Which of the following reactions occurs at the cathode?

Options

A. `2OH^(-) rarr H_(2)O + O + 2e^(-)`
B. `Zn rarr Zn^(2+) + 2e^(-)`
C. `Sn^(2+) rarr Sn^(4+) + 2e^(-)`
D. `Cu^(2+) + 2e^(-) rarr Cu`

Answer

To determine which reaction occurs at the cathode, we need to understand the fundamental concept of electrochemistry, specifically the role of the cathode in electrochemical cells.

### Step-by-Step Solution:

1. **Understand the Role of the Cathode**:
- The cathode is the electrode where reduction occurs. In a reduction reaction, a species gains electrons.

2. **Analyze Each Reaction**:
- We need to evaluate the given reactions to identify which one involves a reduction process.

3. **Examine the First Reaction**:
- Reaction: \( \text{H}_2\text{O} + \text{OH}^- \rightarrow \text{H}_2\text{O} + \text{O} + 2 \text{e}^- \)
- In this reaction, oxygen is being oxidized (going from -2 to 0 oxidation state). This indicates that this reaction occurs at the anode, not the cathode.

4. **Examine the Second Reaction**:
- Reaction: \( \text{Zn} \rightarrow \text{Zn}^{2+} + 2 \text{e}^- \)
- Zinc is being oxidized (going from 0 to +2 oxidation state). This also indicates that this reaction occurs at the anode.

5. **Examine the Third Reaction**:
- Reaction: \( \text{Sn}^{2+} \rightarrow \text{Sn}^{4+} + 2 \text{e}^- \)
- Tin is being oxidized (going from +2 to +4 oxidation state). This indicates that this reaction occurs at the anode as well.

6. **Examine the Fourth Reaction**:
- Reaction: \( \text{Cu}^{2+} + 2 \text{e}^- \rightarrow \text{Cu} \)
- Copper is being reduced (going from +2 to 0 oxidation state). This indicates that this reaction occurs at the cathode.

7. **Conclusion**:
- The reaction that occurs at the cathode is \( \text{Cu}^{2+} + 2 \text{e}^- \rightarrow \text{Cu} \).

### Final Answer:
The reaction that occurs at the cathode is \( \text{Cu}^{2+} + 2 \text{e}^- \rightarrow \text{Cu} \).

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