**Independent Migration of Ions: Kohlrausch’s Law**

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.*

Kohlrausch examined the values of Λ^{0}_{m} of a number of strong electrolytes with common anions or cations and found some regularity in the Λ^{0}_{m} values of various electrolytes. He observed that when the electrolytes were considered in pairs having one common ion the difference between the Λ^{0}_{m} values were constant (Table).

Table: Differences in values of Λ^{0}_{m} for several pairs of electrolytes with a common ion.

These observations led Kohlrausch (1875) to state that the molar conductance at infinite dilution is different for different electrolytes and is equal to the sum of the conductance of the constituent ions of the electrolytes. This is known as the Kohlrausch’s law of independent ionic migration. The law may be expressed in the form

**Λ ^{0}_{m} = λ^{0}_{+} + λ^{0}_{–}**

Where λ^{0}_{+} and λ^{0}_{–} are called the ion conductance of the cation and anion respectively. The above equation means that each ion of an electrolyte contributes independently to the value of Λ^{0}_{m} at infinite dilution. For example, the molar conductance of KCl at infinite dilution is 149.86 Ω^{-1} cm^{2}mol^{-1}. The ion conductance’s of K^{+} and Cl^{–} are 73.50 and 76.30 Ω^{-1} cm^{2}mol^{-1}. According to Kohlrausch law independent ionic migration,

Λ^{0}_{m(KCl)} = λ^{0}_{K+} + λ^{0}_{Cl-}

= 73.50 + 76.30 Ω^{-1} cm^{2}mol^{-1}

= 149.80 Ω^{-1} cm^{2}mol^{-1}

this is in agreement with the value measured directly. The Kohlrausch’s law of independent ionic migration is useful for calculation of Λ° for weak electrolytes for which Λ^{0}_{m} cannot be ascertained from the plot of Λ_{m} vs √C as shown in Table.

Table: Ion conductance at 25°C

The computation is done by addition and subtraction of Λ_{0} values for different strong electrolysis.