Question

The resistance of 0.10 M KCl solution when measured with a conductivity cell at 298 K is 100 \(\Omega\). If the conductivity of 0.10 M KCl solution is 1.29 S m\(^{-1}\), what is the value of cell constant of the same solution at 298 K

• A. \(1.29 m^{-1}\)
• B. \(1.29\times 10^{-2}m^{-1}\)
• C. \(0.129 cm^{-1}\)
• D. \(1.29 cm^{-1}\)
• E. \(0.129 m^{-1}\)

Hint:

Always pay attention to units. Conductivity is often given in S/m or S/cm. Ensure consistency in your calculations.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The question relates three important parameters in electrochemistry: resistance (R), conductivity (\(\kappa\)), and the cell constant (G or l/A). The cell constant is a characteristic of the geometry of the conductivity cell and is independent of the solution measured in it.
Step 2: Key Formula or Approach:
The relationship between conductivity, resistance, and cell constant is given by the formula: \[ \text{Conductivity } (\kappa) = \frac{1}{\text{Resistance } (R)} \times \text{Cell Constant } (G^) \] Rearranging this formula to solve for the cell constant: \[ \text{Cell Constant } (G^) = \text{Conductivity } (\kappa) \times \text{Resistance } (R) \] Step 3: Detailed Explanation:
We are given the following values:

Resistance (R) = 100 \(\Omega\)
Conductivity (\(\kappa\)) = 1.29 S m\(^{-1}\)
Now, we substitute these values into the rearranged formula. Note that the unit Siemens (S) is equivalent to \(\Omega^{-1}\). \[ G^ = (1.29 \text{ S m}^{-1}) \times (100 \, \Omega) \] \[ G^ = (1.29 \, \Omega^{-1} \text{ m}^{-1}) \times (100 \, \Omega) \] \[ G^ = 129 \text{ m}^{-1} \] The calculated cell constant is 129 m\(^{-1}\). Now we must check the units of the options. Options (C) and (D) are in cm\(^{-1}\). We need to convert our answer to cm\(^{-1}\) to compare.
We know that 1 m = 100 cm.
Therefore, 1 m\(^{-1}\) = (100 cm)\(^{-1}\) = \(\frac{1}{100}\) cm\(^{-1}\).
\[ G^ = 129 \times \left(\frac{1}{100} \text{ cm}^{-1}\right) \] \[ G^ = 1.29 \text{ cm}^{-1} \] Step 4: Final Answer:
The value of the cell constant is 1.29 cm\(^{-1}\). This corresponds to option (D).