The lattice energy of an ionic solid is a measure of the strength of bonds in that ionic compound. It is usually defined as the enthalpy of formation of the ionic compound from gaseous ions and as such is invariably exothermic.
- Na+ (g) + Cl− (g) → NaCl (s)
The experimental lattice energy of NaCl is −787 kJ/mol.
Some older textbooks define lattice energy as the energy required to convert the ionic compound into gaseous ions which is an endothermic process, and following this definition the lattice energy of NaCl would be +787 kJ/mol.
The experimental value for the lattice energy can be determined using the Born-Haber cycle.
In 1918 Born
proposed that the lattice energy could be derived from the electrostatic potential of the ionic lattice and a repulsive potential energy term.
- = Avogadros number
- = Madelung constant, relating to the geometry of the crystal.
- = charge of cation
- = charge of anion
- = electron charge in coulombs, 1.6022 C
- = permittivity of free space
- = 1.112 C²/(J m)
- = distance to closest ion
- = Born exponent, a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically.
The Born-Landé equation
gives a reasonable fit to the lattice energy
|| Calculated Lattice Energy
|| Experimental Lattice Energy |
|| −756 kJ/mol
|| −787 kJ/mol |
|| −1007 kJ/mol
|| −1046 kJ/mol |
|| −2170 kJ/mol
|| −2255 kJ/mol |
From the Born-Landé equation it can be seen that the lattice energy of a compound is dependant on a number of factors
- as the charges on the ions increase the lattice energy increases(becomes more negative),
- when ions are closer together the lattice energy increases (becomes more negative)
Barium oxide (BaO), for instance, which has the NaCl structure and therfore the same Madelung constant, has a bond radius of 275 picometers and a lattice energy of -3054 kJ/mol, while sodium chloride (NaCl) has a bond radius of 283 picometers and a lattice energy of -786 kJ/mol.
The Kapustinskii equation
can be used as a simpler way of deriving lattice energies where high precision is not required.