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 cell constant (G*) is a property of the conductivity cell and is given by the formula: G* = Conductivity (\(\kappa\)) × Resistance (R).

Step 2: Detailed Explanation:
Given: Resistance, R = 100 \(\Omega\) Conductivity, \(\kappa = 1.29 \, S m^{-1}\) Cell constant, G* = \(\kappa \times R = 1.29 \, S m^{-1} \times 100 \, \Omega = 129 \, m^{-1}\). Now, convert \(m^{-1}\) to \(cm^{-1}\). Since 1 m = 100 cm, \(1 m^{-1} = 0.01 cm^{-1}\). Therefore, \(129 m^{-1} = 129 \times 0.01 cm^{-1} = 1.29 cm^{-1}\).

Step 3: Final Answer:
The cell constant is \(1.29 cm^{-1}\).