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Relation Between Ka And Kb, Common Ion Effect

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Relation Between Ka And Kb, Common Ion Effect - Lesson Summary

Weak acid is related is related to its conjugate base through equilibrium constant expression k a
HA +H 2O ↔ H 3O + +A -

K a =  [ H 3 O + ][ A - ] [HA]                                                                                                                         

Weak base is related is related to its conjugate acid through equilibrium constant expression k b
BOH + H 2O ↔ B + + OH -

K b =   [B + ][ OH - ] [BOH]   

As the conjugated base pairs are related through the equilibrium constant we can assume that the equilibrium constant for an acid-base pair also related to each other.
Consider the dissociation of weak acid in water
HA +H 2O ↔ H 3O + +A -

 K a =  [ H 3 O + ][ A - ] [HA]     ...........(1)

HA being a weak acid it has strong conjugate base A -
The dissociation equilibrium of strong conjugate base in water is
A -  + H 2O ↔ HA +OH -

 K b = [HA][ A - ] [ A - ]       ...........(2)

Multiplying equation 1 & 2

K a * K b  =  [ H 3 O + ][ A - ] [HA] * [HA][ A - ] [ A - ]  
             = [H 3O + ][ OH -] = k w
 k w  = Ionic product of water
∴  k a * k b = k w

Common ion effect:  The common ion effect is defined as the shift in the position of an ionic equilibrium caused by the addition of a solute that provides an ion which is the part of equilibrium.
Consider the dissociation of acetic acid in water
The equilibrium is represented as 
CH 3COOH (aq) ↔ CH 3COO - +H 3O +
To this solution add a small amount of sodium acetate.
dissociation of sodium acetate is represented as
CH 3COONa → CH3COO - +Na +
Since the concentration of CH3COO -  ions increased in the solution ,according to Le Chatelier,s principle the equilibrium will be shifted to left.
Due to the presence of common ions CH 3COO - the equilibrium will be shifted to the left side. And the dissociation of  CH 3COOH is suppressed.

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