By which of the following methods, `H_(2)O_(2)` can't be synthesised?

Options

A. Lewis addition of ice cold `H_(2)SO_(4)` on `BaO_(2)`
B. Addition of ice cold `H_(2)SO_(4)` on `PbO_(2)`
C. Aerial oxidation of 2-ethyl anthraquinol
D. Electrolysis of `(NH_(4))_(2)SO_(4)` at a high current density

Explanation

To determine which method cannot synthesize hydrogen peroxide (H₂O₂) from the given options, we will analyze each method step by step.

### Step-by-Step Solution:

1. **Method 1: Lewis addition of ice-cold H₂SO₄ on BaO₂**
- When ice-cold sulfuric acid (H₂SO₄) is added to barium peroxide (BaO₂), a reaction occurs that produces barium sulfate (BaSO₄) as a precipitate and hydrogen peroxide (H₂O₂) as a product.
- **Reaction**:
\[ \text{BaO}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{BaSO}_4 (s) + \text{H}_2\text{O}_2 \]
- **Conclusion**: This method can synthesize H₂O₂.

2. **Method 2: Addition of ice-cold H₂SO₄ on PbO₂**
- When ice-cold sulfuric acid is added to lead dioxide (PbO₂), the reaction produces lead sulfate (PbSO₄) as a precipitate and oxygen gas (O₂) instead of hydrogen peroxide.
- **Reaction**:
\[ \text{PbO}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{PbSO}_4 (s) + \frac{1}{2} \text{O}_2 + \text{H}_2\text{O} \]
- **Conclusion**: This method does NOT synthesize H₂O₂.

3. **Method 3: Aerial oxidation of ethyl anthraquinol**
- Ethyl anthraquinol undergoes aerial oxidation, which leads to the formation of hydrogen peroxide.
- **Reaction**:
\[ \text{C}_{14}\text{H}_{12}\text{O} + \text{O}_2 \rightarrow \text{H}_2\text{O}_2 + \text{other products} \]
- **Conclusion**: This method can synthesize H₂O₂.

4. **Method 4: Electrolysis of ammonium sulfate at high current density**
- Electrolysis of ammonium sulfate (NH₄)₂SO₄ produces ammonium ions and sulfate ions. At the anode, sulfate ions can lead to the formation of peroxodisulfate, which can then hydrolyze to produce hydrogen peroxide.
- **Reaction**:
\[ \text{(NH}_4)_2\text{SO}_4 \rightarrow \text{NH}_4^+ + \text{SO}_4^{2-} \]
\[ \text{SO}_4^{2-} \rightarrow \text{H}_2\text{O}_2 \text{ (via peroxo sulfate hydrolysis)} \]
- **Conclusion**: This method can synthesize H₂O₂.

### Final Conclusion:
The method that cannot synthesize hydrogen peroxide (H₂O₂) is **the addition of ice-cold H₂SO₄ on PbO₂**.