To solve the problem of determining the volume of air at N.T.P (Normal Temperature and Pressure) containing 21% oxygen by volume required to completely burn 1000 g of sulfur containing 4% incombustible matter, we can follow these steps:
### Step 1: Calculate the mass of sulfur available for combustion
Given that 4% of the 1000 g of the sample is incombustible matter, we can find the mass of sulfur.
\[
\text{Mass of incombustible matter} = \frac{4}{100} \times 1000 \, \text{g} = 40 \, \text{g}
\]
\[
\text{Mass of sulfur} = 1000 \, \text{g} - 40 \, \text{g} = 960 \, \text{g}
\]
### Step 2: Write the balanced chemical equation for the combustion of sulfur
The balanced equation for the combustion of sulfur is:
\[
S + O_2 \rightarrow SO_2
\]
### Step 3: Determine the moles of sulfur available for combustion
To find the number of moles of sulfur, we use the molar mass of sulfur (S), which is approximately 32 g/mol.
\[
\text{Moles of sulfur} = \frac{\text{Mass of sulfur}}{\text{Molar mass of sulfur}} = \frac{960 \, \text{g}}{32 \, \text{g/mol}} = 30 \, \text{mol}
\]
### Step 4: Calculate the moles of oxygen required for combustion
From the balanced equation, we see that 1 mole of sulfur reacts with 1 mole of oxygen. Therefore, the moles of oxygen required will be equal to the moles of sulfur.
\[
\text{Moles of oxygen required} = 30 \, \text{mol}
\]
### Step 5: Convert moles of oxygen to volume at N.T.P
At N.T.P, 1 mole of gas occupies 22.4 liters. Thus, the volume of oxygen required is:
\[
\text{Volume of oxygen} = \text{Moles of oxygen} \times 22.4 \, \text{L/mol} = 30 \, \text{mol} \times 22.4 \, \text{L/mol} = 672 \, \text{L}
\]
### Step 6: Calculate the volume of air required
Since air contains 21% oxygen by volume, we can find the volume of air required to provide the necessary oxygen.
\[
\text{Volume of air} = \frac{\text{Volume of oxygen}}{0.21} = \frac{672 \, \text{L}}{0.21} \approx 3200 \, \text{L}
\]
### Final Answer
The volume of air required to completely burn 1000 g of sulfur containing 4% incombustible matter is approximately **3200 liters**.
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