State Kohlrausch law of independent migration of ions. Why does the conductivity of a solution decrease with dilution ?

Explanation

Kohlrausch law of independent migration of ions states that limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of anion and cation of the electrolyte.
If `Lambda_(Na^(+))^(@)` and `Lambda_(Cl^(-))^(@)` are the limiting molar conductivities for sodium and chloride ions respectively, then limiting molar conductivity for sodium chloride is given by the equation :
`Lambda_(m)^(@) (NaCl) = lambda_(Na^(+))^(@) + lambda_(Cl^(-))^(@)`
Conductivity of a solution decreases with dilution because the number of ions per unit volume of the solution decreases.