The conductivity of 0.01N KCl solution is 0.0014106 `"ohm"^(-) cm^(-)` at 298 K. When a conductivity cell was filled up with the same solution, it offered a resistance of 484 ohms at 298 K. The same cell was then filled with 0.001 N solution of NaCl at the same temperature which gave a resistance of 5496 ohms. Calculate the value of equivalent conductivity of 0.001 N NaCI solution.

Explanation

To calculate the equivalent conductivity of a 0.001 N NaCl solution, we will follow these steps:

### Step 1: Calculate the Cell Constant
The cell constant (K) can be calculated using the formula:
\[ K = \text{Specific Conductance} \times \text{Resistance} \]

Given that the specific conductance of the 0.01 N KCl solution is \( 0.0014106 \, \text{ohm}^{-1} \text{cm}^{-1} \) and the resistance is \( 484 \, \text{ohms} \), we can substitute these values into the formula:
\[ K = 0.0014106 \, \text{ohm}^{-1} \text{cm}^{-1} \times 484 \, \text{ohms} \]
\[ K = 0.683 \, \text{cm}^{-1} \]

### Step 2: Calculate the Specific Conductance of the 0.001 N NaCl Solution
Using the cell constant calculated in Step 1, we can find the specific conductance of the 0.001 N NaCl solution. The formula is:
\[ \text{Specific Conductance} (k_2) = \frac{K}{R} \]

Where \( R \) is the resistance of the NaCl solution, which is \( 5496 \, \text{ohms} \):
\[ k_2 = \frac{0.683 \, \text{cm}^{-1}}{5496 \, \text{ohms}} \]
\[ k_2 = 0.000124 \, \text{ohm}^{-1} \text{cm}^{-1} \]

### Step 3: Calculate the Equivalent Conductivity
The equivalent conductivity (\( \Lambda \)) can be calculated using the formula:
\[ \Lambda = \frac{k \times 1000}{N} \]

Where:
- \( k \) is the specific conductance of the NaCl solution (from Step 2),
- \( N \) is the normality of the solution (which is \( 0.001 \, N \)).

Substituting the values:
\[ \Lambda = \frac{0.000124 \, \text{ohm}^{-1} \text{cm}^{-1} \times 1000}{0.001} \]
\[ \Lambda = 124.2 \, \text{ohm}^{-1} \text{cm}^2 \text{g}^{-1} \]

### Final Answer
The equivalent conductivity of the 0.001 N NaCl solution is:
\[ \Lambda = 124.2 \, \text{ohm}^{-1} \text{cm}^2 \text{g}^{-1} \]

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