State and explain Kohlrausch's law of independent migration of ions.

Explanation

Statement of Kohlrausch's law : This states that of infinite dilution of the solution, each ion of an electrolyte migrates independently of its co-ions and contributes independently to the total molar conductivity of the electrolyte, irrespective of the nature of other ions present in te solution .
Explanation : Both the ions, cation and anion of the electrolyte make a definite contribution to the molar conductivity of the electrolyte at infinite dilution or zero concentration `(wedge_(0))`.
Of `lambda_(+)^(0)` and `lambda_(-)^(0)` are the molar conductivities of cation and nation respectively at infinite dilution, then
`wedge_(0) = lambda_(+)^(0) + lambda_(-)^(0)` .
This is known as Kohlrausch's law of independent migration of ions.
`wedge_(0KCl) = lambda_(K^(+))^(0) + lambda_(Cl^(-))^(0)` and `wedge_(0NaCl) = lambda_(Na^(+))^(0) + lambda_(Cl^(-))^(0)`
`:. wedge_(0KCl) - wedge_(0NaCl)`
`= (lambda_(K^(+))^(0) + lambda_(Cl^(-))^(0)) - (lambda_(Na^(+))^(0) + lambda_(Cl^(-))^(0)) = lambda_(K^(+))^(0) - lambda_(Na^(+))^(0) + lambda_(I^(-))^(0)`
`:. wedge_(0KI) - wedge_(0NAl) = (lambda_(K^(+))^(0) + lambda_(I^(-))^(0)) - (lambda_(Na^(+))^(0) + lambda_(I^(-))^(0))`
`= lambda_(K^(+))^(0) - lambda_(Na^(+))^(0) = 150.3 - 126.9 = 23.4`
Thus the difference in `wedge_(0)` values for `K^(+)` and `Na^(+)` salts is constant and is independent of the nature of other anions.
This proves the validity of Kohlrausch's law.