SOLUBILITY PRODUCT:

If to a given amount of solvent at a particular temperature, a solute is added gradually in increasing amounts, a stage is reached when some of the solute remains undissolved, no matter how long we wait or how vigorously we stir. The solution is then said to be saturated. A solution which remains in contact with undissolved solute is said to be saturated. At saturated stage, the quantity of the solute dissolved is always constant for the given amount of a particular solvent at a definite temperature.

In case the solute is an electrolyte, its ionisation occurs in solution and degree of dissociation depends on the concentra­tion of dissolved electrolyte at a particular temperature. Thus, in a saturated solution of an electrolyte two equilibria exist and can be represented as:

AB  ↔  AB    ↔         

Solid  unionized           ions

  (dissolved)

Applying the law of action to the ionic equilibrium,

  [A⁺][B^-]/[AB]

Since the solution is saturated, the concentration of unionised molecules of the electrolyte is constant at a particular temperature, i.e., [AB] = K'= constant.

Hence, [A⁺] [B^-] = K[AB] = KK = K_s (constant)

K_s is termed as the solubility product. It is defined as the product of the concentration of ions in a saturated solution of an electrolyte at a given temperature.

Consider, in general, the electrolyte of the type A_xB_y which is dissociated as:

A_xB_y ↔ xA^y+ + yB^x-

Applying law of mass action,

[Ay+]x[Bx-]y/[A_xB_y] = K

     When the solution is saturated,

[A_xB_y] = K' (constant)

or     [A^y+]^x[B^x-]^y = K [A_xB_y] = KK' = K_s (constant)

Thus, solubility product is defined as the product of concentrations of the ions raised to a power equal to the number of times the ions occur in the equation representing the dissociation of the electrolyte at a given temperature when the solution is saturated.

Note:  Solubility product is not the ionic product under all conditions but only when the solution is saturated.