Kohlrausch's law, also known as the law of independent migration of ions, is an important principle in electrochemistry. It states that at infinite dilution, the ionic conductivity of ions is additive. Let's break down the key points to understand this law in detail:

1. Definition of Kohlrausch's Law:
Kohlrausch's law states that the molar conductivity of an electrolyte at infinite dilution is equal to the sum of the molar conductivities of its constituent ions. In other words, the conductivity of an electrolyte solution can be determined by adding up the contributions of its individual ions.

2. Infinite Dilution:
Infinite dilution refers to a scenario where the concentration of an electrolyte is extremely low, approaching zero. At this point, the interactions between ions and solvent molecules are minimized, and the ions behave independently.

3. Ionic Conductivity:
Ionic conductivity is a measure of the ability of ions to carry an electric current through a solution. It depends on the concentration, charge, and mobility of ions. Each ion has its own specific conductivity, and their sum determines the overall conductivity of the electrolyte.

4. Additivity of Ionic Conductivity:
According to Kohlrausch's law, the conductivity of an electrolyte solution is determined by the individual contributions of its constituent ions. This means that the total conductivity of an electrolyte can be calculated by adding up the conductivities of its cations and anions.

5. Mathematical Expression:
Kohlrausch's law can be mathematically expressed as:
Λm = Λ+ + Λ-
where Λm is the molar conductivity of the electrolyte at infinite dilution, Λ+ is the molar conductivity of the cation, and Λ- is the molar conductivity of the anion.

6. Implications of Kohlrausch's Law:
Kohlrausch's law has several important implications in the field of electrochemistry. It allows for the determination of molar conductivity at infinite dilution, which is a fundamental property used to characterize electrolytes. It also provides insights into the behavior of ions in solution and helps in the understanding of conductivity measurements.

In conclusion, Kohlrausch's law states that at infinite dilution, the ionic conductivity of ions is additive. This principle allows for the determination of the molar conductivity of an electrolyte by summing up the contributions of its constituent ions. It is an important concept in electrochemistry and provides valuable insights into the behavior of ions in solution.