What is the solubility of `CaF_2` in a buffer solution containing 0.45 M HCOOH and 0.20 M HCOONa? `K_(sp)(CaF_2) = 3.4 xx 10^(-11), K (HF) = 6.8 xx 10^(-4), K (HCOOH) = 1.7 xx 10^(-4)`

Explanation

To determine the solubility of \( CaF_2 \) in a buffer solution containing 0.45 M formic acid (HCOOH) and 0.20 M sodium formate (HCOONa), we will follow these steps:

### Step 1: Calculate the pH of the buffer solution
The pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{pK}_a + \log \left( \frac{[\text{Salt}]}{[\text{Acid}]} \right) \]
where:
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