State Ostwald’s dilution law.

Explanation

The dissociation of acetic acid can be represented as
`CH_3COOH hArr H^+ +CH_3 COO^-`
The dissociation constant of acetic acids is
`k_(a)=([H^+][CH_3 COO^(-)])/([CH_3 COOH])" "…(1)`

Substituting the equilibrium concentration in equation (1)
`k_(a)=((alpha C)(alpha C))/((1-alpha)C)`
`k_(a)=(alpha^2 C)/(1-alpha)" "...(2)`
We know that weak acid dissociates only to a very small extent compared to one `alpha` is so small and hence in the denominator `(1-alpha) ~=1`. The above expression (2) now becomes.
`k_(a)=alpha^2 C`
`rArr alpha^2 =(K_(a))/(C ) `
`alpha=sqrt((K_a)/(C ))`