To calculate the lattice energy of Calcium oxide CaO using the Born-Haber cycle, we need to consider several energy changes that occur during the formation of CaO from its constituent elements. The Born-Haber cycle is a thermochemical cycle that relates the lattice energy to other measurable energies, such as ionization energy, electron affinity, and enthalpy of formation.Here are the steps involved in the Born-Haber cycle for CaO:1. Sublimation of solid calcium Ca to gaseous calcium Ca g : Ca s Ca g ; H_sublimation = +178 kJ/mol2. Ionization of gaseous calcium Ca g to form a calcium ion Ca g : Ca g Ca g + 2e; H_ionization1 = +590 kJ/mol first ionization energy Since calcium has two ionization energies, we need to add both of them: H_ionization2 = +1145 kJ/mol second ionization energy Total ionization energy: H_ionization_total = H_ionization1 + H_ionization2 = 590 + 1145 = +1735 kJ/mol3. Dissociation of oxygen molecule O into oxygen atoms O : 1/2 O g O g ; H_dissociation = +249 kJ/mol4. Formation of oxide ion O by gaining two electrons by oxygen atom O : O g + 2e O g ; H_electron_affinity = -603 kJ/mol electron affinity of oxygen 5. Formation of CaO from gaseous ions: Ca g + O g CaO s ; H_lattice_energy = ? lattice energy of CaO 6. Enthalpy of formation of CaO: Ca s + 1/2 O g CaO s ; H_formation = -635 kJ/molNow, we can use the Born-Haber cycle to calculate the lattice energy of CaO:H_lattice_energy = H_formation - H_sublimation - H_ionization_total - H_dissociation - H_electron_affinityH_lattice_energy = -635 kJ/mol - +178 kJ/mol - +1735 kJ/mol - +249 kJ/mol - -603 kJ/mol H_lattice_energy = -635 - 178 - 1735 - 249 + 603 = -3194 kJ/molSo, the lattice energy of Calcium oxide CaO is -3194 kJ/mol.Factors that affect the lattice energy of CaO:1. Ionic radii: Smaller ions have a stronger electrostatic attraction between them, leading to higher lattice energy. In the case of CaO, both Ca and O are relatively small ions, resulting in a high lattice energy.2. Charge of the ions: The lattice energy is directly proportional to the product of the charges of the ions. In CaO, the charges of the ions are +2 Ca and -2 O , which contribute to the high lattice energy.3. Crystal structure: The arrangement of ions in the crystal lattice also affects the lattice energy. CaO has a rock-salt structure, which is a highly stable arrangement, contributing to its high lattice energy.