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I think $\ce{HF}$ can be hydrolysis and get $\ce{F-}$ as a conjugate base, so this solution should be a buffer solution. But the correct answer is that this solution is not a buffer. Please explain it to me. I'm very confused.

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What are you talking about? $\ce{HF}$ in water solution is acting like moderately strong acid. It's because:

$$\ce{HF + H2O \rightleftharpoons H3O+ + F-}$$ $$\ce{H3O+ + F- \rightleftharpoons [H3O]F}$$ which is undissociated.Then: $$\ce{F- + HF \rightleftharpoons HF2-}$$

As you can see the large affinity of $\ce{F^-}$ to $\ce{H^+}$ won't allow it to dissociate. The $K_a(HF)(6.6x10^{-4})$ is strongly favoring reactants. So the $\ce{HF}$ in $\ce{H2O}$ isn't buffer because there isn't almost any $\ce{F-}$ to be considered as conjugated acid. So if you add some acid there will not be enough $\ce{F-}$ for it's neutralisation. So if you add some acid or base it will react with water and equilibrium constant will be changed and that will lead to drastic change of pH.

So the buffer is solution which consist of:

  1. salt of strong acid and weak base and the weak base (for example $\ce{NH_{4}Cl}$ and $\ce{HN3}$ ).

  2. salt of weak acid and strong base and the weak acit (for example $\ce{CH3COONa}$ and $\ce{CH3COOH}$).

Hope i helped you. If you have any other questions please ask.

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