The specific conductance of a `0.1 N KCl` solution at `23^(@)C` is `0.012 ohm^(-1) cm^(-1)`. The resistance of cell containing the solution at the same tempreature was found to be `55 ohm`. The cell constant will be

Options

A. `0.142 cm^(-1)`
B. `0.66 cm^(-1)`
C. `0.918 cm^(-1)`
D. `1.12 cm^(-1)`

Explanation

To find the cell constant of the solution, we can use the relationship between specific conductance (κ), resistance (R), and the cell constant (k). The formula is given by:

\[ \kappa = \frac{1}{R} \times k \]

Where:
- \( \kappa \) is the specific conductance,
- \( R \) is the resistance,
- \( k \) is the cell constant.

### Step 1: Write down the known values
- Specific conductance (κ) = 0.012 ohm\(^{-1}\) cm\(^{-1}\)
- Resistance (R) = 55 ohm

### Step 2: Rearrange the formula to find the cell constant (k)
From the formula, we can rearrange it to solve for the cell constant:

\[ k = \kappa \times R \]

### Step 3: Substitute the known values into the equation
Now, substituting the known values into the equation:

\[ k = 0.012 \, \text{ohm}^{-1} \text{cm}^{-1} \times 55 \, \text{ohm} \]

### Step 4: Calculate the cell constant
Now, performing the multiplication:

\[ k = 0.012 \times 55 = 0.66 \, \text{cm}^{-1} \]

### Conclusion
The cell constant \( k \) is 0.66 cm\(^{-1}\).

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