To determine the correct formula for cobalt (III) oxide, we need to understand the charges of the cobalt and oxygen ions.
1. Oxidation State for Cobalt (III):
- The "III" in cobalt (III) indicates that cobalt has an oxidation state of +3. Therefore, a cobalt (III) ion is [tex]\( Co^{3+} \)[/tex].
2. Charge of Oxygen Ion:
- Oxygen typically has an oxidation state of -2 in most of its compounds. Thus, an oxygen ion is [tex]\( O^{2-} \)[/tex].
3. Balancing the Charges:
- To form a neutral compound, the total positive charge must balance the total negative charge. We need to find the ratio of cobalt (III) ions ([tex]\( Co^{3+} \)[/tex]) to oxide ions ([tex]\( O^{2-} \)[/tex]) that results in no net charge.
- The common multiple of 3 (from [tex]\( Co^{3+} \)[/tex]) and 2 (from [tex]\( O^{2-} \)[/tex]) is 6. Therefore:
- Two [tex]\( Co^{3+} \)[/tex] ions will provide a total of [tex]\( 2 \times (+3) = +6 \)[/tex] positive charges.
- Three [tex]\( O^{2-} \)[/tex] ions will provide a total of [tex]\( 3 \times (-2) = -6 \)[/tex] negative charges.
4. Writing the Formula:
- Combine the [tex]\( Co^{3+} \)[/tex] and [tex]\( O^{2-} \)[/tex] ions in the ratio determined above to get a neutral compound. For every 2 cobalt (III) ions, you need 3 oxide ions.
- Therefore, the formula for cobalt (III) oxide is [tex]\( Co_2O_3 \)[/tex].
So, the correct answer is:
[tex]\[ Co_2O_3 \][/tex]
