The specific conductance of a N/10 KCl solution at 18°C is 1.12 x10^–2 mho cm^–1. The resistance of the solution contained in the cell is found to be 65 ohms. Calculate the cell constant.

0.728 cm^–1

The correct answer is option 3. 0.728 cm^–1.

Given:
Resistance ($R$) = 65 $\Omega$

Conductance ($C$) is the reciprocal of resistance:

\(C = \frac{1}{R} = \frac{1}{65 \, \Omega} \approx 0.015385 \, \Omega^{-1}\)

The cell constant ($K$) is the ratio of specific conductance to conductance:

\(K = \frac{\text{specific conductance}}{\text{conductance}}\)

Given:
Specific conductance = $1.12 \times 10^{-2} {mho\text{ } cm^{-1}}$

Converting the specific conductance to $\Omega^{-1} cm^{-1}$:

Specific conductance = $1.12 \times 10^{-2} \Omega^{-1}  cm^{-1}$

Substituting the values into the equation:

\(K = \frac{1.12 \times 10^{-2}  \Omega^{-1} cm^{-1}}{0.015385  \Omega^{-1}}\)

Simplifying:

\(K \approx 0.728 cm^{-1}\)

Therefore, the cell constant is approximately (3) 0.728 cm$^{-1}$.