In 1874, Kohlrausch formulated the law of independent migration of ions based on the experimental data of conductivities of various electrolytes. This law can be stated as follows:

*At infinite dilution, the dissociation of the electrolyte is complete
and hence each ion makes definite
contribution to the equivalent conductivity of the electrolyte irrespective of
the nature of other ions associated with it. *

*Therefore the limiting equivalent conductivity of an
electrolyte is the algebraic sum of limiting equivalent conductivities of its constituent ions.*

i.e., The limiting equivalent conductivity of an electrolyte, Λ_{o}^{electrolyte}

Where λ_{o}^{+} and λ_{o}^{-}
are the limiting equivalent conductivities of cation and anion respectively.

However the Kohlrausch law can also be stated in terms of molar conductivities as:

**The limiting molar conductivity of an electrolyte is the sum of
individual contributions of limiting molar conductivities of its constituent
ions.**

i.e., The molar equivalent conductivity of an electrolyte, μ_{o}^{electrolyte}

Where μ_{o}^{+} and μ_{o}^{-}
are the limiting molar conductivities of cation and anion respectively.

And n_{+} and n_{-} are the stoichiometric numbers of
positive and negative ions formed during the dissociation of electrolyte.

Kohlrausch observed that at infinite dilutions, the difference between the conductivities of sodium and potassium salts is constant irrespective of the associated anions, as tabulated below.

Salt
pair |
Conductivity
(mho cm ^{2} equiv) |
Difference |

NaCl | 108.90 | 21.20 |

KCl | 130.10 | |

NaNO_{3} |
105.33 | 21.17 |

KNO_{3} |
126.50 | |

NaBr | 111.10 | 21.20 |

KBr | 132.30 |

Kohlrausch argued that the constant difference in the conductivities of above pairs can be ascribed to the fact that the mobility of sodium and potassium ions at infinite dilution is not influenced by the nature of counter ions. The ions at such a low concentration migrate in the electric field as they are independent i.e., they show same ionic conductance irrespective of the nature of counter ion.

**1) Calculation of limiting conductivities of weak
electrolytes:** The Kohlrausch law can be used to calculate the limiting conductivities of
weak electrolytes.

E.g., The calculation of limiting equivalent conductance of acetic acid, a weak electrolyte is illustrated below.

According to Kohlrausch law, the limiting equivalent conductance values of CH_{3}COOH,
CH_{3}COONa, HCl and NaCl can be written as follows:

Therefore

**2) Determination of degree of ionization (α)
of weak electrolyte: **The degree of ionization of a weak electrolyte
at a particular concentration is equal to the ratio of actual number of ions
formed due to partial ionization to the expected number of ions formed upon
complete dissociation.

Since the conductance is proportional to the number of ions in the solution, the degree of ionization is equal to the conductance ratio as given below.

Where

Λ_{c}= equivalent conductivity at given concentration.

Λ_{o}= limiting equivalent conductivity.

λ_{o}^{+} = limiting equivalent
conductivity of cation.

λ_{o}^{-} = limiting equivalent
conductivity of anion.