Question

What is the cell constant of a cell containing a solution of resistance \(90\) Ohm with conductivity \(2\times 10^{-3}\ \text{Ohm}^{-1}\text{cm}^{-1}\)?

• A. \(0.50\ \text{cm}^{-1}\)
• B. \(0.18\ \text{cm}^{-1}\)
• C. \(0.029\ \text{cm}^{-1}\)
• D. \(0.70\ \text{cm}^{-1}\)

Hint:

Cell constant equals conductivity multiplied by the resistance of the solution in the cell.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Conductivity is \(\kappa=\dfrac{G^{*}}{R}\), where \(G^{*}\) is the cell constant. So \(G^{*}=\kappa R\).

Step 2: Substitute
\(\kappa=2\times10^{-3}\ \Omega^{-1}\text{cm}^{-1}\) and \(R=90\ \Omega\).

Step 3: Calculation
\(G^{*}=2\times10^{-3}\times90=0.18\ \text{cm}^{-1}\).

Final Answer:
The cell constant is 0.18 per cm. \[ \boxed{\text{(B) }0.18\ \text{cm}^{-1}} \]