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Calculate the solubility of CaF(2) in a ...

Calculate the solubility of `CaF_(2)` in a solution buffered at `pH = 3.0. K_(a)` for `HF = 6.3 xx 10^(-4)` and `K_(sp)` of `CaF_(2) = 3.45 xx 10^(-11)`.

Text Solution

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`[Ca^(2+)] [F^(Theta)] = 3.45 xx 10^(-11)`
The `F^(Theta)` reacts with `H^(o+) (pH = 3.0)` to produce `HF`
`K_(a_(HF)) = ([H^(o+)][F^(Theta)])/([HF]) or 6.3 xx 10^(-4) = (10^(-3)[F^(Theta)])/([HF])`
`:. HF = 1.58 xx [F^(o+)]`
Also the solution contains `[HF] [F^(Theta)] = 2 xx [Ca^(2+)]` or `1.58 xx [F^(Theta)[ + [f^(Theta)] = 2 xx [Ca^(2+)]`
`:. [F^(Theta)] = (2)/(2.58) xx[Ca^(2+)] = 0.775 [Ca^(2+)]`
Let solubility of `CaF_(2)` be S mol `L^(-1) :. [Ca^(2+)] = S`
`:. [F^(Theta)] = 0.775 xx S`
Thus: `S xx (0.775 xx S)^(2) = 3.45 xx 10^(-11)`
`S = 3.86 xx 10^(-4)M`
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