The conductivity of an electrolytic solution is measured with a conductivity cell, which has two electrodes a fixed distance l apart, each with an area of cross-section A. The resistance R of the cell is given by R = ρl/A = l/(κA), where ρ is the resistivity and κ the conductivity of the solution.
The quantity l/A is constant for a given cell; it is denoted by G* and is called the cell constant. It is found by measuring the resistance of the cell filled with a KCl solution whose conductivity is known accurately at various concentrations: G* = l/A = Rκ.
The molar conductivity of a solution, Λm, is its conductivity divided by its molar concentration (Λm = κ/c). Its SI unit is S m2 mol−1 when c is expressed in mol m−3. Conductivity always decreases with decrease in concentration, for both strong and weak electrolytes, because the number of ions per unit volume that carry the current in the solution decreases.
What happens to the molar conductivity when a solution of a weak electrolyte is diluted?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → It increases because the degree of dissociation increases, so one mole of the electrolyte gives more ions
Molar conductivity, Λm = κ/c, is the conducting power of all the ions given by one mole of the electrolyte. A weak electrolyte such as acetic acid is only partly dissociated, and its degree of dissociation increases on dilution:
\( \displaystyle \ce{CH3COOH <=> CH3COO^- + H^+} \)
So on dilution one mole of the acid gives more ions, and Λm increases steeply, most of all at low concentrations.
Why the other options are incorrect
Option (1) It decreases because the weak electrolyte becomes weaker — Incorrect. Dilution makes the electrolyte dissociate more, not less, and Λm rises.
Option (2) It decreases because a given volume contains less electrolyte — Incorrect. Fewer ions per unit volume lowers the conductivity κ, but Λm refers to one mole of electrolyte, and it increases.
Option (3) It increases because the conductivity of the solution increases on dilution — Incorrect. The direction is right but the reason is wrong: the conductivity decreases on dilution, for strong and weak electrolytes alike.
NCERT (2026-27 edition):
2.4.2 Variation of Conductivity and Molar Conductivity with Concentration – “Weak electrolytes like acetic acid have lower degree of dissociation at higher concentrations and hence for such electrolytes, the change in Λm with dilution is due to increase in the degree of dissociation and consequently the number of ions in total volume of solution that contains 1 mol of electrolyte.”