Factors affecting the magnitude of lattice enthalpy

The term lattice enthalpy can be defined by the following ways:

1. The amount of energy released, when one mole of an ionic crystal is made from the requisite number of gaseous cations and anions, is named lattice energy
2. The amount of energy, which is required to break down/ separate one mole of an ionic compound into its constituent isolated gaseous ions
3. The amount of energy, which is liberated when 1 mole of an ionic solid is formed from its constituent gaseous ions.

When an ionic solid MX(s) is dissolved in a polar solvent, the ionic solid is separated into its isolated gaseous ions viz, M⁺(g), and X^– (g) . In this process, some amount of energy is required, which is called the lattice energy of MX(s).

MX(s) + lattice energy ———> M⁺ (g) + X^– (g) (isolated gaseous ions)

Factors affecting the magnitude of lattice enthalpy:

• Charge of ions
• Ionic radius and inter-ionic distance
• Madelung constant

The higher the charge of the ions present in the ionic crystal, the greater is the magnitude of the force of attraction existing between the ions and consequently greater is the magnitude of lattice energy.

Na⁺F^– (914.2 kJ/mole)< Mg²⁺F^–₂ (2882.0) < Mg²⁺O₂ (3895.0 kJ/mole)

K⁺F^– (812.1 kJ/mole) < Ca²⁺ F₂ (2581.0 kJ/mole)< Ca²⁺O^2- (3520.0 kJ/mole)

Born-Lande equation shows that the lattice energy (U) is directly proportional to the charge on ions and inversely proportional to the inter-ionic distance (r_o) between the ions. As r_o is equal to the sum of r₊ and r_–, the smaller is the size of ions, the smaller would be the value of r_o, and hence higher would be the value of U.

Trend of U in case of alkali metal fluorides:

Li⁺ (0.68 Angstrom)< Na⁺ (0.95 Angstrom) < K⁺ (1.33 Angstrom) < Rb⁺ (1.48 Angstrom) < Cs⁺ (1.69 Angstrom)

LiF ( 1034 kJ/mole) > NaF ( 914.2 kJ/mole) > KF ( 812.1 kJ/mole) > RbF (780.3 kJ/mole) > CsF (743.9 kJ/mole)

Trend of U for lithium halides:

Ionic radius: F^– (1.36 Angstrom) < Cl^– ( 1.81 Angstrom) < Br^– ( 1.95 Angstrom) < I^– (2.16 Angstrom)

Lattice enthalpy, U: LiF ( 1034 kJ/mole) > LiCl ( 840.1 kJ/mole)> LiBr ( 781. 2 kJ/mole)> LiI (718.2 kJ/mole)

Trend of U for oxides of alkaline earth metals:

Ionic radius: Be²⁺ (0.31 Angstrom) < Mg²⁺ ( 0.65 Angstrom) < Ca²⁺ (0.99 Angstrom) < Sr²⁺ (1.13 Angstrom)< Ba²⁺ ( 1.69 Angstrom)

U of oxides: BeO (4541 kJ/mole) > MgO (3895 kJ/mole) > CaO (3520 kJ/mole) > SrO (3325 kJ/mole) > BaO (3108 kJ/mole)

The magnitude of lattice energy is directly proportional to the value of M ( Madelung) which depends on the coordination number of each ion and geometric arrangement of ions in the the crystal lattice of the crystal.