# Kohlrausch Law

## What is Kohlrausch Law?

Kohlrausch’s law states that the equivalent conductivity of an electrolyte at infinite dilution is equal to the sum of the conductances of the anions and cations.

The molar conductivity of a solution at a given concentration is the conductance of the volume of solution containing one mole of electrolyte kept between two electrodes with the unit area of cross-section and distance of unit length. The molar conductivity of a solution increases with the decrease in concentration. This increase in molar conductivity is because of the increase in the total volume containing one mole of the electrolyte. When the concentration of the electrolyte approaches zero, the molar conductivity is known as limiting molar conductivity, Ëm°.

Kohlrausch observed certain regularities while comparing the values of limiting molar conductivities of some strong electrolytes. On the basis of his observations, Kohlrausch proposed “limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anions and cations of the electrolyte”. This law is popularly known as Kohlrausch law of independent migration of ions. For example, limiting molar conductivity, Ëm° of sodium chloride can be determined with the knowledge of limiting molar conductivities of sodium ion and chloride ion. Some important applications of Kohlrausch law of independent migration of ions are:

1. Kohlrausch law helps us in the determination of limiting molar conductivities for any electrolyte. Weak electrolytes have lower molar conductivities and lower degree of dissociation at higher concentrations. The graph plotted between molar conductivity and c1/2 (where c is the concentration) is not a straight line for weak electrolytes. The molar conductivity of weak electrolyte increases steeply at lower concentrations. Therefore, limiting molar conductivity, Ëm° cannot be obtained by extrapolation of molar conductivity to zero concentration. Hence, we use the Kohlrausch law of independent migration of ions for the determination of limiting molar conductivity, Ëm° for weak electrolytes.
1. Kohlrausch law also helps us in determining the value of dissociation constant from the value of molar conductivity and limiting molar conductivity for a weak electrolyte at a given concentration.

α =  $\frac {Λ}{{Ë_m}^\circ}$

Where, α = dissociation constant

Λ = molar conductivity

Ëm° = limiting molar conductivity

### Uses of Kohlrausch’s law

• Calculation of Degree of dissociation
• Calculation of solubility of sparingly soluble salt
• Calculation of Dissociation Constant for week electrolytes
• Calculation of Molar Conductivity for week electrolytes at infinite dilution