To solve the problem of determining the percentage purity of copper sulfate (CuSO₄) in the sample, we will follow these steps:
### Step 1: Determine the moles of Na₂S₂O₃ used
We know that the volume of Na₂S₂O₃ solution used is 200 mL and its concentration is 1.0 M.
\[
\text{Moles of Na₂S₂O₃} = \text{Volume (L)} \times \text{Concentration (M)} = 0.200 \, \text{L} \times 1.0 \, \text{mol/L} = 0.200 \, \text{mol}
\]
### Step 2: Determine the moles of iodine (I₂) reacted
From the reaction of Na₂S₂O₃ with iodine, the balanced equation is:
\[
\text{I}_2 + 2 \text{Na}_2S_2O_3 \rightarrow 2 \text{NaI} + \text{Na}_2S_4O_6
\]
From this equation, we see that 1 mole of I₂ reacts with 2 moles of Na₂S₂O₃. Therefore, the moles of I₂ can be calculated as follows:
\[
\text{Moles of I₂} = \frac{0.200 \, \text{mol Na₂S₂O₃}}{2} = 0.100 \, \text{mol I₂}
\]
### Step 3: Determine the moles of CuSO₄ reacted
From the iodimetric reaction given:
\[
2 \text{CuSO₄} + 4 \text{KI} \rightarrow \text{Cu}_2\text{I}_2 + 2 \text{K}_2\text{SO₄} + \text{I}_2
\]
From this equation, we see that 1 mole of I₂ reacts with 2 moles of CuSO₄. Therefore, the moles of CuSO₄ can be calculated as follows:
\[
\text{Moles of CuSO₄} = 2 \times \text{Moles of I₂} = 2 \times 0.100 \, \text{mol} = 0.200 \, \text{mol}
\]
### Step 4: Calculate the mass of CuSO₄ that reacted
The molar mass of CuSO₄ is approximately 159.6 g/mol. Therefore, the mass of CuSO₄ that reacted is:
\[
\text{Mass of CuSO₄} = \text{Moles} \times \text{Molar Mass} = 0.200 \, \text{mol} \times 159.6 \, \text{g/mol} = 31.92 \, \text{g}
\]
### Step 5: Calculate the percentage purity of CuSO₄
The initial mass of the CuSO₄ sample is given as 319.0 g. The percentage purity can be calculated using the formula:
\[
\text{Percentage Purity} = \left( \frac{\text{Mass of pure CuSO₄}}{\text{Total mass of sample}} \right) \times 100
\]
Substituting the values:
\[
\text{Percentage Purity} = \left( \frac{31.92 \, \text{g}}{319.0 \, \text{g}} \right) \times 100 \approx 10.00\%
\]
### Final Answer
The percentage purity of CuSO₄ in the sample is approximately **10%**.
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