Read the passage carefully and answer.
The molar conductivity of a solution at any given concentration is the conductance of the volume of solution containing one mole of electrolyte kept between two platinum electrodes with unit area of cross-section and at a distance of unit length. Both conductivity and molar conductivity change with the concentration of the electrolyte. Kohlrausch examined \( Ʌ°_m \) values for a number of strong electrolytes and observed certain regularities. He noted that the difference in \( Ʌ°_m \) of the electrolytes NaX and KX for any X is nearly constant. On the basis of the above observations, he enunciated the Kohlrausch law of independent migration of ions.
The decrease in molar conductivity of a weak electrolyte on increasing the concentration for a fixed volume is due to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Increase in degree of dissociation on dilution
Molar conductivity, \( \Lambda_m \), measures the conducting power of all the ions given by one mole of electrolyte. For a weak electrolyte only a fraction \( \alpha \) (the degree of dissociation) of the molecules is ionised, so \( \Lambda_m \) depends on how many ions that mole actually gives.
For a weak acid such as acetic acid, the dissociation constant links \( \alpha \) with the concentration:
\( \displaystyle K_a = \frac{c\alpha^{2}}{1-\alpha} \approx c\alpha^{2} \)
\( \displaystyle \alpha \approx \sqrt{\frac{K_a}{c}} \)
\( K_a \) is constant at a given temperature, so when c increases, \( \alpha \) decreases; on dilution, \( \alpha \) increases. A larger concentration therefore means fewer ions per mole and a lower \( \Lambda_m \). Read the other way round, the change in \( \Lambda_m \) is due to the increase in the degree of dissociation on dilution.
Why the other options are incorrect
Option (2) Decrease in degree of dissociation on dilution — Incorrect. Dilution does the opposite: it raises \( \alpha \), since \( \alpha \approx \sqrt{K_a/c} \).
Option (3) Decrease in dissociation constant on increasing the concentration — Incorrect. The dissociation constant depends only on temperature; it does not change with concentration.
Option (4) Increase in dissociation constant on increasing the concentration — Incorrect. For the same reason, \( K_a \) stays constant; only \( \alpha \) changes.
NCERT (2026-27 edition):
Weak Electrolytes
