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 rarr H^(+) + A^(-)`
C 0 0
`C ( 1- alpha )` `C alpha` `C alpha`
`[H^(+)] = C alpha`
`K_(p) = ( C alpha^(2))/( ( 1- alpha))` ( Ostwall dilution law )
`:. C = ( Ka ( 1- alpha))/( alpha^(2))`
`:. [ H^(+) ] = ( K_(a) ( 1- alpha))/( alpha^(2)) xx alpha = ( K_(a) ( 1- alpha))/( alpha)`
`rArr - log [ H^(+) ] = - [ log K_(a) + log ( 1- alpha) - log alpha]`
`rArr pH = - log K_(a) + log"" ( alpha)/((1-alpha)) rArrpH = pK_(a) - log""((1- alpha))/( alpha)`
`rArr log"" ( (1- alpha))/( alpha) = ( p K_(a) - pH ) rArr ( 1- alpha)/( alpha) = 10^((pK_(a)-pH)) rArr ( 1)/( alpha) - 10^((pK_(a) - pH))`
`rArr alpha = ( 1)/( 1+ 10 ^((pK_(a) - pH)))`