Kohlrausch's Law — Core Principles

Core Principles

Kohlrausch's Law, also known as the Law of Independent Migration of Ions, is a fundamental principle in electrochemistry, stating that at infinite dilution, each ion in an electrolyte solution contributes independently to the total molar conductivity, regardless of its counter-ion.

This means the limiting molar conductivity ($\Lambda_m^\circ$) of an electrolyte is the sum of the limiting molar conductivities of its constituent ions, weighted by their stoichiometric coefficients.

Mathematically, for an electrolyte $A_x B_y$, $\Lambda_m^\circ = x\lambda_+^\circ + y\lambda_-^\circ$. This law is crucial because it allows for the indirect calculation of $\Lambda_m^\circ$ for weak electrolytes, which cannot be determined by simple extrapolation of conductivity plots.

Furthermore, it enables the determination of the degree of dissociation ($\alpha = \Lambda_m / \Lambda_m^\circ$), dissociation constants ($K_a = C\alpha^2 / (1-\alpha)$), and the solubility of sparingly soluble salts ($S = (\kappa \times 1000) / \Lambda_m^\circ$).

Understanding its application and limitations (strictly at infinite dilution) is vital for NEET aspirants.

Important Differences

vs Strong Electrolytes vs. Weak Electrolytes (in context of Kohlrausch's Law)

Aspect	This Topic	Strong Electrolytes vs. Weak Electrolytes (in context of Kohlrausch's Law)
Dissociation	Strong Electrolytes: Dissociate almost completely in solution at all concentrations.	Weak Electrolytes: Dissociate partially in solution, and their degree of dissociation increases with dilution.
$\Lambda_m$ vs. $\sqrt{C}$ plot	Strong Electrolytes: Shows a linear decrease in $\Lambda_m$ with $\sqrt{C}$ (Debye-Hückel-Onsager equation). $\Lambda_m^\circ$ can be found by extrapolation.	Weak Electrolytes: Shows a steep, non-linear curve in $\Lambda_m$ vs. $\sqrt{C}$ plot, making extrapolation to find $\Lambda_m^\circ$ impossible.
Direct $\Lambda_m^\circ$ determination	Strong Electrolytes: Yes, by extrapolation of $\Lambda_m$ vs. $\sqrt{C}$ plot.	Weak Electrolytes: No, cannot be determined directly by extrapolation.
Application of Kohlrausch's Law for $\Lambda_m^\circ$	Strong Electrolytes: Kohlrausch's Law can be used to calculate $\Lambda_m^\circ$ from individual ionic conductivities, but it's often directly measured.	Weak Electrolytes: Kohlrausch's Law is *essential* for calculating $\Lambda_m^\circ$ indirectly using $\Lambda_m^\circ$ values of strong electrolytes.
Degree of Dissociation ($\alpha$)	Strong Electrolytes: $\alpha \approx 1$ at all practical concentrations.	Weak Electrolytes: $\alpha = \Lambda_m / \Lambda_m^\circ$, which is less than 1 and varies with concentration.

The primary distinction in the context of Kohlrausch's Law lies in how their limiting molar conductivities ($\Lambda_m^\circ$) are determined. For strong electrolytes, $\Lambda_m^\circ$ can be found by simple graphical extrapolation of molar conductivity versus the square root of concentration. However, for weak electrolytes, due to their incomplete dissociation and the resulting non-linear behavior at low concentrations, direct extrapolation is not feasible. Kohlrausch's Law provides a crucial indirect method for weak electrolytes, allowing their $\Lambda_m^\circ$ to be calculated from the $\Lambda_m^\circ$ values of strong electrolytes. This distinction underpins many numerical applications of the law.