol  NaCl
MgF2 −2922 kJ/mol  rutile
TiO2  −12150 kJ/mol  rutile

Sometimes, in a few textbooks, this energy is defined with the opposite sign (i.e., positive) because of the energy required to convert the crystal into infinitely separated gaseous ions in the vacuum, an endothermic process. As per this convention, the energy of NaCl would be +786 KJ/Mol.



Usually, this energy for solids such as sugar/iodine whose neutral molecules interact by weaker dipole-dipole or Vander Waal forces is considerably less in magnitude when compared to sodium chloride and such crystals, metals like iron, covalently linked materials like a diamond.

The two main factors that contribute to the energy of an ionic solid is:

  • Charge on the ions.

Charge ∝ lattice energy

  • Radius or size of the ions.

Size ∝ 1/Lattice Energy

Usually, Ionic Compounds with smaller energy tend to be more soluble in H2O

Born-Lande Equation: Lattice Energy

In 1918, Born and Lande proposed an equation to derive lattice energy from the repulsive potential energy term and the electric potential of the ionic lattice.

 

Lattice Energy

where
NA is Avogadro Constant;
M is Madelung Constant, relating to the geometry of the crystal;
z+ = charge number of cation;
z = the charge number of anion;
qe = elementary charge, equal to 1.6022×10−19 C;
ε0 = permittivity of free space, equal to 8.854×10−12 C2 J−1 m−1;
r0 = distance to closest ion;
and n is the Born exponent, where 5<n<12, determined experimentally by measuring the compressibility of the solid or derived theoretically.

 

By- Chanapathi Murali Krishna

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