In the reaction : `MnO_(4)^(-)+xH^(+)+n e^(-)rarrMn^(2+)+yH_(2)O` What is the value of n :

Options

A. 5
B. 8
C. 6
D. 3

Answer

To determine the value of \( n \) in the reaction:

\[ \text{MnO}_4^{-} + x\text{H}^{+} + n e^{-} \rightarrow \text{Mn}^{2+} + y\text{H}_2\text{O} \]

we will follow these steps:

### Step 1: Determine the change in oxidation state
- The oxidation state of manganese in \(\text{MnO}_4^{-}\) is \( +7 \).
- The oxidation state of manganese in \(\text{Mn}^{2+}\) is \( +2 \).
- The change in oxidation state is calculated as:
\[ \text{Change} = +7 - (+2) = 5 \]

### Step 2: Balance the manganese atoms
- There is one manganese atom on both sides of the equation:
\[ \text{1 Mn on the left} \quad \text{and} \quad \text{1 Mn on the right} \]
- Therefore, the manganese atoms are already balanced.

### Step 3: Balance the oxygen atoms
- The left side has 4 oxygen atoms from \(\text{MnO}_4^{-}\).
- We can balance the oxygen atoms by adding water (\(\text{H}_2\text{O}\)) on the right side:
\[ \text{4 O from } \text{MnO}_4^{-} \rightarrow \text{4 H}_2\text{O} \]
- Thus, \( y = 4 \).

### Step 4: Balance the hydrogen atoms
- Each water molecule contributes 2 hydrogen atoms. Therefore, 4 water molecules contribute:
\[ 4 \times 2 = 8 \text{ H atoms} \]
- To balance the 8 hydrogen atoms, we need to add \( 8 \text{H}^{+} \) ions on the left side:
\[ x = 8 \]

### Step 5: Balance the charge
- Now we need to balance the charges on both sides of the equation.
- On the left side:
\[ \text{Charge} = -1 (\text{from } \text{MnO}_4^{-}) + 8 (\text{from } 8\text{H}^{+}) = +7 \]
- On the right side:
\[ \text{Charge} = +2 (\text{from } \text{Mn}^{2+}) \]
- To balance the charges, we need to add electrons (\( e^{-} \)) to the left side. Let \( n \) be the number of electrons:
\[ +7 - n = +2 \]
- Rearranging gives:
\[ n = 7 - 2 = 5 \]

### Conclusion
The value of \( n \) is \( 5 \).

### Summary
- The balanced reaction is:
\[ \text{MnO}_4^{-} + 8\text{H}^{+} + 5 e^{-} \rightarrow \text{Mn}^{2+} + 4\text{H}_2\text{O} \]