Prove that the dergee of dissociation of weak acid is given by:
`alpha = (1)/(1+10^(pK_(a)-pH))`
where `K_(a)` is its dissociation constant of the weak acid.

Explanation

For a weak mono protic acid
`{:(HA,hArr,H^(oplus),+,A^(Theta)),(C,,0,,0),(C""(1-alpha),,C alpha,,C alpha):}`
`[H^(o+)] = Calpha`
`K_(a) = (Calpha^(2))/((1-alpha))` (Ostwall dilution law)
`:. C = (K_(a) (1-alpha))/(alpha^(2))`
`:. [H^(o+)] = (K_(a)(1-alpha))/(alpha^(2)) xx alpha = (K_(a)(1-alpha))/(alpha)`
`rArr -log [H^(o+)] =- [log K_(a) +log (1-alpha) - log alpha]`
`rArr pH =- log K_(a) +"log" (alpha)/((1-alpha))`
`rArr pH = pK_(a) - "log" (1-alpha)/(alpha)`
`rArr "log" (1-alpha)/(alpha) = (pK_(a) - pH) rArr (1-alpha)/(alpha)= 10^((pK_(a) -pH))`
`rArr (1)/(alpha) - 1 = 10^((pK_(a)-pH))`
`rArr alpha = (1)/(1+10^((pK_(a)-pH)))`