On dilution, the conductivity (κ) of a solution of an electrolyte decreases, but its molar conductivity (Λm) increases. Which of the following explains the increase in Λm?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → The volume of solution containing one mole of the electrolyte increases, and this more than makes up for the decrease in κ
Molar conductivity is the conductance of the volume V of solution that contains one mole of the electrolyte, placed between electrodes at unit distance:
\( \displaystyle \Lambda_m = \kappa\, V \qquad (2.22) \)
On dilution κ falls, but V, the volume holding one mole, rises more. So the product κV, and with it Λm, increases.
Why the other options are incorrect
Option (1) The number of ions per unit volume that carry the current increases on dilution — Incorrect. On dilution the number of ions per unit volume decreases; that is the reason the conductivity κ falls.
Option (2) The cell constant of the conductivity cell increases on dilution — Incorrect. The cell constant, G* = l/A, depends only on the distance between the electrodes and their area, not on the solution.
Option (4) The limiting molar conductivity (Λ°m) of the electrolyte increases on dilution — Incorrect. Λ°m is the limiting value of Λm as the concentration approaches zero; it is a fixed value for the electrolyte, not something that changes with dilution.
NCERT (2026-27 edition):
2.4.2 Variation of Conductivity and Molar Conductivity with Concentration – “…This can be explained by the fact that the number of ions per unit volume that carry the current in a solution decreases on dilution.”
“…Molar conductivity increases with decrease in concentration. This is because the total volume, V, of solution containing one mole of electrolyte also increases. It has been found that decrease in κ on dilution of a solution is more than compensated by increase in its volume.”