Explain the formation of an ionic compound with respect to lattice energy.

Ionic compounds are formed when atoms of elements with different electronegativities transfer electrons between them to achieve a stable electron configuration. This usually occurs between a metal and a non-metal. The metal atom loses electrons to become a positively charged cation, while the non-metal atom gains electrons to become a negatively charged anion. The resulting ionic compound is a result of the electrostatic attractions between these oppositely charged ions.

Lattice energy is a measure of the energy required to separate one mole of an ionic compound into its separate gaseous ions. It's an indicator of the strength of the electrostatic forces holding the ions together in the crystal lattice. Greater lattice energy corresponds to stronger attractions between the ions and, consequently, more stable ionic compounds.

Lattice energy is determined by two main factors: the charges of the ions and the distance between the ions in the crystal lattice. The energy is directly proportional to the product of the charges of ions and inversely proportional to the distance between their centers. We can represent this relationship with Coulomb's law formula: \[E \propto \frac{Q_{1}Q_{2}}{r}\] Where E is the lattice energy, Q1 and Q2 are the charges of the ions, and r is the distance between the ion centers.

A high lattice energy indicates strong electrostatic forces between the ions in the compound, making the compound more stable and less likely to be broken apart. The formation of an ionic compound is energetically favorable when the lattice energy is sufficiently large to overcome the energy required for electron transfer (ionization energy of the metal and electron affinity of the non-metal). The overall energy change during the formation of an ionic compound can be determined using the Born-Haber cycle, which uses Hess's law to relate lattice energy, ionization energy, electron affinity, and other energy changes involved. In summary, the formation of ionic compounds is driven by the attractive forces between the oppositely charged ions, which are quantified by lattice energy. Stronger attractions between ions result in higher lattice energy and greater stability of the compound.