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:
\(\Lambda^{\circ}_m(\text{CH}_3\text{COOH}) = \Lambda^{\circ}_m(\text{CH}_3\text{COONa}) + \Lambda^{\circ}_m(\text{HCl}) - \Lambda^{\circ}_m(\text{NaCl})\)
Which equation gives the variation of the molar conductivity (Λm) of a strong electrolyte with its concentration (c)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\Lambda_m = \Lambda^{\circ}_m - A\sqrt{c}\)
For a strong electrolyte, the molar conductivity Λm increases slowly on dilution and reaches the limiting value Λ°m as c approaches zero. Its fall from Λ°m is proportional to the square root of the concentration, which gives Option (1).
Why the other options are incorrect
Option (2) \(\Lambda^{\circ}_m = \Lambda_m - A\sqrt{c}\) — Incorrect. This gives \( \Lambda_m=\Lambda^{\circ}_m+A\sqrt{c} \), so Λm would rise with concentration; in fact it falls.
Option (3) \(\Lambda_m = A\sqrt{c} - \Lambda^{\circ}_m\) — Incorrect. At infinite dilution (c → 0) this gives \( \Lambda_m=-\Lambda^{\circ}_m \), a negative molar conductivity, which is impossible.
Option (4) \(\Lambda_m = \Lambda^{\circ}_m - Ac\) — Incorrect. The fall in Λm goes with c1/2, not c; Λm plotted against c is not a straight line.
NCERT (2026-27 edition):
2.4.2 Variation of Conductivity and Molar Conductivity with Concentration – “For strong electrolytes, Λm increases slowly with dilution and can be represented by the equation:
\( \displaystyle \Lambda_m=\Lambda^{\circ}_m-A\,c^{1/2} \qquad (2.23) \)
It can be seen that if we plot … Λm against c1/2, we obtain a straight line with intercept equal to Λ°m and slope equal to ‘–A’.”