Question

You have 50 ml of a complex mixture of weak acids that contains some HF (pKa = 3.18) and some HCN (pKa = 9.21). Which is larger, [F-]/[HF] or [CN-]/[HCN]?

Answer 1

`([F^(-)])/([HF])` is larger

Step-by-step explanation:

`pK_(a)=-logK_(a)` , where
`K_(a)` is the acid dissociation constant.

For a monoprotic acid e.g. HA,
`K_(a)=([H^(+)][A^(-)])/([HA])` and
`([A^(-)])/([HA])=(K_(a))/([H^(+)])`

So, clearly, higher the
`K_(a)` value , lower will the the
`pK_(a)`

In this mixture, at equilibrium,
`[H^(+)]` will be constant.

`K_(a)` of HF is grater than
`K_(a)` of HCN

Hence,
`((F^(-))/([HF])=(K_(a)(HF))/([H^(+)]))>((CN^(-))/([HCN])=(K_(a)(HCN))/([H^(+)]))`

So,
`([F^(-)])/([HF])` is larger