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 first need to understand what a cathodic reaction entails. A cathodic reaction is characterized by the reduction process, which involves the gain of electrons. Conversely, an anodic reaction involves oxidation, which is the loss of electrons.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Cathodic Reaction**: A reaction that occurs at the cathode where reduction (gain of electrons) takes place.
- **Anodic Reaction**: A reaction that occurs at the anode where oxidation (loss of electrons) takes place.

2. **Identify the Reactions**:
- We need to analyze the given options to identify which one represents a reduction (gain of electrons).

3. **Analyze Each Option**:
- **Option 1**: \( \text{Fe} \rightarrow \text{Fe}^{3+} + 3e^- \)
- Here, iron (Fe) is losing electrons (oxidation), so this is not a cathodic reaction.
- **Option 2**: \( 4\text{OH}^- \rightarrow 2\text{H}_2\text{O} + \text{O}_2 + 4e^- \)
- This reaction shows the loss of electrons (oxidation), so it is not a cathodic reaction.
- **Option 3**: \( 2\text{H}_2 \rightarrow 2\text{OH}^+ + 2e^- \)
- This reaction also involves the loss of electrons (oxidation), thus it is not a cathodic reaction.
- **Option 4**: \( 2\text{SO}_4^{2-} \rightarrow \text{H}_2\text{O} + \text{S}^{+6} \)
- Here, we need to analyze the oxidation states. The oxidation state of sulfur decreases from +6 to +5, indicating a gain of electrons (reduction). Therefore, this is a cathodic reaction.

4. **Conclusion**:
- The cathodic reaction among the options provided is **Option 4**: \( 2\text{SO}_4^{2-} \rightarrow \text{H}_2\text{O} + \text{S}^{+6} \).