Derive the hydrogen and hydroxyl ion concentration in aqueous solutions of acids and bases.

Hydrogen and hydroxyl ion concentration in aqueous solutions of acids and bases:

The ionic product is very important quantity in aqueous solutions because it controls the relative concentrations of H⁺ and OH^– ions because their product is constant. In pure water, the concentrations of [H₃O⁺] and [OH^–] ions are equal. But when an acid such as HCl or a base such as NaOH is added to the neutral solution, then concentrations of [H₃O⁺] and [OH^–] ions change and do not remain equal. However the value of ionic product of water, K_w at a particular temperature always remains constant irrespective of the fact whether water is pure or some acid or a base has been added to it.

(i) Change in [H₃O⁺] and [OH^–] ions concentrations on the addition of an acid:
If we add a few drops of acid like HCl to water, the concentration of [H₃O⁺] ions becomes large. Consequently, according to Le-Chatelier’s principle, dissociation equilibrium of water shifts in the reverse direction i.e. H₃O⁺] ions would combine with OH^– ions to form undissociated water molecules so that the value of K_w in the solution may remain the same as that in water. The concentration of OH^– ions may be calculated as:
[OH^–] = K_w / [H₃O⁺]
Hence, the concentration of H₃O⁺ ions will be more than the concentration of OH^– ions in acidic solution.

(ii) Change in [H₃O⁺] and [OH^–] ions concentrations on the addition of a base:
If we add a few drops of base like NaOH to water, the concentration of OH^– ions increases but the concentration of hydrogen ion decreases. The concentration of [H₃O⁺] ions may be calculated as:
[H₃O⁺] = K_w / [OH^–]
Hence, the concentration of H₃O⁺ ions will be less than the concentration of OH^– ions in basic solution.

Hence we can conclude that:
In acidic solution: [H₃O⁺] > [OH^–]
In basic solution: [H₃O⁺] < [OH^–]
In neutral solution: [H₃O⁺] = [OH^–]