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What is Ostwald's law pf Dilution?

Dear Student,

Let’s study the equilibrium in a weak electrolyte such as CH3COOH.When acetic acid is dissolved in water, it dissociates partially into H+ or CH3COO– and ions and the following equilibrium is obtained.

CH3COOH + H2O<-----> CH3COO–  +  H3O+

Applying law of chemical equilibrium, In dilute solution, [H2O] is constant. The product of K and constant [H2O] is denoted as Ka, the ionization constant or dissociation constant of the acid is,Ka = [CH3COO–]×[H3O+]/[CH3COOH] …..(a) 

The fraction of total number of molecules of an electrolyte which ionise into ions is known as degree of dissociation/ionisation α.Let 'C" moles L–1 be the initial molar concentration of acetic acid and α be the degree of dissociation. Therefore, molar concentrations of different species before the ionisation and at equilibrium point are expressed as follows:  

                      CH3COOH (aq)<----> H3O+ (aq)  + CH3COO-(aq)  

Initial conc.            C                         0                          0

Conc. at equil      C(1- α)                  Cα                       Cα                             

Substituting the values of the equilibrium concentrations in equation (a),we get

Ka = Cα.Cα/C(1–α) 

     = C2α2/C(1–α) 

     = Cα2/1–α 

Since for weak electrolytes, the value of α is very small and can be neglected in comparison to 1 i.e., .1 – α = 1.Hence, we get

Kα = Cα2 or α = √Ka/C

Furher, if V is the volume of the solution in litres containing 1 mole of the electrolyte, 

C = 1/V. 

Hence we have

α =√KaV ......(b)

Similarly, for a weak base like NH4OH, we haveα = √Kb/C = √KbV ........(c)

From equations (b) and (c),we can conclude the following statement.

In case of a weak electrolyte at a given temperature, the degree of ionization is inversely proportional to the square root of the molar concentration or directly proportional to square root of the volume of the solution which contains one mole of the electrolyte. This is called Ostwald’s dilution Law. 

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 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 van 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.

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 As per the Arrhenius theory of electrolyte dissociation, the molecules of an electrolyte in a solution are continuously dissociating into ions and the ions are constantly reuniting to form unionized molecules. Hence, a dynamic equilibrium exists between the ions and unionized molecules of the electrolyte in a solution. Ostwald observed that like in chemical equilibrium, law of mass action can be applied to such systems as well.

Let us take the example of 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, the dissociation constant may be expressed 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, the degree of dissociation of a weak electrolyte is proportional to the square root of dilution.

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