Which one of the following reaction occurs at the cathode

Options

A. `2OH^(-) rarr H_(2) O + 1/2 O_(2) + 2e^(-)`
B. `Ag(s) rarr Ag^(+) + e^(-)`
C. `Fe^(2+) rarr Fe^(3+) + r^(-)`
D. `Cu^(2+) + 2e^(-) rarr Cu(s)`

Answer

To determine which reaction occurs at the cathode, we need to understand the basic principles of electrochemistry, particularly the roles of the anode and cathode in an electrochemical cell.

### Step-by-Step Solution:

1. **Understanding the Cathode**: The cathode is the electrode where reduction occurs. Reduction is defined as the gain of electrons by a species.

2. **Identifying Reduction**: In a reduction reaction, a species (let's denote it as X) accepts electrons. For example, if X gains one electron, it becomes an anion (X⁻).

3. **Understanding the Anode**: In contrast, the anode is where oxidation occurs. Oxidation is the loss of electrons by a species. For instance, if a species like silver (Ag) loses one electron, it becomes a cation (Ag⁺).

4. **Analyzing Given Reactions**: To find out which reaction occurs at the cathode, we need to look for a reaction that involves a species gaining electrons.

5. **Conclusion**: The reaction that shows a species gaining electrons is the one that occurs at the cathode. Therefore, among the options provided, the one that represents a reduction process (gain of electrons) will be the correct answer.

### Final Answer:
The reaction that involves the gain of electrons occurs at the cathode.

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