Solubility Product Principle

Solubility Product:

-The product of the concentration of ions of an electrolyte in a saturated solution at a particular temperature.

-It is denoted by $Ks p$ .

Ionic Product:

-The product of concentration of ions.

-It is denoted by $K i p$

At a given temperature if;

i) $K i p < Ks p$ , the solution is said to be unsaturated i.e. more solute can be dissolved in the solution.

ii) $K i p = Ks p$ , the solution is saturated, no precipitation can take place.

iii) $K i p > Ks p$ , the solution is said to be supersaturated, precipitation takes place.

Application of qualitative analysis:

-Encountering many precipitation reactions, like White ppt of $A g Cl$ is formed when $N a Cl$ reacts with $A g N O_{3}$

$N a Cl + A g N O_{3} ⟶ A g Cl ↓ + N a N O_{3}$

Similarly,

$B a C l_{2} + K_{2} S O_{4} ⟶ B a S O_{4} ↓ + 2 K Cl$

These compounds like $A g Cl, B a S O_{4}, P b C l_{2}, e t c$ are insoluble compounds however they are sparingly soluble salts. These undissolved salts goes ionization eg:

$A g Cl (s) ⇋ A g^{+} + C l^{-}$

The equilibrium constant, $K = \frac{[ A g ^{+} ] [ C l ^{-} ]}{A g Cl}$

or, $K \times [A g Cl] = [A g^{+}] [C l^{-}]$

or, $Ks p = [A g^{+}] [C l^{-}]$ $Ks p$ is the solubility product.

General expression for Solubility Product:

Let $A x B y$ be sparingly soluble salt, at equilibrium,

$A x B y (s) ⇋ x A^{y +} (a q) + y B^{x -} (a q)$

Now, $Ks p$ for this system is given as,

$Ks p = [A^{y +} (a q)]^{x} [B^{x -} (a q)]^{y}$

eg;

i) Calcium phosphate $(C a_{3} (P O_{4})_{2})$

$C a_{3} (P O_{4}) 2 ⇋ 3 C a^{2 +} + 2 P O_{4}^{3 -}$

$Ks p = (3 s)^{3} \times (2 s)^{2} = 108 x^{5}$ (s is $s p$ for $C a_{3} (P O_{4})_{2}$ )

ii) Bismuth Sulphide $(B i_{2} S_{3})$ :

$Ks p = (2 s)^{2} \times (3 x)^{3} = 108 x^{5}$

Note:

-Solubility product principle is valid only for saturated solutions in which total concentration of ions is no more than about $0.01 M$ .

Common ion effect:

It is the suppression of ionization of weak electrolyte when a strong is added to weak electrolyte, having one ion common.
This effect cannot be observed in the compounds of transitional metals but is observed in cuprous chloride.
When a soluble salt, say, $A^{+} C^{-}$ is added to a solution of another salt $(A^{+} B^{-})$ containing a common ion $(A^{+})$ , the dissociation of $A B$ is suppressed.

$A B \Leftrightarrow A^{+} + B^{-}$

-By the addition of the salt, $A C$ , the concentration of $A^{+}$ increases. Therefore, according to Le Chatelier's principle, the equilibrium will shift to the left, thereby decreasing the concentration of $A^{+}$ ions. Of that, the degree of dissociation of $A B$ will be reduced.

-A salt of a weak acid is added to a solution of the acid itself, the dissociation of the acid is diminished further.

For example, the addition of sodium acetate to a solution of acetic acid suppresses the dissociation of acetic acid which is already very small. Consider the equilibrium,

$C H_{3} COO H \Leftrightarrow H^{+} + C H 3 CO O^{-}$

-The addition of one of the products of dissociation (example: acetate ion), supplied by the largely dissociated salt (example: sodium acetate)pushes the equilibrium to the left. In other words, the dissociation of acetic acid is suppressed. Similarly, the addition of hydrogen ions furnished by the addition of a largely dissociated acid such as hydrochloric acid , also suppresses the dissociation of acetic acid.

-Thus, the common ion effect is the "suppression of the dissociation of a weak acid or a weak base on the addition of its own ions".

Applications:

Precipitation of sulphides of group $II$ and $III B$ basic radicals.
Precipitation of hydroxides of group $III A$ basic radicals.
Precipitation of group $I V$ basic radicals.

Hydrolysis of salts:

The process of dissolving salt in water to make its aqueous solution which may be acidic, basic or neutral is called hydrolysis of salt.
It is divided into four categories they are:

a. Salts of strong acid and strong base do not go hydrolysis. E.g: $N a Cl, N a N O_{3}, e t c$ .

b. Salts of weak acid and strong base gives basic solution. E.g: $C H_{3} COON a, N a CN, K CN, e t c$ .

c. Salts of weak bases and strong acids yield slightly acidic solution. E.g: $N H_{4} Cl$

d. Salts of weak acids and weak bases gives neutral, basic or acidic depending on the relative hydrolysis of the anions and the cations.