Kohlrausch’s Law

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_–^α, then according to Kohlrausch’s law

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 BaCl₂ furnishes one Ba⁺² ion and two Cl^– ion, therefore,

Ʌ_m^α(BaCI₂) =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 (CH₃COOH) =Ʌ_m^α(CH₃COO 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_m^α is the molar conductance at infinite dilution.

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.