Kohlrausch law of independent migration of ions

Kohlrausch's law of independent migration of ions states that at infinite dilution each ion migrates independently of its co-ion, and contributes to the total molar conductivity of the electrolyte irrespective of the nature of the other ion to which it is associated.

Both the cation and the anion contribute to the molar conductivity of the electrolyte at zero concentration; $\Lambda_0$ is thus the sum of the molar conductivity of the cation and that of the anion at zero concentration:

where $\lambda^0_{+}$ and $\lambda^0_{-}$ are the molar conductivities of the cation and anion respectively, and $n_{+}$ and $n_{-}$ are the number of moles of cation and anion specified in the chemical formula of the electrolyte.

Applications of Kohlrausch theory

1. The theory can be used to calculate the molar conductivity of an electrolyte at zero concentration. For example,

Knowing the molar conductivities of the ions at infinite dilution, the $\Lambda_0$ value of the electrolyte can be obtained.

2. The theory is particularly useful in calculating $\Lambda_0$ values of weak electrolytes from those of strong electrolytes. For example, $\Lambda_0$ of acetic acid can be calculated by knowing those of HCl, NaCl and $\mathrm{CH_3COONa}$, as described below:

$\Lambda_0(\mathrm{HCl}) + \Lambda_0(\mathrm{CH_3COONa}) - \Lambda_0(\mathrm{NaCl})$ …