A: At equilibrium `E_("cell")` becomes zero.
R: At equilibrium reduction potential fo both the electrodes becomes equal.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements then mark (4)

Answer

To solve the question regarding the assertion and reason provided, we will analyze both statements step by step.

### Step-by-Step Solution:

1. **Understanding Assertion (A)**:
- The assertion states that "At equilibrium, \( E_{\text{cell}} \) becomes zero."
- This means that when a galvanic cell reaches equilibrium, there is no net voltage produced by the cell.

2. **Understanding Reason (R)**:
- The reason states that "At equilibrium, the reduction potential of both electrodes becomes equal."
- This implies that the potential difference between the two electrodes (anode and cathode) is zero at equilibrium.

3. **Nernst Equation**:
- The Nernst equation is given by:
\[ E_{\text{cell}} = E^{\circ}_{\text{cell}} - \frac{2.303RT}{nF} \log \frac{[\text{products}]}{[\text{reactants}]} \]
- At equilibrium, the concentrations of products and reactants remain constant, leading to a situation where the logarithmic term becomes constant.

4. **Equilibrium Condition**:
- At equilibrium, the change in Gibbs free energy (\( \Delta G \)) is zero, which can be expressed as:
\[ \Delta G = -nFE_{\text{cell}} = 0 \]
- This indicates that \( E_{\text{cell}} = 0 \).

5. **Implication of \( E_{\text{cell}} = 0 \)**:
- When \( E_{\text{cell}} = 0 \), it indicates that there is no net electron transfer occurring in the cell.
- This also means that the reduction potentials of both electrodes must be equal, as there is no driving force for electron flow.

6. **Conclusion**:
- Since both the assertion and reason are true and the reason correctly explains the assertion, we can conclude that both statements are valid.

### Final Answer:
Both the assertion (A) and reason (R) are true, and the reason is the correct explanation of the assertion.

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