In which of the following reaction the metal is reduced?

Options

A. `[Fe(CN)_4]^(4-) rarr [Fe(CN)_6]^(3-)`
B. `MnO_4^(-)rarr MnO_2`
C. `MnO_4^(2-)rarr MnO_4^-`
D. `Cr_2O_7^(2-)rarr CrO_4^(2-)`

Answer

To determine in which of the given reactions the metal is reduced, we need to analyze the oxidation states of the metals involved in each reaction. Reduction is defined as the gain of electrons or a decrease in oxidation state.

### Step-by-Step Solution:

1. **Identify the Reactions**:
We have several reactions to analyze. Let's denote them as:
- Reaction 1: \( \text{Fe(CN)}_4^{2-} \rightarrow \text{Fe(CN)}_6^{3-} \)
- Reaction 2: \( \text{MnO}_4^{-} \rightarrow \text{MnO}_2 \)
- Reaction 3: \( \text{Cr}_2\text{O}_7^{2-} \rightarrow \text{Cr}_2\text{O}_4^{2-} \)

2. **Calculate Oxidation States**:
- **For Reaction 1**:
- In \( \text{Fe(CN)}_4^{2-} \): Let the oxidation state of Fe be \( x \).
\[ x + 4(-1) = -2 \implies x - 4 = -2 \implies x = +2 \]
- In \( \text{Fe(CN)}_6^{3-} \):
\[ x + 6(-1) = -3 \implies x - 6 = -3 \implies x = +3 \]
- **Change**: From +2 to +3 (oxidation).

- **For Reaction 2**:
- In \( \text{MnO}_4^{-} \): Let the oxidation state of Mn be \( x \).
\[ x + 4(-2) = -1 \implies x - 8 = -1 \implies x = +7 \]
- In \( \text{MnO}_2 \):
\[ x + 2(-2) = 0 \implies x - 4 = 0 \implies x = +4 \]
- **Change**: From +7 to +4 (reduction).

- **For Reaction 3**:
- In \( \text{Cr}_2\text{O}_7^{2-} \): Let the oxidation state of Cr be \( x \).
\[ 2x + 7(-2) = -2 \implies 2x - 14 = -2 \implies 2x = 12 \implies x = +6 \]
- In \( \text{Cr}_2\text{O}_4^{2-} \):
\[ 2x + 4(-2) = -2 \implies 2x - 8 = -2 \implies 2x = 6 \implies x = +3 \]
- **Change**: From +6 to +3 (reduction).

3. **Conclusion**:
- In Reaction 1, Fe is oxidized (oxidation state increases).
- In Reaction 2, Mn is reduced (oxidation state decreases).
- In Reaction 3, Cr is reduced (oxidation state decreases).

Thus, the reactions where the metal is reduced are **Reaction 2** and **Reaction 3**.

### Final Answer:
The metal is reduced in **Reaction 2** \( \text{MnO}_4^{-} \rightarrow \text{MnO}_2 \) and **Reaction 3** \( \text{Cr}_2\text{O}_7^{2-} \rightarrow \text{Cr}_2\text{O}_4^{2-} \).