Let's find the information required step by step:
1. Identifying the Oxidation State of Manganese:
- Manganese(III) oxide indicates that manganese is in the +3 oxidation state.
Therefore, the oxidation state of manganese in this compound is [tex]\( \boxed{3} \)[/tex].
2. Determining the Chemical Formula:
- The compound name manganese(III) oxide suggests that manganese (Mn) has a +3 oxidation state.
- Oxygen (O) typically has a -2 oxidation state.
- To balance these charges in a compound, we need to find the correct ratio of manganese ions to oxide ions.
The chemical formula can be worked out as follows:
- Suppose the formula of the compound is [tex]\( \text{Mn}_x\text{O}_y \)[/tex].
- Manganese has a +3 oxidation state: Total positive charge = [tex]\( 3x \)[/tex].
- Oxygen has a -2 oxidation state: Total negative charge = [tex]\( -2y \)[/tex].
- For the compound to be neutral, the sum of the oxidation states must be zero: [tex]\( 3x - 2y = 0 \)[/tex].
- To balance the charges: [tex]\( 3x = 2y \)[/tex], which simplifies to [tex]\( x/y = 2/3 \)[/tex].
- This means for every 2 manganese atoms, there are 3 oxygen atoms.
Hence, the chemical formula of manganese(III) oxide is [tex]\( \boxed{\text{Mn}_2\text{O}_3} \)[/tex].
So, the oxidation state of manganese in this compound is [tex]\( 3 \)[/tex], and the chemical formula of the compound is [tex]\( \text{Mn}_2\text{O}_3 \)[/tex].
