Explain how the lattice energy of an ionic compound such as \(\mathrm{KCl}\) can be determined using the Born-Haber cycle. On what law is this procedure based?

The Born-Haber Cycle is a thermochemical cycle involving several steps that help in calculating the lattice energy of an ionic compound. In the case of \(KCl\), the steps are ionization of potassium to form \(K^+\), dissociation of chlorine to form \(Cl^-\), formation of \(KCl\) from \(K^+\) and \(Cl^-\), and finally, calculation of the lattice energy.

1. Begin with the atomisation of the constituent elements: \( \mathrm{K_{(s)} \rightarrow K_{(g)} + e^{-}} ; \mathrm{1 / 2 Cl_{2(g)} \rightarrow Cl_{(g)}} \). These are the ionisation energy of potassium and dissociation energy for chlorine respectively. 2. Next is the ionisation of the potassium atom to produce a potassium ion: \( \mathrm{K_{(g)} \rightarrow K^{+}_{(g)} + e^{-}} \). 3. The third step is the electron affinity of the chlorine atom, i.e., the energy released when a chlorine atom gains an electron to become a chloride ion: \( \mathrm{Cl_{(g)}+e^{-} \rightarrow Cl^{-}_{(g)}} \). 4. Finally, is the formation of \(KCl\), the lattice energy, by the combination of ions: \( \mathrm{K^{+}_{(g)} + Cl^{-}_{(g)} \rightarrow KCl_{(s)}} \). By adding all these steps together, we create the Born-Haber cycle.

The Born-Haber cycle is based on Hess's Law of Constant Heat Summation. This law states that the total enthalpy change for a chemical reaction is the same, irrespective of the reaction path.