0.2174 g of the substance gave 0.5825 g of `BaSO_(4)` by Carius method. Calculate the percentage of sulphur.

Answer

To calculate the percentage of sulfur in the given substance based on the mass of barium sulfate (BaSO₄) produced, we can follow these steps:

### Step 1: Determine the molar mass of BaSO₄
The molar mass of BaSO₄ can be calculated by adding the atomic masses of its constituent elements:
- Barium (Ba): 137 g/mol
- Sulfur (S): 32 g/mol
- Oxygen (O): 16 g/mol (and there are 4 oxygen atoms)

So, the molar mass of BaSO₄ is:
\[ \text{Molar mass of BaSO₄} = 137 + 32 + (16 \times 4) = 137 + 32 + 64 = 233 \text{ g/mol} \]

### Step 2: Calculate the mass of sulfur in BaSO₄
From the molar mass, we know that 233 g of BaSO₄ contains 32 g of sulfur. To find out how much sulfur is in 0.5825 g of BaSO₄, we set up a proportion:
\[ \text{Mass of sulfur} = \left( \frac{32 \text{ g S}}{233 \text{ g BaSO₄}} \right) \times 0.5825 \text{ g BaSO₄} \]

Calculating this gives:
\[ \text{Mass of sulfur} = \frac{32}{233} \times 0.5825 \approx 0.0798 \text{ g S} \]

### Step 3: Calculate the percentage of sulfur in the original substance
Now, we can find the percentage of sulfur in the original substance using the formula:
\[ \text{Percentage of sulfur} = \left( \frac{\text{mass of sulfur}}{\text{mass of substance}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage of sulfur} = \left( \frac{0.0798 \text{ g}}{0.2174 \text{ g}} \right) \times 100 \]

Calculating this gives:
\[ \text{Percentage of sulfur} \approx 36.78\% \]

### Final Answer
The percentage of sulfur in the substance is **36.78%**.