How does Arrhenius theory help in comparing the relative strengths of weak acids and weak bases?

The relative strength of weak acids: The relative strength of weak acids can be easily compared in terms of their dissociation constants. In a gaseous solution, the dissociation of weak acid says HA may be represented as,

Since water used as a solvent is present in large quantity, its concentration remains practically constant.

K_a is known as dissociation constant of acid. It is constant at a given temperature for a given acid. Higher the value of K_a, the stronger is the acid.


If we have two weak acids having the same molar concentration in aqueous solution i.e. C mol L , then

Hence the relative strength of two acids having the same molar concentration in aqueous solution may be compared in terms of the square root of their dissociation constants.
Relative strength of weak base:
The dissociation of weak base, say BOH may be represented as,

According to law of chemical equilibrium
                

Since water is used as a solvent, its concentration remains practically constant.

K_b is known as dissociation constant base. It is constant at a given temperature for a given base. Higher the value of K_b, stronger is the base.
 
Similarly, the relative strength of the weak bases may also be compared as,