The specific conductivity of 0.5N solution is `0.01287 ohm^(-1) cm^(-1)`. What would be its equivalent conductance?

Options

A. 257.4
B. 2.574
C. 25.74
D. `0.2574 ohm^(-1) cm^(2) (g.eq)^(-1)`

Answer

To find the equivalent conductance of a solution given its specific conductivity, we can use the following relationship:

\[ \text{Equivalent Conductance} (\Lambda) = \text{Specific Conductivity} (\kappa) \times \frac{1000}{\text{Normality} (N)} \]

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Specific conductivity (\(\kappa\)) = 0.01287 ohm\(^{-1}\) cm\(^{-1}\)
- Normality (N) = 0.5 N

2. **Substitute the Values into the Formula:**
\[ \Lambda = 0.01287 \times \frac{1000}{0.5} \]

3. **Calculate the Equivalent Conductance:**
- First, calculate \(\frac{1000}{0.5}\):
\[ \frac{1000}{0.5} = 2000 \]
- Now, multiply this result by the specific conductivity:
\[ \Lambda = 0.01287 \times 2000 \]

4. **Final Calculation:**
\[ \Lambda = 25.74 \text{ ohm}^{-1} \text{ cm}^2 \text{ g}^{-1} \text{ equivalent}^{-1} \]

### Conclusion:
The equivalent conductance of the 0.5 N solution is **25.74 ohm\(^{-1}\) cm\(^2\) g\(^{-1}\) equivalent\(^{-1}\)**.