In an estimation of S by carius method 0.2175 g of the compound gave 0.5825 g of `BaSO_(4)` Percentage of S is

Options

A. 36.78
B. 45.5
C. 39.48
D. 30.69

Answer

To find the percentage of sulfur (S) in the compound using the Carius method, we can follow these steps:

### Step 1: Understand the formula
The formula to calculate the percentage of sulfur is:
\[ \text{Percentage of S} = \left( \frac{\text{Atomic weight of S}}{\text{Molecular weight of BaSO}_4} \right) \times \left( \frac{\text{Weight of BaSO}_4 \text{ formed}}{\text{Weight of organic compound}} \right) \times 100 \]

### Step 2: Identify the given values
From the question, we have:
- Weight of the organic compound (W) = 0.2175 g
- Weight of BaSO₄ formed = 0.5825 g

### Step 3: Calculate the molecular weight of BaSO₄
To calculate the molecular weight of BaSO₄, we need the atomic weights:
- Atomic weight of Barium (Ba) = 137 g/mol
- Atomic weight of Sulfur (S) = 32 g/mol
- Atomic weight of Oxygen (O) = 16 g/mol (and there are 4 oxygen atoms in BaSO₄)

Calculating the molecular weight:
\[ \text{Molecular weight of BaSO}_4 = \text{Atomic weight of Ba} + \text{Atomic weight of S} + 4 \times \text{Atomic weight of O} \]
\[ = 137 + 32 + (4 \times 16) = 137 + 32 + 64 = 233 \text{ g/mol} \]

### Step 4: Substitute the values into the formula
Now we substitute the values into the formula:
\[ \text{Percentage of S} = \left( \frac{32}{233} \right) \times \left( \frac{0.5825}{0.2175} \right) \times 100 \]

### Step 5: Calculate the values
First, calculate the fraction:
\[ \frac{0.5825}{0.2175} \approx 2.676 \]

Now, substituting this back into the percentage formula:
\[ \text{Percentage of S} = \left( \frac{32}{233} \right) \times 2.676 \times 100 \]

Calculating:
\[ \frac{32}{233} \approx 0.137 \]
\[ 0.137 \times 2.676 \approx 0.366 \]
\[ 0.366 \times 100 \approx 36.78\% \]

### Step 6: Conclusion
Thus, the percentage of sulfur in the compound is approximately **36.78%**.

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