Born-Haber Cycle for Sodium Oxide

The standard enthalpy of formation of sodium oxide is -414kJmol^-1. The equation is:2Na(s) + ½O₂(g) → Na₂O(s)The definition states that the -414kJ is the enthalpy for 1 mole of sodium oxide. The definition of the enthalpy of atomisation is for the formation of 1 mole of sodium atoms but we need to atomise 2 Na(s) so the enthalpy change will be 2x +108 kJ mol^-1. The definition of the enthalpy of atomisation is for the formation of 1 mole of oxygen atoms. So we can use the standard enthalpy of atomisation which is +249 kJmol^-1 as it is. The next step is to ionise the sodium. The equation is:Na(g) → Na⁺(g) + e^-The ionisation energy for sodium is +496 kJ per mole so we double it (we need 2 moles of sodium for each mole of sodium oxide). Mass and charge are conserved for each step. We now have two electron affinities for oxygen. The first is exothermicO(g) + e^- → O^-(g)The second is endothermic.O^-(g) + e^- → O^2-(g)The cycle is completed with the Lattice (formation) enthalpy2Na⁺(g) + O^2-(g) → Na₂O (s)Always include state symbols.