What is degree of ionization is respect of weak acids and weak bases? Derive the relationship between degree of ionization (`alpha`) and ionization constant `(K_(a))` for thke weak acid HX.

Explanation

Degree of Ionization `(alpha)`:
The extent of ionization (or) dissociation of a weak acid or weak base is termed as its Degree of ionization `(alpha)`."Let the concentration of weak acid (HX).be.c molès/it and the degree of ionization be `.alpha.`. Hence at equilibrium,
`{:(HX hArr, H^(+) ,+X^(-)),(C(1-alpha),C alpha ,C alpha):}`
If `.alpha`. is neglected compared to one in denominator,
We have `K_(a)=Calpha^(2) rArr alpha^(2)=(K_(a))/(C) rArr alpha= sqrt((K_(a))/(C))`
Similar equation can be written for the ionization of weak base (BOH) in aq. solution.
`{:(BOH, overset(H_(2)O) hArr, B^(+)+OH^(-)),(C(1-alpha), C alpha, C alpha):}`
`K_(b)=([B^(+)][OH^(-)])/([BOH])=(C alpha xx C alpha)/(C(1-alpha))=(Calpha^(2))/((1-alpha))`
`:. K_(b)=(Calpha^(2))/((1-alpha))`
Neglecting .a. in the denominator, we have
`K_(b)=Calpha^(2) rArr alpha^(2) =(K_(b))/(C)`
`:. alpha= sqrt((K_(b))/(C))`
Therefore strengths of two acids or two bases are compared generally by their `K_(a)` or `k_(b)` values: Higher `K_(a)` or `k_(b)` value, stronger is the acid or base.