**Kohlrausch’s Law of independent migration of ions: **Kohlrausch’s law state that, **‘**At infinite dilution when the dissociation is complete, each ion makes a definite contribution towards molar conductance of the electrolyte irrespective of the nature of the other ion with which it is associated’.

This means that the molar conductance at infinite dilution for a given salt can be expressed as the sum of the contributions from the ions of the electrolyte. If molar conductivity of the cation is denoted by **λ _{+}^{α}** and that of anion by

**λ**then according to Kohlrausch’s law

_{–}^{α},Ʌ_{m}^{α} = υ_{+} λ_{+}^{α } + υ_{– }λ_{–}^{α}

Where, υ_{+}=Number of cation, υ_{– }= Number of anion, λ_{+}^{α }= molar conductivity of the cation, λ_{–}^{α}= molar conductivity of the anion

For example,

(1) One formula unit of NaCI furnishes one Na+ ion and one Cl^{–} ion, therefore,

Ʌ_{m}^{α}(NaCI) =λ^{α}_{Na +}+ λ ^{α}_{ Cl-}

(2) One formula unit of BaCl_{2} furnishes one Ba^{+2} ion and two Cl^{–} ion, therefore,

Ʌ_{m}^{α}(BaCI_{2}) =λ^{α}_{Ba +}+ 2λ^{α}_{ Cl-}

Applications of Kohlrausch’s Law:

1) In the determination of molar conductivity of weak electrolytes at infinite dilution:

Ʌ_{m}^{α} (CH_{3}COOH) =Ʌ_{m}^{α}(CH_{3}COO Na)+ Ʌ_{m}^{α}( HCl)– Ʌ_{m}^{α}(NaCl)

2) To calculate the degree of dissociation of weak electrolytes:

The degree of dissociation of weak electrolytes can be calculated at any concentration as:

α = Ʌ_{m}^{c} / Ʌ_{m}^{α}

Where α is the degree of dissociation, **Ʌ _{m}^{c }**is the molar conductance at concentration C and

**Ʌ**is the molar conductance at infinite dilution.

_{m}^{α }3) To calculate the dissociation constant of weak electrolytes:

4) To determine the solubility of sparingly soluble salt:

5) To determine the ionic product of water.