Oxidation number of manganese in `KMnO_(4). MnO _(2), K_(2) MnO _(4).` respectively is :

Options

A. `+4,+7, +6`
B. `+6,+7,+4`
C. `+4,+6,+7`
D. `+7,+4,+6`

Explanation

To find the oxidation number of manganese (Mn) in the compounds \( KMnO_4 \), \( MnO_2 \), and \( K_2MnO_4 \), we can follow these steps:

### Step 1: Determine the oxidation number of Mn in \( KMnO_4 \)

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

2. **Set up the equation**:
- Let the oxidation number of Mn be \( x \).
- The formula for the compound is \( KMnO_4 \), which contains 1 K, 1 Mn, and 4 O.
- The total charge of the compound must equal 0.
- The equation can be set up as:
\[ 1 + x + 4(-2) = 0 \]

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

Thus, the oxidation number of Mn in \( KMnO_4 \) is **+7**.

### Step 2: Determine the oxidation number of Mn in \( MnO_2 \)

1. **Identify the oxidation states of other elements**:
- Oxygen (O) has an oxidation state of -2.

2. **Set up the equation**:
- Let the oxidation number of Mn be \( x \).
- The formula for the compound is \( MnO_2 \), which contains 1 Mn and 2 O.
- The equation can be set up as:
\[ x + 2(-2) = 0 \]

3. **Solve the equation**:
\[ x - 4 = 0 \\ x = +4 \]

Thus, the oxidation number of Mn in \( MnO_2 \) is **+4**.

### Step 3: Determine the oxidation number of Mn in \( K_2MnO_4 \)

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

2. **Set up the equation**:
- Let the oxidation number of Mn be \( x \).
- The formula for the compound is \( K_2MnO_4 \), which contains 2 K, 1 Mn, and 4 O.
- The equation can be set up as:
\[ 2(1) + x + 4(-2) = 0 \]

3. **Solve the equation**:
\[ 2 + x - 8 = 0 \\ x - 6 = 0 \\ x = +6 \]

Thus, the oxidation number of Mn in \( K_2MnO_4 \) is **+6**.

### Final Answer:
The oxidation numbers of manganese in the compounds are:
- \( KMnO_4 \): +7
- \( MnO_2 \): +4
- \( K_2MnO_4 \): +6