The resistance of 1N solution of four different electrolytes are given below. Arrange them in increasing order of their equivalent conductance values if the same conductivity cell was used to measure the resistance of all the electrolytic solutions:
(A) 250 ohm
(B) 150 ohm
(C) 50 ohm
(D) 280 ohm
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (D), (A), (B), (C)
The conductivity of a solution is obtained from its resistance and the cell constant \( G^* = l/A \) of the conductivity cell. The equivalent conductance is the conductivity divided by the concentration in equivalents:
\( \displaystyle \kappa = \frac{G^*}{R} \)
\( \displaystyle \Lambda_{eq} = \frac{\kappa \times 1000}{N} = \frac{G^* \times 1000}{R\,N} \)
Here the same cell is used (same \( G^* \)) and every solution is 1 N (same N). So \( \Lambda_{eq} \) is inversely proportional to the resistance: the higher the resistance, the lower the equivalent conductance.
\( \displaystyle R:\ \text{(D) } 280 \gt \text{(A) } 250 \gt \text{(B) } 150 \gt \text{(C) } 50\ \Omega \)
\( \displaystyle \Lambda_{eq}:\ \text{(D)} \lt \text{(A)} \lt \text{(B)} \lt \text{(C)} \)
Shortcut: The order of increasing conductance is the order of decreasing resistance: it starts with the 280 Ω solution (D) and ends with the 50 Ω solution (C). Only Option (3) does this.
Note: The question is from beyond the NCERT textbook.