Changing 1 mol of Mg(s) and 1/2 mol of O2 (g) to gaseous atoms requires a total of approximately 150kJ of energy. The first and second ionization energies of Mg are 737kJ/mol and 1450kJ/mol respectively. The first and second electron affinities of Oxygen are -141KJ/mol and +844 kJ/mol respectively. The stardard hear of formation of MgO(s) is -602kJ/mol. Calculate the Lattice Energy of magnesium oxide based on the above given information. (enter the sign and numerical answer without units. Include 4 significant digits in your answer, do not use scientific notation)
To calculate the lattice energy of magnesium oxide (MgO), we need to consider the formation of cations and anions and their corresponding ionization energies and electron affinities.
1. First, we need to find the energy required to form Mg2+ cations from Mg atoms. This can be calculated by subtracting the first and second ionization energies of magnesium from the total energy required for gaseous Mg atoms.
Energy needed to form Mg2+ = (737 kJ/mol + 1450 kJ/mol) - 0 kJ/mol = 2187 kJ/mol
2. Next, we need to find the energy required to form O2- anions from O atoms. This can be calculated by subtracting the first and second electron affinities of oxygen from the total energy required for gaseous O atoms.
Energy needed to form O2- = 0 kJ/mol - (-141 kJ/mol) - 844 kJ/mol = 703 kJ/mol
3. Now, we need to find the energy released (negative) or absorbed when Mg2+ and O2- ions combine to form MgO. This can be calculated using the enthalpy of formation of MgO (which is the negative of the lattice energy).
Energy released = -(-602 kJ/mol) = 602 kJ/mol
4. Finally, the lattice energy can be calculated by summing up the energy required to form Mg2+ cations and O2- anions, and subtracting the energy released during the formation of MgO.
Lattice energy of MgO = Energy needed to form Mg2+ + Energy needed to form O2- - Energy released
= 2187 kJ/mol + 703 kJ/mol - 602 kJ/mol
= 2288 kJ/mol
Therefore, the lattice energy of magnesium oxide is 2288 kJ/mol.