Which of the following is cathodic reaction?

Options

A. `Fe^(2+) rarr Fe^(3+)`
B. `4OH^(-) rarr 2H_(2)O + O_(2)`
C. `2H_(2)O rarr 2OH^(+) + H_(2)`
D. `2SO_(4)^(2-) rarr S_(2)O_(6)^(2-)`

Answer

To determine which of the given reactions is a cathodic reaction, we need to understand the definitions of oxidation and reduction in electrochemistry.

### Step-by-Step Solution:

1. **Understand Oxidation and Reduction**:
- Oxidation is the process where a species loses electrons, resulting in an increase in oxidation state.
- Reduction is the process where a species gains electrons, resulting in a decrease in oxidation state.
- The cathode is the electrode where reduction occurs.

2. **Analyze Each Option**:
- **Option 1**: Iron (Fe) in +2 state converts to iron in +3 state.
- Reaction: \( \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} + e^- \)
- This shows that iron is losing an electron (oxidation). Therefore, this reaction occurs at the anode.

- **Option 2**: Hydroxide ions (OH⁻) produce water and oxygen.
- Reaction: \( 4 \text{OH}^- \rightarrow 2 \text{H}_2\text{O} + \text{O}_2 + 4e^- \)
- Here, hydroxide ions are losing electrons to form water and oxygen, indicating oxidation. However, in the context of the overall reaction, this is typically associated with the cathodic reaction in electrolysis.

- **Option 3**: Water produces hydroxide ions and hydrogen.
- Reaction: \( 2 \text{H}_2\text{O} \rightarrow 2 \text{OH}^- + \text{H}_2 + 2e^- \)
- This shows that water is losing electrons (oxidation), so this reaction occurs at the anode.

- **Option 4**: Sulfate ions (SO₄²⁻) convert to a different sulfate species.
- Reaction: \( 2 \text{SO}_4^{2-} \rightarrow \text{S}_2\text{O}_6^{2-} + 2e^- \)
- This indicates that sulfate is losing electrons (oxidation), so this reaction occurs at the anode.

3. **Conclusion**:
- The only reaction that involves the gain of electrons (reduction) is **Option 2**, where hydroxide ions are involved. Thus, the cathodic reaction is **Option 2**.

### Final Answer:
The cathodic reaction is **Option 2**.