In which of the following compounds manganese has oxidation number equal to that of iodine in `KIO_4`?

Options

A. Potassium manganate
B. Potassium permanganate
C. Dimanganese decacarbonyl
D. Mangenese chloride

Explanation

To determine in which of the given compounds manganese has an oxidation number equal to that of iodine in KIO₄, we will follow these steps:

### Step 1: Determine the oxidation state of iodine in KIO₄

1. **Identify the oxidation states of the elements in KIO₄:**
- Potassium (K) has an oxidation state of +1.
- Oxygen (O) has an oxidation state of -2.

2. **Set up the equation for the oxidation state of iodine (I):**
Let the oxidation state of iodine be \( x \).
The overall charge of the compound is zero, so we can write the equation:
\[ +1 + x + 4(-2) = 0 \]

3. **Simplify the equation:**
\[ +1 + x - 8 = 0 \implies x - 7 = 0 \]

4. **Solve for \( x \):**
\[ x = +7 \]

### Step 2: Determine the oxidation state of manganese in KMnO₄

1. **Identify the oxidation states of the elements in KMnO₄:**
- Potassium (K) has an oxidation state of +1.
- Oxygen (O) has an oxidation state of -2.

2. **Set up the equation for the oxidation state of manganese (Mn):**
Let the oxidation state of manganese be \( y \).
The overall charge of the compound is zero, so we can write the equation:
\[ +1 + y + 4(-2) = 0 \]

3. **Simplify the equation:**
\[ +1 + y - 8 = 0 \implies y - 7 = 0 \]

4. **Solve for \( y \):**
\[ y = +7 \]

### Conclusion

The oxidation state of manganese in KMnO₄ is +7, which is equal to the oxidation state of iodine in KIO₄. Therefore, the compound in which manganese has an oxidation number equal to that of iodine in KIO₄ is:

**Potassium permanganate (KMnO₄)**.