Question

Given below is the plot of the molar conductivity vs \( \sqrt{c} \) concentration for KCl in aqueous solution. If, for the higher concentration of KCl solution, the resistance of the conductivity cell is 100 \( \Omega \), then the resistance of the same cell with the dilute solution is 'x' \( \Omega \). The value of \( x \) is:

Hint:

Molar conductivity and resistance are inversely related in a conductive solution; use the graph for quick estimates.

Answer 1

Correct Answer: 150

Mathematical Derivation

\[ \Lambda_m = \frac{K \times 1000}{C} \]

\[ 100 = \frac{K \times 1000}{0.0225} \]

\[ K = \frac{0.0225}{10} = \frac{1}{R} \times \frac{\ell}{A} \]

\[ \frac{\ell}{A} = \frac{0.0225}{10} \times 100 = 0.0225 \]

For lower concentration:

\[ \Lambda_m = \frac{K \times 1000}{C} \]

\[ 150 = \frac{K \times 1000}{0.01} \]

\[ K = \frac{0.15}{100} \]

\[ K = \frac{1}{R} \times \frac{\ell}{A} \]

\[ \frac{0.15}{100} = \frac{1}{R} \times 0.225 \]

\[ R = \frac{22.5}{0.15} = \frac{2250}{15} = 150\,\Omega \]