Final answer:
Lattice energy decreases with the increase in ion size because the ions have lower charge density and cannot get as close together, resulting in weaker electrostatic forces. The Born-Haber cycle demonstrates how lattice energy is influenced by ion charge, size, and the crystal structure, with higher lattice energies leading to properties like greater melting points and compound hardness.
Step-by-step explanation:
The question regarding why lattice energy decreases as ions get larger can be explained in terms of two closely related factors - charge density and the distance between ions. Firstly, smaller ions have greater charge density, which results in stronger electrostatic attractive forces.
Secondly, smaller ions allow for a shorter distance between the ions in the lattice, further increasing the electrostatic attraction. These two factors contribute to higher lattice energies when ions are smaller and more highly charged.
Both explanations you came across are related and essentially describe the same principle. The charge density is a measure of the electric charge over a given volume; in smaller ions, the charge is concentrated over a smaller volume, which results in a stronger attraction to other ions.
The capability of ions to get closer in the lattice is a consequence of their smaller size; closer proximity increases the electrostatic attraction which enhances the lattice energy.
The Born-Haber cycle is a useful tool for understanding these concepts in more detail, as it illustrates how lattice energy is affected by factors such as ion charge and size, as well as the crystal structure of the solid.
Fundamentally, substances with di- or tripositive cations and/or di- or trinegative anions possess higher lattice energies due to the strong interactions between highly charged ions. Additionally, lattice energy also associates with properties like melting points and hardness of the ionic compounds.