Question

The energy required to separate the ions in the Mg(OH)₂ crystal lattice into individual Mg²⁺(g) and OH⁻(g) ions, as shown in the table below, is known as the lattice energy of Mg(OH)₂(s). As shown in the table, the lattice energy of Mg(OH)₂(s) is greater than the lattice energy of Sr(OH)₂(s).

Explain why in terms of periodic properties and Coulomb's law:
Reaction Lattice Energy (kJ/mol)
Mg(OH)₂(s) → Mg²⁺(g) + 2OH⁻(g) 2900
Sr(OH)₂(s) → Sr²⁺(g) + 2OH⁻(g) 2300

Answer 1

Mg(OH)₂ has a higher lattice energy than Sr(OH)₂ because Mg²⁺ ions are smaller than Sr²⁺ ions, leading to a shorter distance between ions and stronger electrostatic attraction according to Coulomb's law and periodic trends.

Step-by-step explanation:

The lattice energy is the energy required to separate one mole of an ionic solid into its gaseous ions. Mg(OH)₂ has a higher lattice energy than Sr(OH)₂ due to factors explained by Coulomb's law and periodic properties. According to Coulomb's law, the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Since Mg²⁺ is smaller than Sr²⁺, the distance between Mg²⁺ and OH⁻ ions is shorter, leading to a stronger attraction and higher lattice energy. Furthermore, as you move down the group on the periodic table from magnesium to strontium, the size of the cations increases, leading to longer interatomic distances and thus lower lattice energies for Sr(OH)₂ compared to Mg(OH)₂.