To determine the oxidation state of manganese and the chemical formula of Manganese(III) oxide, let's break down the information provided and understand it step-by-step.
1. Manganese(III) oxide:
- The "(III)" indicates that manganese has an oxidation state of +3.
- The "-oxide" means the compound contains oxygen, which typically has an oxidation state of -2 in oxides.
2. Balancing the charges:
- Manganese has an oxidation state of +3.
- Oxygen has an oxidation state of -2.
3. Finding the right proportions:
- To balance the charges in the compound, consider that each manganese ion contributes +3 charge and each oxygen ion contributes -2 charge.
- We need to find a combination where the total positive charge equals the total negative charge.
4. Determining the chemical formula:
- Suppose we have [tex]\(x\)[/tex] atoms of manganese (Mn) and [tex]\(y\)[/tex] atoms of oxygen (O).
- The charge contributed by manganese is [tex]\(3x\)[/tex] (since each Mn is +3).
- The charge contributed by oxygen is [tex]\(-2y\)[/tex] (since each O is -2).
To balance the charges:
[tex]\[
3x = 2y
\][/tex]
Simplifying this equation, we need to find the smallest whole number ratio:
[tex]\[
x = 2 \quad \text{and} \quad y = 3
\][/tex]
5. Resulting chemical formula:
- Therefore, the chemical formula that balances the charges is [tex]\( \text{Mn}_2\text{O}_3 \)[/tex].
Conclusion:
- The oxidation state of manganese in Manganese(III) oxide is +3.
- The chemical formula of Manganese(III) oxide is Mn₂O₃.
So, the answers are:
- The oxidation state of manganese in this compound is [tex]\(3\)[/tex].
- The chemical formula of the compound is [tex]\(Mn_2O_3\)[/tex].
