Conductivity of `0.01` M NaCl solution is `0.00147" ohm"^(-1) cm^(-1)` . What happens to this conductivity if extra 100 ml of `H_(2)O` is added to the above solution?

Options

A. Increases
B. Decreases
C. Remains unchanged
D. First increases and then decreases.

Answer

To solve the problem, we need to analyze what happens to the conductivity of a 0.01 M NaCl solution when we dilute it by adding 100 ml of water.

### Step-by-Step Solution:

1. **Understanding Conductivity**:
- Conductivity (\( \kappa \)) is a measure of a solution's ability to conduct electricity, which is primarily due to the presence of ions in the solution.

2. **Initial Conditions**:
- We start with a 0.01 M NaCl solution, which has a conductivity of 0.00147 \( \Omega^{-1} \text{cm}^{-1} \).

3. **Effect of Dilution**:
- When we add 100 ml of water to the solution, we are effectively diluting it. Dilution means that the concentration of ions in the solution will decrease because the same number of ions is now present in a larger volume.

4. **Calculating New Concentration**:
- The initial volume of the solution can be assumed to be 100 ml (since we are adding another 100 ml). Therefore, the total volume after adding 100 ml of water will be 200 ml.
- The new concentration of NaCl after dilution can be calculated using the formula:
\[ C_1V_1 = C_2V_2 \]
where:
- \( C_1 = 0.01 \, \text{M} \) (initial concentration),
- \( V_1 = 100 \, \text{ml} \) (initial volume),
- \( C_2 \) = new concentration,
- \( V_2 = 200 \, \text{ml} \) (final volume).
- Rearranging gives:
\[ C_2 = \frac{C_1V_1}{V_2} = \frac{0.01 \times 100}{200} = 0.005 \, \text{M} \]

5. **Impact on Conductivity**:
- As the concentration of ions decreases from 0.01 M to 0.005 M, the number of ions per unit volume decreases. Since conductivity is directly related to the concentration of ions, the conductivity will also decrease.

6. **Conclusion**:
- Therefore, after adding 100 ml of water to the 0.01 M NaCl solution, the conductivity will decrease.

### Final Answer:
The conductivity of the solution decreases.