Kohlrausch examined the limiting molar conductivity (Λ°m) of a number of strong electrolytes and observed certain regularities. On the basis of these observations he enunciated the Kohlrausch law of independent migration of ions. The law states that the limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and the cation of the electrolyte. Thus, for sodium chloride:
\(\Lambda^{\circ}_m(\text{NaCl}) = \lambda^{\circ}_{\text{Na}^+} + \lambda^{\circ}_{\text{Cl}^-}\)
Using the Kohlrausch law, it is possible to calculate Λ°m for any electrolyte from the λ° of its individual ions. For a weak electrolyte such as acetic acid, Λ°m can also be obtained from the Λ°m values of strong electrolytes:
\(\Lambda^{\circ}_m(\text{CH}_3\text{COOH}) = \Lambda^{\circ}_m(\text{CH}_3\text{COONa}) + \Lambda^{\circ}_m(\text{HCl}) - \Lambda^{\circ}_m(\text{NaCl})\)
According to the Kohlrausch law, the limiting molar conductivity (Λ°m) of an electrolyte A2B, which dissociates into A+ and B2− ions, is given by
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(2\lambda^{\circ}_{A^+} + \lambda^{\circ}_{B^{2-}}\)
By the Kohlrausch law of independent migration of ions, each ion adds its own limiting molar conductivity, once for every ion that one formula unit gives on dissociation:
\( \displaystyle \Lambda^{\circ}_m=\nu_+\lambda^{\circ}_+ + \nu_-\lambda^{\circ}_- \)
\( \ce{A2B} \) gives two \( \ce{A^+} \) ions and one \( \ce{B^2-} \) ion:
\( \displaystyle \ce{A2B -> 2A^+ + B^2-} \qquad \nu_+=2,\ \nu_-=1 \)
\( \displaystyle \Lambda^{\circ}_m(\ce{A2B})=2\lambda^{\circ}_{A^+}+\lambda^{\circ}_{B^{2-}} \)
NCERT (2026-27 edition):
2.4.2 Variation of Conductivity and Molar Conductivity with Concentration – “… In general, if an electrolyte on dissociation gives ν+ cations and ν− anions then its limiting molar conductivity is given by:
\( \displaystyle \Lambda^{\circ}_m=\nu_+\lambda^{\circ}_+ + \nu_-\lambda^{\circ}_- \qquad (2.25) \)
Here, λ°+ and λ°− are the limiting molar conductivities of the cation and anion respectively.”