Trends in Lattice Energy: Ion Size and Charge

Lattice energy is the energy required to separate one mole of an ionic solid into its component gaseous ions. For sodium chloride, the lattice energy is 769 kJ/mol, meaning 769 kJ must be supplied to convert solid NaCl into gaseous Na+ and Cl– ions. A larger magnitude indicates a more stable ionic compound.

According to Coulomb's law, lattice energy is inversely proportional to the distance between ions, which depends on ionic radius. As ionic size increases down a periodic table column, the bond length increases and ions attract less strongly. Lithium bromide has higher lattice energy (807 kJ/mol) than potassium bromide (682 kJ/mol) because lithium ions are smaller.

Coulomb's law states that potential energy is directly proportional to the product of ion charges. Calcium oxide, with divalent Ca2+ and O2– ions, has lattice energy nearly four times greater than sodium fluoride with monovalent Na+ and F– ions. Doubling both ion charges quadruples the lattice energy when other parameters remain constant.

Lattice energy can be expressed as ΔHlattice = C(Z+)(Z−)/Ro, where C is a structural constant, Z+ and Z– are ion charges, and Ro is the interionic distance. This equation shows lattice energy increases rapidly as ion charges increase and ionic sizes decrease. The relationship demonstrates why both charge and size critically determine ionic compound stability.

When interionic distances are similar, lattice energy depends primarily on ion charges. Lithium fluoride (LiF) with monovalent ions has lattice energy of 1023 kJ/mol, while magnesium oxide (MgO) with divalent ions has 3900 kJ/mol, despite nearly identical interionic distances of about 200 pm. The charge difference explains the dramatic energy difference.

Fluoride ions are significantly smaller than iodide ions, resulting in shorter interionic distances. Magnesium fluoride (MgF2) has lattice energy of 2957 kJ/mol compared to magnesium iodide (MgI2) at 2327 kJ/mol. The smaller ionic size of F– creates stronger electrostatic attractions and requires more energy to separate the ions.

Zinc oxide (ZnO) has higher lattice energy than sodium chloride (NaCl) because both factors favor ZnO: the cation and anion charges are greater, and the interionic distance is smaller. This demonstrates that lattice energy depends on the combined effect of ionic bonding and electron transfer from metals to nonmetals, making ZnO significantly more stable.