In coal, pyrites `(FeS_(2))` is present as a pollution-causing impurity, which is removed by combustion.
`2FeS_(2) + 5O_(2) rarr 4SO_(2) + 2FeO`.
Calculate the moles of `SO_(2)` produced by burning 1.0metric ton `(10^(3) kg)` of coal containing 0.05% by mass of pyrites impurity?

Options

A. `8.32 mol`
B. `4.16 mol`
C. `12.48 mol`
D. `2.08 mol`

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the mass of pyrites (FeS₂) in the coal sample.
- Given that the mass of coal is 1.0 metric ton, which is equal to 1000 kg.
- The percentage of pyrites in coal is 0.05%.

**Calculation:**
\[ \text{Mass of FeS}_2 = \text{Total mass of coal} \times \left(\frac{\text{Percentage of FeS}_2}{100}\right) \]
\[ \text{Mass of FeS}_2 = 1000 \, \text{kg} \times \left(\frac{0.05}{100}\right) = 0.5 \, \text{kg} \]
Convert kg to grams:
\[ 0.5 \, \text{kg} = 500 \, \text{g} \]

### Step 2: Calculate the number of moles of FeS₂.
- The molar mass of FeS₂ is calculated as follows:
- Molar mass of Fe = 55.85 g/mol
- Molar mass of S = 32.07 g/mol
- Therefore, molar mass of FeS₂ = 55.85 + (2 × 32.07) = 55.85 + 64.14 = 119.99 g/mol (approximately 120 g/mol).

**Calculation:**
\[ \text{Number of moles of FeS}_2 = \frac{\text{Mass of FeS}_2}{\text{Molar mass of FeS}_2} \]
\[ \text{Number of moles of FeS}_2 = \frac{500 \, \text{g}}{120 \, \text{g/mol}} \approx 4.17 \, \text{moles} \]

### Step 3: Use the stoichiometry of the reaction to find moles of SO₂ produced.
- The balanced reaction is:
\[ 2 \text{FeS}_2 + 5 \text{O}_2 \rightarrow 4 \text{SO}_2 + 2 \text{FeO} \]
- From the reaction, 2 moles of FeS₂ produce 4 moles of SO₂.

**Calculation:**
\[ \text{Moles of SO}_2 = \text{Moles of FeS}_2 \times \left(\frac{4 \, \text{moles of SO}_2}{2 \, \text{moles of FeS}_2}\right) \]
\[ \text{Moles of SO}_2 = 4.17 \, \text{moles} \times 2 = 8.34 \, \text{moles} \]

### Final Result:
The number of moles of SO₂ produced by burning 1.0 metric ton of coal containing 0.05% by mass of pyrites impurity is approximately **8.34 moles**.

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