It has been found that the pH of a 0.01M solution of an organic acid is 4.15. Calculate the concentration of the anion, the ionization constant of the acid and its `pK_(a)`.

Explanation

`HA hArr H^(o+)+A^(Θ)`
`pH=-log [H^(o+)]` or `log [H^(o+)]=- pH=-4.15=bar(5).85`
`:. [H^(o+)]=7.09xx10^(-5)M=7.08xx10^(-5)M`
`[A^(Θ)]=[H^(o+)]=7.08xx10^(-5)M`
`K_(a)=([H^(o+)][A^(Θ)])/([HA])=((7.08xx10^(-5))(7.08xx10^(-5)))/10^(-2)`
`=5.08xx10^(-7)`
`pK_(a)=-log K_(a) =-log(5.0xx10^(-7))=7-0.699=6.301`
Alternatively
`pH_(W_(A))=1/2(pK_(a)-log C)`
`4.15xx2=pK_(a)-log 10^(-2)`
`8.30-2=pK_(a)`
`pK_(a)=6.30`