To find the mass of `H₂SO₄` produced from `5.52 kg` of `FeS₂`, we will follow these steps:
### Step 1: Write the balanced chemical equations
1. **First reaction**:
\[
4 \, \text{FeS}_2(s) + 11 \, \text{O}_2(g) \rightarrow 2 \, \text{Fe}_2\text{O}_3(s) + 8 \, \text{SO}_2(g)
\]
2. **Second reaction**:
\[
2 \, \text{SO}_2(g) + \text{O}_2(g) \rightarrow 2 \, \text{SO}_3(g)
\]
3. **Third reaction**:
\[
\text{SO}_3(g) + \text{H}_2\text{S}_2\text{O}_7(l) \rightarrow \text{H}_2\text{S}_2\text{O}_7(l)
\]
4. **Fourth reaction**:
\[
\text{H}_2\text{S}_2\text{O}_7(l) + \text{H}_2\text{O}(l) \rightarrow 2 \, \text{H}_2\text{SO}_4(l)
\]
### Step 2: Combine the reactions to find the overall reaction
By combining the balanced equations, we can derive the overall reaction:
\[
4 \, \text{FeS}_2 + 11 \, \text{O}_2 \rightarrow 2 \, \text{Fe}_2\text{O}_3 + 8 \, \text{H}_2\text{SO}_4
\]
### Step 3: Calculate the molar masses
- Molar mass of `FeS₂`:
\[
\text{Fe} = 56 \, \text{g/mol}, \quad \text{S} = 32 \, \text{g/mol}
\]
\[
\text{Molar mass of FeS}_2 = 56 + (2 \times 32) = 56 + 64 = 120 \, \text{g/mol}
\]
- Molar mass of `H₂SO₄`:
\[
\text{H} = 1 \, \text{g/mol}, \quad \text{S} = 32 \, \text{g/mol}, \quad \text{O} = 16 \, \text{g/mol}
\]
\[
\text{Molar mass of H}_2\text{SO}_4 = (2 \times 1) + 32 + (4 \times 16) = 2 + 32 + 64 = 98 \, \text{g/mol}
\]
### Step 4: Calculate the number of moles of `FeS₂`
Given mass of `FeS₂` = `5.52 kg` = `5520 g`
\[
\text{Number of moles of FeS}_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{5520 \, \text{g}}{120 \, \text{g/mol}} = 46 \, \text{moles}
\]
### Step 5: Use stoichiometry to find moles of `H₂SO₄`
From the balanced equation, `4 moles of FeS₂` produce `8 moles of H₂SO₄`. Therefore, for `46 moles of FeS₂`:
\[
\text{Moles of H}_2\text{SO}_4 = \frac{8}{4} \times 46 = 92 \, \text{moles}
\]
### Step 6: Calculate the mass of `H₂SO₄`
\[
\text{Mass of H}_2\text{SO}_4 = \text{moles} \times \text{molar mass} = 92 \, \text{moles} \times 98 \, \text{g/mol} = 9016 \, \text{g}
\]
### Step 7: Convert grams to kilograms
\[
\text{Mass of H}_2\text{SO}_4 = \frac{9016 \, \text{g}}{1000} = 9.016 \, \text{kg}
\]
### Final Answer
The mass of `H₂SO₄` produced is approximately **9.016 kg**.
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