Calculate the volume of `SO_(2)` at STP obtained by burning 500 g of S containing `4%` sand by weight.

Answer

To solve the problem of calculating the volume of \( SO_2 \) at STP obtained by burning 500 g of sulfur containing 4% sand by weight, we can follow these steps:

### Step 1: Calculate the weight of sand in the sample
Given that the sample contains 4% sand by weight, we can find the weight of sand in 500 g of the mixture.

\[ \text{Weight of sand} = \frac{4}{100} \times 500 \, \text{g} = 20 \, \text{g} \]

### Step 2: Calculate the weight of pure sulfur
Now, we subtract the weight of sand from the total weight to find the weight of pure sulfur.

\[ \text{Weight of sulfur} = 500 \, \text{g} - 20 \, \text{g} = 480 \, \text{g} \]

### Step 3: Calculate the number of moles of sulfur
Using the molar mass of sulfur, which is 32 g/mol, we can calculate the number of moles of sulfur.

\[ \text{Moles of sulfur} = \frac{\text{Weight of sulfur}}{\text{Molar mass of sulfur}} = \frac{480 \, \text{g}}{32 \, \text{g/mol}} = 15 \, \text{moles} \]

### Step 4: Determine the moles of \( SO_2 \) produced
From the balanced chemical equation for the combustion of sulfur:

\[ S + O_2 \rightarrow SO_2 \]

We see that 1 mole of sulfur produces 1 mole of \( SO_2 \). Therefore, the moles of \( SO_2 \) produced will also be 15 moles.

### Step 5: Calculate the volume of \( SO_2 \) at STP
At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters. Thus, we can calculate the volume of \( SO_2 \) produced.

\[ \text{Volume of } SO_2 = \text{Moles of } SO_2 \times 22.4 \, \text{L/mol} = 15 \, \text{moles} \times 22.4 \, \text{L/mol} = 336 \, \text{L} \]

### Final Answer
The volume of \( SO_2 \) at STP obtained by burning 500 g of sulfur containing 4% sand by weight is **336 liters**.

---