The solution of nickel sulphate in which nickel rod is dipped is diluted to 10 times. The potential of nickel.

Options

A. Decrease by 60mV
B. Increase by 30V
C. Decreses by 30mV
D. Decreases by 60V.

Explanation

To solve the problem, we need to analyze the electrochemical behavior of a nickel rod dipped in a nickel sulfate solution when the solution is diluted 10 times. We will use the Nernst equation to determine how the potential of the nickel changes upon dilution.

### Step-by-Step Solution:

1. **Identify the Reaction**:
- The nickel rod (Ni) will undergo oxidation to form nickel ions (Ni²⁺) at the anode:
\[ \text{Ni} \rightarrow \text{Ni}^{2+} + 2e^- \]
- The nickel ions in the solution will be reduced back to nickel at the cathode:
\[ \text{Ni}^{2+} + 2e^- \rightarrow \text{Ni} \]

2. **Write the Nernst Equation**:
- The Nernst equation is given by:
\[ E = E^\circ - \frac{0.0591}{n} \log Q \]
- Here, \( n = 2 \) (since 2 electrons are involved) and \( Q \) is the reaction quotient.

3. **Determine the Reaction Quotient (Q)**:
- For the given reaction, the reaction quotient \( Q \) can be expressed as:
\[ Q = \frac{[\text{Ni}^{2+}]}{1} = [\text{Ni}^{2+}] \]
- Since the concentration of solid nickel does not change, it is considered constant.

4. **Effect of Dilution**:
- When the nickel sulfate solution is diluted 10 times, the concentration of Ni²⁺ ions decreases by a factor of 10. If the initial concentration was \( C \), after dilution, it becomes:
\[ [\text{Ni}^{2+}] = \frac{C}{10} \]

5. **Substituting into the Nernst Equation**:
- Substitute \( Q \) into the Nernst equation:
\[ E = E^\circ - \frac{0.0591}{2} \log\left(\frac{C}{10}\right) \]
- This can be simplified to:
\[ E = E^\circ - 0.02955 \log(C) + 0.02955 \log(10) \]
- Since \( \log(10) = 1 \):
\[ E = E^\circ - 0.02955 \log(C) + 0.02955 \]

6. **Final Expression**:
- The final expression for the EMF after dilution becomes:
\[ E = E^\circ + 0.02955 - 0.02955 \log(C) \]
- This indicates that the EMF of the cell decreases by \( 0.02955 \) volts due to the dilution.

### Conclusion:
- The potential of the nickel rod decreases by approximately \( 0.03 \, V \) when the nickel sulfate solution is diluted 10 times.