Question

The resistance of the cell containing the aqueous solution of NaCl at 20°C is 60 ohm. If the specific conductivity of this solution at 20°C is 0.04 ohm^-1.cm^-1,what is the cell constant in cm^-1? 

• A. 2.5
• B. 1.5
• C. 0.5
• D. 0.15
• E. 2.4

Answer 1

Answer: (E)

Given parameters:

• Resistance \( R = 60 \, \Omega \)
• Specific conductivity \( \kappa = 0.04 \, \Omega^{-1}cm^{-1} \)

 

Cell constant formula: \[ \text{Cell constant} (G) = \kappa \times R \]

Calculation: \[ G = 0.04 \, \Omega^{-1}cm^{-1} \times 60 \, \Omega \] \[ G = 2.4 \, cm^{-1} \]

Thus, the correct option is (E): 2.4.

Answer 2

1. Relationship between resistance, specific conductivity, and cell constant:

The relationship between the resistance (\(R\)), specific conductivity (\(\kappa\)), and cell constant (\(G^*\)) is given by:

\[G^* = \kappa \cdot R\]

where:

• \(G^*\) is the cell constant in \(cm^{-1}\)
• \(\kappa\) is the specific conductivity in \(ohm^{-1} \cdot cm^{-1}\)
• \(R\) is the resistance in \(ohms\)

2. Substitute the given values:

\(\kappa = 0.04 \, ohm^{-1} \cdot cm^{-1}\)

\(R = 60 \, ohms\)

\[G^* = 0.04 \cdot 60\]

3. Perform the calculation:

\[G^* = 2.4 \, cm^{-1}\]

4. Final answer:

The cell constant is 2.4 \(cm^{-1}\).