Hydrolysis Constant

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In this article, we shall study hydrolysis of different types of salts and we shall derive expression for hydrolysis constant for each type of salt.

Hydrolysis of salt of strong acid and weak base.

These salts on hydrolysis produce strong acids and weak bases. The resulting solution is acidic in nature.

Consider hydrolysis of ammonium chloride (NH₄Cl). It gives strong acid HCl and weak base NH₄OH, when treated with water and equilibrium exist as,

NH₄Cl + H₂O   ⇌   NH₄OH    + HCl

(weak base )  (strong acid)

Applying ionic theory

NH₄⁺  + Cl^– + H₂O  ⇌     NH₄OH    + H⁺  + Cl^–

Cancelling common ions of both the sides

NH₄⁺  + H₂O  ⇌    NH₄OH    + H⁺

This solution contains free H+ ion. It is acidic to litmus and pH < 7.

Note:

Some salts like CuSO₄, FeCl₃ on hydrolysis do not give clear solution but give turbid solution. It is due to formation of insoluble hydroxides.

Expression for  hydrolysis constant for a salt of strong acid and weak base.

Let one mole of a salt BA of strong acid and weak base be dissolved in water and solution is made Vdm3. The hydrolysis of salt takes place as follows

BA + H₂O         ⇌         BOH    + HA

(weak base )  (strong acid)

Applying ionic theory

B⁺  + A- + H₂O   ⇌   BOH    + H⁺  + A-

Cancelling common ions of both the sides

By applying the law of mass action to above equilibrium,

As water is in large excess [H₂O] = constant

Where K_h is constant called hydrolysis constant.

For a salt of strong acid and weak base h is very small. Hence , 1 – h  = h

Thus, the degree of hydrolysis of a salt of strong acid and weak base is inversely proportional to the square root of concentration and directly proportional to the square root of dilution.

Relation between  hydrolysis constant (K_h) of salt of strong acid and weak base and dissociation constant(K_b) of a weak base.

The hydrolysis of a salt of strong acid and weak base, BA leads to an equilibrium.

B⁺  + H₂O   ⇌   BOH    + H⁺ 

Besides above equilibrium there are two more equilibria.

Weak base BOH which ionizes to small extent.

BOH   ⇌ B⁺ +  OH^–

Where K_b is dissociation constant for the weak base.

Water is slightly ionized.

H₂O      ⇌      H⁺   +    OH ^–

k_w = [H⁺][OH^–] ……….. (3)

Where k_w is ionic product of water

Dividing equation (3) by (2), we get

Thus hydrolysis constant of a salt of strong acid and weak base is a ratio of ionic product of water and dissociation constant of a weak base.

Expression of concentration of [H⁺] in aqueous solution of strong acid and weak base.

The hydrolysis of a salt of strong acid and weak base, BA leads to an equilibrium.

Hydrolysis of salt of weak acid and strong base.

These salts on hydrolysis produce weak acids and strong bases. The resulting solution is basic in nature.

Consider hydrolysis of sodium acetate (CH₃COONa). It gives weak acid CH₃COOH and strong base NaOH, when treated with water and equilibrium exist as,

CH₃COONa  + H 2O ⇌  CH₃COOH + NaOH

(weak acid)  (strong base)

Applying ionic theory

CH₃COO^–  + Na⁺ + H₂O  ⇌    CH₃COOH    + Na⁺  + OH^–

Cancelling common ions of both the sides

CH₃COO^–  +  H₂O   ⇌   CH₃COOH    +  OH^–

This solution contains free OH- ions. It is basic to litmus and pH > 7.

Expression for  hydrolysis constant for a salt of weak acid and strong base.

Let one mole of a salt BA of weak acid and strong base be dissolved in water and solution is made Vdm3. The hydrolysis of salt takes place as follows

BA + H₂O  ⇌    BOH    + HA

(strong base )  (weak acid)

Applying ionic theory

B⁺  + A^– + H₂O  ⇌     B⁺  +  OH^– + HA

Cancelling common ions of both the sides

By applying the law of mass action to above equilibrium,

As water is in large excess [H₂O] = constant

Whre K_h is constant called hydrolysis constant.

For a salt of strong acid and weak base h is very small. Hence, 1 – h  = h

Thus, the degree of hydrolysis  of a salt of weak acid and strong base is inversely proportional to the square root of concentration and directly proportional to the square root of dilution.

Relation between  hydrolysis constant (K_h) of salt of weak acid and strong base and dissociation constant (K_a) of a weak acid.

The hydrolysis of a salt of weak acid and strong base, BA leads to an equilibrium.

A^– + H₂O  ⇌      OH^–  +  HA

Besides above equilibrium there are two more equilibria.

Weak acid which ionizes to small extent.

HA   ⇌ H⁺ +  A ^–

Where Ka is dissociation constant for the weak acid.

Water is slightly ionized.

H₂O      ⇌      H⁺   +    OH ^–

k_w = [H⁺][OH^–] ……….. (3)

Where k_w is ionic product of water

Dividing equation (3) by (2), we get

Thus hydrolysis constant of a salt of weak acid and strong base is a ratio of ionic product of water and dissociation constant of a weak acid.

Expression of concentration of [OH^–] in aqueous solution of weak acid and strong base.

The hydrolysis of a salt of strong acid and weak base, BA leads to an equilibrium.

Hydrolysis of salt of weak acid and weak base:

These salts on hydrolysis produce weak acids and weak bases. The nature of resulting solution depends on the relative strengths of the weak acid and the base formed..

Consider hydrolysis of ammonium acetate (CH₃COONH₄). It gives weak acid CH₃COOH and weak base NH₄OH, when treated with water and equilibrium exist as,

CH₃COONH₄ + H₂O  ⇌ CH₃COOH + NH₄OH

(weak acid)  (weak base)

Applying ionic theory

CH₃COO^–  + NH₄⁺ + H₂O  ⇌ CH₃COOH + NH₄OH

As there are no  free OH^– or H⁺ ions. The relative strength of CH₃COOH and NH₄OH are the same. It is neutral to litmus and pH = 7.

Expression for  hydrolysis constant for a salt of weak acid and weak base.

Let one mole of a salt BA of weak acid and strong base be dissolved in water and solution is made V dm³. The hydrolysis of salt takes place as follows

BA + H₂O  ⇌    BOH    + HA

(weak base )  (weak acid)

Applying ionic theory

By applying the law of mass action to above equilibrium,

As water is in large excess [H₂O] = constant

Where K_h is constant called hydrolysis constant.

For a salt of strong acid and weak base h is very small. Hence, 1 – h  = h

Thus, the degree of hydrolysis  of a salt of weak acid and weak base is independent of  concentration and dilution.

Note:

When h to be found from K_h, use formula

When K_h to be found from h, use formula

Relation between  hydrolysis constant (K_h) of salt of weak acid and weak base, dissociation constant(K_a) of a weak acid and dissociation constant(K_b) of a weak base.

The hydrolysis of a salt of weak acid and weak base, BA leads to an equilibrium.

B⁺  + A^– + H₂O ⇌     BOH + HA

Besides above equilibrium there are three more equilibria.

Weak acid which ionizes to small extent.

Where K_a is dissociation constant for the weak acid.

Weak base BOH which ionizes to small extent.

Where k_b is dissociation constant for the weak base.

Water is slightly ionized.

H₂O      ⇌      H⁺   +    OH ^–

k_w = [H⁺][OH^–] ……….. (4)

Where k_w is ionic product of water

Where KW is ionic product of water

Dividing equation (2) by (3) and (4), we get

.

………  (5)

From equation (1) and (5)