Question

The molar conductivity of 0.02 M solution of an electrolyte is \( 124 \times 10^{-4} \) S m\(^{2}\) mol\(^{-1}\). What is the resistance of the same solution (in ohms), kept in a cell of cell constant 129 m\(^{-1}\)?

• A. 390
• B. 130
• C. 260
• D. 520
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Hint:

Resistance is calculated using \( R = \frac{\text{Cell Constant}}{\kappa} \), where \( \kappa \) is conductivity.

Answer 1

The Correct Option is D

Step 1: Using the Conductivity and Resistance Relation
\[ \kappa = \frac{\lambda_m \times c}{1000} \] where, \( \kappa \) = conductivity
\( \lambda_m \) = molar conductivity = \( 124 \times 10^{-4} \) S m\(^{2}\) mol\(^{-1}\)
\( c \) = 0.02 M
Step 2: Finding Conductivity
\[ \kappa = \frac{(124 \times 10^{-4}) \times 0.02}{1000} \] \[ \kappa = 2.48 \times 10^{-4} \text{ S m}^{-1} \] Step 3: Finding Resistance
\[ R = \frac{\text{Cell Constant}}{\kappa} = \frac{129}{2.48 \times 10^{-4}} \] \[ R = 520 \text{ ohms} \] Thus, the resistance is 520 ohms.
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