When a sparingly soluble salt is dissolved in water then even in the saturated solution, the concentration of the salt is very low. So, whatever little of electrolyte goes into solution, undergoes complete dissociation (due to low concentration). Therefore, in saturated solutions of such electrolytes, the solid electrolyte is in equilibrium with the ions as represented below:
For example, in aqueous solution of silver chloride, following equilibrium exists:
Applying law of chemical equilibrium
K = [Ag+] [Cl -] / [Ag Cl]
The concentration of the undissolved salt is constant (say k) at a particular temperature regardless of the amount of solid silver chloride present. (This is true for any solid that its concentration is independent of the amount of solid). We, therefore, have
K = [Ag +] [ Cl -] / k
The constant K sp is known as the solubility product constant. It is equal to the product of ionic concentrations, termed as ionic product, for a saturated solution. The solubility product constant, K sp’ is the equilibrium constant for the solubility equilibrium of a sparingly soluble ionic compound. In general, for any sparingly soluble salt Ax BY, which dissociates to set up the equilibrium
the solubility product constant may be expressed as:
K SP = [AY+ ]x [ B x-] y
where AY+ and B x- denote the positive and negative ions respectively and x and y represent the number of these ions in the formula of the electrolyte. Thus,
The solubility product of a sparingly soluble salt at a given temperature may be defined as the product of the concentrations of its ions in the saturated solution, with each concentration term raised to the power equal to the number of times the ion occurs in the equation representing the dissociation of the electrolyte.
Equation (28.2) is applicable for a saturated solution i.e., under equilibrium situation.
The expressions of solubility products of some sparingly soluble salts are given below:
Knowing the solubility S, Ks can be calculated. Solubility products of some sparingly soluble salts are given in Table 28.1.
Table 28.1. Solubility Product Constants of Some Sparingly Soluble Salts at 298 K