In which of the following compounds, Mn has highest oxidation state?

Options

A. `K_(2)MnO_(4)`
B. `MnO_(2)`
C. `KMnO_(4)`
D. `Mn_(3)O_(4)`

Explanation

To determine which compound has the highest oxidation state of manganese (Mn), we need to analyze the oxidation states of Mn in each of the given compounds. Let's go through each compound step by step.

### Step 1: Analyze the first compound, \( K_2MnO_4 \)

1. The formula is \( K_2MnO_4 \).
2. Potassium (K) has an oxidation state of +1.
3. Oxygen (O) has an oxidation state of -2.
4. Let the oxidation state of Mn be \( x \).
5. The equation for the compound is:
\[ 2(+1) + x + 4(-2) = 0 \]
Simplifying this gives:
\[ 2 + x - 8 = 0 \implies x - 6 = 0 \implies x = +6 \]

### Step 2: Analyze the second compound, \( MnO_2 \)

1. The formula is \( MnO_2 \).
2. Oxygen (O) has an oxidation state of -2.
3. Let the oxidation state of Mn be \( x \).
4. The equation for the compound is:
\[ x + 2(-2) = 0 \]
Simplifying this gives:
\[ x - 4 = 0 \implies x = +4 \]

### Step 3: Analyze the third compound, \( KMnO_4 \)

1. The formula is \( KMnO_4 \).
2. Potassium (K) has an oxidation state of +1.
3. Oxygen (O) has an oxidation state of -2.
4. Let the oxidation state of Mn be \( x \).
5. The equation for the compound is:
\[ 1 + x + 4(-2) = 0 \]
Simplifying this gives:
\[ 1 + x - 8 = 0 \implies x - 7 = 0 \implies x = +7 \]

### Step 4: Analyze the fourth compound, \( Mn_3O_4 \)

1. The formula is \( Mn_3O_4 \).
2. Oxygen (O) has an oxidation state of -2.
3. Let the oxidation state of Mn be \( x \).
4. The equation for the compound is:
\[ 3x + 4(-2) = 0 \]
Simplifying this gives:
\[ 3x - 8 = 0 \implies 3x = 8 \implies x = \frac{8}{3} \approx +2.67 \]

### Conclusion

After analyzing all four compounds, we find the oxidation states of Mn as follows:
- In \( K_2MnO_4 \): +6
- In \( MnO_2 \): +4
- In \( KMnO_4 \): +7
- In \( Mn_3O_4 \): \( \frac{8}{3} \) or approximately +2.67

The highest oxidation state of Mn is found in \( KMnO_4 \), which is +7.

### Final Answer
The compound in which Mn has the highest oxidation state is \( KMnO_4 \).

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