The balanced chemical equation for the reaction between aluminium and oxygen to form aluminium oxide is:

4Al + 3O2 -> 2Al2O3

From the equation, we can see that 3 moles of O2 are required to react with 4 moles of Al to produce 2 moles of Al2O3.

Therefore, if 0.78 mol of O2 reacts, we can calculate the number of moles of Al2O3 formed using stoichiometry:

Moles of Al2O3 = (Moles of O2 reacted) * (Moles of Al2O3 produced / Moles of O2 required)

Moles of Al2O3 = (0.78 mol) * (2 mol Al2O3 / 3 mol O2)

Moles of Al2O3 = 0.52 mol

Therefore, 0.52 moles of Al2O3 are formed when 0.78 mol of O2 reacts with aluminium.