To calculate the lattice energy of magnesium oxide MgO , we can use the Born-Haber cycle and the Coulomb's law. The lattice energy U can be calculated using the following formula:U = k * Q1 * Q2 / rwhere k is the electrostatic constant 8.9875517923 10^9 N m^2 C^-2 , Q1 and Q2 are the charges of the ions, and r is the distance between the ions.First, we need to convert the distance between the ions from to meters:2.1 = 2.1 10^-10 mNow, we can calculate the lattice energy:U = 8.9875517923 10^9 N m^2 C^-2 * +2e * -2e / 2.1 10^-10 m where e is the elementary charge 1.602176634 10^-19 C .U = 8.9875517923 10^9 N m^2 C^-2 * 3.204353268 10^-19 C ^2 / 2.1 10^-10 m U = 8.9875517923 10^9 N m^2 C^-2 * 1.027376583 10^-37 C^2 / 2.1 10^-10 m U = 9.233 10^-28 N mNow, we need to convert the lattice energy from N m to kJ/mol. We can do this by multiplying by Avogadro's number 6.02214076 10^23 mol^-1 and dividing by 1000:U = 9.233 10^-28 N m * 6.02214076 10^23 mol^-1 / 1000U = 5555.8 kJ/molSo, the lattice energy of magnesium oxide MgO is approximately 5556 kJ/mol.