Ostwald's dilution law

The strength of an acid or a base is experimentally measured by determining the dissociation or ionisation constant. 

When acetic acid (a weak electrolyte) is dissolved in water, it dissociates partially into H⁺ or H3O⁺ and CH3COO^- ions and the following equilibrium is obtained,

Applying law of chemical equilibrium, 

In dilute solution, [H₂O] is constant. The product of K and constant [H₂O] is denoted as K_a, the ionization constant or dissociation constant of the acid is,

                            .....(i)

The fraction of the total amount of molecules of an electrolyte which ionise into the ions is called as degree of dissociation/ionisation α.

If 'C' represents the initial concentration of the acid in moles L^-1 and α degree of dissociation, then the equilibrium concentration of ions (CH₃COO^- and H₃O⁺) is equal to the Cα and that of the undissociated acetic acid

= C(1-α) i.e., we have

Initial conc      C                                 0                     0

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

Putting the values of the equilibrium concentrations in equation one we get

                     .....(ii)

In case of weak electrolytes, the value of α is very small and can be neglected in comparison to 1 which means 1- α = 1.

Hence, we obtain

                                .....(iii)

The degree of dissociation, α can therefore be calcualted at a given concentration, C if K_a is known. Furher, if V is the volume of the solution in litres containing 1 mole of the electrolyte, C=1/V. Hence we have

                                                      .....(iv)

Similarly, for a weak base like NH₄OH, we have

                              .....(v)

The equations given above lead to the following result

"For a weak electrolyte, the degree of ionisation is inversely proportional to the square root of molar concentration or directly proportional to the square root of volume containing one mole of the solute."

This is called Ostwald's dilution law.

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