0.395 g of an organic compound by Carius method for the estimation of S gave 0.582 g of `BaSO_4`. The percentage of S in the compound is

Options

A. `20.24%`
B. `35.62%`
C. `12.24%`
D. `40.65%`

Explanation

To find the percentage of sulfur (S) in the organic compound using the data provided, we can follow these steps:

### Step 1: Calculate the moles of BaSO₄ produced
We know the mass of BaSO₄ produced is 0.582 g. The molar mass of BaSO₄ is given as 233 g/mol.

\[ \text{Moles of BaSO₄} = \frac{\text{Mass of BaSO₄}}{\text{Molar mass of BaSO₄}} = \frac{0.582 \, \text{g}}{233 \, \text{g/mol}} \approx 0.0025 \, \text{mol} \]

### Step 2: Determine the moles of sulfur in BaSO₄
From the formula of BaSO₄, we can see that there is 1 mole of sulfur in 1 mole of BaSO₄. Therefore, the moles of sulfur will be the same as the moles of BaSO₄.

\[ \text{Moles of S} = 0.0025 \, \text{mol} \]

### Step 3: Calculate the mass of sulfur
Using the molar mass of sulfur (32 g/mol), we can find the mass of sulfur.

\[ \text{Mass of S} = \text{Moles of S} \times \text{Molar mass of S} = 0.0025 \, \text{mol} \times 32 \, \text{g/mol} = 0.08 \, \text{g} \]

### Step 4: Calculate the percentage of sulfur in the organic compound
Now, we can calculate the percentage of sulfur in the organic compound using the formula:

\[ \text{Percentage of S} = \left( \frac{\text{Mass of S}}{\text{Mass of organic compound}} \right) \times 100 \]

Substituting the values:

\[ \text{Percentage of S} = \left( \frac{0.08 \, \text{g}}{0.395 \, \text{g}} \right) \times 100 \approx 20.25\% \]

### Final Answer
The percentage of sulfur in the organic compound is approximately **20.25%**.

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