Kohlrausch's law is used for the determination of
(A). Molar conductivity of a weak electrolyte.
(B). Degree of dissociation of a weak electrolyte.
(C). Dissociation constant.
(D). Solubility of sparingly soluble salts.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B), (C) and (D)
Kohlrausch’s law of independent migration of ions states that the limiting molar conductivity of an electrolyte is the sum of the limiting molar conductivities of its cation and anion:
\( \displaystyle \Lambda_m^{\circ} = \nu_{+}\lambda_{+}^{\circ} + \nu_{-}\lambda_{-}^{\circ} \)
Its value for a weak electrolyte cannot be found by extrapolating a graph of \( \Lambda_m \) against \( \sqrt{c} \), because the curve rises steeply near zero concentration. The law gives it from the values for strong electrolytes, and from it the other quantities follow.
(A) Molar conductivity of a weak electrolyte. — Correct. The law gives the limiting molar conductivity (at infinite dilution) of a weak electrolyte, for example acetic acid:
\( \displaystyle \Lambda_m^{\circ}(\ce{CH3COOH}) = \Lambda_m^{\circ}(\ce{HCl}) + \Lambda_m^{\circ}(\ce{CH3COONa}) - \Lambda_m^{\circ}(\ce{NaCl}) \)
(B) Degree of dissociation of a weak electrolyte. — Correct. With the measured \( \Lambda_m \) at concentration c:
\( \displaystyle \alpha = \frac{\Lambda_m}{\Lambda_m^{\circ}} \)
(C) Dissociation constant. — Correct. For a weak acid such as acetic acid, using α from (B):
\( \displaystyle K_a = \frac{c\,\alpha^{2}}{1 - \alpha} \)
(D) Solubility of sparingly soluble salts. — Correct. A saturated solution of a salt such as AgCl is so dilute that \( \Lambda_m \approx \Lambda_m^{\circ} \), which Kohlrausch’s law gives from the ionic values. With the measured conductivity κ of the saturated solution, the solubility (in mol L−1) is:
\( \displaystyle S = \frac{1000\,\kappa}{\Lambda_m^{\circ}} \quad (\kappa \text{ in S cm}^{-1},\ \Lambda_m^{\circ} \text{ in S cm}^{2}\,\text{mol}^{-1}) \)
NCERT (2026-27 edition):
Applications of Kohlrausch Law
Variation of Conductivity and Molar Conductivity with Concentration – “… At infinite dilution (i.e., concentration c → zero) electrolyte dissociates completely (α = 1), but at such low concentration the conductivity of the solution is so low that it cannot be measured accurately. Therefore, Λ°m for weak electrolytes is obtained by using Kohlrausch law of independent migration of ions (Example 2.8). At any concentration c, if α is the degree of dissociation then it can be approximated to the ratio of molar conductivity Λm at the concentration c to limiting molar conductivity, Λ°m. Thus we have:
\( \displaystyle \alpha = \frac{\Lambda_m}{\Lambda_m^{\circ}} \)
But we know that for a weak electrolyte like acetic acid (Class XI, Unit 7),
\( \displaystyle K_a = \frac{c\alpha^2}{(1-\alpha)} = \frac{c\Lambda_m^2}{\Lambda_m^{\circ 2}\left(1-\frac{\Lambda_m}{\Lambda_m^{\circ}}\right)} = \frac{c\Lambda_m^2}{\Lambda_m^{\circ}\left(\Lambda_m^{\circ}-\Lambda_m\right)} \)”