Question

What is the lattice energy of magnesium oxide (MgO) given that the ionization energy of Mg is 738 kJ/mol, the electron affinity of O is -141 kJ/mol, and the distance between the ions in MgO is 2.1 Å? Show your work and units.

Answer 1

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.