1. Determine the chemical formula of aluminum oxide:

* Aluminum has a +3 charge (Al³⁺)

* Oxygen has a -2 charge (O²⁻)

* To balance the charges, we need two aluminum ions for every three oxygen ions.

* The chemical formula is Al₂O₃.

2. Understand the mole ratio:

* The formula Al₂O₃ tells us that for every 1 mole of aluminum oxide (Al₂O₃), there are 3 moles of oxygen ions (O²⁻).

3. Calculate the moles of O²⁻ ions:

* You have 0.65 moles of aluminum oxide (Al₂O₃).

* Multiply the moles of Al₂O₃ by the mole ratio from the formula: 0.65 moles Al₂O₃ * (3 moles O²⁻ / 1 mole Al₂O₃) = 1.95 moles of O²⁻ ions

Therefore, there are 1.95 moles of O²⁻ ions in 0.65 moles of aluminum oxide.