247. How the Kohlrausch’s law is used to determine the degree of ionization of weak electrolyte?

 Kohlrausch’s law of independent migration of ions states molar conductivity of an electrolyte at infinite dilution can be expressed as the sum of the contribution of individual ions. If molar conductivity of cations and anions are represented by λ^∞₊ and λ^∞_– respectively.

${\mathrm{\lambda }}_{\mathrm{m}}^{\infty } ={\mathrm{V}}_{+}{\mathrm{\lambda }}_{+}^{\infty } + {\mathrm{V}}_{-}{\mathrm{\lambda }}_{+}^{\infty }$

where v₊ and v_– are number of cations and anions per formula of electrolyte e.g.,

Λ^∞ CaCl₂ = λ^∞ (Ca²⁺) + 2 λ^∞ (CI^–)
Λ = KCl = λ^∞ (K⁺) + λ^∞ (CI^–)

Uses 1. It is used to find molar conductivity of weak electrolyte at infinite dilution which 
cannot be obtained by extrapolation.

2. It is used to calculate degree of dissociation of weak electrolyte at a particular concentration.
Degree of dissociation 
$\mathrm{\alpha } =\frac{{\mathrm{\Lambda }}_{\mathrm{m}}}{{\mathrm{\Lambda }}_{\mathrm{m}}^{°}}$
where Λ_m is molar conductivity of weak electrolyte at a particular concentration and Λ^e_mis molar conductivity of weak electrolyte at infinite dilution.