Hydrogen peroxide oxidises `[Fe(CN)_(6)]^(4-)` to `[Fe(CN)_(6)]^(3-)` in acidic medium but reduces `[Fe(CN)_(6)]^(3-)` to `[Fe(CN)_(6)]^(4-)` in alkaline medium. The other products formed are, respectively

Options

A. `H_(2)O" and "(H_(2)O+OH^(-))`
B. `(H_(2)O+O_(2)) " and "H_(2)O`
C. `(H_(2)O+O_(2))" and "(H_(2)O+OH^(-))`
D. `H_(2)O" and "(H_(2)O+O_(2))`

Answer

To solve the problem, we need to analyze the reactions of hydrogen peroxide (H₂O₂) with the complex ions \([Fe(CN)_6]^{4-}\) and \([Fe(CN)_6]^{3-}\) in acidic and alkaline media, respectively. Let's break it down step by step.

### Step 1: Identify the Reactions

1. **In Acidic Medium:**
- Hydrogen peroxide oxidizes \([Fe(CN)_6]^{4-}\) to \([Fe(CN)_6]^{3-}\).
- The oxidation state of iron changes from +2 in \([Fe(CN)_6]^{4-}\) to +3 in \([Fe(CN)_6]^{3-}\).

2. **In Alkaline Medium:**
- Hydrogen peroxide reduces \([Fe(CN)_6]^{3-}\) back to \([Fe(CN)_6]^{4-}\).
- The oxidation state of iron changes from +3 in \([Fe(CN)_6]^{3-}\) to +2 in \([Fe(CN)_6]^{4-}\).

### Step 2: Write the Balanced Reactions

#### Reaction in Acidic Medium
1. **Oxidation Reaction:**
- The half-reaction can be written as:
\[ H_2O_2 + 2Fe^{2+} + 2H^+ \rightarrow 2Fe^{3+} + 2H_2O \]
- The overall reaction is:
\[ H_2O_2 + 2[Fe(CN)_6]^{4-} + 2H^+ \rightarrow 2[Fe(CN)_6]^{3-} + 2H_2O \]

#### Reaction in Alkaline Medium
2. **Reduction Reaction:**
- The half-reaction can be written as:
\[ 2Fe^{3+} + 2OH^- \rightarrow 2Fe^{2+} + O_2 + 2H_2O \]
- The overall reaction is:
\[ H_2O_2 + 2[Fe(CN)_6]^{3-} + 2OH^- \rightarrow 2[Fe(CN)_6]^{4-} + O_2 + 2H_2O \]

### Step 3: Identify the By-products

- In the acidic medium reaction, the by-product is water (\(H_2O\)).
- In the alkaline medium reaction, the by-products are oxygen (\(O_2\)) and water (\(H_2O\)).

### Final Summary of Reactions

1. **Acidic Medium:**
\[ H_2O_2 + 2[Fe(CN)_6]^{4-} + 2H^+ \rightarrow 2[Fe(CN)_6]^{3-} + 2H_2O \]
- By-product: Water (\(H_2O\))

2. **Alkaline Medium:**
\[ H_2O_2 + 2[Fe(CN)_6]^{3-} + 2OH^- \rightarrow 2[Fe(CN)_6]^{4-} + O_2 + 2H_2O \]
- By-products: Oxygen (\(O_2\)) and Water (\(H_2O\))

### Conclusion

The other products formed in the respective reactions are:
- In acidic medium: Water (\(H_2O\))
- In alkaline medium: Oxygen (\(O_2\)) and Water (\(H_2O\))