Wilhelm Ostwald’s dilution law is a relationship proposed in 1888 between the dissociation constant Kd and the degree of dissociation α of a weak electrolyte. The law takes the form
K d = [ A + ] [ B − ] [ AB ] = α 2 1 − α ⋅ c 0 {\displaystyle K_{d}={\cfrac {{\ce {[A+] [B^{-}]}}}{{\ce {[AB]}}}}={\frac {\alpha ^{2}}{1-\alpha }}\cdot c_{0}}
Where the square brackets denote concentration, and c0 is the total concentration of electrolyte. Using α = Λ c / Λ 0 {\displaystyle \alpha =\Lambda _{c}/\Lambda _{0}} , where Λ c {\displaystyle \Lambda _{c}} is the molar conductivity at concentration c and Λ 0 {\displaystyle \Lambda _{0}} is the limiting value of molar conductivity extrapolated to zero concentration or infinite dilution, this results in the following relation:
K d = Λ c 2 ( Λ 0 − Λ c ) Λ 0 ⋅ c 0 {\displaystyle K_{d}={\cfrac {\Lambda _{c}^{2}}{(\Lambda _{0}-\Lambda _{c})\Lambda _{0}}}\cdot c_{0}}
Derivation Consider a binary electrolyte AB which dissociates reversibly into A+ and B− ions. Ostwald noted that the law of mass action can be applied to such systems as dissociating electrolytes. The equilibrium state is represented by the equation:
AB ↽ − − ⇀ A + + B − {\displaystyle {\ce {AB <=> {A+}+ B^-}}}
If α is the fraction of dissociated electrolyte, then αc0 is the concentration of each ionic species. (1 - α) must, therefore be the fraction of undissociated electrolyte, and (1 - α)c0 the concentration of same. The dissociation constant may therefore be given as
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