Oxidation numbers of Mn in its compounds `MnCl_(2),Mn(OH)_(3),MnO_(2)` and `KMnO_(4)` respectively are:-

Options

A. `+2, +4, +7, +3`
B. `+2,+3,+4,+7`
C. `+7,+3,+2,+4`
D. `+7,+4,+3,+2`

Explanation

To determine the oxidation numbers of manganese (Mn) in the compounds \( \text{MnCl}_2 \), \( \text{Mn(OH)}_3 \), \( \text{MnO}_2 \), and \( \text{KMnO}_4 \), we will analyze each compound step by step.

### Step 1: Determine the oxidation state of Mn in \( \text{MnCl}_2 \)

1. Let the oxidation state of Mn be \( X \).
2. Chlorine (Cl) has an oxidation state of -1. Since there are 2 Cl atoms, the total contribution from Cl is \( 2 \times (-1) = -2 \).
3. The overall charge of the compound is neutral (0), so we set up the equation:
\[ X + (-2) = 0 \]
4. Solving for \( X \):
\[ X = +2 \]
5. Therefore, the oxidation state of Mn in \( \text{MnCl}_2 \) is **+2**.

### Step 2: Determine the oxidation state of Mn in \( \text{Mn(OH)}_3 \)

1. Let the oxidation state of Mn be \( X \).
2. The hydroxide ion (OH) has an oxidation state of -1. Since there are 3 OH groups, the total contribution from OH is \( 3 \times (-1) = -3 \).
3. The overall charge of the compound is neutral (0), so we set up the equation:
\[ X + (-3) = 0 \]
4. Solving for \( X \):
\[ X = +3 \]
5. Therefore, the oxidation state of Mn in \( \text{Mn(OH)}_3 \) is **+3**.

### Step 3: Determine the oxidation state of Mn in \( \text{MnO}_2 \)

1. Let the oxidation state of Mn be \( X \).
2. Oxygen (O) has an oxidation state of -2. Since there are 2 O atoms, the total contribution from O is \( 2 \times (-2) = -4 \).
3. The overall charge of the compound is neutral (0), so we set up the equation:
\[ X + (-4) = 0 \]
4. Solving for \( X \):
\[ X = +4 \]
5. Therefore, the oxidation state of Mn in \( \text{MnO}_2 \) is **+4**.

### Step 4: Determine the oxidation state of Mn in \( \text{KMnO}_4 \)

1. Let the oxidation state of Mn be \( X \).
2. Potassium (K) has an oxidation state of +1. Oxygen (O) has an oxidation state of -2. Since there are 4 O atoms, the total contribution from O is \( 4 \times (-2) = -8 \).
3. The overall charge of the compound is neutral (0), so we set up the equation:
\[ +1 + X + (-8) = 0 \]
4. Simplifying the equation:
\[ X - 7 = 0 \implies X = +7 \]
5. Therefore, the oxidation state of Mn in \( \text{KMnO}_4 \) is **+7**.

### Final Answer

The oxidation numbers of Mn in the compounds \( \text{MnCl}_2 \), \( \text{Mn(OH)}_3 \), \( \text{MnO}_2 \), and \( \text{KMnO}_4 \) are respectively:
- \( \text{MnCl}_2 \): **+2**
- \( \text{Mn(OH)}_3 \): **+3**
- \( \text{MnO}_2 \): **+4**
- \( \text{KMnO}_4 \): **+7**

Thus, the final answer is **+2, +3, +4, +7**.