The chemical formula for phosphorus III oxide is P₂O₃. Here's how we arrive at that:

* Phosphorus III indicates that phosphorus has an oxidation state of +3.

* Oxide means the compound contains oxygen. Oxygen typically has an oxidation state of -2.

To create a neutral compound, we need to balance the charges. Since we have two phosphorus atoms with +3 oxidation state each (+6 total) and three oxygen atoms with -2 oxidation state each (-6 total), the charges balance out.