Law of dilution

Wilhelm Ostwald’s dilution law is a relationship between the dissociation constant and the degree of dissociation of a weak electrolyte (acids, bases).

$\mathsf{K_p = \frac{c(K^+) \cdot c(A^-)}{c(KA)} = \frac{\alpha^2}{1-\alpha} \cdot c_0}$

where:

• K_p: constant of protolysis
• α: degree of dissociation (or degree of protolysis)
• c(A^-): concentrations of anions
• c(K⁺): concentration of cations
• c₀: overall concentration
• c(KA): concentration of associated electrolyte.

Concerning conductivity, this results in the following relation:

$\frac{\Lambda_c^2}{(\Lambda_0 - \Lambda_c)\Lambda_0}\cdot c = K_c$ According to Arrhenius theory of electrolyte dissociation, the molecules of an electrolyte in solution are constantly splitting up into ions and the ions are constantly reuniting to form unionized molecules. Therefore, a dynamic equilibrium exists between ions and unionized molecules of the electrolyte in solution. It was pointed out by Ostwald that like chemical equilibrium, law of mass action can be applied to such systems also.

Consider a binary electrolyte AB which dissociates into A+ and B- ions and the equilibrium state is represented by the equation:

                               AB ↔  A+ + B-

       Initially t = o       C         0     0

       At equilibrium     C(1-α)   Cα    Cα

So, dissociation constant may be given as

               K = [A+][B-]/[AB] = (Cα * Cα)/C(1-α)

                  =   Cα2 /(1-α)                                         ....... (i)

For very weak electrolytes,

                α <<< 1,  (1 - α ) = 1

      .·.                    K = Cα2

                             α = √K/C                             ....... (ii)

Concentration of any ion = Cα = √CK .

From equation (ii) it is a clear that degree of ionization increases on dilution.

Thus, degree of dissociation of a weak electrolyte is proportional to the square root of dilution.

Limitations of Ostwald's dilution law:

The law holds good only for weak electrolytes and fails completely in the case of strong electrolytes. The value of 'α' is determined by conductivity measurements by applying the formula Λ/Λ∞. The value of 'α' determined at various dilutions of an electrolyte when substituted in Eq. (i) gives a constant value of K only in the case of weak electrolytes like CH3COOH, NH4OH, etc. the cause of failure of Ostwald's dilution law in the case of strong electrolytes is due to the following factors"

(i) The law is based on the fact that only a portion of the electrolyte is dissociated into ions at ordinary dilution and completely at infinite dilution. Strong electrolytes are almost completely ionized at all dilutions and Λ/Λ∞ does not give accurate value of 'α'.

(ii) When concentration of the ions is very high, the presence of charges on the ions appreciably effects the equilibrium. Hence, law of mass action its simple form cannot be strictly applied in the case of strong electrolytes.

• K_c: constant of dissociation
• Λ_c: equivalent conductivity
• Λ₀: boundary conductivity
• c: concentration of electrolyte.

See also

Autosolvolysis